Seismic Loads Guide To The Seismic Load Provisions of ASCE 7-16 by Finley Allan Charney, Thomas F. Heausler, Justin D. Marshall

Seismic Loads

Other Titles of Interest ASCE 7 Hazard Tool Delivers a quick, efficient way to look up key design parameters specified by Standard ASCE/SEI 7-10 and 7-16 through a web-based application that retrieves load data for each of seven hazards, visualizes them on a map, and generates a unified report of results. (ASCE 2016) (http://ascetools.online) Minimum Design Loads and Associated Criteria for Buildings and Other Structures, ASCE/SEI 7-16 Provides requirements for general structural design and includes means for determining dead, live, soil, flood, wind, snow, rain, atmospheric ice, and earthquake loads and their combinations that are suitable for inclusion in building codes and other documents. A detailed commentary of explanatory and supplementary information is included. (ASCE 2016) (ISBN 978-0-7844-1424-8) Significant Changes to the Minimum Design Load Provisions of ASCE 7-16 by GARY CHOCK, P.E., D.CE.; S. K. GHOSH, PH.D.; MICHAEL O’ROURKE, PH.D., P.E.; AND T. ERIC STAFFORD, P.E. Describes the revisions to the minimum design load requirements set forth in Standard ASCE/SEI 7-16. (ASCE Press 2018) (ISBN 978-0-7844-1457-6) Seismic Loads: Guide to the Seismic Load Provisions of ASCE 7-10 BY FINLEY A. CHARNEY, PH.D., P.E. Provides clear explanations of the seismic design provisions contained in Standard ASCE/SEI 7-10. (ASCE Press 2015) (ISBN 978-0-7844-1352-4) Seismic Evaluation and Retrofit of Existing Buildings, ASCE/SEI 41-17 Describes deficiency-based and systematic procedures that use performance-based principles to evaluate and retrofit existing buildings to withstand the effects of earthquakes. (ASCE 2017) (ISBN 978-0-7844-1485-9) Earthquake Protection of Building Equipment and Systems: Bridging the Implementation Gap BY JEFFREY A. GATSCHER, GARY L. MCGAVIN, AND PHILIP J. CALDWELL Presents a framework for applying the latest earthquake engineering research to the nonstructural elements of individual building projects, concentrating on mechanical and electrical systems. (ASCE Press 2012) (ISBN 978-0-7844-1152-0)

Seismic Loads

Seismic Loads Guide to the Seismic Load Provisions of ASCE 7-16

Finley A. Charney, Ph.D., P.E. Thomas F. Heausler, P.E., S.E. Justin D. Marshall, Ph.D., P.E.

Seismic Loads

Library of Congress Cataloging-in-Publication Data Names: Charney, Finley Allan, author. | Heausler, Thomas F., author. | Marshall, Justin D, author. Title: Seismic loads : guide to the seismic provisions of ASCE 7-16 / Finley A. Charney, Ph.D., P.E., Thomas F. Heausler, P.E., S.E., Justin D. Marshall, Ph.D., P.E. Other titles: Seismic loads (2020) Description: Reston, Virginia : American Society of Civil Engineers, 2020. | Includes bibliographical references and index. | Summary: “Authors Charney, Heausler, and Marshall provide clear, authoritative explanations of the seismic design provisions contained in Minimum Design Loads and Associated Criteria for Buildings and Other Structures, Standard ASCE/SEI 7-16”– Provided by publisher. Identifiers: LCCN 2019051180 | ISBN 9780784415504 (print) | ISBN 9780784482704 (pdf) | ISBN 9780784482728 (epub) Subjects: LCSH: Earthquake resistant design–Standards. | Earthquake resistant design–Case studies. Classification: LCC TA658.44 .C3824 2020 | DDC 624.1/762021873–dc23 LC record available at https://lccn.loc.gov/2019051180 Published by American Society of Civil Engineers 1801 Alexander Bell Drive Reston, Virginia 20191-4382 www.asce.org/bookstore | ascelibrary.org Any statements expressed in these materials are those of the individual authors and do not necessarily represent the views of ASCE, which takes no responsibility for any statement made herein. No reference made in this publication to any specific method, product, process, or service constitutes or implies an endorsem*nt, recommendation, or warranty thereof by ASCE. The materials are for general information only and do not represent a standard of ASCE, nor are they intended as a reference in purchase specifications, contracts, regulations, statutes, or any other legal document. ASCE makes no representation or warranty of any kind, whether express or implied, concerning the accuracy, completeness, suitability, or utility of any information, apparatus, product, or process discussed in this publication, and assumes no liability therefor. The information contained in these materials should not be used without first securing competent advice with respect to its suitability for any general or specific application. Anyone utilizing such information assumes all liability arising from such use, including but not limited to infringement of any patent or patents. ASCE and American Society of Civil Engineers—Registered in US Patent and Trademark Office. Photocopies and permissions. Permission to photocopy or reproduce material from ASCE publications can be requested by sending an email to [emailprotected] or by locating a title in the ASCE Library (http://ascelibrary.org) and using the “Permissions” link. Errata: Errata, if any, can be found at https://doi.org/10.1061/9780784415504. Copyright © 2020 by the American Society of Civil Engineers. All Rights Reserved. ISBN 978-0-7844-1550-4 (print) ISBN 978-0-7844-8270-4 (PDF) ISBN 978-0-7844-8272-8 (ePub) Manufactured in the United States of America. 26 25

24 23 22 21

2 3 4 5

Seismic Loads

Contents Preface

Abbreviations and Symbols

Table of Conversion Factors

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Overview of the ASCE 7 Seismic Load Provisions 1.1

Intent of the Seismic Load Provisions

1.2

Brief History of ASCE 7 Seismic Load Provisions

1.3

Overview of the Update Process for ASCE 7

1.4

Signiﬁcant Changes in ASCE 7-16 Relative to ASCE 7-10

Risk Category 2.1

Overview

2.2

Examples

1 2

5 7

Determining Ground Motion Parameters 3.1

Examples

3.2

Using the ASCE 7 Hazard Tool

21 23

Site Class Procedure for Seismic Design 4.1

Gathering Data

4.2

Site Class Determination

4.3

Site Classiﬁcation Example

4.4

Comments on Site Classiﬁcation

28 28 31 33

Developing an Elastic Response Spectrum 5.1

Chapter 6

xvii

Development of an Elastic Vertical Response Spectrum

Importance Factor and Seismic Design Category 6.1

Seismic Importance Factor Ie

6.2

Seismic Design Category

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Contents

Chapter 7

Selection of Structural Systems

7.1

Structural Conﬁguration Issues

7.2

Bearing Wall Systems

7.3

Dual Systems

7.4

Coupled Reinforced Concrete Shear Wall Systems

7.5

Cantilevered Column Systems

52 54

7.6 Steel Frame Systems Not Speciﬁcally Detailed for Seismic Resistance 55 7.7

Chapter 8

Alternate and Nonconforming Systems

Combinations of Lateral Load Resisting Systems

8.1 Combinations of Framing Systems in the Same Direction or in Different Directions 58 8.2

Combinations of Structural Systems in the Vertical Direction

8.3 Computing Approximate Periods of Vibration for Combined Systems 64 8.4 Vertical Combination When the Lower Section Is Stiff Relative to the Upper Portion 65

Chapter 9

Diaphragm Flexibility

9.1 Example Classiﬁcation of Diaphragm Flexibility Using Section 12.3.1.3 69 9.2

Accidental Torsion in Systems with Semirigid Diaphragms

Chapter 10 Horizontal Structural Irregularities

Chapter 11

10.1

Torsional Irregularities (Types 1a and 1b)

10.2

Reentrant Corner Irregularity (Type 2)

10.3

Diaphragm Discontinuity Irregularity (Type 3)

10.4

Out-of-Plane Offset Irregularity (Type 4)

10.5

Nonparallel System Irregularity (Type 5)

10.6

Consequences of Horizontal Irregularities

Vertical Structural Irregularities

80 81

11.1

Soft Story (Stiffness) Irregularities (Types 1a and 1b)

11.2

Weight (Mass) Irregularity (Type 2)

11.3

Vertical Geometric Irregularity (Type 3)

92 93

11.4 In-Plane Discontinuity in Vertical Lateral Force-Resisting Element Irregularity (Type 4) 93 11.5 Discontinuity in Lateral Strength–Weak Story Irregularity (Types 5a and 5b) 94 11.6

Consequences of Vertical Irregularities

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Contents

Chapter 12

Redundancy Factor

Chapter 13

Load Combinations

105

13.1

Basic Load Combinations

106

13.2 Special Seismic Load Combinations, Including the Overstrength Factor 111

Chapter 14

Chapter 15

Selection of Structural Analysis Procedures 14.1

Selection of Structural Analysis Procedures

14.2

Examples for Computing TS and Comparing to 3.5 TS

14.3

Structural Analysis Considerations

114 115

117

Structural Modeling Requirements 15.1

Chapter 16

113

119

Overview of Mathematical Modeling Requirements

Effective Seismic Weight (Mass)

119

125

16.1 Example 1: 4-Story Book Warehouse and Ofﬁce Building in Burlington, Vermont 125 16.2

Chapter 17

Example 2: Low-Rise Industrial Building

133

Period of Vibration 135 17.1

Approximate Fundamental Period Ta

135

17.2 Computing Ta for Masonry and Concrete Shear Wall Structures 141

Chapter 18

17.3

Periods of Vibration for Three-Dimensional Systems

17.4

Differences Between CuTa and Tcomputed

143

146

Description and Use of the Equivalent Lateral Force Procedure 147 18.1

Overview of the ELF Procedure

148

18.2 Use of the ELF Procedure for Purposes Other than Final Design 153

Chapter 19

Drift and P-delta Effects 19.1

Example Building

19.2

P-delta Effects

157

160

164

19.3 Back-Calculation of Stability Ratios when P-delta Effects are Included in Analysis 166 19.4

Computation of Actual Story Overstrength

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168

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Contents

Chapter 20 Accidental Torsion and Ampliﬁcation of Accidental Torsion 171 20.1 Application of Accidental Torsion in Systems with Relatively Flexible Semirigid Diaphragms 178

20.2 Application of Accidental Torsion and Torsional Ampliﬁcation in Modal Response Spectrum and Linear Response History Analysis 179

Chapter 21

Equivalent Lateral Force Analysis

185

21.1

8-Story Building

21.2

Two-Stage ELF Procedure According to Section 12.2.3.2

186

Chapter 22 Modal Response Spectrum Analysis 22.1

Overview

22.2

Response Spectrum Used for Analysis

22.3

System Modeling

208

22.4

Modal Properties

208

198

205

206 207

22.5 Number of Modes to Include in the Analysis and Modal Combination Procedure 209 22.6 Initial Scaling of Results (Determining Modal Response Parameters) 211 22.7

Analysis Results

22.8

Determination of Force Results

211 214

Chapter 23 Linear Response History Analysis 23.1

Overview

23.2

Response Spectrum Used for Analysis

23.3

System Modeling

224

23.4

Modal Properties

224

221

222 223

23.5 Number of Modes to Include in the Analysis and Modal Combination Procedure 225 23.6

Ground Motion Selection and Modiﬁcation

23.7

Analysis Results

225

234

Chapter 24 Comparison of Computed Response Using ELF, MRS, and LRH Analysis 249 24.1

Inelastic Story Drift Comparisons

24.2

Elastic Base Shear Comparisons

249 251

Chapter 25 Nonlinear Response History Analysis

261

25.1

Development Process

25.2

Overview of the ASCE 7-16 Chapter 16 Provisions

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263 264

Contents

Chapter 26 Diaphragms and Collectors

269

Nonstructural Components

277

Chapter 27

27.1 Example of Empirical Method for 4-Story Reinforced Concrete Building 280 27.2

Development and Use of Floor Response Spectra

27.3

1% Damping

292

Chapter 28 Nonbuilding Structures 28.1

287

Example 1: Pipe Rack

293 295

28.2 Example 2: Large Equipment Structures on a Pile Supported Mat 306

Chapter 29 Complete Seismic Load Analysis of Simple Building 309 29.1

Simple Building Details

29.2

Seismic Design

29.3

Accidental Torsion

29.4

Member and Connection Checks

309

310 312

Chapter 30 Frequently Asked Questions

314

321

I. Questions Covering General Issues

321

II. Questions Covering Design Issues

324

III. Questions Covering Structural Analysis Issues

329

Appendix A Overview of Modal Response History and Modal Response Spectrum Analysis 345 A.1

Overview of the MRS Procedure

A.2

Overview of the Modal Response History Procedure

A.3

Uniﬁed Approach

A.4

Direct Response History Analysis

A.5

Advantages of Response History Analysis

346

348 348 348

Appendix B 8-Story Building Case Study Structure References Index

361

365

About the Authors

373

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351

347

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Preface The purpose of this guide is to provide theoretical background and examples related to the use of the Standard ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures (2017a). The guide is also pertinent to users of recent editions of the International Building Code (ICC 2017), because the IBC refers directly to ASCE 7.

Sections of ASCE 7 Pertinent to the Guide Seismic Loads: Guide to the Seismic Load Provisions of ASCE 7-16 (the guide) has content pertinent to the following chapters of ASCE 7: Chapter 1: General Chapter 2: Combinations of Loads Chapter 11: Seismic Design Criteria Chapter 12: Seismic Design Requirements for Building Structures Chapter 13: Seismic Design Requirements for Nonstructural Components Chapter 15: Seismic Design Requirements for Nonbuilding Structures Chapter 16: Nonlinear Response History Analysis Chapter 20: Site Classification Procedure for Seismic Design Chapter 22: Seismic Ground Motion, Long-Period Transition, and Risk Coefficient Maps Seismic material excluded from the guide are Chapter 14 (“Material-Specific Design and Detailing Requirements”), Chapter 17 (“Seismic Design Requirements for Seismically Isolated Structures”), Chapter 18 (“Seismic Design Requirements for Structures with Damping Systems”), Chapter 19 (“Soil– Structure Interaction for Seismic Design”), and Chapter 21 (“Site-Specific Ground Motion Procedures for Seismic Design”). These topics are beyond the scope of this edition of the guide and may be included in future editions. The vast majority of the examples in the guide relate to Chapters 1, 2, 11, 12, and 22. Chapters 13, 15, 16, and 20 are covered in less detail and include worked examples for Chapters 13, 15, and 20. The material in Chapter 16 (“Nonlinear Response History Analysis”) presents an overview without a detailed example. The principal purpose of the guide is to illustrate the application of the ASCE 7 provisions and not to provide background on the theoretical basis of the provisions. Hence, theoretical discussion is kept to a minimum. However,

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Preface

explanations are provided in a few instances. The reference section of the guide contains a list of all technical publications cited in the chapters. Additional background is provided in the commentary to ASCE 7-16. One of the more important resources is the FEMA P-1051 report (FEMA 2016), which contains numerous detailed design examples that incorporate many of the requirements of ASCE 7-16. These examples (which cover also Chapters 16, 17, and 21 of ASCE 7-16) are much more detailed than those provided in this guide and concentrate on the structural design aspects of earthquake engineering, rather than the loads and structural analysis, which is the focus of the guide. The National Institute of Building Standards (part of NIST) provides another excellent set of seismic analysis and design references. These “technical briefs” cover a variety of subjects, including diaphragm behavior, design of moment frames, design of braced frames, and nonlinear structural analysis. The briefs can be downloaded at no charge from www.nehrp-consultants.org.

How to Use This Guide This guide is organized into a series of individual chapters. With the exceptions of Chapters 21 through 24 and Appendix B (which are based on the same 8-story building), each chapter stands alone and does not depend on information provided in other examples. This means that in some cases information is provided in the beginning of the example that requires some substantial calculations, but these calculations are not shown. For instance, in the example on drift and P-Delta effects (Chapter 19), the details for computing the lateral forces used in the analysis are not provided, and insufficient information is provided for the reader to back-calculate these forces. However, reference is made to other examples in the guide where similar calculations (e.g., finding lateral forces) are presented. The reader should always be able to follow and reproduce all new numbers (not part of the given information) that are generated in the examples. Equation, Table, and Figure Numbering: The examples presented in the guide often refer to sections, equations, tables, and figures in ASCE 7. All such items are referred to directly, without specific reference to ASCE 7. For instance, a specific example might contain the statement, “The response modification factor R for the system is provided in Table 12.2-1 of the standard.” References to sections, equations, tables, and figures that are unique to the guide are always preceded by the letter G and use bold text. For example, the text may state that the distribution of forces along the height of the structure is provided in Table G12-3 and illustrated in Figure G12-5. In this citation, the number 12 is the guide chapter number, and the number after the dash is the sequence number of the item (i.e., third table or fifth figure). Notation and Definitions: The mathematical notation in the guide follows directly the notation provided in Chapter 11 of ASCE 7. However, because the guide does not use all of the symbols in ASCE 7, a separate list of symbols

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Preface

actually used in the guide is provided in a separate section titled “Symbols Unique to the Guide.” This list also provides deﬁnitions for symbols that have been introduced in the guide.

Computational Units: All examples in the guide are developed in the US customary (English) system, as follows (with the standard abbreviation in parentheses): Length units: inches (in.) or feet (ft) Force units: 1,000 pounds (lb) or 1 kip (k) Time units: seconds (s). All other units (e.g., mass) are formed as combinations of the aforementioned units. A unit conversion table is provided. Appendixes and Frequently Asked Questions: In addition to the 30 individual chapters, the guide contains two appendixes. Appendix A provides an overview of the linear dynamic analysis procedures in Section 12.9 of the standard. Detailed examples that use the procedures are provided in Chapters 22 and 23 of the guide. Appendix B describes the 8-story steel building that is utilized in Chapters 21 through 24. Chapter 30 is titled “Frequently Asked Questions” (FAQ) in which several common questions are posed, together with the authors’ answers. In some cases, an interpretation of ASCE 7 is required, especially when the standard is ambiguous. The FAQ chapter is divided into sections on general requirements, design, and structural analysis. User Comments: Users are requested to notify the authors of any ambiguities or errors that are found in this guide. Suggestions for improvement or additions are welcomed and will be included in future versions. All questions should be sent to [emailprotected], with “Question about Guide to ASCE 7-16” provided as the subject matter of the email. Disclaimer: The interpretations regarding ASCE 7 requirements and any and all other opinions presented in this guide are those of the authors and do not necessarily represent the views of the ASCE 7 Standard Committee or ASCE.

Acknowledgments The authors would like to acknowledge the following individuals for their contributions to the guide: Kevin Aswegan, P.E., Magnusson Klemencic Associates, Seattle, Washington Ozgur Atalayan, Ph.D., P.E., Walter P Moore, San Francisco, California James R. Harris, Ph.D., P.E., J. R. Harris & Company, Denver, Colorado John Hooper, P.E., S.E. Magnusson Klemencic Associates, Seattle, Washington C. J. Smith, P.E., and Thomas Moore, Schnabel Engineering Associates, Blacksburg, Virginia (authors of the example on Site Class analysis, Chapter 4)

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Abbreviations and Symbols Abbreviations 2D 3D ACI AISC ANSI ASCE ASTM ATC BRB BSSC CBF CQC DE EBF ELF FEMA IBC ICC kcf LL LRH MCE MRS NEHRP NIST NGA NRH OC PEER RC SDC SRSS USGS

Two-dimensional Three-dimensional American Concrete Institute American Institute of Steel Construction American National Standards Institute American Society of Civil Engineers ASTM International formerly American Society for Testing and Materials Applied Technology Council Buckling-restrained brace Building Seismic Safety Council Concentrically braced frame Complete quadratic combination Design earthquake Eccentrically braced frame Equivalent lateral force Federal Emergency Management Agency International Building Code International Code Council kips per cubic foot Live load Linear response history Maximum considered earthquake Modal response spectrum National Earthquake Hazard Reduction Program National Institute of Standards and Technology Next-generation attenuation Nonlinear response history Occupancy Category Paciﬁc Earthquake Engineering Research Center Reinforced concrete Seismic Design Category Square root of the sum of the squares United States Geological Survey

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xvi

Abbreviations and Symbols

Symbols Unique to the Guide Symbol

Deﬁnition

Introduced in Chapter

CS FP K K M MpCk MpGk R Reff S Sai Sdi Tcomputed TMF TMN Vyi Γ δi Δo ΔCENTER ΔEDGE Δf ϕ ω

Combined scale factor Fundamental period scale factor Lateral stiffness of component Structural stiffness matrix Structural mass matrix Plastic moment strength of column k Plastic moment strength of girder k Modal excitation vector Effective response modiﬁcation coefﬁcient Suite scale factor Spectral acceleration in mode i Spectral displacement in mode i Period computed by structural analysis Period at which Equation (12.8-5) controls Cs Period at which Equation (12.8-6) controls Cs Story strength Modal participation factor Displacement in mode i Drift computed without P-delta effects Drift at geometric center of building Drift at edge of building Drift computed with P-delta effects Mode shape Circular frequency of vibration

Seismic Loads

6 6 9 20 20 10 10 20 7 6 20 20 10, 17 7 18 10 20 20 19 9 9 19 20 20

Table of Conversion Factors US customary units

International System of Units (SI)

1 inch (in.) 1 foot (ft) 1 statute mile (mi) 1 square foot (ft2) 1 cubic foot (ft3) 1 pound (lb) 1 pound (force) 1 pound per square foot (lb/ft2) 1 pound per cubic foot (lb/ft3) 1 degree Fahrenheit (°F) 1 British thermal unit (Btu) 1 degree Fahrenheit per British thermal unit (°F/Btu)

25.4 millimeters (mm) 0.3048 meter (m) 1.6093 kilometers (km) 0.0929 square meter (m2) 0.0283 cubic meter (m3) 0.4536 kilogram (kg) 4.4482 newtons (N) 0.0479 kilonewton per square meter (kN/m2) 16.0185 kilograms per cubic meter (kg/m3) 1.8 degrees Celsius (°C) 1.0551 kilojoules (kJ) 1.7061 degrees Celsius per kilojoule (°C/kJ)

xvii

Seismic Loads

1 Overview of the ASCE 7 Seismic Load Provisions

This chapter begins with an overview of the intent of the seismic load provisions of ASCE 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures. This is followed by a brief history of the standard, starting with the 1945 edition of ANSI A58-1 and proceeding through ASCE 7-16. Also described is the process for updating the standard.

1.1 Intent of the Seismic Load Provisions The intent of the ASCE 7-16 seismic load provisions is to provide a minimum level of reliability against collapse for buildings and other structures. The system-level target reliabilities are provided in terms of a conditional probability of failure in Table 1.3-2. For example, for systems assigned to Risk Category II, the target performance is that there is less than a 10% probability that the system will fail (collapse) when subjected to the maximum considered earthquake (MCE). There are no stated requirements for performance at any other limit state, such as limited displacement or limited damage under more frequently occurring events. However, there is an expectation that significant damage will appear during earthquakes that occur more frequently than the MCE. In fact, the damage (inelastic response of the seismic force–resisting system), when controlled by special design and detailing procedures, is desirable because it allows the system to be designed for forces significantly less than would occur if it remained elastic and suffered little or no damage. This design procedure, often called ductilitybased design, is facilitated for building structures in Chapter 12 of ASCE 7-16 by use of performance coefficients R, Cd, and Ω0, in association with a linear static or dynamic analysis. Similar procedures are used for the design of nonstructural components (Chapter 13) and nonbuilding structures (Chapter 15).

Seismic Loads

For special structures, such as hospitals or tall buildings, it is becoming common for performance-based design procedures to be used, in which the system is evaluated for multiple limit states. Such procedures are allowed in ASCE 7-16, with requirements provided in Section 1.3.1.3. Nonlinear analysis procedures are often utilized in performance-based design. Chapter 16 of ASCE 7-16 provides the requirements for nonlinear dynamic analysis. Additional details on the methodology for building and analyzing nonlinear dynamic analysis models are provided in the Paciﬁc Earthquake Engineering Research (PEER) Center’s document Guidelines for Performance-Based Design of Tall Buildings (PEER 2017).

1.2 Brief History of ASCE 7 Seismic Load Provisions ASCE 7 has an almost 100-year history, with numerous groups of engineers incrementally developing seismic loading procedures that resulted in ASCE 7-16. Included in the evolution of the standard are a host of building codes, standards, prestandards, and tentative or recommended provisions developed by the International Conference of Building Officials (and its predecessors), the American National Standards Institute (ANSI), the Structural Engineers Association of California (SEAOC), the Applied Technology Council (ATC), and the Building Seismic Safety Council (BSSC). Although the development process was initially haphazard with various groups producing somewhat different requirements in a variety of building codes at almost random intervals, the current procedure is now more deliberate. ASCE 7 is currently revised every 6 years, with most of the significant changes being developed in concert with BSSC and ASCE. The resulting document is adopted, with minor differences, by the International Building Code (IBC), which itself is updated on a 3-year cycle. ASCE 7-16 is the twelfth publication in a sequence of minimum design load standards. The National Bureau of Standards (NBS) published the first edition, American standard A58.1, in 1945. This edition, American Standard Building Code Requirements for Minimum Design Loads in Buildings and Other Structures, contained a total of 27 pages for all loads and included three pages of earthquake loading requirements. (This standard was preceded with a 1925 NBS report Minimum Live Loads Allowable for Use in Design of Buildings.) In ANSI A58.1-1945, the earthquake loading on the structural system was computed as V = CW, where C was taken as 0.2 and W is the total dead weight of the building, including 50% of the live load. Regional seismicity, structural dynamics, and ductility were not considered in any explicit manner. The A58.1 standard was updated in 1955. This document is titled Minimum Design Loads on Buildings and Other Structures. The seismic loading requirements (by use of an appendix) included references to differing seismicity in different regions of the country but provided no specific requirements for accounting for these differences. The design lateral force was still based on the formula V = CW, where W is the dead load plus total live load, and C varied over the height as function of the number of stories in the building. This was the first recognition, albeit in a very rudimentary manner, of lateral forces being

Seismic Loads

Overview of the ASCE 7 Seismic Load Provisions

related to the first mode shape. There was still no explicit recognition of the role of ductility in the structural system. In 1959, the seismology committee of SEAOC began publishing a document called Recommended Lateral Force Requirements and Commentary. Here, the design lateral force was V = KCW, where K is a system-dependent parameter, which ranged from 0.67 for moment-resisting frames to 1.33 for a shear wall system. This was the first occurrence of a factor that explicitly accounted for reduction in seismic design loads for systems deemed to exhibit better performance. The ⅓ coefficient C was taken as 0.05/T , where T is the period of vibration that is related only to building height and width. An exception allowed the period to be taken as 0.1 times the number of stories (N) for moment-resisting frames. Forces were distributed along the height in a triangular pattern for systems taller than two stories, and for slender buildings, 10% of the total lateral force was shifted to the top of the structure to account for higher mode effects. The term W was taken as the total dead load, plus 25% of live load for storage and warehouse occupancies. The SEAOC seismic design recommendations (often referred to as the Blue Book because of its blue cover) were periodically updated, and in general, these updates were absorbed into future editions of the A58.1 standard and into the earthquake loading provisions of the Uniform Building Code (UBC). However, before the publication for the first Blue Book, the UBC (itself first published in 1927) had rudimentary requirements for seismic loading. Because the A58.1 standard was intended to apply to the entire United States, it was necessary to include a zone factor Z, into the lateral force formula, and this first appears in the 1972 edition where V = ZKCW. Maps were provided that identified three zones, with Z = 0.25 for Zone 1, 0.5 for Zone 2, and 1.0 for Zone 3. The 1982 edition of ANSI A58.1 introduced two additional terms into the equation for determining total seismic base shear, where V = ZIKCSW. The term I was an occupancy importance factor, set as 1.25 for buildings with occupancy greater than 300 persons in one area, 1.5 for essential facilities, and 1.0 for all other buildings. The soil profile coefficient, S, recognized increased ground acceleration on softer soils, and ranged from 1.0 to 1.5. The number of seismic zones was expanded to Zones 0 to 4, for which the coefficient for Zone 4 is 1.0 and reduces to 0.125 for Zone 0. Before the release of ANSI A58.1-1982, the NBS and the National Science Foundation (NSF) funded the development of a new concept in seismic provisions for seismic loads. The new provisions, referred to as ATC 3-06, were developed by a team of practitioners and academics and were published by the Applied Technology Council as Tentative Provisions for the Development of Seismic Regulations for New Buildings (ATC 1978). Several significant changes in philosophy were implemented into ATC 3-06, including the following: 1.

Design basis was shifted from working stress to ultimate strength,

Seismic risk was changed from quasi-deterministic (seismic zones and zone factors) to probabilistic,

Seismic Loads

Structures were designated in terms of Seismic Performance Category, which ranged from A to D, and speciﬁc analysis and design requirements were tied to these categories, and

Assessment of the system to determine the presence of horizontal and vertical irregularities was required, with a variety of consequences, penalties, or restrictions being imposed if such irregularities exist.

The seismic base shear formula became V = CSW, where CS is taken as 1.2Av S/RT 2/3 but not greater than 2.5 Aa/R. The terms Av and Aa were probabilistic peak ground accelerations (obtained from maps), and R is the seismic response modification coefficient. R values and corresponding deflection amplification factors, Cd, were provided for 21 systems. Example R values are R = 8 for special moment frames, R = 5.5 for reinforced concrete shear wall systems, and R = 5 for steel braced frames. The R values were based on judgment and data available at the time of writing, as opposed to coefficients that could be determined mathematically or by analysis, and it was acknowledged that the values would need to be revised periodically as seismic behavior became better understood. The ATC 3-06 provisions also provided for the first time explicit requirements for modal response spectrum analysis and the inclusion of P-delta effects in analysis. The provisions were updated in 1982, with the update containing approximately 250 changes relative to the original document. In 1979, the Building Seismic Safety Council was formed, initially to debate and discuss ATC 3-06 (Harris 1992). Included in the evaluation of ATC 3-06 were a comprehensive series of trial designs, leading to further modifications of the provisions. In 1986, FEMA published the first edition (1985) of the NEHRP Recommended Provisions for the Development of Seismic Regulations for New Buildings (note that the word “Recommended” replaced the word “Tentative” in the ATC 3-06 document). This was essentially a revision of ATC 3-06 and included changes that resulted from the BSSC deliberations and trial designs. Shortly after the release of the 1985 NEHRP provisions, ANSI A58.1 was updated and identified as ASCE 7-88. The name change reflected the increased role that the ASCE Technical Division on Codes and Standards had in the development of seismic loads standards. ASCE 7-88 was essentially identical to ANSI A58.1-1982, and thus had not yet shifted to the ATC 3-06/NEHRP provisions philosophy. In 1988, the first revision to the NEHRP provisions was released, and this formed the basis for ASCE 7-93, which was published in 1994. This was the first edition of ASCE 7 to fully embrace the concepts developed in ATC 3-06. The cycle of ASCE 7 updates following updates of the NEHRP provisions has continued until present, wherein ASCE 7-16 was updated shortly after the 2015 NEHRP provisions were published. Additional information regarding the relationship between the NEHRP provisions and ASCE 7 is provided subsequently in this chapter. Although the NEHRP provisions were the foundation for updates to ASCE 7, revisions to the seismic load provisions in the UBC did not fully follow suit.

Seismic Loads

Overview of the ASCE 7 Seismic Load Provisions

Table G1-1. Updates to Various Codes and Standards Documents

Code or standard ANSI A58.1 ASCE 7 SEAOC Blue Book UBC NEHRP provisions IBC

Year of published updates 1945, 1955, 1988, 1993, 1959, 1966, 1927, 1935, in 1997 1985, 1988, 2000, 2003,

1972, 1995, 1973, 1937,

1982 1998, 2002, 2005, 2010, 2016 1974, 1988, 1996, 1999 and every 3 years thereafter, concluding

1991, 1994, 1997, 2003, 2010, 2015 2006, 2009, 2012, 2015, 2018

Figure G1-1. Number of pages (exclusive of commentary) for ANSI A58.1 and ASCE 7. Whereas many of the basic concepts of the provisions were adopted, the UBC only gradually transitioned from a working stress basis to a strength basis (deferred until 1997) and never fully transitioned from zone maps to probabilistic seismic hazard maps. Starting with the 2000 International Building Code (IBC), the seismic provisions are essentially fully compliant with the latest release of ASCE 7, because the IBC adopts ASCE 7 by reference (with a few speciﬁed changes). Table G1-1 provides a summary of the updates of ANSI A58.1, ASCE 7, the Blue Book, the NEHRP provisions, UBC, and IBC. Also provided is Figure G1-1, which shows a history of the number of pages (exclusive of commentary) of the seismic provisions from 1945 to 2016. The large increase in page numbers that occurred in 1993 is because of the shift inspired by ATC 3-06.

1.3 Overview of the Update Process for ASCE 7 ASCE 7 is updated every 6 years. The work to revise the seismic provisions in the standard is performed by the Seismic Subcommittee. This subcommittee consisted of approximately 70 individuals for ASCE 7-16, including practitioners, government employees, academicians, industry representatives, and others.

Seismic Loads

There are several task committees (e.g., general provisions, ground motions, nonstructural components, nonbuilding structures, seismic isolation, and added damping systems). Most of the task committee members also participate as a member of the Seismic Subcommittee. The Seismic Subcommittee and the related task committees operate under a set of rules established by the ASCE Codes and Standards Committee and are approved by ANSI. Further, the Seismic Subcommittee follows its own charter and operating procedures. The charter lists the following goals: 1.

Simplify and clarify the requirements to the extent possible, which is also a goal of the main committee;

Review and ballot proposed changes to the previous edition of ASCE 7 prepared by external users;

Review changes being developed for the NEHRP provisions, and based on them, create ballot change proposals to ASCE 7 for potential incorporation;

Review the proposed changes to other standards (e.g., ACI–318, AISC 341), and based on these, propose changes to ASCE 7;

Review other source documents (e.g., the latest version of IBC) and, based on the results, propose changes to ASCE 7;

Create other proposals as appropriate to correct errors or improve the seismic provisions of ASCE 7, including other areas of the standard that are directly part of seismic design (e.g., load combinations); and

Edit the ASCE 7 seismic provisions to address errors and formatting issues as required.

Proposed changes to the standard may be submitted by anyone but must include a reason or rationale for the proposed change. The proposals not initiated by the ASCE Seismic Committee or the NEHRP Provisions Update Committee (PUC) are first reviewed by a joint coordinating committee (JCC) to determine whether they should be initially processed by the PUC. If approved by the PUC they will be forwarded to the Seismic Subcommittee for further action. The PUC also develops a series of proposed changes and these are published as Part 1 of the NEHRP provisions. Such proposals are automatically considered but not necessarily adopted (at all or without extensive modifications) by the Seismic Subcommittee. The Seismic Subcommittee and the various task committees may also develop proposals. The Seismic Subcommittee and the various task committees meet two to three times a year during the first two or three years of the update process. Meetings last approximately 2 days, with task committees meeting first, and then reporting to the full Seismic Subcommittee. Proposed changes are then balloted by the Seismic Subcommittee and must be approved by two-thirds of the voting members before they are sent to the ASCE 7 Main Committee. Members voting no are required to provide a written basis for their negative vote. Before full revisions of the standard are developed, supplements may be issued. These supplements in general correct errors in the first printing, provide minor

Seismic Loads

Overview of the ASCE 7 Seismic Load Provisions

updates, or in some cases make signiﬁcant changes if a current provision is deemed unsafe. For example, a supplement to ASCE 7-10 replaced a minimum base shear requirement that was eliminated in the initially published document. The replacement was based on new research ﬁndings that were not available during the previous cycle’s development process. In another example, Supplement 1 to ASCE 7-10’s seismic provisions included an extensively expanded commentary.

1.4 Signiﬁcant Changes in ASCE 7-16 Relative to ASCE 7-10 There were numerous changes to the seismic provisions in ASCE 7-16 relative to the 2010 edition. These are too numerous to enumerate fully in this guide, although it is noted that locations of changes are clearly identiﬁed by vertical bars next to the changed item. The following is an example from Chapter 11 of ASCE 7-16: BASE SHEAR: Total design lateral force or shear at the base. BOUNDARY ELEMENTS: Portions along wall and diaphragm edges for transferring or resisting forces. Boundary elements include chords and collectors at diaphragm and shear wall perimeters, edges of openings, discontinuities, and reentrant corners. BUILDING: Any structure whose intended use includes shelter of human occupants. In the remainder of this guide, those changes that are most relevant to the materials presented are listed in the beginning of each chapter. However, this is not a complete list of changes. The following is an example from Chapter 14 of this guide: Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • • • •

Linear response history (LRH) analysis was removed from Chapter 16 and new requirements were written and placed in Chapter 12. Section 12.9 was retitled “Linear Dynamic Analysis,” and the modal response spectrum (MRS) procedure and LRH analysis were placed in this section. The Chapter 16 procedures for nonlinear response history (NRH) analysis were rewritten. Three-dimensional mathematical models must be used in MRS and LRH analysis. Scaling requirements for MRS and LRH analyses were changed to require the dynamic base shear computed using these procedures to be not less than 100% of the equivalent lateral force (ELF) seismic base shear. The previous requirement was scaling to at least 85% of the ELF base shear.

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2 Risk Category

Changes in ASCE 7-16, relative to ASCE 7-10 that affect this chapter: •

There are no changes to ASCE 7-16 relative to ASCE 7-10 that inﬂuence this chapter.

This chapter covers the selection of risk category for a variety of buildings and other structures.

2.1 Overview Risk category is used in several places in ASCE 7, including • • • • •

Determination of importance factor, Ie (Section 11.5.1 and Table 1.5-2), Requirements for protected access for Risk Category IV structures (Section 11.5.2), Determination of Seismic Design Category (Section 11.6 and Tables 11.6-1 and 11.6-2), Determination of drift limits (Section 12.12.1 and Table 12.12-1), and Determination of importance factor for nonstructural components (Section 13.1.3).

Table 1.5-1 provides general descriptions for all risk categories. The risk categories range from I (buildings and other structures that represent a low risk to human life in the event of failure) to IV (buildings and other structures that are designated as essential facilities and/or pose a substantial hazard to the community in the event of a failure). Risk category is not related to the speciﬁc

Seismic Loads

hazard for which the loads are determined. However, the magnitude of the loads and other design criteria associated with a given hazard is usually a function of the risk category (or the importance factor, Ie). Owing to the broad risk category descriptions in Table 1.5-1, the table is likely to be insufficient for classifying risk in many cases. More detailed descriptions of risk category are provided in Table 1604.5 of the 2018 International Building Code (ICC 2017). In several cases the IBC risk category descriptions include reference to occupancy groups, specifically Occupancy Group I, which is used for institutional facilities. These groups, which are defined in Section 308 of IBC, are further subdivided into four separate subgroups as follows: • • • •

I-1: Structures or portions thereof for more than 16 persons who reside on a 24 hour (h) basis in a supervised environment and receive custodial care. Examples include assisted living facilities and convalescent care facilities. I-2: Buildings and other structures used for medical care on a 24 h basis for more than five persons who are incapable of self-preservation. Examples include hospitals and nursing homes. I-3: Buildings and other structures that are inhabited by more than five persons who are under restraint or security. Examples include detention centers, jails, and prisons. I-4: Buildings and other structures used for day care, where more than five persons of any age receive custodial care for less than 24 h per day.

Also of interest are Group E occupancies (Section 305 of IBC) that are facilities used for education, up to the 12th grade, and are used by more than six persons at one time. Several of the risk category descriptions in IBC Table 1604.5 depend on the “occupant load” of the building. Chapter 2 of IBC defines the occupant load as “the number of persons for which the means of egress of a building or portion thereof is designed.” Occupant load is determined in accordance with Chapter 10 of IBC. Some of the specific IBC triggers for classification of the higher occupancies are (Table 1604.5):

Risk Category III:

• Buildings used primarily for public assembly with occupant load greater than 300, • Buildings containing Group E occupancies with occupant load greater than 250, • Buildings containing educational occupancies above 12th grade with occupant load greater than 500, • Group I-2 facilities with occupant load greater than 50 and without surgery or emergency treatment, • Group I-3 occupancies, • Any other occupancy with an occupant load greater than 5,000, and • Facilities containing materials deemed toxic to humans.

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Risk Category

Risk Category IV: • • • • • • • •

Group I-2 occupancies having surgery or emergency treatment, Fire, rescue, ambulance, and police stations, Emergency vehicle garages, Designated earthquake or hurricane emergency shelters, Designated emergency preparedness and communication centers, Aircraft control towers, Buildings and other structures critical to national defense, and Facilities containing materials deemed highly toxic to humans.

In regard to toxic materials, the risk category can be reduced to II if an assessment is made in accordance with Section 1.5.3 of ASCE 7 that the release of the materials is not sufficient to pose a threat to the public. For those working outside the United States and using ASCE 7, the local building code and/or the Authority Having Jurisdiction should be consulted for risk category guidance, because the requirements of IBC may not be applicable. In the following examples, the use of Table 1.5-1 of ASCE 7 in conjunction with Table 1604.5 of IBC is demonstrated through several scenarios. For each example, the structure is briefly described, and the risk category is presented followed by discussion. Note that selection of risk category can be somewhat subjective. When in doubt, the local building official should be consulted. Although each individual example in this chapter provides a geographic location for the building or structure under consideration, this location is not relevant to the selection of the risk category. These locations are provided simply to add some realism to the scenarios given.

2.2 Examples Example 1 A 3-story building on a university campus in Blacksburg, Virginia, housing offices and classrooms. The occupant load is 375. Answer: Risk Category = II. Explanation: Risk Category II was chosen because the building has an occupant load of less than 500, which is the threshold of classifying the building as Risk Category III. Note that a high school (secondary school) building with an identical configuration would be considered Risk Category III because it is classified as Group E and the occupant load is greater than 250.

Example 2 A 6-story medical ofﬁce building with outpatient surgical facilities located in Austin, Texas. The occupant load for the building is 400.

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Answer: Risk Category = II. Explanation: Risk Category II is used because the building is not open 24 h per day and thus is not considered as an IBC Occupancy Group I-2 building. In general, the surgical facilities are not used in the case of emergencies and are not considered critical.

Example 3 A one-story elderly care facility (Alzheimer’s care and nursing home) with an occupant load of 120, located in Savannah, Georgia. Answer: Risk Category = III. Explanation: Risk Category III is used because the facility falls under IBC Occupancy Group I-2 (i.e., residents are usually incapable of self-preservation in the event of an evacuation), and has an occupant load of more than 50, but has no surgery or emergency care capability.

Example 4 A 40-story casino and hotel in Reno, Nevada. Gambling rooms, ballrooms, and theaters accommodate as many as 800 people each. Total hotel occupant load is 6,500 as calculated in IBC Chapter 10. Answer: Risk Category = III. Explanation: Risk Category III is selected because the facility has an occupant load greater than 5,000 people.

Example 5 Municipal courthouse and ofﬁce building, containing two prisoner holding cells (a maximum of 15 prisoners in each) and a sheriff’s department radio dispatcher facility, located in Richmond, California. Courtrooms have a maximum capacity of 120. Answer: Risk Category = III. Explanation: In this case, the driving factor is the prisoner holding cells, which are in IBC Occupancy Group I-3. If the radio dispatcher facility were ofﬁcially designated as an emergency communication center, the risk category would advance to IV.

Example 6 Retail ﬁreworks building in Chattanooga, Tennessee, of approximately 10,000 ft2. The occupancy load is 125. Answer: Risk Category = II or III.

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Risk Category

Explanation: Although fireworks can be considered explosive, the energy released by the explosions is relatively small (compared to, for example, a facility that stores military munitions). For this reason, Risk Category II is selected. This is a case in which a discussion with the local building official would be useful because there is some potential for classification as Risk Category III.

Example 7 Major television network news afﬁliates ofﬁce building in Tallahassee, Florida, that contains two studios for broadcasting local news. The facility is not a designated emergency communication center. The occupant load is 235. Answer: Risk Category = II. Explanation: Risk Category II is selected because the building is not designated as an emergency communication center.

Example 8 A 95-story, mixed-use building in Chicago, Illinois, containing two ﬂoors of retail facilities (shops and restaurants with a maximum capacity of 60), 50 levels of ofﬁce building space, and 43 levels of apartments. Answer: Risk Category III. Explanation: A building of this size would have an occupant load greater than 5,000.

Example 9 A one-story bus station in Santa Fe, New Mexico. Buses enter the facility to load and unload passengers. The computed occupant load is 350. Answer: Risk Category = III. Explanation: Risk Category III is selected because the occupant load is greater than 300 and because Section 303.4 of IBC classiﬁes transportation waiting areas as public areas of assembly.

Example 10 Beverage manufacturing, warehouse, and distribution facility in Golden, Colorado. The occupant load for this building is 125. Answer: Risk Category = II. Explanation: Risk Category II is used because higher categories are not appropriate. The facility cannot be designated as Risk Category I because it is not a minor storage facility.

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Example 11 Grandstand for a college football stadium with seating for 15,000 individuals in Lubbock, Texas.

Answer: Risk Category = III. Explanation: For this structure the occupant load is greater than 5,000, so Risk Category III is required.

Example 12 Dockside cargo storage warehouse adjacent to the Houston Ship Channel. The building is one story with a gross floor area of 30,000 ft2. Cargo is transported by forklifts and overhead cranes and is moved in and out daily. The cargo may contain certain liquids in metal drums considered toxic to humans. The occupant load is 60. Answer: Risk Category = III Explanation: Although the principal use of this nonessential facility is for storage, there is significant human activity in the structure, so a classification of Risk Category I is not appropriate. In general, the storage of toxic materials requires Risk Category III. According to Section 1.5.3 of ASCE 7 (and similar language in footnote b of IBC Table 1604.5), the structure may be classified as Risk Category II if it can be demonstrated through a hazard assessment and risk management plan that the release of toxic materials does not pose a threat to the public.

Example 13 Grain storage silo in Hays, Kansas. Answer: Risk Category = I. Explanation: This assignment is based on the classiﬁcation of this nonbuilding structure as an agricultural facility that poses a low threat to human life in the event of a failure.

Example 14 Pedestrian bridge between a baseball stadium and an adjacent parking lot. One end of the bridge is supported by the stadium superstructure. The bridge spans over a spur of an interstate highway. Estimated maximum number of people on the bridge at any time is 220. The bridge is in San Antonio, Texas. Answer: Risk Category = III. Explanation: The stadium would have Risk Category III because the stadium occupant load would be substantially greater than 5,000. The bridge is given Risk

Seismic Loads

Risk Category

Category III because it is a means of egress from the stadium and is thereby classiﬁed as part of the stadium. An additional consideration is the fact that a full or partial collapse of the bridge onto the interstate would inhibit the movement of emergency vehicles.

Example 15 The entry foyer for a regional hospital in St. Louis, Missouri. The 1,800 ft2, glassenclosed structure is separate from, but closely adjacent to, the hospital. The main purpose of the foyer is for visitors to the hospital to gain access to the main hospital building. A reception desk and several unmanned information kiosks are also in the foyer. There is a covered walkway between the main hospital and the foyer. Hospital staff and emergency personnel and ambulances gain access through other portals. Answer: Risk Category = II or IV. Explanation: The hospital is clearly a Risk Category IV facility. If the foyer were an operational entry into the hospital, Section 11.5.2 of ASCE 7 would require the foyer to be classified as Risk Category IV as well. However, because hospital staff and emergency personnel do not gain access through the foyer, the entry foyer may be considered nonoperational, and hence, may be classified as a Risk Category II structure. Consultation with the local building official would be appropriate before a final designation is made. See also Section 1.5.2 that discusses systems with multiple risk categories.

Seismic Loads

3 Determining Ground Motion Parameters

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • •

The seismic hazard maps have been updated, which affects the determination of the seismic coefficients SS, S1, and PGA. The values for the site coefficients Fa and Fv in Tables 11.4-1 and 11.4-2, respectively, have changed considerably. Requirements for site specific procedures have been expanded.

In this example, the design basis spectral accelerations SDS and SD1 are found for sites in speciﬁc geographical locations. They are ﬁrst approximately determined by hand, using maps and tables provided by ASCE 7, and are then checked through the use of a software utility provided by the Applied Technology Council (ATC). The use of the new ASCE Hazard Tool is also illustrated. The basic ground motion parameters in ASCE 7 are SS and S1. SS is the “short period” spectral acceleration (T = 0.2 s), and S1 is the 1 s (T = 1.0 s) spectral acceleration for sites on the boundary of Site Class B and C. These accelerations are based on the risk-targeted maximum considered earthquake (MCER), for which there is approximately a 2% probability of being exceeded in 50 years (i.e., occurs once every 2,475 years) and 5% damping. It should be noted that in ASCE 7 the terms SS and S1 (and related derived values SDS and SD1) are referred to as “spectral acceleration response parameters.” The units associated with the values assigned to these parameters are not consistent throughout the ASCE 7-16. For example, in the maps of Chapter 22, values of

Seismic Loads

acceleration are given in terms of percent of gravity (e.g., a mapped value for SS of 30 in Figure 22-1 is 0.3g). Where used with Equation 12.8-6, S1 is unitless. In the development of response spectra, Figure 11.4-1 indicates that the units are g. In this chapter and in other chapters of this guide, spectral acceleration response parameters are typically (but not always) shown in units of g, regardless of use. SS and S1 are used in several ways in ASCE 7, including the determination of the design-level acceleration parameters SDS and SD1. The design accelerations include a site coefficient factor (Fa or Fv), which accounts for soil characteristics different from firm rock, and a multiplier of 2/3, which effectively converts from the MCER basis to a somewhat lower level of shaking, called the design earthquake (DE). The site coefficients are obtained directly or by interpolation from values provided in Tables 11.4-1 and 11.4-2. SS and S1 are obtained from maps (Figures 22-1 through 22-8) that are provided in Chapter 22. Peak ground acceleration (PGA) values are provided in Figures 22-9 through 22-13. Long-period transition periods TL are provided in Figures 22-14 through 22-17. Owing to the large scale of the maps, the SS and S1 values that are obtained from the maps may be very imprecise. Thus, it is more common to determine the values of SS and S1 from a web-based tool. This example illustrates the use of the maps and tables and is then reworked using a tool provided by the ATC. Also illustrated is the use of the ASCE 7 Hazard Tool. The site coefficients Fa and Fv have changed considerably relative to ASCE 7-10: 1.

Values of Fa and Fv, provided in Tables 11.4-1 and 11.4-2, respectively, have been changed for several site class/ground motion combinations.

Both tables now provide a value of Fa and Fv less than 1.0 for ground motion magnitudes on Site Class B. However, these values are applicable only if site-speciﬁc shear wave velocity measurements have been made. If such measurements have not been made, both Fa and Fv are to be taken as 1.0 for all ground motion magnitudes. See Section 11.4.3.

When Site Class D is taken as the default site class (not based on measurements), the value of Fa should not be taken as less than 1.2. This limit will control for values of Ss > 0.75g. See Section 11.4.4.

It is now required to perform a site-speciﬁc hazard analysis for SS > 0.75g in Site Class E, and/or for S1 > 0.1g. See Section 11.4.8.

When determining Fv in Site Class D and E, where S1 is greater than or equal to 0.2g, a site-speciﬁc hazard analysis is required. An exception allows for the use of the tabulated values for Fv when T is less than or equal to 1.5Ts. For longer periods, the seismic coefﬁcient Cs must be multiplied by 1.5. See Section 11.4.8.

Several of the values for FPGA have changed in Table 11.8-1, and the tabulated values for Site Class B must be increased from 0.9 to 1.0 if site-speciﬁc shear wave velocity measurements are not available. See Section 11.4.3.

ASCE 7-16 provides commentary for background regarding the technical basis for the changes.

Seismic Loads

Determining Ground Motion Parameters

Table G3-1 is similar to Table 11.4-1, with the exception that extra rows have been added for the Site Class B locations without velocity measurements and for the default Site Class D situation. Table G3-2 is similar to Table 11.4-2, except that a row was added for Site Class B without shear wave velocity measurements. Table G3-3 is similar to Table 11.8-1, except that a row was added for Site Class B without shear wave velocity measurements.

Table G3-1. Short-Period Site Coefﬁcients Fa Site class A B B C D D E

(w/ m) (w/o m) (investigated) (default)

SS ≤ 0.25

SS = 0.50

SS = 0.75

SS = 1.0

SS = 1.25

SS ≥ 1.5

0.8 0.9 1.0 1.3 1.6 1.6 2.4

0.8 0.9 1.0 1.3 1.4 1.4 1.7

0.8 0.9 1.0 1.2 1.2 1.2 1.3

See 11.4.8

0.8 0.9 1.0 1.2 1.1 1.2 See 11.4.8 See 11.4.8

0.8 0.9 1.0 1.2 1.0 1.2 See 11.4.8 See 11.4.8

Note: Similar to Table 11.4-1. B (w/ m) indicates that Site Class B was established with the use of on-site geophysical measurements of shear wave velocity; B (w/o m) indicates without on-site measurements as described in Section 11.4.3. D (investigated) indicates that soil properties were investigated, and the shear wave velocities were determined in accordance with Chapter 20. D (default) indicates that soil properties are not known in sufﬁcient detail as described in Section 11.4.3 and are thus subject to a minimum Fa of 1.2 per Section 11.4.4.

Table G3-2. Long-Period Site Coefﬁcients Fv Site class A B B C D D E F

(w/ m) (w/o m) (investigated) (default)

S1 ≤ 0.10

S1 = 0.20

S1 = 0.30

S1 = 0.40

S1 = 0.50

S1 ≥ 0.6

0.8 0.8 1.0 1.5 2.4 2.4 4.2 See 11.4.8

0.8 0.8 1.0 1.5 2.2* 2.2* 3.3* See 11.4.8

0.8 0.8 1.0 1.5 2.0* 2.0* 2.8* See 11.4.8

0.8 0.8 1.0 1.5 1.9* 1.9* 2.4* See 11.4.8

0.8 0.8 1.0 1.5 1.8* 1.8* 2.2* See 11.4.8

0.8 0.8 1.0 1.4 1.7* 1.7* 2.0* See 11.4.8

Seismic Loads

0.8 0.9 1.0 1.3 1.6 1.6 2.4 See 11.4.8

A B B C D D E F

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0.8 0.9 1.0 1.2 1.4 1.4 1.9 See 11.4.8

PGA = 0.2 0.8 0.9 1.0 1.2 1.3 1.3 1.6 See 11.4.8

PGA = 0.3 0.8 0.9 1.0 1.2 1.2 1.2 1.4 See 11.4.8

PGA = 0.4

0.8 0.9 1.0 1.2 1.1 1.1 1.2 See 11.4.8

PGA = 0.5

0.8 0.9 1.0 1.2 1.1 1.1 1.1 See 11.4.8

PGA ≥ 0.6

Note: Similar to ASCE 7-16 Table 11.8-1. B (w/ m) indicates that Site Class B was established with the use of on-site geophysical measurements of shear wave velocity; B (w/o m) indicates without on-site measurements as described in Section 11.4.3. D (investigated) indicates that soil properties were investigated, and the shear wave velocities were determined in accordance with Chapter 20. D (default) indicates that soil properties are not known in sufﬁcient detail as described in Section 11.4.3 and are thus subject to a minimum Fa of 1.2 per Section 11.4.4.

(investigated) (default)

(w/ m) (w/o m)

PGA ≤ 0.1

Site class

Table G3-3. Site Coefﬁcients FPGA

20 Seismic Loads

Determining Ground Motion Parameters

Tables G3-1 and G3-2 reﬂect modiﬁcations made in Supplement 1 of ASCE 7-16, effective December 12, 2018.

3.1 Examples Example 1. Find Ground Motion Values for a Site in Savannah, Georgia For this example, a site in downtown Savannah, Georgia, is considered. Shear wave tests have been conducted and indicate that the soil matches the characteristics of Site Class D. ASCE 7 provides only large-scale maps in Figures 22-1 and 22-2. Savannah lies on the coast, just below the border between South Carolina and Georgia. Figure G3-1 shows the building site location marked with a small star. Site latitude–longitude coordinates are (32.06, −81.09). The maps provided in Chapter 22 of the standard do not have the resolution required to determine the ground motion parameters. Fortunately, two webbased tools are available for determining the ground motion values. The first of these is developed by the ATC, and can be found at https://hazards.atcouncil.org/. The tool uses site coefficients consistent with ASCE 7-16. The site location may be specified in several ways, but the preferred approach is usually to specify the site’s latitude and longitude. Figure G3-2 shows the page with relevant data entered for the chosen site, and Figure G3-3 shows some additional data provided by the program. The following values are provided in the detailed report: SS = 0.310g S1 = 0.113g PGA = 0.168g

Fa = 1.552 Fv = 2.374 FPGA = 1.464

SMS = 0.481g SM1 = 0.268g PGAM = 0.246g

SDS = 0.320g SD1 = 0.179g

The long-period transition period TL is not provided in the tool but can easily be determined from Figure 22-14, which indicates TL = 8.0 s. Also not provided by the tool is the transition period TS which can be calculated as follows: TS = SD1/SDS = 0.179/0.320 = 0.559 s.

Example 2. Find Ground Motion Values for a Site in Raleigh Hills, Oregon This example is for the steel frame building described in detail in Appendix B. The site is located at latitude–longitude coordinates (45.48, −122.76), and the soil has been classiﬁed as Site Class C (determined by use of shear velocity tests). Values provided by use of the ATC tool are SS = 0.885g S1 = 0.402g PGA = 0.401g

Fa = 1.200g Fv = 1.500g FPGA = 1.200g

SMS = 1.062g SM1 = 0.603g PGAM = 0.481g

SDS = 0.708g SD1 = 0.402g

The long-period transition period TL is not provided in the tool but can easily be determined from Figure 22-14, which indicates TL = 16.0 s. Also not provided by the tool is the transition period TS = SD1/SDS = 0.402/0.708 = 0.568 s.

Seismic Loads

Figure G3-1. Site location in Savannah, Georgia.

Figure G3-2. Screenshot of parameters entered into the ATC Hazard Tool for Site Class D in Savannah. If the shear wave velocity tests indicate that the site class is D, the ATC tool returns the following parameters: SS = 0.885g S1 = 0.402g PGA = 0.401g

Fa = 1.146g Fv = 1.898g FPGA = 1.199g

SMS = 1.014g SM1 = 0.763g PGAM = 0.481g

SDS = 0.676g SD1 = 0.568g

The transition period TS = 0.568/0.676 = 0.840 s. It is very important to note, however, that the report also indicates that because S1 > 0.2g for this site, a sitespeciﬁc seismic hazard analysis may be required. See Section 11.4.8 for details.

Seismic Loads

Determining Ground Motion Parameters

Figure G3-3. Additional data from ATC Hazard Tool for Site Class D in Savannah.

3.2 Using the ASCE 7 Hazard Tool ASCE created the ASCE 7 Hazard Tool that can be accessed (by subscription only) at https://asce7hazardtool.online/. Readers can click on “Guest” and see wind and tsunami data free or they can click on subscribe and see hazard data for all seven hazards including wind, seismic, ice, rain, ﬂood, snow and tsunami. Readers can also view a video on the ASCE 7 corporate page at https:// www.asce.org/asce-7/. For seismic design, it is again convenient to enter latitude and longitude (45.479, −122.7559). Values provided in the ASCE 7 Hazard Tool’s report for Site Class C are the same as those given by the ATC tool: SS = 0.885g S1 = 0.402g

SMS = 1.062g SM1 = 0.603g

SDS = 0.708g SD1 = 0.402g

Fa = 1.200 Fv = 1.500

Figures G3-4 through G3-6 show images captured from the report. The preceding Fa and Fv values are not reported by the ASCE tool and were back-calculated from the given values. The PGA values also are not reported. When the tool is used for the Site Class D condition, the results are provided as shown in Figure G3-7, in which the results for the long-period accelerations (SM1, SD1) are reported as “null.” This is attributed to the note (superscript a) in

Seismic Loads

Figure G3-4. ASCE 7 Hazard Tool input parameters for Site Class C in Oregon.

Figure G3-5. ASCE 7 Hazard Tool intermediate results for Site Class C in Oregon.

Seismic Loads

Determining Ground Motion Parameters

Figure G3-6. ASCE 7 Hazard Tool results for Site Class C in Oregon.

Figure G3-7. ASCE 7 Hazard Tool results for Site Class D in Oregon. Table 11.4-2 that directs one to Section 11.4.8, which states that a site-specific seismic hazard analysis must be carried out for Site Class D locations where S1 is greater than or equal to 0.2g. However, the site-specific analysis need not be carried out if the value of the seismic response coefficient Cs (see Section 12.8.1) is increased by a factor of 1.5 for structures with periods less than 1.5Ts. It is the engineer’s responsibility to make this adjustment when computing Cs.

Seismic Loads

4 Site Class Procedure for Seismic Design

Changes in ASCE 7-16, relative to ASCE 7-10 that affect this chapter: •

There are no changes to ASCE 7-16 relative to ASCE 7-10 that inﬂuence this chapter.

This example illustrates the development of site class in accordance with Chapter 20 of ASCE 7. Site class is used to characterize the type and properties of soils at a given site and account for their effect on the site coefficients, Fa and Fv, used in developing the design response spectrum (e.g., generalized simplified seismic analysis, per Chapter 12). The procedure can also require a site response analysis in accordance with Section 21.1, depending on the site class determination. However, the site classification procedure does not encompass evaluation of potential geologic and seismic hazards (Section 11.8). The example set forth is applicable for the site classification procedure provided in Chapter 20 of ASCE 7. See Chapter 11 for definitions pertaining to the site classification procedure. Based on the competency of the soil and rock material, a site is categorized as Site Class A, B, C, D, E, or F. The site classes range from hard rock to soft soil profiles as presented in Table G4-1. This table appears in ASCE 7 as Table 20.3-1. For this example, the shear wave velocity criteria are not covered in detail. Shear wave velocity correlations and direct measurement require considerable

Seismic Loads

Table G4-1. Site Classiﬁcation

Site class A. B. C. D. E.

vs ( ft/s)

Hard rock Rock Very dense soil and soft rock Stiff soil Soft clay soil

F. Soils requiring site response analysis in accordance with Section 21.1.

N or N ch (blows/ft)

su (lb/ft2)

>5,000 NA NA 2,500 to 5,000 NA NA 1,200 to 2,500 >50 >2,000 600 to 1,200 15 to 50 1,000 to 2,000 25 ft (7.6 m) with PI > 75] (see Section 20.3.1 for possible exceptions); or

Very thick soft to medium stiff clays [H > 120 ft (37 m)] with su < 1,000 lb/ft2 (50 kPa) (see Section 20.3.1 for possible exceptions).

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Unless one of the preceding exceptions is met, a site response analysis (Section 21.1) shall be performed for sites determined to be Site Class F. Site response analysis exceptions vary depending on the speciﬁc site condition.

Step 2: Check Site Class E (Section 20.3.2) If a proﬁle contains a soft clay layer with all the following characteristics, the site shall be classiﬁed as Site Class E: 1.

Hlayer > 10 ft (3 m),

PI > 20,

w ≥ 40%, and

su < 500 lb/ft2 (25 kPa).

Step 3: Check Site Class C, D, E (Section 20.3.3), or A, B (Sections 20.3.4 and 20.3.5) Using one of the following three methods, categorize the site using Table G4-1. All computations of vs , N, N ch , and su shall be performed in accordance with Section 20.4. vs Method: An advantage of using shear wave velocity data is that the measured behavior better characterizes the subsurface proﬁle than data collected from point locations (i.e., borings). Disadvantages of the method include the relatively expensive cost, as well as experience required, to perform and interpret the data. If appropriate shear wave velocity data are available, vs shall be calculated for the top 100 ft (30 m) using Equation (20.4-1) and the appropriate site class determined from Table G4-1. If the classiﬁcation falls into criteria of either Site Class A or B in Table G4-1, the following additional criteria shall be considered: • •

Site Class A or B shall not be assigned to a site if there is more than 10 ft (3 m) of soil between the rock surface and the bottom of the spread footing or mat foundation (Section 20.1). Shear wave velocity criteria speciﬁed in Section 20.3.4 for Site Class B, and in Section 20.3.5 for Site Class A, shall be observed.

The applicable site class depends on which of the preceding criteria are met. N Method: Using standard field penetration values for all soil and rock layers, N shall be calculated for the top 100 ft (30 m) using Equation (20.4-2). N and other similar symbols are defined in Section 11.3. The following should be considered regarding standard field penetration values (Section 20.4.2): •

ASCE 7 states that standard penetration resistance values as “directly measured in the ﬁeld without corrections” should be used. The author believes that energy corrections based on the type of hammer used should

Seismic Loads

Site Class Procedure for Seismic Design

•

• •

be applied because this difference is fundamental in the values measured. For instance, the standard penetration values from an automatic hammer should be appropriately increased to safety hammer (N60) values to reflect the high efficiency of the automatic hammer. Equation (20.4-2) requires a single N value for each distinct layer in the profile. Where multiple boring values are available from a single layer, average the values or choose conservative values to characterize each distinct layer. Use a maximum of 100 blows/ft. See Section 20.4.2 for discussion. Where refusal is met for a rock layer, N shall be taken as 100 blows/ft.

Nch and su Method: Divide the 100 ft (30 m) profile into cohesionless and cohesive layers in accordance with the definitions presented in Section 20.3.3. Using standard field penetration values for the cohesionless layers, N ch shall be calculated using Equation (20.4-3). The comments on standard field penetration values listed in the section titled “N Method” apply to N ch . Using undrained shear strength values for the cohesive layers, su shall be calculated using Equation (20.4-4). As stated in Section 20.4.3, undrained shear strength values shall be determined in accordance with ASTM D2166 or ASTM D2850. Determining a site class requires two steps, first using N ch as the classification criterion, and second using su as the classification criterion (Table G4-1). If the site classes differ, the site shall be assigned a site class corresponding to the softer soil (Section 20.3.3).

4.3 Site Classification Example The site profile presented in this example represents highly idealized subsurface conditions. Interpretation of actual subsurface data and soil properties requires substantial judgment by the geotechnical professional. The site profile used in the example is shown in Figure G4-2. The blow counts in the example represent N60 values obtained from a safety hammer. As noted in the “N Method” section, the author believes these are the appropriate values to be used in seismic site class determination. The steps previously outlined are applied to the subsequent example.

Step 1: Check Site Class F If the profile meets any of the criteria in Section 20.3.1, the site shall be classified as Site Class F. This profile has been chosen to ensure that Site Class F does not apply. However, this check should not be overlooked in practice.

Step 2: Check Site Class E If the proﬁle contains any layers meeting all of the criteria in Section 20.3.2, the site shall be classiﬁed as Site Class E. Soft clay layer criteria are checked next:

Seismic Loads

Figure G4-2. Subsurface proﬁle. Note: Standard penetration values presented as N60 values (ASTM 2004). Soil designations are based on USCS classiﬁcation (ASTM 2011).

Soft clay: Layer 2: Layer 4:

H > 10 ft H = 11 ft H = 12 ft

PI > 20 PI = 27 PI = 23

w ≥ 40% w = 16% w = 34%

su < 500 lb/ft2 su = 1,200 lb/ft2 su = 400 lb/ft2

where bold indicates a criterion that is not met. Layer 2 does not qualify based on its water content and undrained shear strength. Layer 4 does not qualify based on its water content. Because neither layer satisﬁes all of the soft clay layer criteria, the site does not automatically qualify for Site Class E.

Step 3: Check Site Class C, D, E, or A and B For this step, use the N method to determine site class. Using this method automatically excludes Site Class A or B because they are based on shear wave velocity. Using the notation from Equation (20.4-2), the following information was determined from the example proﬁle in Table G4-2. Based on the value of N = 100/8.65 = 12 calculated using Equation (20.4-2), the site classiﬁes as Site Class E (N < 15) in accordance with Table G4-1. Some observations that can be made from the values in Table G4-2 are the following:

Seismic Loads

Site Class Procedure for Seismic Design

Method. Table G4-2. Summary of N Layer i

Soil or rock designation

1 2 3 4 5 6 7 8

SC (ﬁll) CL SC CL SM SP-SM Rock Rock

Cohesionless*

Cohesive*

X X X X X X X X

Ni (blows/ft)

di (ft)

di/Ni

17 9 13 3 15 26 62 100

7 11 13 12 17 15 10 15

0.41 1.22 1.00 4.00 1.13 0.58 0.16 0.15

Total 100 Total 8.65 N = 100/8.65 = 12 * Based on ASCE 7-16 deﬁnition; Section 20.3.3.

• •

Standard penetration value of 50 blows/in. at refusal (85 ft) was assigned a maximum value allowed of 100 blows/ft (Section 20.4.2); and Based on the known geology, this blow count was then used from refusal to a depth of 100 ft to complete the site proﬁle, resulting in a 15 ft layer with blow counts of 100 blows/ft.

4.4 Comments on Site Classification Although highly idealistic, the site profile used in this example illustrates the need for adequate site investigation. Had only the data from shallow boring (B-1) been available, the designer would be unaware of the potentially soft clay layer encountered in B-2 and B-3. Other important considerations that may impact the site classification and require the use of engineering judgment, because they are not explicitly covered by the code, include: • • • •

Where to begin the site profile for below-grade structures, Incorporating planned site grading (cut and fill) at the site, Applicability of the design response spectrum method (generalized simplified seismic analysis) to structures supported on deep foundations, and Characterizing highly variable site profiles (e.g., layer thickness and/or properties) within a given site.

A brief discussion of these considerations can be found in the code commentary, Section C20.3.

Seismic Loads

5 Developing an Elastic Response Spectrum

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • • •

Section number changes in Chapter 11 because of the insertion of a new Section 11.4.1; Ground motion acceleration parameters have been changed (new maps); Site coefﬁcients Fa and Fv presented in Tables 11.4-1 and 11.4-2, respectively, have changed considerably; and New procedures are provided in Section 11.9 for developing vertical response spectra.

In this example, an elastic horizontal acceleration response spectrum is generated for a site near Savannah, Georgia. The development of an elastic vertical acceleration response spectrum is also illustrated. An elastic spectrum is used directly in the modal response spectrum analysis approach (Section 12.9.1), as a target for spectrum matching in linear response history analysis (Section 12.9.2) and as a target for spectrum matching or ground motion scaling in nonlinear response history analysis (Section 16.2.3). The basic form of the design response spectrum for horizontal acceleration is shown in Figure 11.4-1 of ASCE 7. This spectrum, which represents the total acceleration of the mass (ground acceleration plus acceleration of the mass relative to the ground), has four branches: 1.

Straight-line ascending portion between T = 0 and T = T0 [Equation (11.4-5)],

Seismic Loads

Constant acceleration portion between T = T0 and T = TS (Sa = SDS),

Descending constant velocity region between T = TS and T = TL [Equation (11.4-6)], and

Descending constant displacement region beyond TL [Equation (11.4-7)].

The four branches of the spectrum are controlled by the design earthquake spectral accelerations SDS and SD1, by Equation (11.4-5), which describes the ﬁrst branch of the spectrum, and by the long-period transition period TL, which is provided by the contour maps of Figures 22-14 through 22-17. The other transitional periods, T0 and TS, are computed according to Section 11.4.6 as follows: T 0 = 0:2T S T S = S D1 =S DS The spectral acceleration between T = 0 and T=T0 is given by Equation (11.4-5). When T = 0, this equation produces an acceleration of 0.4(SDS). This result approximates the design-level peak ground acceleration. More accurate values of peak ground acceleration can be found from Figures 22-9 through 22-13 of the standard or from the ATC Hazard Tool (https:/hazards.atcouncil.org/). Figure G5-1 shows the total acceleration spectrum (as designated previously) and the associated relative velocity and a relative displacement (deformation) spectra that were plotted for an unspeciﬁed site where SDS = 0.6g, SD1 = 0.3g, and TL = 4.0 s. The transitional periods T0 and TS are 0.1 and 0.5 s, respectively. For the purpose of plotting the spectra, the units on SDS and SD1 are in terms of g, the acceleration of gravity. Using g = 386.4 in./s2, the relative velocity spectrum is obtained by multiplying all ordinates of the acceleration by 386.4/(2π/T), and the relative displacement spectrum is obtained by multiplying all ordinates of the acceleration spectrum by 386.4/(2π/T)2. The constant acceleration, constant velocity, and constant displacement regions of the spectra are clearly visible from Figures G5-1(a–c), respectively. A more detailed presentation of the construction of both a horizontal and vertical acceleration response spectrum is illustrated next. The parameters for the default Site Class D location are as follows: SS = 0.312g Fa = 1.55 SMS = 0.484g SDS=0.322

S1 = 0.120g Fv = 2.36 SM1 = 0.283 SD1=0.189

TL = 8.0 s

Chapter 22 Tables 11.4-1 and 11.4-2 Equations (11.4-1) and (11.4-2) Equations (11.4-3) and (11.4-4)

The horizontal acceleration response spectrum to be used in modal response spectrum analysis is constructed for periods up to 4.0 s because it is expected that the fundamental period of the structure is less than this. Note, however, that for the purpose of developing spectrally matched ground motions or scaling ground motions for use in response history analysis, the period range for the spectrum should be extended beyond the fundamental period by a factor of 1.2

Seismic Loads

Developing an Elastic Response Spectrum

(b)

(a)

(c)

Figure G5-1. Acceleration, velocity, and displacement spectra: (a) horizontal total acceleration; (b) horizontal relative velocity; and (c) horizontal relative displacement. for linear response history analysis (Section 12.9.2.3.1) and by a factor of not less than 1.5 for nonlinear response history analysis (Section 16.2.3.1). For Site Class D, the acceleration at T = 0 is 0.4 SDS = 0.4(0.322) = 0.129g. The transitional period TS = SD1/SDS=0.189/0.322 = 0.587 s. The constant acceleration portion of the spectrum begins at T = 0.2TS = 0.2(0.587) = 0.117 s and ends at TS. The complete horizontal acceleration response spectrum for the Site Class D location is plotted with a black line in Figure G5-2. Because the spectrum is plotted for a maximum period of 4.0 the “constant displacement” branch is not shown. For use in a structural analysis program, the response spectrum is often presented in a table of period-acceleration values. In some cases, the spectrum is automatically generated from values of SDS, SD1, and TL. When creating a table of spectrum values, it is important to provide sufficient resolution in the curved portions. Discrete spectral values are provided in Table G5-1 and the same points are represented by squares on Figure G5-2 for the Site Class D spectrum. It is important to recognize that the elastic response spectrum developed in this example has not been adjusted by the importance factor Ie, nor by the response modification coefficient R. These two parameters, as well as the deflection

Seismic Loads

Figure G5-2. Elastic design response spectra (R = 1, Ie= 1) for various site classes for which SS = 0.313g and S1 = 0.120g. Table G5-1. Elastic Design Spectral Ordinates (R = 1, Ie = 1) for a Site Class D Location Period T (s)

Spectral acceleration Sa (g)

0 0.117 (T0) 0.587 (Ts) 0.65 0.75 1.00 1.50 2.00 2.50 3.00 3.50 4.00

0.134 0.322 0.322 0.290 0.252 0.189 0.126 0.094 0.076 0.063 0.054 0.047

amplification parameter Cd, are applied in modal response spectrum analysis (Section 12.9.1) and linear response history analysis (Section 12.9.2). For illustrative purposes only, response spectra are also shown in Figure G5-2 for Site Classes A, B, and C. Parameters used to draw the curves are provided in Table G5-2. Figure G5-2 shows that site class can have a profound effect on the level of ground acceleration for which a structure must be designed. For the example given, SDS for Site Class D is 1.72 times the value when the site class is B. SD1 increases by a factor of 2.94 when the site class changes from B to D. Note also the significant increase in the transitional period TS as the site class moves from A to D. This can have an influence on the permitted analysis method because, as indicated in Table 12.6-1, the equivalent lateral force method of analysis is not allowed for some systems where T exceeds 3.5 TS.

Seismic Loads

Developing an Elastic Response Spectrum

Table G5-2. Elastic Design Response Spectrum Parameters (R = 1, Ie= 1) for Various Site Classes for which SS = 0.312g and S1 = 0.120g

Site class A B C D

SDS (g)

SD1 (g)

TS (s)

0.80 0.90 1.30 1.55

0.80 0.80 1.50 2.36

0.166 0.187 0.270 0.322

0.061 0.064 0.120 0.188

0.365 0.342 0.444 0.585

5.1 Development of an Elastic Vertical Response Spectrum Section 11.9 of the standard provides procedures for developing a vertical response spectrum. This spectrum could theoretically be used in association with modal response spectrum analysis but is intended to provide an alternate to the Section 12.4.2.2 requirements for including vertical seismic load effects. This procedure is only required to be used for three classes of nonbuilding structures according to Section 15.1.4 of the standard. Also, the spectrum developed is for the MCE level ground motions. To convert to the design earthquake the spectral acceleration values must be multiplied by 2/3; this step is not shown in this example. Equations (11.9-1) through (11.9-4) deﬁne the shape of the spectrum as follows: S aMv = 0.3C v S MS S aMv = 20C v S MS ðT v − 0:025Þ + 0.3C v S MS

for T v ≤ 0:025 s

(11.9-1)

for 0.025 < T v ≤ 0.05 s

(11.9-2)

Figure G5-3. Vertical acceleration spectrum for Site Class D and SMS = 0.484g.

Seismic Loads

S aMv = 0.8 C v S MS

for 0.05 < T v ≤ 0.15 s

(11.9-3)

S aMv = 0.8C v S MS ð0.15=T v Þ0.75

for 0.15 < Tv ≤ 2.0 s

(11.9-4)

where SMS is the 0.2 s MCE horizontal ground acceleration, Cv is a vertical coefﬁcient obtained from Table 11.9-1, and Tv is the vertical period of vibration corresponding to the vertical acceleration that is being computed. For the previous example, SMS = 0.484g. Interpolating from Table 11.9-1, Cv = 0.908 is obtained. The vertical response spectrum calculated from these parameters is shown in Figure G5-3.

Seismic Loads

6 Importance Factor and Seismic Design Category

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • •

Owing to new hazard maps, ground motion values Ss and S1 have changed The values of the site coefﬁcients Fa and Fv presented in Tables 11.4-1 and 11.4-2, respectively, have changed considerably. It is more likely that a site-speciﬁc analysis will be required for softer soils in higher seismic hazard regions.

This chapter demonstrates the determination of the seismic importance factor and the seismic design category.

6.1 Seismic Importance Factor Ie The seismic importance factor (Ie) is a function of the risk category and is provided in Table 1.5-2. The values of Ie are Ie = 1.0 for Risk Categories I and II, Ie = 1.25 for Risk Category III, and Ie = 1.5 for Risk Category IV. The primary use of the importance factor is in the determination of design lateral forces. For example, Equation (12.8-2) provides the response coefﬁcient Cs for short period systems (i.e., T < Ts) as follows: S C s = DS R Ie

Seismic Loads

(12.8-2)

Seismic Loads

in which Ie appears to be a modiﬁer of R, which is an incorrect interpretation because R is a system-dependent parameter that is independent of risk. Another interpretation of Ie is obtained when Equation (12.8-2) is written as follows:

Cs =

S DS I e R

(G6-1)

In the revised equation, Ie appears to act as a multiplier of the design spectral acceleration. This also is an incorrect interpretation because the level of ground motion felt by a building is not a function of risk. The true purpose of the importance factor is to provide additional strength for risk-critical facilities. For the same level of ground motion and type of detailing, a stronger building will have lower ductility demand and less damage than a weaker system. Ductility demand is also reduced by limiting drift, and Ie (indirectly) serves this purpose as well. This can be seen by the allowable drifts provided in Table 12.12-1, which are a function of the risk category, and through Table 11.5-1 are also directly related to the importance factor. Thus, when considering both strength and deformation, a Risk Category IV building of a given R value, with Ie = 1.5, would be designed for 1.5 times the strength and, for most structures (see “all other structures” in Table 12.12-1), would have half of the allowable drift of an identical structure designed with a risk category of I or II. The comparison of system behaviors with different importance factors is shown through a set of idealized force-deformation plots in Figure G6-1. The Risk Category IV building with Ie = 1.5 would have a signiﬁcantly lower ductility demand and probably would sustain less damage than the system with Ie = 1.0. Damage is reduced, but not eliminated, in Risk Category IV systems. The seismic importance factor also appears in the computation of story drift [Equation (12.8-15)]: δx =

C d δxe Ie

(12.8-15)

Figure G6-1. Force-displacement plots for system designed with various Ie.

Seismic Loads

Importance Factor and Seismic Design Category

where the Ie in the denominator cancels the Ie that is included in the computation of δxe, which is directly proportional to Cs [see Equation (G6-1)]. This avoids an effective double counting of the importance factor because the computed drift and the drift limits are both either directly or indirectly related to importance factor. A similar situation appears in Equation (12.8-16) θ=

P x ΔI e V x hsx C d

(12.8-16)

In this case, the Ie in the numerator replaces the Ie that was removed in Equation (12.8-15), and the Cd in the denominator of Equation (12.8-16) removes the same term that is in the numerator of Equation (12.8-15). This results in the term VxCd/ΔIe being a true measure of story elastic stiffness, which is effectively being compared to the story geometric stiffness Px/hsx.

6.2 Seismic Design Category Seismic design category (SDC) is deﬁned in Section 11.6 and Tables 11.6-1 and 11.6-2. The parameters that affect SDC are the risk category and the design level spectral accelerations SDS and SD1, or for very high-level ground motions, the mapped maximum considered earthquake (MCER) spectral acceleration S1 (Section 11.4). The SDC depends on the site class because SDS and SD1 are directly related to the site class via Equations (11.4-1) and (11.4-2). In the examples that follow, two sites, one in eastern Tennessee and the other near Concord, California, are considered. For each site, consideration is given to the same structure constructed on soils with Site Class B or D. Consideration is given also to two different risk categories for each site: II and IV. The results of the calculations are presented in Tables G6-1 and G6-2 for the eastern Tennessee and Concord locations, respectively. For the eastern Tennessee site, which is of relatively low seismicity, the SDC for the Site Class B location is B for Risk Category II buildings and C for Risk Category IV buildings. For Site Class D, the SDC is C for the Risk Category II building and D for the Risk Category IV building. The increased SDC on

Table G6-1. Determination of Seismic Design Category for Site in Eastern Tennessee Ground motion parameters (g) Site class B D

SDS

0.42 0.42

0.13 0.13

0.280 0.409

Seismic design category

SD1

Risk Category II

Risk Category IV

0.087 0.203

B D

C D

Seismic Loads

Table G6-2. Determination of Seismic Design Category for Site in Concord, California Ground motion parameters (g)

Site class B D

Seismic design category

SDS

SD1

Risk Category II

Risk Category IV

1.74 1.74

0.60 0.60

1.16 1.16

0.40 0.68

D D

Site Class D soils is attributable to the soil ampliﬁcation represented by the factors Fa and Fv (see subsequent calculations). Thus, in eastern Tennessee, the SDC ranges from B to D, depending on use and site. Moving from SDC B to D has signiﬁcant effects on the selection, design, and detailing of the structural system. In Concord, the SDC is D in all cases. Had the ground motions been somewhat stronger, with S1 greater than 0.75g, the SDC would be increased to E for Risk Category I, II, and III structures and increased to F for Risk Category IV structures.

Detailed Calculations for Eastern Tennessee From Figures 22-1 and 22-2 (or from the ASCE 7 Hazard Tool), SS = 0.42g and S1 = 0.13g. For Site Class B (site-speciﬁc velocity measurements not made): F a = 1:0 and F v = 1:0

(Tables 11.4-1 and 11.4-2)

2 2 S DS = F a S S = ð1.0Þð0.42Þ = 0.280g 3 3

[Equations (11.4-1) and (11.4-3)]

2 2 S D1 = F v S 1 = ð1.0Þð0.13Þ = 0.087g 3 3

[Equations (11.4-2) and (11.4-4)]

SDC = B for Risk Category II

(Tables 11.6-1 and 11.6-2)

SDC = C for Risk Category IV

(Tables 11.6-1 and 11.6-2)

For Site Class D (measured): F a = 1:46 and F v = 2:34

(Tables 11.4-1 and 11.4-2)

2 2 S DS = F a S S = ð1.46Þð0.42Þ = 0.409g 3 3

Seismic Loads

[Equations (11.4-1) and (11.4-3)]

Importance Factor and Seismic Design Category

2 2 S D1 = F v S 1 = ð2.34Þð0.13Þ = 0.203g 3 3

[Equations (11.4-2) and (11.4-4)]

SDC = D for Risk Category II

(Tables 11.6-1 and 11.6-2)

SDC = D for Risk Category IV

(Tables 11.6-1 and 11.6-2)

Detailed Calculations for Site near Concord, California From Figures 22-1 and 22-2 (or from the ASCE 7 Hazard Tool), SS = 1.74g and S1 = 0.60g. For Site Class B (site-speciﬁc velocity measurements not made): F a = 1:0 and F v = 1:0

(Tables 11.4-1 and 11.4-2)

2 2 S DS = F a S S = ð1.0Þð1.74Þ = 1.16g 3 3

[Equations (11.4-1) and (11.4-3)]

2 2 S D1 = F v S 1 = ð1.0Þð0.60Þ = 0.40g 3 3

[Equations (11.4-2) and (11.4-4)]

SDC = D for Risk Category II

(Tables 11.6-1 and 11.6-2)

SDC = D for Risk Category IV

(Tables 11.6-1 and 11.6-2)

For Site Class D (measured, see Section 11.4.8 Item 3, which requires site-speciﬁc ground motion, or Section 11.4.8 Exception 2 for additional requirements): F a = 1:00 and F v = 1:70

(Tables 11.4-1 and 11.4-2)

2 2 S DS = F a S S = ð1.00Þð1.74Þ = 1.16g 3 3

[Equations (11.4-1) and (11.4-3)]

2 2 S D1 = F v S 1 = ð1.70Þð0.60Þ = 0.68g 3 3

[Equations (11.4-2) and (11.4-4)]

SDC = D for Risk Category II

(Tables 11.6-1 and 11.6-2)

SDC = D for Risk Category IV

(Tables 11.6-1 and 11.6-2)

Seismic Loads

Seismic Design Category Exception for Buildings with Short Periods Under certain circ*mstances, determining the SDC on the basis of SDS only is permitted. The speciﬁc requirements are listed as four numbered points in Section 11.6. This provision applies only for systems with very short periods of vibration (with the approximate period Ta less than 0.8TS). This exception, where applicable, may result in the lowering of the SDC from, say, C to B, where the SDC of C would be required if the exception were not evaluated.

Seismic Loads

7 Selection of Structural Systems

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • •

•

No new structural systems were added. A new Section 12.2.1.1 was added that describes procedures for analysis and design of “Alternate Structural Systems” not included in Table 12.2-1. Such systems would be typically analyzed using the nonlinear response history procedure that is described in the fully revised Chapter 16. New Section 12.2.1.2 was added that provides requirements and exceptions for detailing members of the seismic force-resisting system.

In this chapter the basic concepts of selecting a structural system are discussed, and the factors that are most likely to affect the choice of a system are reviewed. This is followed by a brief overview of some of the different types of structural systems allowed in the standard. The best structural system for a particular building depends on a large number of factors, such as architectural and functional requirements, labor, fabrication, construction costs, and inspection requirements. These issues are so variable that they cannot be addressed in this guide. However, another consideration in the system selection can be addressed, and this chapter explains how the provisions of ASCE 7 may affect or restrict choices that may be made. Section 12.2.1, together with Table 12.2-1, provides the basic rules for the selection of seismic force resisting systems. Table 12.2-1 is divided into broad categories, such as bearing wall systems, building frame systems, and dual

Seismic Loads

systems, and it provides a number of system types within each category. Limitations are placed on the use of each system in terms of SDC and structural height hn. For example, ordinary steel concentrically braced frames (System 3 under the Building Frame Systems category) are not permitted (NP) in SDC F, are allowed only up to heights of 35 ft in SDC D and E, and are allowed with no height limit (NL) in SDC B and C. Section 12.2.5.4 provides conditions under which certain highly ductile building frame systems may have their structural height limits increased above the values shown in Table 12.2-1. For each system, three design parameters are speciﬁed: • • •

Response modification coefficient R, System overstrength factor Ω0, and Deflection amplification factor Cd.

Among the different parameters listed in Table 12.2-1, R is very important for system selection because the seismic base shear V is inversely proportional to this parameter via the seismic response coefﬁcient Cs. Aside from R, another important value involved in system selection is the period of vibration T, because the base shear V is also inversely proportional to this value. For the purpose of determining seismic base shear, T is usually taken as CuTa, which is the upper limit on the computed period. Please see Chapter 17 of this guide, “Period of Vibration,” for additional details. Equations (12.8-2) through (12.8-4) form three branches of the design response spectrum. It is noted, however, that it would be extremely rare for Equation (12.8-4) to control the design of a building because T for buildings is almost always less than the minimum value of TL = 4 s. See “Frequently Asked Questions,” G5, for more details on the use of TL. Cs =

S DS R=I e

Equation (12.8-2) applies where T ≤ TS

Cs =

S D1 TðR=I e Þ

Equation (12.8-3) applies where TS < T ≤ TL

Cs =

S D1 T L T 2 ðR=I e Þ

Equation (12.8-4) applies where T > TL

where TS = SD1/SDS

Section 11.4.6.

Three inelastic design spectra for an unspeciﬁed site with SDS = 0.5 and SD1 = 0.2 are presented in Figure G7-1. The three curves, from top to bottom, are for a special concentrically braced frame (CBF) (R = 6), a steel plate shearwall (SPSW) (R = 7), and a special steel moment frame (SSMF) (R = 8). In all cases the importance factor Ie = 1.0. Two horizontal lines are also drawn. The upper line represents the minimum value of Cs given by Equation (12.8-5) as 0.044SDSIe, which is applicable for SS < 0.6. The lower line is the absolute minimum value of Cs = 0.01 when SS < 0.6. Each of the plotted lines has two markers, one for a

Seismic Loads

Selection of Structural Systems

Figure G7-1. Inelastic design spectrum for 2- and 10-story systems. system that is 2 stories tall with hn = 25 ft., and the other for a system that is 10 stories tall with hn = 125 ft. Some observations made from Figure G7-1 are as follows: 1.

For the two-story system: The design base shear for the CBF and the SPSW is controlled by Equation (12.8-2), with Cs = 0.0833 and 0.0714, respectively. The SMF system is controlled by Equation (12.8-3), with Cs = 0.0453. Thus, the base shear in the CBF is 1.17 times that of the SPSW, and 1.84 times that of the SSMF. These factors are related to differences in the R values and in the period of vibration T = CuTa because both R and T appear in the denominator of Equation (12.8-3).

For the 10-story system: The design base shear for the CBF and SPSW system is controlled by Equation (12.8-3) with Cs = 0.0297 and 0.0254, respectively. For the SSMF system, the Cs value is controlled by the minimum base shear requirement of Equation (12.8-5), with Cs = 0.022 (which is signiﬁcantly greater than the lower limit of 0.01).

For the 10-story SSMF system, the effective R value is 4.55, and is signiﬁcantly less than the designated value of 8.0 provided in Table 12.2-1. Note that the effective R value is the value of R, when used in Equation (12.8-3) that would produce the same base shear as given by Equation (12.8-5). Because the effective R value for the SSMF is so much less than 8, it seems that there might be some false economy provided by the SSMF system.

The basic point that is made by the preceding discussion is that system economy is related to a number of factors, with R being among the most important parameters. However, other factors such as deﬂection limits, period of vibration, and minimum base shear requirements can be important when deciding on a structural system. Another important point to be made is that there is no restriction on highly ductile systems being used in low seismic hazard areas. However, where such systems are used, the detailing must be as speciﬁed in the material standard, for

Seismic Loads

example, AISC 341-16 (AISC 2015) or ACI 318-14 (ACI 2014), even if wind forces in combination with gravity forces control the sizing of the structural components. Thus, costly detailing that is not required may again be leading to false economy.

7.1 Structural Conﬁguration Issues An important consideration for structural economy is related to the placement of the lateral load resisting systems within the building plan. For architectural reasons it is often necessary to place shear walls and braced frames away from the façade of the building, and a logical choice is to place these components within the service core. (See Chapter 10 of this guide and Figure G10.3 for a graphic illustration of this effect). Placing all of the lateral load resistance within the core tends to produce torsionally irregular systems that are subject to a host of penalties including the application of accidental torsion, and the requirement to evaluate drift at the edges of the building. In addition, it is not unusual for an initially torsionally irregular building to be extremely irregular when components are removed to evaluate structural redundancy. If this happens (or if the system is initially extremely irregular), the redundancy factor ρ becomes 1.3, which increases all seismic design forces by 30%. See Section 12.3.4 of the standard and Chapters 10, 12, and 13 of this guide for additional discussion on these issues.

7.2 Bearing Wall Systems Section 11.2 defines bearing wall systems (under the definition for “Wall”) as systems in which bearing walls support all or major parts of the vertical load. Presumably, a major portion would be more than 50% of the total vertical load. Bearing walls are defined as (1) a “metal or wood stud wall that supports more than 100 lb/linear ft of vertical load in addition to its own weight,” or (2) a “concrete or masonry wall that supports more than 200 lb/linear ft of vertical load in addition to its own weight.” Given this definition, the likelihood is that most metal or wood stud walls or concrete/masonry walls would be classified as bearing walls. The main difference between bearing wall systems and building frame systems (which encompass the same lateral load resisting elements) is that the R values for bearing wall systems are usually lower than those for the corresponding building frame system. Values of Cd for bearing walls can be equal to or less than the value for the corresponding building frame system. Height limitations are the same for a given bearing wall and corresponding building frame system. In addition, there are no bearing wall systems in structural steel, except for lightframed systems with steel sheets or light strap bracing. Consider the system shown in Figure G7-2. This system, 1-story high, has ordinary precast concrete walls around the perimeter. Where designated as a bearing wall system (A5 in Table 12.2-1), the design values are R = 4, Ω0 = 2.5,

Seismic Loads

Selection of Structural Systems

North

B B=Bearing Wall

N = Nonbearing wall

Figure G7-2. Concrete shear wall system, Scheme 1 building frame system, R = 5; not a bearing wall system. and Cd = 4. If designated as a building frame system (B8 in Table 12.2-1), the corresponding values are R = 5, Ω0 = 2.5, and Cd = 4.5. The roof framing consists of steel interior tube columns and steel beams and joists. There are also steel columns between the walls on the east and west faces of the building, and these columns support the steel beams. The walls on the north and south side of the building, designated by “B,” are clearly bearing walls. The walls on the east and west faces would be classified as bearing walls if the loading delivered into these walls by the roof deck exceeds 200 lb/linear ft. For the purpose of this example, it is assumed that this tributary loading is less than 200 lb/linear ft, and that these walls, designated by “N” in Figure G7-2, would not be designated as bearing walls. The tributary vertical gravity load carried by the columns is shown by the shaded region in the interior of the structure. This region represents approximately 65% of the total load, so the bearing walls carry only 35% of the total vertical load. Hence, by definition, this system is not a bearing wall system and would be classified as a building frame system. In Figure G7-3, the system is changed such that there is only one line of columns in the interior, and the center walls on the east and west side of the building support reactions from the steel girder. Hence, these walls become bearing walls. The shaded region, representing the tributary vertical load carried by the columns, is slightly more that 50% of the total area, so the system could still be classified as a building frame system. If the steel columns were removed in their entirety and the joists spanned the full width of the building, as shown in Figure G7-4, the building would be classified as a bearing wall system for loads acting in the east–west direction. For loads acting in the north–south direction, the walls resisting the lateral load are not

Seismic Loads

North

B B=Bearing Wall

N = Nonbearing wall

Figure G7-3. Concrete shear wall system, Scheme 2 building frame system, R = 5; not a bearing wall system. B

North

B B=Bearing Wall

N = Nonbearing wall

Figure G7-4. Concrete shear wall system, Scheme 3: for east–west seismic, it is a bearing wall system, R = 4; for north–south seismic, it is a building frame system, R = 5; not a bearing wall system. bearing walls, and the system could be classiﬁed as a nonbearing wall system for loads acting in this direction. Additional discussion related to bearing wall systems may be found in Ghosh and Dowty (2007).

7.3 Dual Systems A variety of dual systems are provided in Table 12.2-1. The higher ductility dual systems (D1–D13) combine a special moment resisting frame with a building

Seismic Loads

Selection of Structural Systems

frame system such as a shear wall or braced frame. Less ductile systems (E1–E8) incorporating intermediate moment frames are also allowed in some SDCs. Combinations of materials can be used, and in this sense a steel special moment resisting frame could be combined with a special reinforced concrete shear wall. Aside from performance enhancements discussed subsequently, the principal advantage of the dual system over independent systems is a greater R value than that which would be applied to the building frame system and increased height limits in some cases. For example, for a steel special concentrically braced frame, R = 6 and the height limit is 160 ft in SDC D. When combined with a special moment resting frame, R = 7 and there is no height limit. As specified in Section 12.2.5.1, the moment resisting frame in any of the specified dual systems must be capable of resisting at least 25% of the seismic design forces. The total seismic force resistance is to be provided by the combined system. Although not specifically stated in the standard, it is reasonable to use for the dual system the period of vibration Ta (or CuTa) that is applicable for the building frame system (e.g., buckling restrained braced frame or concentrically braced frame). See FAQ A8 for additional discussion on determining the period for dual systems. Unfortunately, the standard is not clear on how the 25% rule is to be applied, because there are two possible interpretations. The first of these is that one analysis of the full system is required, and in that analysis the sum of the column shears at the first story in the moment frame should be not less than 25% of the seismic base shear. The second interpretation is that the full system be analyzed under 100% of the lateral load, that the moment frame is separately analyzed for 25% of the lateral forces, and that the largest of the moment frame component forces from the two analyses be used. It seems that the first approach is more rational because it provides a more realistic distribution of design forces in the moment frame, requires only one mathematical model, and is applicable to all methods of analysis. It is noted, however, that the Commentary to the SEAOC Blue Book (SEAOC 1999) clearly indicates that “the special moment resisting frame, acting independently, shall be designed to resist not less than 25% of the total required force.” Aside from the practical advantages mentioned previously (e.g., lower R values and increased height limits) the physical advantages of dual systems arise from the symbiotic interaction between the relatively flexible moment resisting frame and the stiffer wall or braced frame. This concept is illustrated in Figure G7-5, which shows that, because of deformation compatibility requirements, interactive forces develop in the diaphragms. These interactive forces strongly influence the internal forces in the individual systems, with one significant advantage being relatively uniform bending moments in the beams along the height of the moment frame. It is interesting to note that where the moment frame is separately analyzed and designed for 25% of the lateral load, the frame is being designed for a force distribution that is completely different than that which includes the interaction. See FAQ A14 for additional discussion.

Seismic Loads

Systems Acting Independently

Moment Frame

Shear Wall

(Shear Mode)

(Cantilever Mode)

Dual System and Interactive Forces

Moment Frame

Shear Wall

Figure G7-5. Frame–truss (wall) interaction.

7.4 Coupled Reinforced Concrete Shear Wall Systems Two (or more) special reinforced concrete shear walls that are connected with deep beams are referred to as coupled wall systems and are very popular in highrise residential construction. Such a system is shown in Figure G7-6. The vertical lines in the ﬁgure represent thickened boundary elements, which are not always required. The principal advantage of coupled walls, compared to the use of two walls without the coupling beams, is increased lateral stiffness and reduced drift. In addition, owing to frame action, there is a signiﬁcant reduction in the bending moments at the base of the walls relative to that which would be obtained using uncoupled walls. Inelastic performance is also enhanced as a result of the ductile behavior of the coupling beams. However, Table 12.2-1 does not have an individual listing for coupled wall systems. Hence, when using the

Coupling Beam

Special Reinforced Concrete Shear Wall

Figure G7-6. Coupled special reinforced concrete shear walls.

Seismic Loads

Selection of Structural Systems

system, the system performance parameters R, Cd, and Ω0 are taken as those for the special reinforced concrete shear wall system. Design and detailing requirements for the wall and the coupling beams can be found in Chapter 18 of ACI 318-14 (ACI 2014).

7.5 Cantilevered Column Systems Cantilevered column systems are discussed in Section 12.2.5.2 and are listed in Part G of Table 12.2-1. A typical system is illustrated in Figure G7-7, where it is seen that all of the resistance is provided at the base of the columns (the moment at the top of the columns is zero owing to the pinned connection.) Because of a lack of redundancy, these systems have some of the lowest R values in Table 12.2-1 and are never allowed to exceed 35 ft in height. Consider, for example, the cantilever column system G3, which must be detailed in accordance with the requirements for columns in special reinforced concrete moment frames. For this system R = 2.5 and the height limit is 35 ft in SDC D. (This is compared to a special concrete moment frame system with R = 8 and no height limit.) In Section 12.2.5.2, cantilever column systems must have factored axial forces less than 15% of the axial capacity of the column, and foundation and other supporting elements must be designed to resist seismic load effects, including overstrength Ω0.

7.6 Steel Frame Systems Not Specifically Detailed for Seismic Resistance Part H of Table 12.2-1 provides design values and system limitations for steel systems not specifically detailed for seismic resistance. For these systems any combination of moment frames and braced frames may be used, and they are designed using the Specification for Structural Steel Buildings (AISC 2015), and do not rely on the requirements of the Seismic Provisions for Structural Steel Buildings (AISC 2016b). In some cases, R = 3 systems may be more economical than systems with higher R values (e.g., ordinary steel moment frames with R = 3.25) that are allowed for use in the same SDC.

Inelastic Behavior

Figure G7-7. Cantilever column system.

Seismic Loads

7.7 Alternate and Nonconforming Systems If a system is not listed in Table 12.2-1, it may not be used as part of the seismic force resisting system unless it satisﬁes the requirements of Section 12.2.1.1, “Alternative Structural Systems.” If a system provided in Table 12.2-1 is used but certain required aspects of that system (e.g., structural height limitations) are not met, the system may be used if it is approved by the local building ofﬁcial (i.e., Authority Having Jurisdiction) and if it is analyzed using the nonlinear response history procedures of Chapter 16, and is shown to meet all the acceptance requirements stated in that chapter.

Seismic Loads

8 Combinations of Lateral Load Resisting Systems

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

There are no changes that affect this chapter.

This chapter covers Sections 12.2.2 and 12.2.3 of the standard, which deals with a variety of issues related to the combination of different structural systems in one direction, two directions, or along the height of the building. At issue is the height limitation for the combined system and the appropriate values of R, Ω0, and Cd to use for the systems. Also discussed is the two-stage analysis procedure of Section 12.2.3.2 that provides a variation of the application of the equivalent lateral force procedure for systems with stiff lower levels and ﬂexible upper levels. Figures G8-1 and G8-2 illustrate the different types of combinations of lateral force resisting systems that might be used in a building. Buildings 1 and 2 in Figure G8-1 utilize the same system in both directions, and there is no variation in system with height, so they are not covered by Sections 12.2.2 or 12.2.3. Building 3 of Figure G8-1 has a full-height shear wall system in the north–south direction, and a full height special moment frame in the east–west direction and is covered by Section 12.2.2. Building 4 of Figure G8-1 has a single fullheight special moment frame in the east–west direction, but there is a combination of full-height systems in the north–south direction. These different systems can be considered separately in accordance with the requirements of

Seismic Loads

Special R/C Moment Frame

Special R/C Shear Wall

N Building 1

Building 2

Building 4

Building 3

Figure G8-1. Plan-wise combinations of structural systems.

Section 12.2.3.3, or they may be considered as a dual system (Section 12.2.5.1) if the moment frame has the capability to resist at least 25% of the total design base shear in the direction under consideration. Figure G8-2(a and b) illustrate a variety of systems for which the lateral load resisting system is constant along the height (Buildings A and B) or varies along the height (Buildings C and D). This situation is covered by Section 12.2.3.1. Where the lower portion of the system is signiﬁcantly stiffer than the upper part of the system, a special equivalent lateral force procedure may be used in accordance with Section 12.2.3.2 of the standard.

8.1 Combinations of Framing Systems in the Same Direction or in Different Directions Where different seismic force resisting systems are used in the two orthogonal directions of a building, and where there is no interaction (shared structural components) between these systems, Section 12.2.2 speciﬁes that the system limitations set forth in Table 12.2-1 apply independently to the two orthogonal directions. The exception, of course, is that the lower of the height limitations among all utilized systems controls for the whole building. Consider, for example, the buildings shown in Figure G8-1, where the lateral load systems extend the full height of the buildings. Each of the buildings is assigned to Seismic Design Category D. The special reinforced concrete shear wall systems are considered building frame systems and not bearing wall systems.

Seismic Loads

Combinations of Lateral Load Resisting Systems

Building A

Building B

Building C

Building D

Figure G8-2. Vertical combinations of structural systems: (a) Buildings A and B, and (b) Buildings C and D. Buildings 1 and 2 have the same type of lateral system in each direction. The system limitations and design parameters are taken directly from Table 12.2-1 as follows:

Building 1: Special RC Moment Frame in Both Directions Height limit for SDC D = No Limit

Seismic Loads

R=8 Ω0 = 3 Cd = 5.5

Building 2: Special RC Shear Wall in Both Directions Height limit for SDC D = 160 ft R=6 Ω0 = 2.5 Cd = 5.0 The height limit for Building 2 could be increased to 240 ft if the requirements of Section 12.2.5.4 are met. Building 3 has different systems in the two orthogonal directions, but there is only one system in each individual direction. Clearly, the height limitation for the building is controlled by the shear wall. The design values for each system are as speciﬁed for that system in Table 12.2-1. The values for Building 3 are as follows:

Building 3: Special RC Moment Frame in the East–West Direction and Special RC Shear Wall in the North–South Direction Height limit for SDC = D = 160 ft (240 ft if Section 12.2.5.4 is applicable) For Special RC Moment Frame in the East–West Direction: R=8 Ω0 = 3 Cd = 5.5 For Special RC Shear Wall in the North–South Direction: R=6 Ω0 = 2.5 Cd = 5.0 Building 4 has a single system in the east–west direction and a combination of systems in the north–south direction. Assuming that the combined system is not designed as a dual system, Section 12.2.3 states that the more stringent system height limitation must be used in the north–south direction, hence the shear wall would control, and the height limitation for the structure would be 160 ft. The design parameters for the moment frames acting in the east–west direction would be taken directly from Table 12.2-1. For the north–south direction, Section 12.2.3.3 states that the value of R used for the combined system would be the least value of R for any system used in the given direction. For the structure under north–south loading, the shear wall has the lowest R, and thus

Seismic Loads

Combinations of Lateral Load Resisting Systems

R = 6 is assigned. Section 12.2.3.3 further stipulates that the Cd and Ω0 values for the combined system would be taken from the system that governs R, thus again, the shear wall values control. The design values for Building 4 are summarized as follows:

Building 4: Special RC Moment Frame in the East–West Direction, Combination of Special RC Moment Frame and Special RC Shear Wall in the North–South Direction; Not Designed as a Dual System in the North–South Direction Height limit for SDC = D = 160 ft For the Moment Frames in the East–West Direction: R=8 Ω0 = 3 Cd = 5.5 For the Combined System Acting in the North–South Direction: R=6 Ω0 = 2.5 Cd = 5.0 It would probably be beneﬁcial to design the combined moment frame–shear wall as a dual system. The dual system (System D-3 in Table 12.2-1) has no height limitation, and the R value is 7, compared to that for the combined (nondual) system, which has R = 6. However, the moment frame in the dual system must be designed to resist at least 25% of the design base shear. The parameters for Building 4 with the north–south direction designed as a dual system are as follows:

Building 4: Special RC Moment Frame in the East–West Direction, Combination of Special RC Moment Frame and Special RC Shear Wall in the North–South Direction; Designed as a Dual System in the North– South Direction Height limit for SDC = D = No Limit For the Moment Frames in the East–West Direction: R=8 Ω0 = 3 Cd = 5.5 For the Dual System Acting in the North–South Direction: R=7 Ω0 = 2.5 Cd = 5.5

Seismic Loads

8.2 Combinations of Structural Systems in the Vertical Direction Section 12.2.3.1 provides the requirements for buildings with different systems in the vertical direction. This kind of system is shown as Buildings C and D in Figure G8-2(b). Building C has an X-braced system on the bottom six levels and a moment frame in the top six levels. Building D in the same ﬁgure is just the opposite, with the moment frame at the bottom and the braced frame at the top. Buildings A and B of Figure G8-2(a) consist of a moment frame or a braced frame for the full height. In all cases, the moment frame is a special steel moment resisting frame, and the braced frame is a special steel concentrically braced frame. The height of each of the buildings is 150 ft, and the buildings are assigned to Seismic Design Category C. Buildings A and B have a single system along the full height, and their limitations and design parameters come directly from Table 12.2-1. The system values are summarized for these two buildings as follows:

Building A: Special Steel Moment Frame Height limit for SDC C = No Limit R=8 Ω0 = 3 Cd = 5.5

Building B: Special Steel Concentrically Braced Frame Height limit for SDC C = No Limit R=6 Ω0 = 2.0 Cd = 5.0 Building C has a special steel concentrically braced frame (R = 6) in the bottom six stories and a special steel moment frame (R = 8) in the top six stories. Section 12.2.3.1 provides the requirements for selecting the system limitations and design parameters. Subparagraph 1 of this section is applicable because the lower system has a smaller R value than does the upper system. Hence, the upper system is designed for the R, Ω0, and Cd values for the upper system, and the lower system is designed for the R, Ω0, and Cd values for the lower system. In addition, the forces transferred from the upper system to the lower system must be multiplied by the ratio (in this case 8/6) of the upper system’s R value to the lower system’s R value. Section 12.2.3.1 does not state explicitly which height limitation would apply, but this situation is irrelevant for the given example because each system has a height limit that is greater than the height of the building. In cases for which there is a potential for the height limit for one of the components of a vertically

Seismic Loads

Combinations of Lateral Load Resisting Systems

combined system to be less than the intended height of the building, it is recommended that the height for the entire building be taken as the minimum of the limits for the different components.

The design values for Building C are as follows:

Building C: Stories 1 through 6 (Special Steel Concentrically Braced Frame) R=6 Ω0 = 2.0 Cd = 5.0

Building C: Stories 7 through 12 (Special Steel Moment Frame) R=8 Ω0 = 3.0 Cd = 5.5 There could be some question as to how the exterior columns in the lower six stories of Building C would be designed. These columns are shown within the dotted line regions of Figure G8-2(b) (Building C). Strictly speaking, these columns are part of the special moment frame because they transmit the overturning moment of the upper six levels to the base of the building. These columns should be detailed as special moment frame columns. Building D has a special moment frame in the lower six stories and special steel CBF in the upper six stories. According to Section 12.2.3.1, the entire structure should be designed using the R, Ω0, and Cd values for the upper system. Hence, the design values for the structure are as follows:

Building D: Special Steel Moment Frame for Stories 1 through 6 R=6 Ω0 = 2.0 Cd = 5.0

Building D: Special Steel Concentrically Braced Frame for Stories 7 through 12 R=6 Ω0 = 2.0 Cd = 5.0 As with Building C, a question arises with regard to the design of the discontinuous columns in Building D, in which the interior columns are at issue. These columns are enclosed by dotted lines in Figure G8-2(b) (Building D).

Seismic Loads

Section 12.3.3.3 requires that elements supporting discontinuous frames be designed using load factors that include the overstrength factor Ω0 when a Type 4 vertical irregularity (in-plane discontinuity irregularity) exists. It is not clear whether an irregularity exists because there is no apparent overturning moment transfer offset in the lateral load resisting system, and because it is not clear whether there is a reduction in stiffness below the transition. However, some engineers might consider the offset in the lateral load resisting system to be inﬁnite, thereby requiring the design of the interior columns with the factor Ω0. (The author would not be inclined to use the Ω0 factors for the exterior columns of Building C but would use the Ω0 factors for the interior columns of Building D.) As a ﬁnal point, ASCE 7 places severe restrictions on systems similar to Building C in Figure G8-2(b) (moment frames above braced frames) when such systems are used in buildings assigned to SDC D and above. These restrictions, given in Section 12.2.5.5, are not applicable to the buildings in this example because the SDC was C.

8.3 Computing Approximate Periods of Vibration for Combined Systems It is almost always necessary to determine the approximate period of vibration, Ta, for a structure. This period is used in computing the seismic base shear when the equivalent lateral force (ELF) method of analysis is used and for scaling the results of a modal response spectrum or linear response history analysis when the base shear from such an analysis is less than 100% of the ELF base shear (Sections 12.9.1.4.1 and 12.9.2.5). The approximate period is computed using Equation (12.8-7), which uses the parameters Ct and x. Table 12.8-2 provides these parameters for a variety of well-defined systems but does not specifically address combined or dual systems. Hence, dual systems or systems combined in the same direction would apparently fall under the “All other structural systems” category. This approach seems overly conservative, and it would seem reasonable to use a weighted average based on the parameters in Table 12.8-2. For example, the period for Building D of Figure G8-2(b) could be estimated as the average of the period of a 12-story moment frame and a 12-story braced frame. However, the average of the periods of a 6-story moment frame (the top half) and a 6-story braced frame (the bottom half) would not be appropriate. Neither would it be appropriate to use one period for the upper half of the building and a different period for the lower half. For dual systems it would be appropriate to use Ta for the stiffer component of the system as the period of the dual system. Although not specifically allowed in the standard, this seems reasonable because use of Ta for “all other structural systems” in Table 12.8-2 is overly conservative where the stiffer component is a buckling restrained braced frame system or an eccentrically braced frame. For additional information on this issue, see FAQ A8 in Chapter 30 of this guide.

Seismic Loads

Combinations of Lateral Load Resisting Systems

8.4 Vertical Combination When the Lower Section Is Stiff Relative to the Upper Portion Where the lower portion of a building is much stiffer than the upper portion, it is permitted to use a two-stage ELF procedure to determine design forces. This procedure will likely result in significantly reduced story shears in the flexible upper levels of the building relative to forces obtained using the traditional application of the ELF procedure. However, the benefit occurs only if the lower levels of the building also have significantly more mass than the upper levels. Section 12.2.3.2 requires that the two-stage analysis be limited to systems in which the lower portion is at least 10 times as stiff as the upper portion and for which the period of the entire structure is not greater than 1.1 times the period of the upper portion of the structure, with the upper portion fixed at its base. A typical structure that can benefit from a two-stage analysis is a typical mixeduse structure with light-frame wood or cold-formed steel on the upper, residential floors, and a concrete podium structure that houses commercial and/or parking uses on the lower floors. Failure to use a two-stage analysis in a structure like this will result in excessive design forces being applied to the upper floors. The stiffness requirements are difficult to apply because the standard does not specify how the stiffness is to be computed, and there can be several measures of the stiffness of a structure. Because of these complexities, examples of this type of system are deferred to Chapter 21 of this guide, which covers the equivalent lateral force method.

Seismic Loads

9 Diaphragm Flexibility

Changes in ASCE 7-16, relative to ASCE 7-10 that affect this chapter: •

Aside from slight changes in the nomenclature used to classify diaphragms as ﬂexible (Figure 12.3-1), there are no signiﬁcant changes to the procedures used to classify diaphragm stiffness.

For analysis purposes, roof and floor diaphragms must be classified as either flexible, semirigid, or rigid. Each of these terms are related to in-plane loads and deformations. The standard does not address out-ofplane (bending) stiffness of diaphragms. For some structures, such as light-frame wood shear wall systems, there is an advantage in classifying the diaphragm as flexible because accidental torsion is not required, and the individual wall systems can be analyzed separately in two dimensions with the distribution of forces to the resisting elements based on tributary mass. In some situations the diaphragms can be classified as rigid. Here, a three-dimensional model is usually required, but the diaphragm need not be modeled in detail. In the past there was a significant computational benefit to using a rigid diaphragm, but this advantage has essentially disappeared as the storage capacity and processing speed of computers has increased. Where diaphragms are neither flexible or rigid, they are classified as semirigid and must be modeled in three dimensions in such a manner that the in-plane flexibility of the diaphragm is appropriately captured. This chapter demonstrates the procedure ASCE 7 uses to determine a diaphragm’s stiffness and illustrates by example the procedure to determine analytically if a diaphragm can be classified as flexible.

Seismic Loads

Section 12.3 of the standard provides the requirements for classifying the diaphragms as flexible, rigid, or semirigid. The classification is used in Section 12.7 to determine if the mathematical model should explicitly include the diaphragm stiffness, and in Section to 12.8.4, which allows buildings with flexible diaphragms to be analyzed using tributary mass (which ignores both inherent and accidental torsion). Section 12.3.1.1 provides the conditions under which the diaphragm can automatically be classified as flexible. Wood structural panel diaphragms are usually considered flexible. As another example, the diaphragm can be considered as flexible in buildings with vertical steel braced frames and with diaphragms constructed using untopped steel decking. The same diaphragm would not be classified as flexible if the lateral system were a steel moment frame. Thus, the stiffness of the diaphragm relative to the frame is an important consideration. If the diaphragm cannot be classified as flexible under Section 12.3.1.1 and it is desired to model the diaphragm as flexible, an analytical procedure is provided in Section 12.3.1.3. In this procedure the computed maximum in-plane diaphragm deflection (δMDD) is compared to the average deflection at the diaphragm supports (ΔAVE), and if δMDD/ΔAVE is greater than 2.0 the diaphragm can be considered as flexible. An example calculation is provided subsequently in this chapter. Unless very simple models are used to determine δMDD and ΔAVE, it is likely to be more difficult to determine if the diaphragm is flexible than it is to go ahead and model the diaphragm as semirigid. In addition, it is rare that the diaphragm will be classified as flexible using the analytical procedure. An example of a simple model to determine diaphragm flexibility is provided in the 2015 Special Design Provisions for Wind and Seismic (AWC 2015). In this procedure, the midspan diaphragm deformation consists of three parts: bending, shear, and chord slip. The vast majority of the deformation is contributed by shear and chord slip. Similarly, when computing deformations in metal deck diaphragms, the shear deformations must be included with a reduced shear stiffness to account for connection slip. Section 12.3.1.2 provides the requirements for classifying the diaphragm as rigid. For diaphragms with span-to-depth ratios of 3 or less, and where the diaphragm is constructed with concrete slabs or slabs over metal deck, the diaphragm is permitted to be classified as rigid. Span is the distance between the vertical supports at either end of the diaphragm. Section 12.3.1.2 also states that the diaphragm cannot be classified as rigid if any horizontal irregularity (Table 12.3-1) exists. This includes even a marginal torsional irregularity, or a diaphragm in which a reentrant corner irregularity is marginally triggered. Although not specifically stated in the same section, the authors recommend that the diaphragm be modeled as semirigid where there is a significant difference in the lateral stiffness of the various lateral load resisting elements, such as might be the case in a dual system.

Seismic Loads

Diaphragm Flexibility

9.1 Example Classification of Diaphragm Flexibility Using Section 12.3.1.3 The structure in this example is shown in plan and elevation in Figure G9-1. The purpose of the unusual structure is storage for hazardous chemicals. The lateral load–resisting system in the transverse directions consists of four reinforced concrete shear walls, each 10 in. thick. The diaphragm, also constructed from concrete, is 4 in. thick. The lateral load–resisting system in the longitudinal direction consists of 10 in. thick walls, 11 ft long, placed at the center of each bay. The length of the diaphragm between walls is 44 ft, and the depth of the diaphragm is 12 ft, producing a span-to-depth ratio of 3.67. According to Section 12.3.1.2, the diaphragm cannot automatically be considered rigid because the span-to-depth ratio is greater than 3.0. Note: Figure 12.3-1 of ASCE 7 indicates that the span of a diaphragm should be taken as the distance between lateral load–resisting elements. This rather unrealistic example was devised to produce a span-to-depth ratio greater than 3.0 for a single diaphragm segment. An analysis must be performed to determine if the diaphragm is flexible or semirigid. According to Section 12.3.1.3 and the related Figure 12.3-1, the diaphragm is flexible if the maximum diaphragm deflection (δMDD) is greater than 2.0 times the average drift of vertical elements (ΔADVE). An analysis to determine the quantities δMDD and ΔADVE was performed using the SAP2000 (CSI 2019) finite-element analysis program. Thin-shell elements were used to model the walls and diaphragms. These elements automatically include in-plane shear deformations, which are essential for diaphragm analysis. Figure G9-2 shows the finite-element model. Loading consisted of a 10 kip force applied in the y-direction at each node along the edge of the diaphragm. A uniform load applied to the edge of the diaphragm may also be used and would be more appropriate where the shell elements are not of a consistent width.

12 ft

(a) Plan

11 ft (typ)

18 ft

44 ft

(b) Elevation

Figure G9-1. Three-bay concrete structure analyzed for diaphragm ﬂexibility.

Seismic Loads

Figure G9-2. Finite-element model for computing diaphragm ﬂexibility.

Figure G9-3. Diaphragm displacements for a 4.0 in. thick slab. Figure G9-3 shows the deflections computed along the edge of the diaphragm. In the end span, the average drift of the vertical walls that bound the end bay (Figure 12.3-1) is ΔADV E = ð0:0136 þ 0:0295Þ=2 = 0:0216 in: The maximum diaphragm deflection (MDD) is computed by subtracting the average drift from the maximum deflection of the diaphragm (at midspan) as follows: δMDD = 0:0425 0:0216 = 0:0209 in:

Seismic Loads

Diaphragm Flexibility

The ratio of the maximum to the average displacement is

δMDD =ΔADV E = 0:0209=0:0216 = 0:968 This ratio, 0.967, is less than 2.0, so according to Section 12.3.1.3, the diaphragm may not be considered flexible. With a 10 kip force applied at each edge node, the total load applied to the structure is 250 kips. Figure G9-4 shows the distribution of these forces to the interior and exterior walls for a variety of assumptions. For the computed assumption, based on the finite-element analysis, each exterior wall resists 38.4 kips, and the interior walls carry 83.0 kips each, for a total (all four walls) of 242.8 kips. This total is slightly less than 250 kips, because the longitudinal walls carry some shear, which is delivered to the foundation through weak-axis bending in these walls. For a fully rigid diaphragm, the 250 kip force would be expected to be equally distributed to the walls because the walls have the same lateral stiffness. This situation would result in a force of 62.5 kips in each wall. For a fully flexible diaphragm, the distribution of forces would be distributed on a tributary area basis with 1/6 of the total force, or 41.7 kips, going to the exterior walls, and 1/3 of the force, or 83.3 kips, going to each of the interior walls. The finite-element results appear to be more consistent with the flexible diaphragm assumption than with the rigid diaphragm assumption. This has nothing to do with diaphragm flexibility. Because the walls have virtually no torsional stiffness about the vertical axis, these supports emulate the condition of a pinned support more than a fixed support in a three-span continuous beam. For example, a three-span continuous beam subjected to the same loading as that used in the finite-element analysis would have exterior support reactions of 33.3 kips and interior reactions of 91.7 kips. This result, shown as the beam assumption in Figure G9-4, is valid regardless of the stiffness of the beam, as long as each span has the same flexural stiffness. Therefore, a prudent designer should consider how sensitive the results are to the assumptions made. Other parameters, such as cracking in walls and diaphragms, and rocking or uplift in

Figure G9-4. Distribution of forces in walls for diaphragm thickness of 4.0 in.

Seismic Loads

Figure G9-5. Diaphragm displacements for a 2.0 in. thick slab. the walls, can influence the force distribution in the lateral system. If the results are sensitive to various parameters, the design should be based on a bounded solution. If the diaphragm is assumed to be only 2.0 in. thick (e.g., concrete over a metal deck), the results of the finite analysis still indicate that the diaphragm is semirigid. The deflected shape for this condition is provided in Figure G9-5. The computations are as follows: ΔADV E = ð0:0134 þ 0:0297Þ=2 = 0:0215 in: The maximum diaphragm deflection, δMDD, is δMDD = 0:0595 0:0215 = 0:0380 in: The ratio of the maximum to the average displacement is δMDD =ΔADV E = 0:0380=0:0215 = 1:77 This value is less than 2.0, so even the system with the 2.0 in. slab is classified as semirigid. The computed reactions at the base of the walls are close to those determined for the system with the 4.0 in. thick diaphragm. Again, this example shows that diaphragm flexibility has little influence on how the shears are distributed. However, this behavior is not necessarily applicable to all buildings.

9.2 Accidental Torsion in Systems with Semirigid Diaphragms Section 12.7.3 of ASCE 7 states that structures with semirigid diaphragms must be modeled to include the representation of the diaphragm stiffness (ﬂexibility)

Seismic Loads

Diaphragm Flexibility

and that additional degrees of freedom, aside from the two lateral displacements and one rotation at each level, must be included in the model. Because any model that includes these effects is three-dimensional, the de facto requirement of ASCE 7 is that systems with semirigid diaphragms must be modeled in three dimensions and presumably using a finite-element approach, wherein the diaphragm is discretized into a number of shell elements, as shown in Figure G9-2. Where either of the dynamic analysis methods of Section 12.9 is used, the diaphragm’s mass must be appropriately distributed over the diaphragm in a realistic manner. The question arises as to whether the ELF method of analysis may be used to analyze the structure shown in Figure G9-2. Table 12.6-1 is silent on this issue because the only factor that excludes the possibility of using ELF, in Seismic Design Categories D through F, is a fundamental period greater than 3.5 TS, or a system with a structural height greater than 160 ft and a horizontal irregularity of Type 1a or 1b or a vertical irregularity of Types 1a, 1b, 2, or 3. In the authors’ opinion, the use of ELF for structures with semirigid diaphragms is not always appropriate, particularly if the diaphragm is somewhat flexible or highly irregular in shape. In ELF analysis, the lateral loads are applied at the center of mass, and if the diaphragms are modeled using shell elements, considerable local deformations and stress concentrations occur at the location of the applied load. The deformation and stress patterns in the actual diaphragm are quite different because the inertial forces in the diaphragm are distributed throughout the diaphragm, not at a single point. Some improvement would be obtained if the ELF story forces were applied to the diaphragms in a distributed manner. However, what this pattern should be is not clear because the pattern depends on the total accelerations at each point in the diaphragm and this pattern is unknown at the beginning of the analysis. A modal response spectrum analysis or a linear modal response history analysis produces realistic distributions of inertial forces (if the diaphragm masses are distributed throughout the diaphragm and if a sufficient number of modes are used in the analysis) and is therefore more appropriate than ELF.

Seismic Loads

10 Horizontal Structural Irregularities

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • •

There are no changes that influence the determination of the presence of horizontal irregularities. There is a significant change with respect to the consequence of a system having a torsional or extreme torsional irregularity. In ASCE 7-10, accidental torsion needed to be considered in all systems where the diaphragm was not flexible. In ASCE 7-16 the requirements for including accidental torsion in analysis are dependent on whether a torsional irregularity or an extreme torsional irregularity exists.

Section 12.3.2.1 is used to determine if one or more horizontal structural irregularities exist in the structural system. The ﬁve basic irregularity types are described in Table 12.3-1. This chapter explores each of these irregularities but concentrates primarily on horizontal structural irregularity Types 1a and 1b (torsion and extreme torsion).

10.1 Torsional Irregularities (Types 1a and 1b) Based on the deﬁnitions in Table 12.3-1, a Type 1a torsional irregularity exists if the maximum story drift computed including accidental torsion with Ax = 1.0 at one edge of the building is more than 1.2 times the average of the story drifts at the two ends of the structure. If the ratio of maximum edge to average story drift is greater than 1.4, the system has an extreme (Type 1b) torsional irregularity.

Seismic Loads

In this guide the ratio of maximum edge story drift to average story drift is referred to as the torsional irregularity factor (TIF). The mathematical model used to compute the TIF must be three-dimensional and may be based on rigid diaphragm analysis without P-delta effects included. The lateral loading should be as determined in Section 12.8 of the standard, and accidental torsion should be applied in accordance with Section 12.8.4.2. Story drifts are computed at the edge of the building in accordance with Section 12.8.6, although it is noted that multiplication of computed displacements by the ratio of Cd/Ie is not necessary because these terms cancel out when computing the TIF at each story. Computation of the TIF is illustrated for each of four possible torsional eccentricities in Figure G10-1. A torsional or extreme torsional irregularity applies to the entire system even if the relevant TIF limit (1.2 or 1.4, respectively) is exceeded only at one story of the building and only under one of four possible accidental eccentricities. Two examples are provided for determining if a torsional irregularity exists. In the ﬁrst example, a simple one-story structure with symmetrically placed shear walls is analyzed to determine the effect of the placement of the walls on the torsional behavior of the system. The second example is more realistic in the sense that it determines whether torsional irregularities occur in a typical 6-story ofﬁce building.

Figure G10-1. Computing the torsional irregularity factor for four accidental eccentricities.

Seismic Loads

Horizontal Structural Irregularities

(a)

Figure G10-2a. Simple building for accidental torsion evaluation plan view with walls symmetrical about centroid. For the first example, consider first a simple one-story system shown in Figure G10-2(a). The lateral system for the building consists of four walls, each with an in-plane lateral stiffness k. The out-of-plane lateral stiffness of each wall is assumed to be zero. The walls are placed symmetrically in the system; the parameter α is used to locate the walls some distance from the center of mass, which is located at the geometric center of the building. A value of α of 0.5 places the wall on the perimeter of the building. The diaphragm is assumed to be rigid. The lateral load V is applied at an accidental eccentricity of 0.05 times the building width, L. Given this configuration, the displacement at the center of the building is ΔCENTER =

V 2k

(G10-1)

and the deﬂection at the edge of the building is ΔEDGE =

V 0.05V L + ð0.5LÞ 2k 2kðα2 L2 + α2 B2 Þ

(G10-2)

The deﬂection at the center of the building is the same as the average of the deﬂections at the extreme edges of this rigid diaphragm building. Using Equations (G10-1) and (G10-2) and simplifying, the ratio of the displacement at the edge to the center is ΔEDGE 0.025 2 i ≡ TIF = 1 + h ΔCENTER α2 1 + BL

(G10-3)

Figure G10-2(b and c) depict some extremes of the building aspect ratio and wall placement. Figure G10-2(b) has a square-shaped plan and walls are located near the perimeter. This arrangement is very resistant to accidental torsion. Figure G10-2(c) has a slender rectangular plan and the walls are located close to the centroid. This arrangement is much less resistant to

Seismic Loads

(b)

Figure G10-2b. Simple building α = 0.5; B/L = 1.0; TIF = 1.05 < 1.2. Not torsionally irregular.

(c)

Figure G10-2c. Simple building α = 0.24; B/L = 0.25; TIF = 1.4. At limit of extremely torsionally irregular.

accidental torsion. Figure G10-3 is a plot of Equation (G10-3) for four values of B/L and for α values ranging from 0.1 (all walls near the center of the building) to 0.5 (all walls on the perimeter of the building). Also shown are the limits for a torsional irregularity (TIF = 1.2) and for an extreme torsional irregularity (TIF = 1.4). For the rectangular building with B/L = 0.25, the torsional irregularity occurs when α is approximately 0.34 and the extreme irregularity occurs when α = 0.24. These conditions are labeled as Points A and B on the ﬁgure. For the square building (B/L = 1), the torsional and extreme torsional irregularities occur at α = 0.25 and 0.18, respectively, and are represented on the ﬁgure as Points C and D. Three important observations may be drawn from the results: 1.

Torsional irregularities may occur even when the lateral load resisting system is completely symmetric.

The closer the walls are to the center of the building (i.e., lower values of α), the greater the possibility of encountering a torsional irregularity. Thus, buildings with interior reinforced concrete core-walls or interior core bracing as the only lateral load resisting system are very likely to be torsionally irregular.

Seismic Loads

Horizontal Structural Irregularities

Figure G10-3. Effect of wall placement on torsional irregularity.

Torsional irregularities are more likely to occur in rectangular buildings than in square buildings.

The second example for checking if a torsional irregularity occurs is based on a 6-story building with a typical ﬂoor plan as shown in Figure G10-4. The lateral load resisting systems consist of moment frames on Grid lines A and D and braced frames on Lines 2, 3, 4, and 5. There is no bracing on Grid line 6, so the center of mass and the center of rigidity do not coincide with respect to loading in the transverse direction. The height of the ﬁrst story is 16 ft, and the height of Stories 2 through 6 are 13 ft, giving a total building height of 81 ft.

Figure G10-4. Plan view of 6-story building for evaluation of torsional irregularity.

Seismic Loads

Table G10-1. Torsional Irregularity Check for the Building in Figure G10-4.

Story

Fi (kips)

Tai (ft-kips)

δi Line 1 (in.)

Δi Line 1 (in.)

δi Line 7 (in.)

Δi Line 7 (in.)

Ratio

6 5 4 3 2 1

207.0 160.1 111.9 70.9 37.9 15.0

1283.3 992.6 693.5 439.7 235.0 93.0

2.575 2.058 1.555 1.160 0.799 0.459

0.517 0.503 0.395 0.361 0.340 0.459

3.863 3.178 2.471 1.864 1.281 0.693

0.685 0.707 0.607 0.583 0.588 0.693

1.140 1.169 1.212* 1.235* 1.267* 1.203*

Note: Ratio = Δi line 7 ÷ Δi average of Line 1 and Line 7. * Result is greater than 1.2 so a Type 1a horizontal irregularity exists.

The results of the torsional analysis for loading in the transverse direction are shown in Table G10-1. The analysis was run using a rigid diaphragm assumption. Column 2 of the table shows the lateral forces at each level computed according to the equivalent lateral force procedure of Section 12.8. Column 3 of the table provides the torsional moments at each level, which are equal to the story force times 6.2 ft (0.05 times the width of the building). The accidental torsion analysis is based on the lateral forces applied to the right of Frame line 4 because this produces the largest displacements at the edge of the building. (In a more complicated building, this would not be apparent, and both directions for the eccentricity would be checked.) Column 4 of the table provides the computed story displacements at the left edge of the building (2.0 ft to the left of Grid 1), Column 5 lists the associated story drifts. Columns 6 and 7 contain the computed displacements (Δ) and story drifts (δ) at the right edge of the building (2.0 ft to the right of Grid line 7). The ratio of the drift at the right edge of the building to the average drift of the edges is shown in Column 8. As may be observed in Column 8, the ratio of edge drift to average drift exceeds 1.2, but is less than 1.4, for Stories 1 through 4, so the structure has a Type 1a torsional irregularity (according to Table 12.3-1). This building is very close to being torsionally regular, and thus it would be advisable to modify the design to eliminate the irregularity. The purpose of the aforementioned checks is for the determination of existence of torsional irregularity (Type 1a) and extreme torsional irregularity (Type 1b). Table 12.3-1 lists the sections of the standard which are triggered as a result of those classiﬁcations. When a torsional irregularity does not exist, Section 12.8.4.2 permits accidental torsion to be omitted when determining the seismic forces E (see Section 12.4.2) in the design of the structure and in determining the design story drift.

10.2 Reentrant Corner Irregularity (Type 2) According to Table 12.3-1, a reentrant corner irregularity only occurs when both plan projections beyond the corner are greater than 15% of the length of the plan

Seismic Loads

Horizontal Structural Irregularities

Figure G10-5. Building with four re-entrant corners and with a reentrant irregularity. dimension in the direction of the projection. Figure G10-5 shows the plan of a building with four reentrant corners, marked A through D. For this building, only Corner D would be considered a reentrant corner irregularity because both projections are greater than 15% of the dimension of the building in the direction being considered. In some cases, a notch in the edge of the building may trigger a re-entrant corner irregularity. See the following discussion on diaphragm irregularities for more details.

10.3 Diaphragm Discontinuity Irregularity (Type 3) According to Table 12.3-1, diaphragm discontinuity irregularities occur if the area of a cutout or hole in the diaphragm is greater than 50% of the gross enclosed diaphragm area, or if the in-plane stiffness of the diaphragm at one level is less than 50% of the stiffness at an adjacent level. Unfortunately, the standard does not provide a deﬁnition for gross enclosed area, so this is open to interpretation as indicated subsequently. Figures G10-6(a–d) show four different diaphragms. In Figure G10-6(a), the opening is a notch and has less than 50% of the gross enclosed area, so the diaphragm is not irregular. Note the presence of the exterior window wall, which is required if the shown opening is to be considered as part of the enclosed area. If this window wall did not exist, the opening might in fact cause a re-entrant corner irregularity because the projections caused by the opening are greater than 15% of the building width. This situation is shown in Figure G10-7. In Figures G10-6(b and c), the diaphragm openings are at the interior of the building, and neither triggers a diaphragm irregularity because the areas of the

Seismic Loads

(a)

(b)

(c)

(d)

Figure G10-6. Diaphragm openings and irregularities.

Figure G10-7. Diaphragm notch causing a reentrant corner irregularity. openings are less than 50% of the gross enclosed area. The opening in Figure G10-6(d) does cause a diaphragm irregularity. The 50% cutout should be reviewed in future editions of the standard because the diaphragm shown in Figure G10-6(c) has an abrupt change in stiffness and is clearly irregular from an analytical perspective.

Seismic Loads

Horizontal Structural Irregularities

Figure G10-8. Finite-element model for determining diaphragm stiffness. A diaphragm irregularity can also occur if the in-plane stiffness at one level is less than 50% of the stiffness at an adjacent level. Calculations to determine diaphragm stiffness are not straightforward, but in some cases can be accomplished using finite-element analysis. For example, a finite-element model for the diaphragm in Figure G10-6 is shown in Figure G10-8. The diaphragm stiffness would be computed as the quantity V/Δ. Another way of modeling the diaphragm would be to provide simple supports on the left and right sides of the diaphragm and apply a lateral pressure to the faces of the shell elements to determine the midspan deflection for comparison to the diaphragms above and below. For more complex systems, with multiple diaphragm segments and multiple lateral load resisting elements, the determination of diaphragm stiffness is essentially impossible in terms of the definition provided in Table 12.3-1, and engineering judgment must be used. A diaphragm irregularity based on a differing stiffness of adjacent stories may in fact be irrelevant. Consider, for example, a rectangular building with no diaphragm openings. At one level, the floor slab is 4 in. thick; at an adjacent level, the thickness is 10 in. Clearly the 10 in. thick diaphragm is more than twice as stiff as the 4 in. thick diaphragm, but in terms of stiffness relative to the lateral load resisting system, both may be considered rigid. Hence, the different stiffness of the diaphragms has virtually no effect on the analysis and performance of the building, with the exception that the increased thickness may cause a mass irregularity. However, regardless of the actual diaphragm behavior, the classification of the diaphragm as discontinuous cannot be ignored when addressing the consequences of the irregularity (e.g., increased collector forces required by Section 12.3.3.4).

10.4 Out-of-Plane Offset Irregularity (Type 4) Out-of-plane irregularities occur when the lateral forces in a lateral load– resisting element are transferred to an element that is not in the same plane

Seismic Loads

Figure G10-9. Plan of Imperial County Services Building.

as that element. An example is shown in Figure G10-9, which is a plan view of the Imperial County Services Building, which was severely damaged during the October 15, 1979, Imperial Valley earthquake. In this building, Wall A, an exterior wall, occurs on Stories 2 through 6 and must transfer its shear to Wall B, which exists only on the ﬁrst story and is inset. Overturning moment is transferred to the columns adjacent to but offset from Wall A. The three walls labeled C extend the full height of the building. The lateral system in the long direction consists of moment resisting frames. During the earthquake, the columns immediately adjacent to Wall A but not on the same line as Wall A failed because of the combined effect of overturning in the transverse direction and moment frame action in the longitudinal direction. A photograph of the building is shown in Figure G10-10(a), and damage to the columns is shown in Figure G10-10(b). (The failure of the columns could also be considered to be caused by a vertical irregularity because of the difference in stiffness between Wall A and the slightly offset columns that support it. A lack of ductile detailing in the columns was also a problem).

Figure G10-10. Photograph of Imperial County Services Building. (a) entire building with solid wall A in foreground dropped several inches: and (b) damage in ﬁrst-story columns adjacent to Wall A.

Seismic Loads

Horizontal Structural Irregularities

Figure G10-11. A structure with a nonparallel system irregularity.

10.5 Nonparallel System Irregularity (Type 5) Nonparallel system irregularities occur when any element of the lateral load resisting system is not parallel to one of the orthogonal axes of the lateral load resisting system of the entire structure. Such a system is shown in Figure G10-11, which is a plan view of a reinforced concrete frame-wall system. In Figure G10-11, the axes marked x and y represent the principal axes of the entire structural system. Clearly, the line of action of the lateral load resisting elements are not parallel to either the x- or the y-axis, so a nonparallel system irregularity occurs.

10.6 Consequences of Horizontal Irregularities Horizontal irregularities are primarily of signiﬁcance when the structure under consideration is assigned to SDC D or above, or in some cases, SDC C. The third and fourth columns of Table 12.3-1 provide the consequences of the irregularities in terms of the Seismic Design Category. A few examples of these consequences are provided as follows: • • •

• •

Section 12.3.3.1 provides circ*mstances in which certain horizontal irregularities are prohibited. An extreme torsional irregularity for systems in SDC D requires the redundancy factor to be set at 1.3 (Section 12.3.4.2). A Type 5 horizontal irregularity triggers the requirement for consideration of orthogonal load effects (Section 12.5.3.1) in buildings assigned to SDC C and above and requires three-dimensional analysis in all SDC levels (Section 12.7.3). Structures in SDC B with a Type 1b horizontal (extreme torsion) irregularity must include accidental torsion in the design (Section 12.8.4.2). Structures in SDC C and above with a Type 1a or 1b (torsion or extreme torsion) irregularity must include accidental torsion in the analysis and design (Section 12.8.4.2).

Seismic Loads

•

Table 12.6-1 (Permitted Analytical Procedures) contains restrictions on the use of the ELF analysis method when certain irregularities exist.

An omission in Table 12.3-1 is the fact that the presence of any horizontal irregularity effectively precludes the classiﬁcation of diaphragms as rigid (see Section 12.3.1.2). In accordance with Section 12.7.3 any horizontal irregularity would require that diaphragms be modeled as semirigid.

Seismic Loads

11 Vertical Structural Irregularities

Changes in ASCE 7-16, relative to ASCE 7-10 that affect this chapter: •

There are no signiﬁcant changes to ASCE 7-16 that affect the examples presented in this chapter.

Section 12.3.2.2 is used to determine if one or more vertical structural irregularities exist in the lateral load–resisting system. The ﬁve basic irregularity types are described in Table 12.3-2. This chapter explores each of these irregularities but concentrates primarily on irregularity Types 1a and 1b (soft story) and Types 5a and 5b (weak story).

11.1 Soft Story (Stiffness) Irregularities (Types 1a and 1b) The standard provides two methods to determine if a soft story irregularity exists. The ﬁrst is a stiffness-based check, which is described in Table 12.3-2. The second method is provided in an exception to Section 12.3.2.2, wherein story drift ratios are used. The second method is simpler than the ﬁrst method because drift is easier to obtain than is story stiffness. A second exception in Section 12.3.2.2 states that soft story irregularities need not be checked for any one-story building, or for two-story buildings in SDC B, C, and D.

Seismic Loads

The first step in a soft story irregularity check is to use the first exception in Section 12.3.2.2. If the relative drift criteria are met, there is no soft story irregularity and the check is complete. If the drift criteria are not met, the irregularity must be accepted, or the stiffness-based check of Table 12.3-2 must be performed. The stiffness check has three possible results: no irregularity exists, a soft story irregularity exists (Type 1a), or an extreme soft story irregularity exists (Type 1b). For the drift-based check, the structure is subjected to the design lateral loads, and story drift ratios are computed for each story. If the drift ratio in each story is less than 1.3 times the drift ratio in the story directly above it, there is no stiffness irregularity. When performing the drift check, the top two stories of the building need not be evaluated, and accidental torsion need not be included. Where threedimensional analysis is used, drifts shall be computed at the center of mass in accordance with Section 12.8.6. Although ASCE 7 requires that the design-level lateral loads be used in the check, this is not strictly necessary when linear analysis is performed. It is important, however, that the vertical distribution of the lateral loads be reasonably correct. On the basis of this concept, the lateral loads used for the stiffness irregularity check based on the exception may be based on the equivalent lateral force method described in Section 12.8. The result of the calculation may show, however, that the ELF method may not be used for the final design of the structure. Applicability of the ELF method is covered in Section 12.6 and Table 12.6-1. For this example, we consider a 6-story reinforced concrete moment frame located in a region of high seismicity (SD1 > 0.4g). For simplicity, we assume that the story weight for each level is 1,500 kips and that all story heights are equal to 12.5 ft, except for one tall story, which has a height of 18.5 ft. Two separate analyses are run: one for which the tall story is the first story of the building, and one for which the tall story is the second story of the building. Elevations of these frames are shown in Figure G11-1. The columns at the first story are assumed to be fixed at the base.

(a) Tall 1st Story

(b) Tall 2nd Story

Figure G11-1. Building used to investigate soft story irregularity.

Seismic Loads

Vertical Structural Irregularities

The period of vibration of the structure is estimated (from Section 12.8.2) as T = CuT a

where Cu is taken from Table 12.8-1 and where T a = C t hxn

(12.8-7)

For our structure, hn is 81 ft, and for a concrete moment frame, Ct = 0.016 and x = 0.9 (Table 12.8-2). Hence, T a = C t hxn = 0.016 × 810.9 = 0.835 s Note that T = CuTa may only be used if a properly substantiated (computer) analysis has been used to determine the true analytical period (called Tcomputed in this guide). For this example, we assume that such an analysis has been performed and that Tcomputed exceeds CuTa, thereby setting CuTa as the upper limit on period. This result produces a more realistic value of the exponent k than the use of Ta alone. Because of the high seismicity, Cu = 1.4 (Table 12.8-1) and T = C u T a = 1.4 × 0.835 = 1.17 s Based on the text in Section 12.8.3, the exponent k can be computed as k = 1 when T is less than or equal to 0.5 s, k = 0.5 T + 0.75 when 0.5 < T < 2.5 s, and k = 2 when T is greater than or equal to 2.5 s. For the current example k = 0.5 T + 0.75 = 0.5ð1.17Þ + 0.75 = 1.33 For computing the lateral force, a total base shear of 100 kips is assumed, and this shear is distributed vertically according to Equation (12.8-12). The 100 kips shear is used in lieu of the actual design seismic base shear for simplicity because the ratios of story drift or story stiffness are independent of the shear force used. Tables G11-1 and G11-2 show the lateral load computations for the structures with the tall first and second stories, respectively. The resulting story displacements, story drifts, story drift ratios, and ratio of story drift ratios are shown in Tables G11-3 and G11-4. These computations do not include the deflection amplification factor Cd or the importance factor Ie because these factors cancel out when calculating the ratios of the story drift ratios. In Table G11-3, which is for the structure with the tall first story, the interstory drift ratio (IDR) in the tall bottom story (0.43%) is actually smaller than the drift ratio at the next story above (0.53%). The first-story drift ratio divided by the second-story drift ratio is 0.811. This rather unexpected result occurs because

Seismic Loads

Table G11-1. Development of Lateral Loads for Structure with Tall First Story

Story 6 5 4 3 2 1

H (ft)

h (ft)

w (kips)

whk

whk/total

F (kips)

12.5 12.5 12.5 12.5 12.5 18.5

81.0 68.5 56.0 43.5 31.0 18.5

1,500 1,500 1,500 1,500 1,500 1,500 Total

521,128 416,898 318,811 227,765 145,080 72,968 1,702,650

0.306 0.245 0.187 0.134 0.085 0.043 1.000

30.6 24.5 18.7 13.4 8.5 4.3 V = 100.0

Table G11-2. Development of Lateral Loads for Structure with Tall Second Story Story 6 5 4 3 2 1

H (ft)

h (ft)

w (kips)

whk

whk/total

F (kips)

12.5 12.5 12.5 12.5 18.5 12.5

81.0 68.5 56.0 43.5 31.0 12.5

1,500 1,500 1,500 1,500 1,500 1,500 Totals

521,128 416,898 318,811 227,765 145,080 43,297 1,672,979

0.311 0.249 0.191 0.136 0.087 0.026 1.000

31.1 24.9 19.1 13.6 8.7 2.6 V = 100.0

Table G11-3. Drift-Based Soft-Story Check for Structure with Tall First Story Story 6 5 4 3 2 1

H (in.)

δ (in.)

Δ (in.)

IDR (%)

IDRn/IDRn+1

150 150 150 150 150 222

4.29 3.88 3.25 2.50 1.75 0.96

0.41 0.63 0.75 0.74 0.79 0.96

0.27 0.42 0.50 0.50 0.53 0.43

— 1.56 1.19 1.00 1.06 0.811

Note: IDR = Δ/H × 100%.

the fixed-base condition stiffens the bottom story relative to the upper stories. This effect may be seen in the deflected shape profile, which is presented in Figure G11-2(a). The maximum ratio of IDRs in Table G11-3 is 1.56, which is for the fifth story relative to the sixth story. Although this ratio is greater than 1.3, it does not result in a soft story classification because the first exception in Section 12.3.2.2 states that the top two stories of the structure may be excluded from the check.

Seismic Loads

Vertical Structural Irregularities

Table G11-4. Drift-Based Soft-Story Check for Structure with Tall Second Story

Story 6 5 4 3 2 1

H (in.)

δ (in.)

Δ (in.)

IDR (%)

IDRn/IDRn+1

150 150 150 150 222 150

4.60 4.18 3.54 2.75 1.93 0.46

0.42 0.65 0.78 0.82 1.47 0.46

0.28 0.43 0.52 0.55 0.66 0.31

— 1.54 1.21 0.96 1.20 0.47

(a) Tall 1st Story

(b) Tall 2nd Story

Figure G11-2. Deflected shape profiles. The drift calculations are shown for the structure with the tall second story in Table G11-4. Here, the second-story drift ratio (0.66%) is 1.2 times the drift ratio of the third story (0.55%). A soft story condition does not occur because this value is less than 1.3. The deflected shape profile for the structure with the soft second story is shown in Figure G11-2(b). Based on the preceding results, both of the structures shown in Figure G11-1 are exempt from the stiffness-based soft story check described in the first two rows of Table-12.3-2. However, there are circ*mstances in which this check may be required. To illustrate this procedure, a stiffness-based soft story check is performed for the building with the tall second story [Figure G11-1(b)], although such a check is not actually required for this structure. The first step in the analysis is the determination of the story stiffness. This determination is done on a story-by-story basis by applying equal and opposite lateral forces V at the top and bottom of the story, computing the story drift Δ in the story, and defining the story stiffness as Ki = Vi/Δi. The procedure is illustrated in Figure G11-3. See FAQ A1 in Chapter 30 of this guide for more discussion of this procedure. After the story stiffnesses are determined, they are compared according to the requirements of Table 12.3-2. A soft story irregularity exists if, for any story,

Seismic Loads

Figure G11-3. Computing stiffness for Story i. Table G11-5. Stiffness-Based Soft Story Analysis for Structure with Soft Second Story Story 6 5 4 3 2 1

Δ (in.)

K (kips/in.)

Kn/Kn+1

Kn/Avg Kn+1

0.763 0.691 0.622 0.511 1.042 0.290

131 145 161 196 96 345

— 145/131 = 1.11 161/145 = 1.11 196/161 = 1.22 96/196 = 0.490 345/96 = 3.59

— — — 196/146 = 1.35 96/167 = 0.575 345/151 = 2.28

Note: Avg Kn+1 = average stiffness, K, of the three stories above.

the stiffness of that story is less than 70% of the stiffness of the story above, or if the stiffness of the story is less than 80% of the average stiffnesses of the three stories above. The irregularities are considered extreme if for any story the stiffness of that story is less than 60% of the stiffness of the story above, or if the stiffness of the story is less than 70% of the average stiffnesses of the three stories above. The results for the frame of Figure G11-1(b) are shown in Table G11-5. A story shear of V = 100 kips was used in the analysis. Based on this check, the structure has an extreme soft story irregularity. However, the structure need not be classified as such because the drift-based check of the same structure exempted this structure from the stiffness-based check. Based on this observation, one should always perform the drift-based check first because this step may exempt a structure from being classified as having a soft story irregularity, thereby allowing the designer to skip the more time-consuming stiffness-based check.

11.2 Weight (Mass) Irregularity (Type 2) Vertical weight irregularities are relatively straightforward to determine, and no example is presented. Note, however, that the story weight used in the calculation is the effective seismic weight, as deﬁned in Section 12.7.2. Also, the same

Seismic Loads

Vertical Structural Irregularities

exception (the drift ratio test) that applies to stiffness irregularities may be applied to weight irregularities. It is possible that this exception may supersede the mass ratio test provided in Table 12.3-2.

11.3 Vertical Geometric Irregularity (Type 3) A vertical geometric irregularity occurs when the horizontal dimension of the lateral resisting system at one level is more than 130% of that for an adjacent story. Based on this deﬁnition, on the one hand, the structure shown in Figure G11-4(a) has a vertical geometric irregularity because the moment resisting frame has three bays on the third story and only two bays on the fourth story. On the other hand, the structure shown in Figure G11-4(b) does not have a vertical geometric irregularity because the braced frame, which is the lateral resisting system, has the same horizontal dimension for the full height. The setbacks on the upper three stories have no inﬂuence on the vertical geometric irregularity of the braced frame system because the two exterior bays resist gravity loads only, and as such, are not part of the lateral load–resisting system. It is likely that both systems in Figure G11-4 have a weight irregularity.

11.4 In-Plane Discontinuity in Vertical Lateral Force-Resisting Element Irregularity (Type 4) An in-plane discontinuity occurs when there is a horizontal offset in the lateral load–resisting system that causes an overturning moment demand on a supporting structural element, which can be a beam, column, truss, or slab. Based on this deﬁnition, the system shown in Figure G11-5(a) has an irregularity because the offset produces overturning moment demands on the columns that support the upper three stories of the X-braced frame. For the system shown in Figure G11-5(b), the offset again produces overturning moment demands on the two columns supporting the upper three stories.

(a) Moment Frame

(b) Braced Frame

Figure G11-4. Example of vertical geometric irregularity.

Seismic Loads

Figure G11-5. Example of an in-plane discontinuity irregularity. In the system shown in Figure G11-5(a), Columns C and D (dotted rectangles) under the discontinuous braced frame would be subject to the requirements of Section 12.3.3.3, thereby requiring them to be designed with load cases that include the overstrength factor Ω0. Column C in Figure G11-5(b) would also be subject to the requirements of Section 12.3.3.3, because the offset transfers an overturning moment to this column. However, Column B in the same structure would not be required by the ASCE 7 standard to be designed for load cases including Ω0 because this column would carry overturning forces even if the offset did not exist [Figure G11-5(c)].

11.5 Discontinuity in Lateral Strength–Weak Story Irregularity (Types 5a and 5b) Weak story irregularities are difﬁcult to detect because the concept of story strength is not well deﬁned, even for relatively simple systems, such as moment frames and X-braced frames. Providing a full numerical example of this type of

Seismic Loads

Vertical Structural Irregularities

irregularity is beyond the scope of this guide because the computation of story strength depends on rules established in the material speciﬁcations, such as ACI 318-14 (ACI 2014) or the AISC seismic provisions (AISC 2016b). Some discussion is warranted, however. Consider the case of a momentresisting frame shown in Figure G11-6. In Figure G11-6(a), it is assumed that a column mechanism has formed. This kind of mechanism can form if the columns are weak relative to the beams (which is not allowed for special moment frames in steel or reinforced concrete). The mechanism shown in Figure G11-6(b) is a beam mechanism. This mechanism, as shown, is in fact incorrect because a single-story beam mechanism cannot occur; plastic hinges would need to form in all beams at all stories. In addition, it would be necessary for hinges to form at the base of the columns (if the columns are ﬁxed at the base). The beam mechanism could occur at one level only; however, if the columns in the story above and the story below the beam with the plastic hinges had a moment-free hinge at midheight. On the basis of these assumptions, the commentary to the 2005 AISC seismic provisions (AISC 2005) provided formulas for computing the story strength for the mechanisms shown in Figure G11-6. The intended use of the AISC expressions is related to frame stability and not system irregularity. For the story mechanism [Figure G11-6(a)], which is applicable for systems that do not satisfy the strong column–weak beam criterion, the story strength of story, Vyi, (AISC 2005) is P 2 m k = 1 M pCk V yi = (C3-3) H For the beam (girder) mechanism that does satisfy the strong column–weak beam requirements [Figure G10-6(b)], the AISC expression for computing story strength (AISC 2005) is P 2 nj= 1 M pGj (C3-2) V yi = H

Figure G11-6. Moment frame mechanisms.

Seismic Loads

where k and j = Integer counters, m = Number of columns, MpCk = Plastic moment strength of column k under minimum factored load, n = Number of bays, MpGj = Plastic moment strength of beam j, and H = Story height. The preceding formulas would be equally applicable to structures of reinforced concrete and are suitable for computing story strength in association with the requirements of Table 12.3-2. For steel or concrete, the effect of the axial force in the columns on moment strength of the plastic hinges must be considered. For braced frames, the story strength depends primarily on the bracing configuration, the axial strength of the brace, and the angle of attack θ of the brace, as shown in Figure G11-7. In Figure G11-7(a), the system is a buckling restrained braced frame, for which the strength of the single brace is the same in tension as it is in compression. For the concentrically braced frame, the strength of the tension and compression brace is different, and this difference has to be taken into consideration. Finding the story strength of other systems, such as frame-wall systems in concrete or moment frames in combination with braced frames in steel, is not straightforward and must be computed using nonlinear static analysis. A loading similar to that used to determine story stiffness (Figure G11-3) could be used. Such analysis should include gravity load effects if it is expected that the gravity loads have an influence on member strength. A rigorous analysis would include P-delta effects as well. Weak structure irregularities are highly undesirable and should be avoided if at all possible. Fortunately, such irregularities are uncommon in structures designed according to ASCE 7 and the material specifications (e.g., AISC 2016a, b). The irregularity is rare because the design story shears always

(a) Buckling Restrained Braced Frame

(b) Concentrically Braced Frame

Figure G11-7. Brace frame strength irregularities.

Seismic Loads

Vertical Structural Irregularities

increase from the top to the bottom of the structure, and, hence, the story strengths should increase from the top to the bottom as well.

11.6 Consequences of Vertical Irregularities Vertical irregularities are signiﬁcant primarily when the structure under consideration is assigned to SDC D or above, or in some cases, SDC C. The second and third columns of Table 12.3-2 provide the consequences of the irregularities in terms of the seismic design category. A few of the more important consequences are the following: • • • • •

Systems with vertical irregularities of Type 5b are not allowed in SDC D (12.3.3.1). Systems with vertical irregularities of Type 1b, 5a, or 5b are not allowed in SDC E or F (12.3.3.1). Systems with vertical irregularity of Type 5b shall not be greater than two stories (or 30 ft) in height (12.3.3.2). Structural elements supporting discontinuous frames that have vertical irregularity of Type 4 shall be designed to resist seismic loads including the effect of overstrength (12.3.3.3). The equivalent lateral force procedure is prohibited for some systems with vertical structural irregularities in SDC D, E, and F (Table 12.6-1).

Seismic Loads

12 Redundancy Factor

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

There are no signiﬁcant changes that affect the determination of the redundancy factor.

Section 12.3.4 describes the methodology for determination of the redundancy factor, ρ, which is used in several of the seismic load combinations that are speciﬁed in Section 12.4. This chapter demonstrates how the redundancy factor is determined for several structural systems. The use of the redundancy factor in the context of the load combinations is demonstrated in Chapter 13 of this guide. The redundancy factor, ρ, is used in association with the seismic load combinations that are speciﬁed in Section 12.4, in particular, in accordance with Equation (12.4-3) E h = ρQE

(12.4-3)

where Eh is the effect of horizontal seismic forces, and QE is a component or connection force that results from application of horizontal loads. When used in conjunction with Equation (12.4-3), the value of the redundancy factor, ρ, is either 1.0 or 1.3, depending on the seismic design category and the structural conﬁguration. The factor can be different in the two horizontal directions. Where the redundancy factor is determined to be 1.3 in one direction, it applies to all connections and components in the structure that are designed to resist seismic loads generated from the seismic load case in that direction. Section 12.3.4.1 lists a variety of conditions wherein ρ can be taken as 1.0 without further evaluation. For example, ρ can be taken as 1.0 in the design of nonstructural components. The factor ρ can also be taken as 1.0 in drift and P-delta calculations. Note,

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100

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however, that the allowable story drifts must be divided by ρ for moment frames in SDC D, E, and F (Section 12.12.1.1). For structures in SDC B and C, ρ is taken as 1.0 in each direction. For structures in SDC D, E, and F, the redundancy factor is 1.3, but may be reduced to 1.0 if it passes either a configuration test or a calculation test. These tests are stipulated in Section 12.3.4.2. The configuration test is described in subparagraph (b) of Section 12.3.4.2, which states that ρ may be taken as 1.0 where the structure has no horizontal structural irregularities and where at least two bays of perimeter seismic force– resisting elements exist on each side of the building for each story of the building resisting more than 35% of the seismic base shear. The number of bays for a shear wall shall be considered as the total length of the wall (in one plane) divided by the story height, or two times the total length of the wall divided by the story height for light-frame construction. Subparagraph (a) of Section 12.3.4.2, in association with Table 12.3-3, describes the calculation test. In this test, a lateral load-resisting element (or connection) is removed from the structure to determine if removal of the element or connection causes an extreme torsional irregularity (where one was not present before), or if the lateral strength of the structure is reduced by more than 33%. If the extreme torsional irregularity or excessive strength loss does not occur, the redundancy factor may be taken as 1.0. Note that the torsional irregularity test fails (ρ must be taken as 1.3) if the structure has an extreme torsional irregularity before the component or connection is removed. As stated previously, ρ = 1.0 may be used in SDC D, E, and F structures if either Condition (a) or (b) applies. The Condition (a) test is much more difficult to apply, so Test (b) should be applied first. The loss-of-strength test under Condition (a) rarely occurs and providing a logical argument (performing the calculation by inspection) that a 33% strength loss is impossible for the given configuration is usually acceptable. The torsion test is more problematic, particularly when the structure has a torsional irregularity before the component or connection is removed. Figure G12-1 illustrates several cases for which Condition (b) may be evaluated. The floor plans in the figure are applicable at levels for which the seismic base shear is greater than 35% of the base shear. Only Building A satisfies the Condition (b) test. The building has no horizontal structural irregularities, the walls on each side of the building are long enough to provide two equivalent bays on each side, and the walls are located on the perimeter. Building B violates the criteria because the two walls marked with asterisks are not on the perimeter. (Note that the perimeter frame requirement in Section 12.3.4.2 does not specify that all frames be on the perimeter. It is the authors’ interpretation, however, that all of the lateral load resistance be provided by at least two bays of perimeter framing on each side of the building for ρ to default to 1.0.) Building C, which is assumed to have no irregularities, does not satisfy the criteria in the y-direction because the plan length of the walls marked with asterisks is insufficient to provide two equivalent bays on each side of the building.

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101

Redundancy Factor

Figure G12-1. Evaluation of the redundancy factor for various buildings. Buildings D, E, and F cannot automatically be classified with ρ = 1.0 because each has a horizontal structural irregularity. In Building F, the irregularity occurs because of an out-of-plane offset of the shear walls marked with asterisks. The walls at the upper level are on the interior of the building and transfer to the exterior at the lower levels. The fact that Condition (b) has not been satisfied for a given building does not mean that the redundancy factor is 1.3. This situation would be the case only if Condition (a) in Section 12.3.4.2 is also not met. Consider again Building B of Figure G12-1. In this shear wall system, each wall has a plan length greater than the height of the wall. Thus, the height-to-width ratio of the walls is less than 1.0, and the system defaults to Other lateral force–resisting elements in Table 12.3-3. Presumably, therefore, this system can be assigned a redundancy factor of 1.0 in. each direction because no requirements dictate otherwise. The same situation appears to occur even if the walls marked by asterisks in Building B of Figure G12-1 are removed entirely. In the opinion of the authors, this situation violates the spirit of the redundancy factor concept, and a factor of 1.3 should be assigned in this case. In Building C of Figure G12-1, each wall marked with an asterisk has a length less than the story height. Removal of one of these walls does not cause an extreme torsional irregularity. At first glance, the removal of one wall appears to reduce the strength of the system by only 25% in the y-direction. However, this situation does not consider the effect of torsion. The reduction in strength must be based on the questions, “How much lateral load can be applied in the y-direction for the system with one wall missing, and how does that compare with the strength of the system with the wall in place?” Two interpretations exist for evaluation of the strength of the system with elements removed. The first is based on elastic analysis, and the second is based on inelastic analysis. An important consideration of the use of an inelastic

Seismic Loads

102

Seismic Loads

analysis is that the system must be sufﬁciently ductile to handle the continued application of loads after the lateral load–resisting elements begin to yield. Consider, for example, the system shown in Figure G12-2. This system has eight identical walls, marked A through H, each with a force–deformation relationship as shown in Figure G12-3. The lateral load–carrying capacity of each wall is 100 kips. The system is evaluated on the basis of the following situations: 1.

Elastic behavior with all walls in place,

Elastic behavior with one wall removed,

Inelastic behavior analysis with all walls in place, and

Inelastic behavior with one wall removed.

For each situation, the lateral force V is applied in the y-direction at an eccentricity of 5% of the width (eccentricity = 0.05 × 125 ft = 6.25 ft) of the

Figure G12-2. System with one wall (C) removed.

Figure G12-3. Force–deformation relationship for shear wall.

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103

Redundancy Factor

building in the x-direction. The eccentricity of 5% of the plan width is consistent with the accidental torsion requirements of Section 12.8.4.2. New to ASCE 7-16 is a relaxation of the accidental torsion requirements (Section 12.8.4.2). Most often, accidental torsion is now only applied for determination of horizontal irregularities, and if none exist, accidental torsion need not be included in the determination of seismic forces and drifts. For the following calculations, however, accidental torsion is included because redundancy determination is a function of the existence of a horizontal irregularity. The analysis was performed for this example using a computer program that can model inelastic structures. This analysis provided the curves shown in Figure G12-4. The upper curve represents the behavior of the system with all four walls in place, and the lower curve is for the system with Wall C removed. The elastic analysis for each system is represented by the response up to first yield (the first change in slope of the curves), and the inelastic response is represented by the full curve. From the perspective of the elastic analysis, the structure with all walls in place can resist a lateral load V of 370 kips. At this load, Walls C and D on the right side of the building carry 100 kips, and Walls A and B carry 85 kips. The ratio of the displacement δ2 relative to the displacement δ1 is 1.14, so according to Table 12.3-1, the structure does not have a torsional irregularity. When the inelastic response is considered, the structure can carry additional lateral load because Walls A and B can each resist an additional 15 kips before they reach their 100 kip capacity. With four walls resisting 100 kips each, the total lateral capacity of the system is 400 kips. Recall that the force– displacement plot for this four-wall system is shown by the upper curve in Figure G12-4. The displacement shown in the figure is the y-direction displacement, δ2. The first change of slope in the curve occurs when Walls C and D yield, and the second change occurs when Walls A and B yield.

Figure G12-4. Force–deformation plot for structure with three or four walls using inelastic analysis.

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104

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When Wall C is removed, the center of rigidity moves 9.375 ft to the left. When an elastic analysis is performed, the system can resist a lateral load of only 230 kips, because Wall D reaches its 100 kip capacity. At this point, Walls A and B resist 65 kips each. In addition, the ratio of the displacement at point δ2 with respect to the displacement at point δ1 is 1.35. Hence, a torsional irregularity, but not an extreme irregularity, exists. The ratio of the resisting force of the three-wall system to that of the four-wall system is 230/370 or 0.621. On this basis, the system must be designed with ρ = 1.3 because it loses more than 33% of its strength. From the perspective of an inelastic analysis, the three-wall system can resist a total of 300 kips. This is shown by the force–displacement diagram (the lower curve) in Figure G12-4. The ratio of the inelastic resisting force of the threewall system to that of the four-wall system is 300/400 = 0.75. In this case, the system could theoretically be designed with ρ = 1.0 because it passes both the strength and the nonextreme torsion irregularity tests. See ASCE 7-16 commentary Figure C12.3-6 for a ﬂowchart of this procedure. Two ﬁnal points are made regarding the use of the redundancy factor: 1.

When it is determined that ρ = 1.3 in a given direction, the factor of 1.3 applies only to load combinations where seismic forces are applied in that direction. Also, the load combination with ρ = 1.3 is used for all components and connections developing seismic forces when the load is applied in that direction. This includes elements and components from the bottom to the top of the structure and is not limited to those elements and components in levels resisting more than 35% of the seismic base shear.

The Condition (a) test of Section 12.3.4.2 applies for buildings with different types of lateral load–resisting elements in a given direction. For example, for a dual momentframe shear wall system, the test would be performed with a single wall removed, and then with a single beam removed from the moment frame.

Seismic Loads

13 Load Combinations

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

• • • • •

The numbering and the details of the strength-based seismic load combinations in Chapter 2 have changed. The seismic load combinations are now provided in Section 2.3.6 and are numbered as Combinations 6 and 7 for the cases of maximum and minimum gravity load, respectively. Similar changes have been made to the allowable stress combinations. Some of the nomenclature ﬁrst used in Chapter 12 of ASCE 7-10 was moved to Chapter 2 of ASCE 7-16. A new section (11.9) was added that is used to develop a vertical acceleration spectrum. This is used primarily in Chapter 15, “Nonbuilding Structures.” Accidental torsion is no longer required for some buildings and this will reduce the number of load combinations (12.8.4.2). New terminology has been introduced to represent a capacity-limited horizontal seismic load effect, Ecl (12.4.3.2). This factor supersedes the use of Emh = Ω0QE in some cases. New provisions for response history analysis in Chapter 12 and Chapter 16 require three-dimensional analysis with bidirectional loading consisting of 100% of the ground motions being applied simultaneously in each direction.

This chapter explores the use of the strength design load combinations that include earthquake load effects. These load combinations, numbered 6 and 7 in Section 2.3.6 of ASCE 7, are then discussed in context with the requirements of Section 12.4. Also discussed in this chapter are requirements for including direction of loading (Section 12.5), accidental torsion (Section 12.8.4.2), and ampliﬁcation of accidental torsion (Section 12.8.4.3).

105

Seismic Loads

106

Seismic Loads

13.1 Basic Load Combinations Chapter 2 of ASCE 7 provides the required load combinations for both strengthbased and allowable stress-based designs. This chapter covers only the use of the strength-based load combinations. There are ﬁve basic load combinations provided in Section 2.3.1 and two basic load combinations with seismic load effects in Section 2.3.6. Each member and connection of the structure must be designed for the maximum force or interaction of forces (e.g., axial force plus bending) produced by any one of these basic combinations. For any given member, such as a reinforced concrete girder, it might be found that different combinations control different aspects of the design. For example, load Combination 2 in Section 2.3.2 might control the requirements for bottom reinforcement at midspan, whereas Combination 6 controls requirements for top reinforcement at the ends of the member. A speciﬁc example of this circ*mstance is provided subsequently. The remainder of this example concentrates on Combinations 6 and 7, which are as follows (where the term E is not yet divided into horizontal and vertical effects): Combination 6: Combination 7:

1.2D + 1.0E + 1.0L + 0.2S 0.9D + 1.0E

In each of these combinations, the factor on earthquake load effects, E, is 1.0. This is because the spectral design accelerations SDS and SD1, produced from the requirements of Chapter 11, are calibrated to be consistent with an ultimate load. The factor on live load in Combination 6 may be reduced to 0.5 in most cases (See Exception 1 in Section 2.3.6). The adopted building code may provide load combinations that are somewhat different from those specified in ASCE 7. If so, these combinations must be used in lieu of the ASCE 7 requirements. For example, recent editions of IBC (ICC 2017) specify a factor of 0.7 on snow load in Combination 6 for configurations (such as sawtooth roofs) that do not shed snow off the structure. The snow load in Combination 6 is always included when S > 0. There might also be a snow load effect in E in both Combinations 6 and 7 because the effective seismic weight, W, is required to include 20% of the design snow load when the flat roof snow load exceeds 30 lb/ft2 (Section 12.7.2). There are two ways in which the combinations are used. The first, covered in Section 12.4.2, is applicable to all elements and connections in the structure and may be considered the basic load combinations. The second, covered in Section 12.4.3, is for those special elements or connections that must be designed with the overstrength factor, Ω0. ASCE 7 provides several specific cases where the overstrength load combination must be used: • • •

Section 12.2.5.2, which requires that the foundation and other elements contributing to the overturning resistance of cantilever column structures be designed with the overstrength factor; Section 12.3.3.3, which pertains to elements supporting discontinuous walls or frames; Section 12.10.2.1, which pertains to collector elements, their splices, and their connections to resisting elements;

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Load Combinations

• •

Sections 12.10.1.1 and 12.10.3.3, transfer forces in diaphragms; and Sections 12.13.8.4, 12.13.8.5, and 12.13.8.6, batter piles, pile anchorage, and pile splices.

In addition, the materials standards have provisions that require/allow the use of the overstrength factor in some cases. For example, Section 18.4.3 of ACI 318-14 (ACI 2014) stipulates that the seismic shear demand in columns of intermediate moment frames be based on the nominal ﬂexural strength or on the computed force multiplied by Ω0. In this case, the use of the overstrength is a simpler calculation but is likely to be conservative relative to the use of the nominal strength. Similarly, AISC 341-16 (2016b) requires that steel columns and column base anchorages include overstrength, Ω0, for special, intermediate, and ordinary systems, for most common situations. Section 12.4.2 of ASCE 7 provides details on the standard seismic load effect. For use in load Combination 6, the seismic load effect E is given as E = Eh + Ev

(12.4-1)

and for use in load Combination 7 as E = Eh − Ev

(12.4-2)

E h = ρQE

(12.4-3)

Ev = 0:2S DS D

(12.4-4a)

where

and

The term Eh represents the horizontal seismic load effect. The term ρ in Equation (12.4-3) is the redundancy factor, computed in accordance with Section 12.3.4. This value is 1.0 for all buildings assigned to SDC B or C and is either 1.0 or 1.3 in SDC D through F. This factor applies to the entire structure but may be different in the two orthogonal directions. See Chapter 12 in this guide for details on determination of the redundancy factor. The term Ev represents the effect of vertical ground acceleration, which is not considered explicitly elsewhere, with the exception of Section 12.4.4, which provides requirements for minimum upward forces in horizontal cantilevers for buildings in SDC D through F. New in ASCE 7-16 is an exception in Section 12.4.2.2 that replaces Ev = 0.2SDSD with the term 0.3SavD [Equation (12.4-4b)], where Sav is the appropriate ordinate of the vertical acceleration spectrum as determined from Section 11.9. Although it might be possible to use 0.3Sav in lieu of 0.2SDS for building structures, a vertical period of vibration would be required to determine Sav, and this period would likely be much shorter than the fundamental sway period and difﬁcult to identify. Thus, although not speciﬁcally stated in the standard, it appears that use of Exception 1 and Equation (12.4-4b) in Section 12.4.2.2 should be restricted to use in association with Chapter 15, “Nonbuilding Structures,” of the standard (15.1.4).

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QE in Equation (12.4-3) is the seismic effect on an individual member or connection. This value is produced by the seismic analysis of the structure and includes direct loading (e.g., application of equivalent lateral forces), accidental torsion and torsional ampliﬁcation (if applicable), and orthogonal loading effects (if applicable). QE might represent, for example, a bending moment at a column support, an axial force in a bracing member, or a stress in a weld. In some cases, QE might represent an interaction effect, such as an axial-force bending moment combination in a beam column. In such cases, both the axial force and bending moment occur concurrently and should be taken from the same load combination. When Equations (12.4-1) through (12.4-4) are substituted into the basic load combinations, the following detailed combinations for strength design are obtained: Combination 6: Combination 7:

(1.2 + 0.2SDS)D + ρQE + 1.0L + 0.2S (0.9 − 0.2SDS)D + ρQE

The use of these load combinations is illustrated in Figures G13-1 and G13-2. Each ﬁgure shows a simple frame with gravity and seismic loading. Snow loading is not present. Figure G13-1(a and b) show only the gravity portion of the load, with the heavy gravity case shown in Figure G13-1(a) and the light gravity case shown in Figure G13-1(b). In Figure G13-1(c and d), the loading is shown for seismic effect acting to the east or to the west. Moment diagrams are drawn for each loading, and these diagrams are presented on the tension side. The moment values (units not important) are shown for each loading.

(a) Heavy Gravity

(b) Light Gravity

(d) Lateral West

Figure G13-1. Basic load combinations for simple frame.

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109

Load Combinations

(a) Heavy Gravity + Lateral East

(b) Heavy Gravity + Lateral West

(d) Light Gravity + Lateral West

Figure G13-2. Combinations of basic combinations for worst effect. Figure G13-2 shows the combination of gravity and earthquake load. Figure G13-2(a and b) give the total moments for load Combination 6, with heavy gravity plus seismic acting to the east on in Figure G13-2(a) and heavy gravity plus seismic acting to the west in Figure G13-2(b). Figure G13-2(c and d) show Combination 7 with light gravity and seismic acting to the east or west. Controlling moments are circled. As may be seen in Figure G13-2, each load combination must be exercised twice, once for positive seismic and once for negative seismic, to produce the controlling effect in each member or connection. For the given example, the controlling tension on the top moment is 10 at both ends of the beam, and the controlling tension on the bottom moment is 4 for the full beam span. Of course, other load combinations (without seismic) provided in Chapter 2 of ASCE 7 must also be exercised to determine if they control. It is important to recognize, however, that the seismic detailing requirements associated with any system must be provided, regardless of the loading combination that controls the strength of the member or connection. For example, a member in an intermediate moment frame that has a wind-based design force twice as high as the seismic design force would be sized on the basis of the wind forces but must be detailed according to the requirements for intermediate moment frames. The lateral forces shown in Figures G13-1 and G13-2 include the effects of accidental torsion (where required), as well as the effect of seismic loads acting simultaneously in orthogonal directions (where required). Accidental torsion (12.8.4.2) must be included for any nonﬂexible diaphragm building in SDC B that

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110

Seismic Loads

has an extreme torsional irregularity, or for nonflexible diaphragm buildings in SDC C through F that have a torsional irregularity or an extreme torsional irregularity. The accidental torsion must be amplified in SDC C through F but only if the accidental torsion is applied statically. Where accidental torsion is accommodated by a physical mass offset in modal response spectrum or linear response history analysis, amplification is not required (Sections 12.9.1.5 and 12.9.2.2.2). Direction of load effects are covered in Section 12.5. For structures in SDC B, the analysis (including accidental torsion effects) may be performed independently in each direction and the structure may be designed on that basis. For structures in SDC C through F, the direction of load effects must be explicitly considered wherever a Type 5 horizontal nonparallel systems irregularity occurs (Table 12.3-1). In addition, orthogonal load effects must be included in SDC D through F, in which elements common to two or more lateral load resisting systems (i.e., columns and walls) develop axial forces caused by seismic effects in excess of 20% of their axial capacity. Where accidental torsion or orthogonal effects are required, the development of the forces represented by QE can become quite complex. Consider, for example, a system wherein the ELF method of analysis is required, in which • • • •

Lateral forces must be applied in positive and negative directions, Accidental torsion may or not be required, Orthogonal load effects may or may not be required, and The redundancy factor may be different in the two orthogonal directions.

This complexity is represented by Equation (G13-1) in which the “combined” effect caused by seismic forces acting principally in the x-direction, ρE X is ρE X = ρX ðF X T eY Þ DY ρY F Y

(G13-1)

where ρX = Redundancy factor in the x-direction (1.0 or 1.3), FX = Forces computed owing to lateral forces applied in the x-direction without accidental torsion, TeY = Forces computed owing to story accidental torques resulting from x-direction forces applied at a y eccentricity, DY = Directionality factor for forces applied in the y-direction (0.0 or 0.3), ρY = Redundancy factor in the y-direction (1.0 or 1.3), and FY = Forces computed owing to lateral forces applied in the y-direction without accidental torsion. The ± symbol in the equation indicates positive or negative loading, and all permutations must be considered. This results in eight possible sets of member earthquake forces for the application of principal x-direction forces. A similar equation, Equation (G13-2), can be written for lateral loads acting principally in the y-direction, which results in an additional eight sets of member earthquake forces as

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111

Load Combinations

ρE Y = ρY ðF Y T eX Þ DX ρX F X

(G13-2)

Thus, when gravity effects are considered in load Combinations 6 and 7, a total of 2(8+8) = 32 different sets of member earthquake forces would be needed when both accidental torsion and orthogonal load effects are required. This number would be reduced to only eight sets if accidental torsion and orthogonal loading are not required (this being +FX, −FX, +FY, −FY for each of Combinations 6 or 7). The manner in which the different load effects are considered becomes further complicated when the modal response spectrum analysis procedure is used. These complications arise from the need to scale force and/or displacement results, the ability to accommodate accidental torsion by use of a mass offset, and the possibility of combining orthogonal loads statistically rather than by direct addition. Similar complications exist for the linear response history analysis procedure. See guide Chapters 22 and 23 for detailed requirements for each procedure.

13.2 Special Seismic Load Combinations, Including the Overstrength Factor As mentioned, there are a variety of circ*mstances in which the load combinations with overstrength must be used. The special load combinations that include the overstrength factor are (after combining terms) the following: Combination 6: Combination 7:

(1.2 + 0.2SDS)D + Emh + 1.0L + 0.2S (0.9 − 0.2SDS)D + Emh where Emh = Ω0QE

where the only difference with respect to the standard load combination is that the term Ω0 replaces the redundancy factor ρ. It is very important to emphasize that the load combinations incorporating overstrength usually apply to individual components; they never apply to the complete structural system. Analogous with load combinations including redundancy, the component force resulting from a combination of direct load, accidental torsion, and orthogonal loading could be represented in Equations (G13-3) and (G13-4) as Ω0 EX = Ω0 ½ðF X T eY Þ DY F Y

(G13-3)

Ω0 E Y = Ω0 ½ðF Y T eX Þ DX F X

(G13-4)

in which it is important to note that the overstrength factor is not directional—it applies only to the specific component under consideration and is specified in Table 12.2-1 for the specific structural system of which the component is a part. The standard allows Emh to be calculated as the capacity-limited horizontal seismic load effect, Ecl (12.4.3.2). Chapter 11 indicates that Ecl is determined from a rational plastic mechanism analysis, which would most likely be performed using a nonlinear static pushover procedure.

Seismic Loads

14 Selection of Structural Analysis Procedures

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • • • •

Linear response history (LRH) analysis was removed from Chapter 16 and new requirements were written and placed in Chapter 12. Section 12.9 was retitled “Linear Dynamic Analysis,” and the modal response spectrum (MRS) procedure and LRH analysis were placed in this section. The Chapter 16 procedures for nonlinear response history (NRH) analysis were rewritten. Three-dimensional mathematical models must be used in MRS and LRH analysis. Scaling requirements for MRS and LRH analyses were changed to require the dynamic base shear computed using these procedures to be not less than 100% of the equivalent lateral force seismic base shear. The previous requirement was scaling to at least 85% of the ELF base shear.

This chapter covers the selection of the structural analysis procedures, and speciﬁcally Table 12.6-1 of the standard. Also discussed is the question as to the appropriate period of vibration T that should be compared to 3.5 Ts when determining if the equivalent lateral force (ELF) procedure is allowed for taller buildings.

113

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114

Seismic Loads

14.1 Selection of Structural Analysis Procedures Structures in SDC A may be analyzed using the lateral forces designated in Section 1.4.2, “General Structural Integrity.” Section 12.6 and Table 12.6-1 provide the requirements for selection of the seismic analysis procedure to be used for structures in SDC B and above. Four basic procedures are provided in Table 12.6-1: 1.

Equivalent lateral force (ELF) analysis (Section 12.8),

Modal response spectrum (MRS) analysis (Section 12.9.1),

Linear response history (LRH) analysis (Section 12.9.2), and

Nonlinear response history (NRH) analysis (Chapter 16).

Under certain (very limited) circ*mstances, the simpliﬁed procedure provided in Section 12.14 may be used. This chapter of the guide concentrates on ELF, MRS, and LRH analyses. Although the NRH procedures are effective and can be used for any system, they are usually reserved for special circ*mstances, such as validation of alternate structural systems that do not conform to all the requirements of Chapter 12. See Section 12.2.1.1 for speciﬁc requirements for nonconforming systems. Detailed technical descriptions and examples of use of the ELF, MRS, and LRH procedures are presented in Chapters 21, 22, and 23 of this guide, respectively. In these examples, the three procedures are applied to the same structure and a comparison of results and a general discussion of the advantages and disadvantages of each method is provided in Chapter 24. An overview of the NRH procedure (without an example) is presented in Chapter 25.

Selection of Method of Analysis Procedure Table 12.6-1 is used to determine the minimum (in the sense of complexity) analysis procedure that may be used for the final analysis, which consists of the determination of deformations and component forces. Where the ELF analysis procedure is allowed for the final analysis, there is no restriction against using MRS, LRH, or even NRH analyses. Where the ELF analysis procedure is not allowed for the final analysis, it is allowed for use in preliminary design and is in fact necessary for intermediate steps in the seismic design process. For example, an ELF analysis is used to determine if certain configuration irregularities exist. Chapters 18 and 21 of this guide provide additional information on the uses of the ELF analysis procedure. Table 12.6-1 can be summarized as follows: 1.

MRS, LRH, and NRH analysis is permitted for all structures in all SDC.

ELF analysis is permitted for all structures in SDC B and C.

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Selection of Structural Analysis Procedures

ELF is permitted for structures in SDC D, E, or F with structural height h ≤ 160 ft and where none of the following irregularities exist: ○

Type 1a and 1b horizontal irregularity (torsional or extreme torsional),

○

Type 1a and 1b vertical irregularity (soft story and extreme soft story),

○

Type 2 vertical irregularity (weight or mass), or

○

Type 3 vertical irregularity (vertical geometric).

ELF is permitted for regular structures in SDC D, E, or F with h > 160 ft and T < 3.5TS.

The limitations related to irregularity are enforced because the presence of any of these irregularities violates the premise on which the ELF method was developed. The limitation related to height and/or TS is in place because higher mode effects cannot be adequately captured by the ELF analysis procedure for taller systems. For buildings located in SDC B or C, the ELF analysis procedure is allowed for all systems and there is little incentive for performing MRS or LRH analyses. However, the more advanced procedures should be considered for highly irregular systems and for tall buildings. In ASCE 7-10, a signiﬁcant motivator for performing MRS or LRH analysis when ELF analysis was allowed was the potential reduction in base shear to 85% of the ELF base shear. However, in ASCE 7-16, this provision was changed to require that the MRS or LRH results be scaled to 100% of the ELF base shear.

14.2 Examples for Computing TS and Comparing to 3.5 TS In this example, calculations are performed to determine the permitted analysis procedures for a regular steel moment frame and a regular concentrically braced frame system situated in a moderate seismic hazard area, (SS = 0.75, S1 = 0.3) and on soil Site Classes B or D. For Site Class B, site-specific velocity measurements were made. The assignment of Site Class D was determined from site conditions. The building is used for offices, and the risk category is II. The systems have a structural height, hn, of 168 ft which is greater than the 160 ft limit, so it is necessary to determine if the period T exceeds 3.5 TS, as defined in Section 11.4.6: TS =

S D1 S DS

Physically, TS is the period at which the constant acceleration [Equation (12.8-2)] and the constant velocity [Equation (12.8-3)] branches of the response spectrum intersect (Figure 11.4-1). When determining if T > 3.5 Ts, the standard is not clear on which period T should be used in the comparison: Ta, CuTa, or Tcomputed. Tcomputed is the fundamental period in the direction of response determined from

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a rational (e.g., eigenvalue) analysis. Note that the symbol “Tcomputed” is used only in this guide and is not deﬁned in the standard.

The approximate period Ta is deﬁned as follows: T a = C t hxn

(12.8-7)

According to Table 12.8-2, Ct and x are, respectively, 0.028 and 0.8 for steel moment-resisting frames, and 0.02 and 0.75, respectively, for concentrically braced frames. In the ELF method, T = CuTa must be used for determining the seismic base shear when Tcomputed is greater than CuTa. Cu is a function of the 1 s spectral coefficient, SD1, with values ranging from 1.4 to 1.7 supplied in Table 12.8-1. The calculations are performed first using the period T = CuTa, and then recalculated using the other options. (Use of Fv = 2.0 for Site Class D would need to be based on a site-specific analysis in accordance with footnote a in Table 11.4-2, which refers to Section 11.4.8.) For systems on Site Class B: For SS = 0.75 Fa = 0.9 Table 11.4-1 For S1 = 0.30 Fv = 0.8 Table 11.4-2 SDS = (2/3) Fa SS = (2/3) × 0.90 × 0.75 = 0.45 Equations (11.4-1) and (11.4-3) SD1 = (2/3) Fv S1 = (2/3) × 0.8 × 0.3 = 0.16 Equations (11.4-2) and (11.4-4) SDC = C (Risk Category II) Tables 11.6-1 and 11.6-2 ELF analysis is allowed for both systems by Table 12.6-1 because the SDC is C.

For systems on Site Class D: For SS = 0.75 Fa = 1.2 Table 11.4-1 For S1 = 0.30 Fv = 2.0 Table 11.4-2 SDS = (2/3) Fa SS = (2/3) × 1.2 × 0.75 = 0.60 Equations (11.4-1) and (11.4-3) SD1 = (2/3) Fv S1 = (2/3) × 2.0 × 0.3 = 0.40 Equations (11.4-2) and (11.4-4) SDC = D (Risk Category II) Tables 11.6-1 and 11.6-2 Here it is possible that ELF will not be allowed because the SDC is D.

It must be determined if T is greater than TS because hn > 160 ft TS = SD1/SDS = 0.40/0.60 = 0.667 s 3.5TS = 3.5(0.667) = 2.33 s For SD1 = 0.4, Cu = 1.40

Section 11.4.5 Table 12.8-1

Determine if ELF is allowed using T = CuTa For the steel moment frame: Ct = 0.028 and x = 0.8 and T = CuTa = 1.40 × 0.028 × 1680.8 = 2.36 s 2.36 > 3.5Ts, so use MRS or LRH analysis

Table 12.6-1

For the steel concentrically braced frame: Ct = 0.02 and x = 0.75 and T = CuTa = 1.40 × 0.020 × 1680.75 = 1.30 s 1.30 < 3.5Ts, so use ELF, MRS, or LRH

Table 12.6-1

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Selection of Structural Analysis Procedures

Now what if T = Ta is used? For steel moment frame T = Ta = 0.028 × 1680.8 = 1.68 s 1.68 < 3.5Ts, so use ELF, MRS or LRH For steel braced frame T = Ta = 0.02 × 1680.75 = 0.93 s 0.93 < 3.5Ts, so use ELF or MRS or LRH For the moment frame ELF is now allowed. For the braced frame the answers did not change relative to using T = CuTa.

Now what if Tcomputed is used, which is 3.20 s for the moment frame and 2.50 s for the braced frame? For the steel moment frame 3.20 > 3.5Ts, so use MRS or LRH For the steel braced frame 2.50 > 3.5Ts, so use MRS or LRH In this case, ELF is prohibited for both systems.

Which period should be used in the calculation? Theoretically, the answer is Tcomputed because this corresponds to the period that would be used in the MRS or LRH analysis. Also, this period is almost always greater than CuTa and would be more likely to require MRS or LRH analysis in lieu of the less accurate ELF analysis procedure. In the author’s opinion, it would be very unconservative to use Ta because this is an extreme lower bound period and would be far less likely to disallow the less accurate ELF analysis procedure.

14.3 Structural Analysis Considerations After the method of analysis is determined, it is necessary to establish the details of the analysis. Considerations include the necessity to model in two or three dimensions when the ELF analysis procedure is used (three-dimensional is required for all MRS or LRH analysis in ASCE 7-16), and whether the diaphragms should be modeled as rigid or semirigid. These aspects of structural analysis are discussed in Chapter 15 of this guide.

Seismic Loads

15 Structural Modeling Requirements

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • •

Three-dimensional models are required where MRS or LRH analysis is used. Accidental torsion is required only for structures with a Type 1b extreme torsional irregularity in SDC B, and for structures with either a Type 1a or 1b torsional irregularity in structures assigned to SDC C, D, E, and F.

This chapter discusses the requirements for the development of the structural analysis model and the associated requirements of Section 12.7.3 of the standard.

15.1 Overview of Mathematical Modeling Requirements Two-Dimensional or Three-Dimensional Modeling Three-dimensional (3D) modeling is required in ASCE 7-16 for MRS (Section 12.9.1.8), LRH (Section 12.9.2.2), and NRH analysis (Section 16.3.1). Where the ELF procedure is used, Section 12.7.3 states that a 3D model is required where there exists a horizontal irregularity of Type 1a (torsion), Type 1b (extreme torsion), Type 4 (out-of-plane offset), or Type 5 (nonparallel system).

119

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In addition, the same section requires that diaphragms that are not rigid be modeled as semirigid. Where diaphragms are modeled as semirigid, a 3D mathematical model is required because the diaphragms would be represented using either membrane or shell finite elements. Section 12.3.1.2 states that the presence of any horizontal irregularity disallows the use of rigid diaphragms, and hence, the presence of any horizontal irregularity effectively requires a 3D analysis. It is somewhat ironic that two-dimensional (2D) models are allowed in ELF analysis if a torsional irregularity does not exist, but that a 3D model is required to determine the presence of the irregularity. Given this and the fact that modern analysis software makes is easy to generate and analyze 3D models, it would seem that 2D mathematical models would be rarely used unless the diaphragms can be classified as flexible.

Diaphragm Modeling Where the diaphragm is semirigid, Section 12.7.3 requires that the mathematical model should include a representation of the in-plane diaphragm stiffness characteristics and that sufficient degrees of freedom be used to account for the system’s dynamic properties. Two issues are involved in the modeling of the diaphragm: (1) the use of membrane or shell finite elements, and (2) the fineness of mesh used to model the diaphragm. Regarding the type of finite element to use, a shell element is usually required if the diaphragm is not horizontal but can be used for horizontal diaphragms. Such elements have six degrees of freedom per node and have both in-plane and out-of-plane stiffness. It is usually desirable to minimize (to near zero) the out-ofplane (bending) stiffness to avoid the diaphragm inadvertently contributing to the lateral stiffness of the system. If the out-of-plane stiffness is set to exactly zero, the element effectively becomes a membrane element and it may be necessary to restrain the vertical degrees of freedom and all three rotational degrees of freedom at several nodes of the element. Membrane elements should be used only for horizontal diaphragms. The fineness of the mesh used to model in the diaphragm depends on whether the stresses in the diaphragm need to be recovered. If these stresses need not be recovered, a coarse mesh consisting of perhaps a 3-by-3 or 4-by-4 mesh per bay is appropriate. If the stresses are to be recovered, a much finer mesh may be required, and the fineness of the mesh depends on the geometry of the diaphragm and the details of any local discontinuities. A trial-and-error approach is usually necessary to determine the appropriate mesh for the application.

Shear Deformation in Frame Elements Most modern software includes shear deformations in frame elements by default. Where this is not the default, shear deformations should be activated because they can be an important source of ﬂexibility in steel moment frames, deep beams, and shear walls.

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Cracked Section Properties in Reinforced Concrete Structures Section 12.7.3 requires that stiffness properties of concrete and masonry elements consider the effect of cracked sections. In such structures, cracking can have a significant influence on the cross-sectional stiffness of the structural elements. Table 10-5 of ASCE 41-17 (ASCE 2017b) provides recommendations for determining the effective stiffness of reinforced concrete beams, columns, slabs, and walls. This table is duplicated in Table G15-1 herein, in which recommendations for flexural, shear, and axial rigidly are provided. For example, for nonprestressed beams it is recommended that flexural rigidity be taken as 0.3EcIg, and the shear rigidity be taken as 0.4EcAw. The reduction in flexural stiffness is very significant because only 30% of the gross property is used. On first glance, it appears that a significant reduction is also taken in shear, except it is noted that the term 0.4Ec is an estimate of the shear modulus of the concrete. Hence, 0.4EcAw is in fact the gross (uncracked) shear stiffness. In some cases, such as deep link beams in coupled wall systems, cracking can significantly reduce the stiffness in shear. It is recommended therefore, that for cases in which shear deformations can be important, appropriate reductions in shear stiffness be used. See Park and Paulay (1975) for some guidelines. In addition, where there is considerable uncertainty in estimating the cracked properties, it is recommended that analysis be bounded with an appropriate range of properties.

Table G15-1. Effective Stiffness Values for Concrete Structures (From ASCE 41-13)

Component Beams—nonprestresseda Beams—prestresseda Columns with compression caused by design gravity loads ≥ 0.5 Agfc′ Columns with compression caused by design gravity loads ≤ 0.1 Agfc′ or with tension Beam–column joints Flat slabs–nonprestressed Flat slabs–prestressed Walls-crackedb

Flexural Rigidity

Shear Rigidity

Axial Rigidity

0.3EcIg EcIg 0.7EcIg

0.4EcAw 0.4EcAw 0.4EcAw

— — EcAg

0.3EcIg

0.4EcAw

EcAg (compression) EsAs (tension)

Refer to Section 10.4.2.2.1 Refer to Section 10.4.4.2 Refer to Section 10.4.4.2 0.5EcAg

EcAg 0.4EcAg

—

0.4EcAg

—

0.4EcAw

EcAg (compression) EsAs (tension)

For T-beams, Ig can be taken as twice the value of Ig of the web alone. Otherwie, Ig should be based on the effective width as deﬁned in Section 10.3.1.3. For columns with axial compression falling between the limits provided, ﬂexural rigidity should be determined by linear interpolation. If interpolation is not performed, the more conservative effective stiffnesses should be used.

See Section 10.7.2.2.

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Beam–Column Joint Deformations in Steel (and Concrete) Moment Frames Very large shear stresses can develop in the beam–column joint (panel zone) region of steel moment frames, and the deformations associated with these stresses can contribute signiﬁcantly to the lateral displacements of the frames. Section 12.7.3 requires that these deformations be considered in the structural analysis. There are basically three approaches to account for these deformations: 1.

Use centerline analysis,

Use a scissors model, or

Use a Krawinkler model.

These models are illustrated in Figure G15-1. The centerline model, Figure G15-1(a), is effective because it underestimates the shear deformations in the joint and overestimates the ﬂexural deformations in the joint. These errors tend to offset, producing a reasonably accurate model. In the scissors model, Figure G15-1(b), the shear deformation in the panel zone is transformed into a rotational deformation within a rotational spring. The model shown in Figure G15-1(c) is much more complex and explicitly represents the deformation in the panel zone. In most cases the use of the centerline model is adequate and satisﬁes the requirements of Section 12.7.3. However, many commercial analysis programs allow and simplify the use of the more sophisticated models. See Charney and Marshall (2006) for more background on the various models. ASCE 7 does not require that beam-column joint deformations be considered in reinforced concrete moment frames. In some cases, such deformations can be

(a) Centerline

(b) Scissors

(d) Centerline with Rigid Region

Figure G15-1. Various panel zone models.

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Structural Modeling Requirements

important and can be represented by models similar to those used for steel structures. If the centerline model is used, it might be appropriate to model some portion of the joint region as rigid to account for the fact that panel zone deformations in concrete frames are usually not as signiﬁcant as they are in steel frames. Such a model is illustrated in Figure G15-1(d). See Section 10.4.2.2.1 of ASCE 41-13 (ASCE 2013) for details.

Modeling Structural Framing that Is Not Part of the Lateral Force Resisting System Section 12.7.3 of the standard states that “the model shall include the stiffness and strength of elements that are signiﬁcant to the distribution of forces and deformations in the structure.” This statement refers to the main lateral force resisting system and should not be applied to structural components that are expected to carry gravity load, but not lateral load. For such components, they should either be omitted from the model or modeled such they have no lateral stiffness. However, for SDC D, E, and F, the deformation compatibility requirements of standard Section 12.12.5 will apply to the gravity-only components. Comments related to modeling gravity columns to capture 3D P-delta effects are presented subsequently. Please see also FAQ A19 in Chapter 30 of this guide for comments on the development of forces in the weak axis of components of the main lateral load resisting system.

Modeling for Accidental Torsion Section 12.8.4.2 requires that accidental torsion be included in the analysis of SDC B buildings with an extreme torsional irregularity and for SDC C, D, E, and F systems with a torsional or extreme torsional irregularity. Where ELF analysis is used, the effects of accidental torsion (including ampliﬁcation as required by Section 12.8.4.3) are accounted for by applying the lateral forces at the appropriate eccentricity or by applying static story torsions. Where MRS analysis is used, it is permitted to run the analysis without accidental torsion and to add the torsional effects in the same manner as used for ELF. Alternately, it is permitted to modify the mass layout in the diaphragms such that the center of mass is shifted 5% of the building dimension perpendicular to the direction of loading. (See Chapter 20 of this guide for a discussion of where the use of a 5% mass offset in MRS analysis is deemed to be unsafe in some situations.) Where accidental torsion is accounted for by use of mass offset, it is not necessary to amplify the torsional effects (Section 12.9.1.5). Where LRH analysis is used, it is required to include accidental torsion by use of a mass offset (Section 12.9.2.2.2). See Chapter 20 of this guide for a discussion of approaches for providing the mass offset.

Mass Modeling The mathematical model must include mass if the periods of vibration are to be determined or if the MRS or LRH analysis procedures are used. Although the mass associated with the structural system can be represented by use of mass density, it is recommended that this be avoided, and that point, line, and area

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masses be used. This provides more control in mass modeling and facilitates the shifting of the center of mass if it is necessary to include accidental torsion. Some programs, such as ETABS (CSI 2018), provide a means to automatically shift the center of mass, and this requires that the mass be assigned to diaphragm elements. There are certain advantages to this approach.

P-delta Effects Section 12.7.3 of the standard states that the mathematical model should account for P-delta effects. However, the standard does not require that P-delta effects be considered explicitly; instead it uses an ad hoc procedure that determines if such effects are important, and if so, provides a methodology to modify the computed results to account for such effects. This procedure was adopted when the inclusion of P-delta effects in the analysis was not practical. However, modern structural analysis software allows such effects to be included with very little effort, and it is therefore recommended that P-delta effects be included in all analysis. (In fact, ASCE 7-16 requires that P-delta effects be explicitly included in LRH and NRH analysis). Section 12.8.7 and Equation (12.8-17) establishes limits on the reduction in lateral stiffness that is associated with P-delta effects. See Chapter 19 of this guide for rational procedures for complying with this requirement where P-delta effects are explicitly included in the analysis. Where the system is modeled in three dimensions, and where P-delta effects are required, it is necessary that the gravity load be distributed realistically throughout the structural system; this will often require the explicit modeling of gravity columns that are not part of the main lateral load resisting systems. These models must have a realistic axial stiffness, but the lateral stiffness should be zero. This can be accomplished by providing moment releases at the top and bottom of the columns or using section property reduction factors (for bending only).

Foundation Modeling As stated in Section 12.7.1 the standard does not require that the foundation be explicitly modeled. However, if it is desirable to do so, the provisions of Section 12.13.3 or Chapter 19 should be followed. Recommendations for modeling foundations can be found in the report, Soil-Structure Interaction for Building Structures (NIST 2012).

Seismic Loads

16 Effective Seismic Weight (Mass)

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

There are no changes to ASCE 7-16 relative to ASCE 7-10 that inﬂuence this chapter.

Computation of effective seismic weight W is covered in Section 12.7.2 of the standard. In this chapter, the effective seismic weight is computed for an ofﬁce and warehouse building in Burlington, Vermont. The example demonstrates the requirements for including both storage live load and snow load in the effective weight calculations. An additional example is provided to illustrate the computation of effective seismic weight for a one-story building with heavy wall panels.

16.1 Example 1: 4-Story Book Warehouse and Office Building in Burlington, Vermont The building used for this example is an office and warehouse building in Burlington, Vermont. Plans and an elevation of the building are shown in Figure G16-1. The first floor, at grade level, is used for both storage and office space, with about 70% of the area dedicated to storage. The second and third floors are used for storage only, and the fourth floor consists only of office space. The storage area is used primarily for boxes of textbooks to be used in the Burlington area public schools.

125

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The structural system for the building is a prestressed concrete flat slab. This system supports gravity loads and acts as a moment-resistant frame for both wind and seismic forces. For seismic design, the frame is classified as an ordinary moment-resisting frame. It is expected that the ELF method will be used for the structural analysis of the system. The slabs, constructed from lightweight structural concrete with a density of 115 lb/ft3, have a basic thickness of 9 in. and are thickened to 12 in. (3 in. drop panels) at the second and third floor column areas to provide resistance to one-way shear (i.e., punching shear). The slabs at the fourth level (the office floor) and the roof do not have drop panels. A small mechanical penthouse, constructed from steel, is built over the roof slab, as shown in Figure G16-1(b and c). The penthouse is braced laterally and is sufficiently rigid to transfer its roof and snow loads to the main roof level; hence, it is not considered a separate story. For this example, it is assumed that the columns are also constructed from 115 lb/ft3 lightweight concrete. In most cases, normal-weight concrete would be used for the columns of a concrete building. The building is clad with lightweight precast concrete architectural panels with a thickness of 4 in. The concrete used for these panels has a density of 90 lb/ft3. These panels have window openings that cover approximately 35% of the façade. These window areas weigh 12 lb/ft2. The exterior wall extends 4 ft above the roof to form a solid parapet. The panels are supported vertically at grade and at levels 2, 3, and 4. The detailing of the panel connections is such that the panels are considered as effective seismic weight in each direction. The books are stored in plastic containers, which in turn are supported by a steel rack system. The racks cover approximately 70% of the floor area. Small forklifts (not to be classified as permanent equipment) are used to place and remove pallets of containers from the shelves. The rack storage system, which is anchored to the slab, weighs approximately 20 lb/ft2. The racking system is laterally braced in two orthogonal directions with steel X bracing. The system is sufficiently rigid to transfer the storage loads to the floor slabs. Table 4.3-1 describes live load for light storage warehouse at 125 psf and library stack rooms with live load of 150 psf. Table 4.3-1 directs the user to “Also See Section 4.13”, which describes a limitation of 90 in. tall, 2 ft wide bookshelves, with 3 ft aisles between shelf units. Although the book storage in this building does not meet that limitation, it was deemed similar and appropriate to use a design live load of 150 lb/ft2. The office area on the fourth floor of the building is designed for a live load of 50 lb/ft2. A variety of workspaces are formed by a combination of fixed and movable partitions. A partition allowance of 15 lb/ft2 is used in the design of the office floors (as a live load according to Section 4.3.2). Two-thirds of this value, 10 lb/ft2, is used for effective seismic weight as required by item 2 in Section 12.7.2. The design dead load value used for the ceiling and mechanical areas of the main building is 15 lb/ft2. Floor finishes in the office area are assumed to weigh 2.5 lb/ft2. The floors in the storage areas are bare concrete.

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Effective Seismic Weight (Mass)

Figure G16-1. Plans and elevation of book warehouse: (a) second and third floor plans; (b) roof plan (fourth floor similar, without mechanical room); and (c) elevation. The second and third floors have two openings, one (15 × 20 ft) to accommodate a hydraulic elevator for use in transporting the books (including the small forklifts), and the other (15 × 10 ft) for an elevator that services the offices on the fourth floor. The fourth floor and roof have only the smaller opening. Other minor openings exist in the floors and roof, but these openings are small and are

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not considered when computing the effective seismic weight. Two stairwells are also present in the building (not shown on plan), but the weights of these are, on a pound per square foot basis, approximately the same as the floor slab. The mechanical room contains a variety of heating, air conditioning, and ventilating equipment. The average dead load for the entire mechanical room, including the steel framing, roof, and equipment, is 60 lb/ft2. The roofing over the remainder of the building (that area not covered by the mechanical room) is assumed to weigh 15 lb/ft2. The ground snow load for the building site is 60 lb/ft2. Based on the procedures outlined in Chapter 7 of ASCE 7, it has been determined that the flat roof snow load is 42 lb/ft2. Calculation of the effective seismic weight, W, is based on the requirements of Section 12.7.2. The weight includes all dead load, a minimum of 25% of the floor live load in the storage areas, a 10 lb/ft2 partition allowance where appropriate, total operating weight of permanent equipment, and 20% of the uniform design snow load when the flat roof snow load exceeds 20 lb/ft2. Each of these load types is pertinent to the building under consideration.

Dead Load The seismic load for the first-floor level (a slab on grade) transfers directly into the foundation, so this load need not be considered as part of the effective seismic weight. The loading for the second floor consists of the slab, drop panels, columns, storage rack system, ceiling and mechanical system, and exterior cladding. Slab: Total area = 160 × 110 − 15 × 20 − 15 × 10 = 17,150 ft2 Unit weight = (9/12) × 115 = 86.2 lb/ft2 Weight = 17,150 × 86.2/1,000 = 1,478 kips Drop panels: 30 panels × 100 ft2 per panel = 3,000 ft2 Unit weight = (3/12) × 115 = 28.8 lb/ft2 Weight = 3,000 × 28.8/1,000 = 86 kips Columns: Clear height of first story = 13 ft Clear height of second story = 13 ft Height tributary to second level = (13 + 13)/2 = 13 ft Column area = 4.91 ft2 Weight = 30 columns × 4.91 × 13 × 115/1,000 = 220 kips Storage rack system: Total area = 17,150 ft2 (no deduction taken for area of columns) Effective area =0.7 × 17,150 = 12,005 ft2

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Effective Seismic Weight (Mass)

Unit weight = 20 lb/ft2 Weight = 12,005 × 20/1,000 = 240 kips Ceiling and mechanical system: Total area = 17,150 ft2 (no deduction taken for area of columns) Unit weight = 15 lb/ft2 Weight = 17,150 × 15/1,000 = 257 kips Exterior cladding: Perimeter = 2(160 + 110) = 540 ft Height tributary to second level = 14 ft Area of 4 in. thick precast = 0.65 × 540 × 14 = 4,914 ft2 Unit weight of panel = (4/12) × 90 = 30.0 lb/ft2 Total panel weight = 4,914 × 30.0/1,000 = 147 kips Area of glass windows = 0.35 × 540 × 14 = 2,646 ft2 Unit weight of glass = 12 lb/ft2 Total glass weight = 2,646 × 12/1,000 = 32 kips Total cladding weight = 147 + 32 = 179 kips Total dead load at second level = 1,478 + 86 + 220 + 240 + 257 + 179 = 2,460 kips The dead load on the third level is almost identical to that on the second level. The only difference is that the absence of the drop panels at the fourth story has a slight inﬂuence on the clear length of the columns at the third story. For this example, this small difference is ignored, and the same dead load is used for the second and third levels. The dead load for the fourth level is computed as follows: Slab: Total area = 160 × 110 − 15 × 10 = 17,450 ft2 Unit weight = (9/12) × 115 = 86.2 lb/ft2 Weight = 17,450 × 86.2/1,000 = 1,504 kips Columns: Clear height of third story = 13.25 ft Clear height of fourth story = 11.25 ft Height tributary to fourth level = (13.25 + 11.25)/2 = 12.25 ft Column area = 4.91 ft2 Weight = 30 columns × 4.91 × 12.25 × 115/1,000 = 208 kips Partitions: Total area = 17,450 ft2 (no deduction taken for area of columns) Unit weight = 10 lb/ft2 (see Section 12.7.2, item 2) Weight = 17,450 × 10/1,000 = 175 kips Floor ﬁnish: Total area = 17,450 ft2 (no deduction taken for area of columns) Unit weight = 2.5 lb/ft2 Weight = 17,450 × 2.5/1,000 = 44 kips

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Ceiling and mechanical system: Total area = 17,450 ft2 (no deduction taken for area of columns) Unit weight = 15 lb/ft2 Weight = 17,450 × 15/1,000 = 262 kips Cladding: Perimeter = 2(160 + 110) = 540 ft Height tributary to fourth level = 0.5(14 + 12) = 13 ft Area of 4 in. thick precast = 0.65 × 540 × 13 = 4,563 ft2 Unit weight of panel = (4/12) × 90 = 30 lb/ft2 Total panel weight = 4,563 × 30/1,000 = 137 kips Area of glass windows = 0.35 × 540 × 13 = 2,457 ft2 Unit weight of glass = 12 lb/ft2 Total glass weight = 2,457 × 12/1,000 = 29 kips Total cladding weight = 137 + 29 = 166 kips Total dead load at fourth level = 1,504 + 208 + 175 + 44 + 262 + 166 = 2,359 kips. The dead load for the roof level is computed as follows: Slab: Total area = 160 × 110 − 15 × 10 = 17,450 ft2 Unit weight = (9/12) × 115 = 86.2 ft2 Weight = 17,450 × 86.2/1,000 = 1,504 kips Columns: Clear height of fourth story = 11.25 ft Height tributary to roof level = (11.25)/2 = 5.62 ft Column area = 4.91 ft2 Weight = 30 columns × 4.91 × 5.62 × 115/1,000 = 95 kips Ceiling and mechanical system: Total area = 17,450 ft2 (no deduction taken for area of columns) Unit weight = 15 lb/ft2 Weight = 17,450 × 15/1,000 = 262 kips Rooﬁng: Total area of main roof = 160 × 110 − 40 × 35 = 16,200 ft2 Unit weight = 15 lb/ft2 Weight = 16,200 × 15/1,000 = 243 kips Mechanical area: Total area = 40 × 35 = 1,400 ft2 Unit weight = 60 lb/ft2 (estimated) Weight = 1,400 × 60/1,000 = 84 kips Cladding: Perimeter = 2(160 + 110) = 540 ft Height tributary to roof = 6 ft (excluding parapet)

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Area of 4 in. thick precast = 0.65 × 540 × 6 = 2,106 ft2 Unit weight of precast = (4/12) × 90 = 30 lb/ft2 Total panel weight = 2,106 × 30/1,000 = 63 kips Area of glass windows = 0.35 × 540 × 6 = 1,134 ft2 Unit weight of glass = 12 lb/ft2 Total glass weight = 1,134 × 12/1,000 = 14 kips Total cladding weight = 63 + 14 = 77 kips Parapet: Perimeter = 2(160 + 110) = 540 ft Height tributary to roof = 4 ft Area of 4 in. thick precast = 540 × 4 = 2,160 ft2 Unit weight of precast = (4/12) × 90 = 30 lb/ft2 Total parapet weight = 2,160 × 30/1,000 = 65 kips Total dead load at the roof = 1,504 + 95 + 262 + 243 + 84 + 77 + 65 = 2,330 kips. The total dead weight for the building, including the mechanical level, is 9,609 kips. Using a building volume exclusive of the mechanical area of (160 × 110) × 54 = 950,400 ft3, the dead load density for the building is 9,609/950,400 = 0.0101 kips/ft3 or 10.0 lb/ft3. This weight is a bit heavier than that which would be appropriate for a low-rise ofﬁce building, but it is reasonable for a concrete warehouse building. Calculation of building density is a good reality check on effective seismic weight. In general, low-rise buildings have a density in the range of 7 to 10 lb/ft3, depending on material and use.

Contribution from Storage Live Loads at Levels 2 and 3 As mentioned in the building description, the building has a design storage live load of 150 lb/ft2. However, only 70% of each ﬂoor is reserved for storage, and the remainder is used for aisles, stairs, and restrooms. The openings for elevators are considered separately. Building use statistics indicate that the storage racks are near capacity in the summer months when school is not in session and reduce to about 30% capacity during the fall and winter months. Section 12.7.2 states that a minimum of 25% of storage live load shall be used as effective seismic weight. For this facility, the 25% minimum is used. However, others might argue that, on the basis of use statistics, a larger portion of the load should be used. Note: The design of combined building–rack storage systems is considerably more complex than indicated in this example. See Chapters 13 and 15 of ASCE 7 for requirements for the design and attachment of rack systems to the building superstructure. See also the Speciﬁcations for the Design, Testing, and Utilization of Industrial Steel Storage Racks 2012 (ANSI 2012). The basis for the 25% is a combination of (1) probability that full capacity will occur simultaneously with earthquake, (2) that density is such that there may be low live load in aisles and vacant space, and (3) a portion of the mass may be

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ineffective because it is loose and not tied to the structure and thus provides some energy dissipating friction attributed to relative movement.

The live load contribution to effective seismic weight is as follows for the second and third levels: Total area = 160 × 110 − 15 × 20 − 15 × 10 = 17,150 ft2 Effective area = 0.7 × 17,150 = 12,005 ft2 Effective live load = 0.25(150) = 37.5 lb/ft2 Total live load contribution to seismic weight = 12,005 × 37.5/1,000 = 450 kips

Contribution of Snow Load at Roof Level Section 12.7.2 indicates that 20% of the uniform design snow load must be included in the effective seismic weight when the flat roof snow load exceeds 30 lb/ft2. The flat roof snow load for this building is 42 lb/ft2, so snow load must be included. The building has a flat roof (both the main roof and the mechanical room), so the uniform snow load is 42 lb/ft2. Using a total area of 160 × 110 = 17,600 ft2, the contribution from snow to the effective seismic weight is the following: Total area = 17,600 ft2 Effective snow load = 0.2(42) = 8.4 lb/ft2 Total snow load contribution to seismic weight = 17,600 × 8.4/1,000 = 148 kips The effective seismic weight for the entire system is summarized in Table G16-1. The design seismic base shear [Equation (12.8-1)] should be based on these weights, as should the distribution of forces along the height of the building [Equations (12.8-11) and (12.8-12)]. These forces should be placed at the center of mass of floors of the building, as appropriate. For this building, the center of mass is slightly offset from the plan center because of the floor openings and the somewhat eccentric location of the mechanical room. The weights shown in Table G16-1 are to be used in an ELF analysis of the system. If a three-dimensional modal analysis is used, the mass moments of inertia are required for each floor. When heavy cladding is used, it may be appropriate to include this cladding as line masses, situated at the perimeter.

Table G16-1. Summary of Effective Seismic Weight Calculations Load contribution (kip) Level

Dead

Live

Snow

Total

2 3 4 R Total

2,460 2,460 2,359 2,330 9,609

450 450 0 0 900

0 0 0 148 148

2,910 2,910 2,359 2,478 10,657

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If the mechanical penthouse covered more area, it might be appropriate to consider this as a separate level of the building. Section 12.2.3.1 covers situations when different lateral load resisting systems are used along the height of the building. The light rooftop structure used in this example is exempt from the requirements of Section 12.2.3.1 via 12.2.3.1, Exception 1. Consideration should also be given to the design, detailing, and anchorage of the steel rack system used in this building. Chapters 13 and 15 provide the requirements for the analysis and design of the system.

16.2 Example 2: Low-Rise Industrial Building In the previous example, the weight of the cladding parallel to and perpendicular to the direction of loading was included in the effective seismic weight in each direction. Thus, the effective seismic weight is the same in each direction. For low-rise buildings with heavy walls (“hard walls,” e.g., concrete tilt-up, precast, or masonry), the load path from the walls, through the diaphragm and into the shear walls must be considered to appropriately implement the seismic weight. Consider the building shown in Figure G16-2. The walls are 7.25 in. tilt-up concrete with no ﬁnish (91 psf). The walls are 22 ft tall with a 2 ft parapet. Windows and doors are small and their lesser weight (compared to concrete) is neglected. The weight of the roof is 20 psf. This weight includes the wood framing, rooﬁng, and an estimate of the average weight of mechanical components likely to exist throughout the entire roof area. For this example, Cs = 0.26, and it was derived from Equation (12.8-1), V = Cs W, and Equation (12.8-2), Cs = SDS/(R/Ie). For earthquake in the north–south direction, the following weights and forces are calculated: Walls at lines A and B = 91 psf [(20 ft/2) + 2 ft parapet] 120 ft (2 walls lines) = 262 kips

Figure G16-2. Framing plan of low-rise industrial building.

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Figure G16-3. Elevation of low-rise industrial building. Roof = 20 psf (50 × 120 ft) = 120 kips V at roof = (0.26)(262 kips + 120 kips) = (0.26) 382 kips = 99.3 kips This load is distributed by the roof diaphragm equally to lines 1 and 2. V wall 1 roof = 99.3 kips/2 = 50 kips W wall 1 self-weight = 91 psf (22 × 50 ft) = 100 kips V wall 1 attributed to self-weight of wall only = (0.26) 100 kips = 26 kips V at bottom of wall 1 = 50 kips + 26 kips = 76 kips (See Figure G16-3) V at bottom of wall 2 = 76 kips V total north–south direction = 76 kips + 76 kips = 152 kips For earthquake in east–west direction, calculations are similar. Walls at line 1 and 2 = 91 psf [(20 ft/2) + 2 ft parapet] 50 ft (2 wall lines) = 109 kips Roof = 20 psf (50 × 120 ft) = 120 kips V at roof = (0.26)(109 kips + 120 kip) = 60 kips This load is distributed by the roof diaphragm equally to lines A and B. W wall A self-weight = 91 psf (22 × 120 ft) = 240 kips V wall A attributed to self-weight of wall only = (0.26)240 kip = 62 kips V at bottom of wall A = 60 kips + 62 kips = 122 kips V at bottom of wall B = 122 kips V total east–west direction = 122 kips + 122 kips = 244 kips Notice that the east–west total base shear is not the same value as the north– south total base shear. This example accurately follows the load path from the perpendicular walls, through the diaphragm and into the parallel to force shear walls. Note that the diaphragm may be designed for the lower forces at the roof level (50 kips in Figure G16-3), but the shear walls must be designed for the total load at the base of the wall (76 kips in Figure G16-3).

Seismic Loads

17 Period of Vibration

Changes in ASCE 7-16, relative to ASCE 7-10 that affect this chapter: •

There are no changes to ASCE 7-16 relative to ASCE 7-10 that inﬂuence this chapter.

This chapter explores the computation of the period of vibration of building structures. This example reviews the empirical methods that ASCE 7 provides for computing periods, computes periods for a few simple buildings, and then does a more detailed analysis wherein the empirical periods are compared to the period based on rational analysis.

17.1 Approximate Fundamental Period Ta Section 12.8.2.1 addresses the computation of the approximate period of vibration of buildings. Three basic formulas are provided: T a = C t hxn

(12.8-7)

T a = 0:1 N

(12.8-8)

0.0019 T a = pffiffiffiffiffiffiffi hn Cw

(12.8-9)

Note that Equation (12.8-9) as shown is for use with length units in feet. A new term in ASCE 7-16 (Cq) is used to adjust to metric units. All three formulas are highly empirical and are to be used for seismic analysis of building structures only. Equation (12.8-7) applies to all buildings, Equation (12.8-8) applies to

135

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certain moment frames, and Equation (12.8-9) is applicable only for masonry or concrete shear wall structures. The primary use of Ta is in the computation of seismic base shear V. The period (in relation to TS) is also used in determination of the appropriate method of analysis (Table 12.6-1). In Equation (12.8-7), the coefficient Ct and the exponent x come from Table 12.8-2 and depend on the structural system and structural material. In general, moment-resisting frames are the most flexible, and this is reflected by the coefficients in Table 12.8-2. The lowest periods are associated with “all other systems” in the table, and these systems include shear walls and braced frames. Buckling-restrained braced frames and eccentrically braced frames (EBFs) have, for a given height, periods between those that would be calculated for moment frames and “other systems.” This is logical owing to the lower crosssectional area in buckling-restrained braces (BRBs) relative to braces in concentrically braced systems and owing to the eccentric connections in eccentrically braced frame systems. Also, the coefficients used for eccentrically braced steel frames are applicable only if the eccentrically braced frame is designed and detailed according to the requirements of the AISC 341-16 (AISC 2016b). Table 12.8-2 does not provide specific coefficients for dual systems, and it is expected that the coefficients for “all other systems” be used. However, it would seem that a dual system would be slightly more flexible and would have a somewhat greater period than the stiffer component of that system (e.g., the braced frame). To illustrate the use of the Equations (12.8-7) and (12.8-8), consider a 6-story steel structure with 13 ft story heights, giving hn = 13 × 6 = 78 ft. Using Equation (12.8-7), yields the following: For a steel moment frame

T a = C t hxn = 0.028ð78Þ0.8 = 0.914 s

For a steel concentrically braced frame For a steel EBF or BRB Using instead Equation (12.8-8) for the moment frame

T a = C t hxn = 0.02ð78Þ0.75 = 0.525 s T a = C t hxn = 0.03ð78Þ0.75 = 0.787 s Ta = 0.1 N = 0.1(6) = 0.60 s

The use of the same equations is illustrated more generally in Figure G17-1, which plots the computed periods with height for the same systems and also for a concrete moment frame. For the Ta = 0.1N formula, the story height was assumed to be 12.5 ft. The trends are as expected, and it is noted also that the period for the steel moment frame is slightly larger than for a concrete frame of the same height. When applying Equation (12.8-7), the basic uncertainty is in the appropriate value to use for the structural height hn, which is defined as “the vertical distance from the base to the highest level of the seismic force resisting system of the structure.” Section 11.2 of ASCE 7 defines the base as “the level at which the horizontal seismic ground motions are considered to be imparted to the structure.” For a building on level ground without basem*nts, the base may be taken as the grade plane (see definition of grade plane in Chapter 11 of the standard). In many cases, however, it may not be easy to establish an exact location of the base. This is particularly true when the building is constructed on

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Figure G17-1. Periods of vibration for different systems. a sloped site or when there are one or more basem*nt levels. Also of some concern is the deﬁnition of the highest level of the structure. This height should not include parapets, small mechanical rooms, or other minor rooftop appurtenances. For buildings with sloped roofs, the structural height should be taken from the base to the average height of the roof. See also commentary Section 11.2 for deﬁnitions and illustrations of the base. Consider, for example, the X-braced steel frame structures shown in Figure G17-2(a–c). The structure in Figure G17-2(a) has no basem*nt. Here, the height hn is the distance from the grade level to the roof, not including the penthouse. The structure in Figure G17-2(b) is the same as the structure in Figure G17-2(a) but has a full basem*nt. At the grade level, the slab is thickened, and the horizontal seismic force at the grade level is partially transferred through the plane of the diaphragms to exterior basem*nt walls. Here again, the effective height should be taken as the distance from the grade level to the main roof. However, a computer model would produce a longer (greater) period for the structure in Figure G17-2(b) relative to structure in Figure G17-2(a) because of the axial deformations that occur in the subgrade

(a) (b)

(c)

Figure G17-2. Finding the effective height hn for a braced frame.

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columns and braces of the braced frame of structure Figure G17-2(b). In structure Figure G17-2(c), the first-grade slab is not thickened, and it is not expected that the braced frame shear forces will be completely transferred out through the first-floor diaphragm. However, some lateral support is provided by the soils adjacent to the basem*nt walls. Here, the period of vibration is longer than for either structure in Figure G17-2(a and b) but may not be long as determined using the distance from the main roof to the top of the basem*nt slab. Thus, a height from the midlevel of the basem*nt to the main roof might be appropriate. Engineering judgment may be required. When in doubt, use the shortest reasonable height for hn because this height produces the most conservative base shear.

Period T Used in the Equivalent Lateral Force Method The total base shear and the distribution of lateral forces along the height of the structure are both functions of the period of vibration, T. To compute these quantities, the approximate period Ta may be used, giving T = Ta. In general, this choice is conservative because periods computed on the basis of a rational structural analysis are almost always greater than those computed from the empirical formulas. In recognition of this fact, ASCE 7 (Section 12.8.2) allows the use of a modified period T = CuTa, for which the coefficient Cu is provided in Table 12.8-1. The modifier may be used only if a period, called Tcomputed herein, is available from a properly substantiated structural analysis. Consider the braced frame structure [Figure G17-2(a)] discussed previously, with Ta = 0.525 s. A computer analysis has predicted a period of Tcomputed = 0.921 s for the structure, so the modified period T = CuTa may be used. Assuming that the structure is in a region of moderate seismicity with SD1 = 0.25g and interpolating from Table 12.8-1, then C u = 0.5ð1.4 + 1.5Þ = 1.45 T = C u T a = 1.45 × 0.525 = 0.761 s The period of 0.761 s must be used in the determination of the set of equivalent lateral forces from which the strength of the structure is to be evaluated, although the rational period Tcomputed was somewhat longer at 0.921 s. As explained in a separate example (Chapter 19), Section 12.8.6.2 of the standard allows the computed period to be used in the development of an alternate set of equivalent lateral forces that are used only for drift calculations.

What if the Computed Period Tcomputed is Less Than T = CuTa? The computed period may turn out to be less than the upper limit period CuTa. Continuing with the braced frame, assume that the computed period Tcomputed = 0.615 < CuTa = 0.761 s. Although ASCE 7 is silent on this possibility, it is recommended that the lower period (in this case Tcomputed) be used in the calculations. In the unlikely event that the computed period turned out to be less than Ta = 0.525 s, the period T = Ta = 0.525 s may be used because there is no requirement that a Tcomputed shall be determined. If the computed period is

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Table G17-1. Summary of Period Values to Be Used in Calculations.

Situation Tcomputed ≤ Ta Ta < Tcomputed < CuTa Tcomputed ≥ CuTa

Period T to be used in strength calculations

Period T to be used in drift calculations

Ta Tcomputed CuTa

Ta Tcomputed Tcomputed

signiﬁcantly different from CuTa, for example, less than 0.5 CuTa or more than 2 CuTa, the computer model should be carefully inspected for errors. Table G17-1 summarizes the period values that should be used in the strength and drift calculations.

Period Computed Using Equivalent Lateral Forces and Resulting Displacements Most commercial structural analysis computer programs can calculate the periods of vibration of building structures. If this capability is not available, the period can be accurately determined from the displacements produced from a set of lateral forces. The lateral force distributions provided by Equations (12.8-11) and (12.8-12) are well suited to this calculation, but these forces depend on the exponent k, which in turn depends on T, which we are trying to find. For the purpose of computing the lateral forces required for the period calculation, it is recommended that k be based on a trial period of T = CuTa. The formula for computing the approximate period is based on a first-order Rayleigh analysis and is as follows: ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2W δ i Pi = 1 i T computed = 2π (G17-1) g ni= 1 δi F i where Fi = Lateral force at level i, δi = Lateral displacement at level i, Wi = Weight at level i, n = Number of levels, and g = Acceleration of gravity. When using Equation (G17-1), the displacements δ are those that result directly from the application of the lateral forces F, and they do not include the deflection amplifier Cd. Also important is that this period would be considered as Tcomputed (and not as Ta) because it is based on the actual structural system properties and not on an empirical formula.

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Table G17-2. Determination of Period Using the Analytical Method

Level i 6 5 4 3 2 1

Fi (kip)

δi (in.)

Wi (kip)

δiFi (kip-in.)

Σδi2Wi (kip-in.2)

301 245 190 137 87 40

3.95 3.15 2.40 1.70 1.05 0.5

1,100 1,100 1,100 1,100 1,100 1,100

1,189 772 456 233 91 20 Σ = 2,761

17,163 10,914 6,336 3,179 1,213 275 Σ = 39,080

The use of Equation (G17-1) is illustrated in Table G17-2 for the braced frame in Figure G17-2(a). For the example, it is assumed that the story weights are uniform at 1,100 kips per level. The mechanical penthouse is not included in the analysis. Using T = CuTa = 0.761 s, k = 1.13. The period computed from the information provided in Table G17-2 is as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 39,080 T = 2π = 1.20 s 386.4 2,761 A slight improvement in the period could be obtained by computing a new exponent k based on this period, developing a new set of lateral forces, and repeating the calculation. In this case, the updated value of k is 1.351, and the revised period is 1.18 s. This difference is frankly not large enough to justify the additional effort.

Period Computed Using Computer Programs Most commercially available structural analysis programs can calculate the period of vibration. The computed period depends directly on the assumptions made in modeling the mass and stiffness of the various components of the structure and on the manner in which the boundary conditions (supports) are represented. In many cases, determination of the appropriate component stiffness is not straightforward because these properties depend on a variety of factors, including the effective rigidity of connections, the degree of composite action, and the degree of cracking in concrete. Although it is beyond the scope of this guide to provide detailed information on modeling, the following points are noted. Deformations in the panel zones of the beam–column joints of steel moment frames are a significant source of flexibility in these frames. Two mechanical models for including such deformations are summarized in Charney and Marshall (2006). These methods are applicable to both elastic and inelastic systems. For elastic structures, it has been shown that the use of centerline analysis provides reasonable, but not always conservative, estimates of frame flexibility. Fully rigid end zones, as allowed by many computer programs, should never be used because they always result in an overestimation of lateral stiffness

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in steel moment resisting frames. The use of partially rigid end zones may be justified in certain cases, such as when doubler plates are used to reinforce the panel zone. Partially rigid end zones are also appropriate in the modeling of the joints of reinforced concrete buildings. The effect of composite slabs on the stiffness of beams and girders may be warranted in some circ*mstances. When composite behavior is included, due consideration should be paid to the reduction in effective composite stiffness when portions of the slab are in tension (Schaffhausen and Wegmuller 1977, Liew 2001). For reinforced concrete buildings, it is necessary to represent the effects of axial, flexural, and shear cracking in all structural components. Recommendations for computing cracked section properties may be found in Park and Paulay (1975) and other similar texts. In terms of the degree of cracking to use in the analysis, Table 10-5 of ASCE 41-17 (ASCE 2017b) provides reduction factors that can be used to represent flexural cracking. For example, ASCE 41-13 recommends that 30% of the gross section moment of inertia be used in modeling beams and girders in nonprestressed structures, and that 70% of the gross section moment of inertia be used for columns in compression with gravity loads 0 greater than or equal to 0.5Ac f c . It is noted that ASCE 41-13 does not reduce shear rigidity attributable to cracking. In the authors’ opinion, this is not appropriate because the reduction in shear stiffness caused by cracking can be significant (Park and Paulay 1975). Shear deformations should be included in all structural analyses. Such deformations can be significant in steel moment frames. In addition, shear deformations in reinforced concrete shear wall systems can actually dominate the flexibility when the walls have height-to-width ratios of less than 1.0.

17.2 Computing Ta for Masonry and Concrete Shear Wall Structures Section 12.8.2.1 prescribes an alternate method for computing Ta for masonry or concrete shear wall structures. The following equations are provided: 0.0019 T a = pffiffiffiffiffiffiffi hn CW

CW =

(12.8-9)

x 100 X Ai h i AB i = 1 1 + 0.83 hn 2 Di

where AB = Area of the base of the structure (ft2), Ai = Area of the web of wall i (ft2), Di = Plan length of wall i (ft), and x = Number of walls in the direction under consideration.

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(12.8-10)

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The constant 0.0019 in Equation (12.8-9) is for ft units. The use of the equations is based on Goel and Chopra (1998) and is limited to buildings with a structural height less than or equal to 120 ft and for which all of the walls extend the full height of the building. These equations are exercised using the structure shown in Figure G17-3. The building has eight walls, with dimensions shown in the ﬁgure. The analysis is performed with nine different assumptions on the height of the building. In all cases, the total building area is 15,000 ft2. The results of the analysis are provided in Table G17-3 together with the period computed using Equation (12.8-7) (using Ct = 0.02 and x = 0.75). As seen in the table, the period for the 26 ft tall system has a period of 0.113 s when Equations (12.8-9) and (12.8-10) are used and increases to 0.230 s when Walls 1,2,7, and 8: Thickness = 10 in., Length = 12 ft Walls 3,4,5, and 6: Thickness = 12 in., Length = 16 ft

100 ft

150 ft

Figure G17-3. Concrete shear wall system used for period determination. Table G17-3. Computing the Period for Masonry and Concrete Shear Wall Structures Building height (ft)

Using Equations (12.8-9) and (12.8-10)

Using Equation (12.8-7) with Ct = 0.02 and x = 0.75

Ta (s)

13 26 39 52 65 78 91 104 117

0.0385 0.1811 0.0992 0.0597 0.0395 0.0280 0.0207 0.0160 0.0127

0.038 0.113 0.235 0.404 0.621 0.886 1.19 1.56 1.96

0.136 0.230 0.312 0.378 0.458 0.525 0.589 0.651 0.711

Note: Values in bold for the 78 ft story height are discussed in the text.

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Equation (12.8-7) is used. On the other hand, for the 78 ft tall system, the period using Equations (12.8-9) and (12.8-10) is 0.886 s and is signiﬁcantly less (0.525 s) when computed using Equation (12.8-7). The difference is even more extreme for the 117 ft tall system. Given the very large discrepancy between the computed periods using the different formulas for Ta, the engineer should be cautious when using Equations (12.8-9) and (12.8-10), particularly for structures greater than 60 ft in height. In addition, it is the authors’ opinion that the use of the formula T = CuTa is not applicable when Equations (12.8-9) and (12.8-10) are utilized [or that Cu should be taken as 1.0 when Equations (12.8-9) and (12.8-10) are used]. This is because these equations are based on a rigorous structural analysis and not strictly on empirical observations. A sample calculation for the 78 ft tall building is provided as follows: hn = 78 ft Ab = 15,000 ft2 Aw = (10/12) × 12 = 10 ft2 Aw = (12/12) × 16 = 16 ft2 Ai 10 2 i = h 2 i = 0.277 For Walls 1, 2, 7, 8: h hn 1 + 0.83 Di 1 + 0.83 78 12 Walls 1, 2, 7, and 8 Walls 3, 4, 5, and 6

Ai 16 2 i = h 2 i = 0.772 For Walls 3, 4, 5, 6: h hn 1 + 0.83 Di 1 + 0.83 78 16 CW =

x 100 X Ai 100 h i= ½4 × 0.2773 + 4 × 0.7720 = 0.0280 AB i = 1 1 + 0.83 hn 2 15000 Di

0.0019 0.0019 T a = pffiffiffiffiffiffiffi hn = pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 78 = 0.886 s CW 0.0289 A better approach for determining the period of vibration of a shear wall system is to model the system accurately in a finite-element analysis program. This is done quite conveniently with modern software.

17.3 Periods of Vibration for Three-Dimensional Systems A computer program is required to determine the periods of vibration for threedimensional structures. The program reports periods (frequencies) for as many modes as the user requests. For regular rectangular buildings (regular in the sense of structural irregularities as described in Section 12.3.2), the first three modes usually represent the two orthogonal lateral modes and the torsional mode. These modes can occur in any order, and it is possible (although not usually desirable) that the first or second mode can be a torsional mode. It is also possible that the first mode (or any of the first several modes) can represent the

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vibration of a flexible portion of the system, such as a long cantilever, a long span beam, or even an error in connectivity. Thus, before using the periods in an analysis, the engineer should plot and animate the mode shapes to make sure that the proper periods are being used. Reviewing the mass participation of each mode is also a good indicator of structural behavior. Interpretation and use of the modes and the periods of irregular buildings is often complex because even the first mode shape may represent a coupled lateral–torsional response. The period associated with the mode that has the highest mass participation factor in the direction under consideration should be used for the determination of the seismic forces in that direction. As with regular systems, the mode shapes should always be plotted and animated to make sure that they are reasonable. An illustration of the first six mode shapes and periods for a highly irregular steel building are shown in Figure G17-4. The first two modes are predominantly lateral, and the third mode is predominantly torsional.

Figure G17-4. Mode shapes and periods for a highly irregular building.

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Note: N.S. = not speciﬁed.

Steel special moment resisting frame (Table 6-4)

Steel buckling restrained braced frame (Table 5-4)

Steel special concentrically braced frame (Table 5-3)

Special RC shear wall (Table 4-2)

Structural system 2 3 4 5 2SCBFDmax 3SCBFDmax 6SCBFDmax 12SCBFDmax 16SCBFDmax 2BRBFDmax 3BRBFDmax 6BRBFDmax 12BRBFDmax 16BRBFDmax 2RSA 3RSA 4RSA 5RSA 6RSA

Archetype 2 4 8 12 2 3 4 12 16 2 3 4 12 16 2 4 8 12 20

Number of stories N.S. N.S. N.S. N.S. ELF ELF ELF ELF MRS ELF ELF ELF ELF MRS MRS MRS MRS MRS MRS

Design basis 0.31 0.52 0.87 1.17 0.26 0.49 0.82 1.38 1.81 0.40 0.73 1.23 2.06 2.56 0.58 0.95 1.64 2.25 3.37

CuTa

0.50 0.55 0.76 0.99 0.40 0.58 1.05 1.91 3.16 0.50 0.80 1.35 2.82 3.73 0.91 1.62 2.29 3.12 4.47

Tcomputed

2.60 1.12 0.76 0.72 2.37 1.40 1.64 1.92 3.05 1.56 1.20 1.10 1.87 1.45 2.46 2.91 1.95 1.93 1.76

[Tcomputed/CuTa)2]

Table G17-4. Empirical versus Computed Periods of Vibration for a Variety of Systems from ATC 76

Period of Vibration

145

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17.4 Differences Between CuTa and Tcomputed It is of some interest to compare the approximate period CuTa to Tcomputed for a variety of systems. This information is presented in Table G17-4, which uses period values presented in NIST (2010), which is a set of examples of the FEMA P-695 (FEMA 2009) procedure for computing design values (R, Cd, Ω0) for new systems not listed in Table 12.2-1. As can be seen in the table, in most cases the computed period is significantly greater than CuTa. The last column of the table provides the ratio (Tcomputed/CuTa)2 which is an estimate of the flexibility of the system based on computed properties relative to that for the approximate properties. These ratios are close to 3 in some cases, which would seem to be hard to justify if the empirical values (based on observation of real buildings during real earthquakes) are realistic. It is likely that the “error” is in the computed period, because it does not account for many sources of stiffness in the actual system (e.g., nonstructural components, the gravity system, modeling cracked sections, ignoring composite action). However, even considering all these sources of stiffness, it seems that the difference in CuTa and Tcomputed is difficult to justify. See Question A17 in Chapter 30 of this guide for additional discussion.

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18 Description and Use of the Equivalent Lateral Force Procedure

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • •

•

There are no signiﬁcant changes to the equivalent lateral force analysis procedure in terms of developing the lateral forces to use for design. A signiﬁcant change in ASCE 7-16 is that accidental torsion need not be included in the analysis where an extreme torsional irregularity does not exist in SDC B, and where a torsional irregularity does not exist in structures assigned to SDC C, D, E, and F (12.8.4.2). Scaling of modal response spectrum results has changed to produce a modal response spectrum base shear that is not less than 100% of the ELF base shear (as opposed to 85% in ASCE 7-10) (12.9.1.4.1).

This chapter describes the equivalent lateral force analysis procedure and discusses the use of the procedure in final design (where ELF is permitted as the final analysis procedure) and in other situations in which the procedure is used to perform various supporting tasks in the analysis, such as determining whether certain irregularities exist, computing P-delta stability ratios, and computing diaphragm forces. No specific examples are presented in this chapter, but the procedures discussed are used in other chapters of this guide. Table 12.6-1 is used to determine the permitted analytical procedure. The term permitted refers to the procedure used to determine member forces and story

147

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drifts that would be used in the design. However, there are a number of situations in which the ELF procedure is used (must be used) for other purposes even when it is not allowed for ﬁnal design. Such uses include 1.

Preliminary design of the lateral load resisting system,

Determining the presence of certain horizontal or vertical irregularities,

Computing the torsional ampliﬁcation factors,

Application of accidental torsion,

Computing P-delta stability ratios,

Determining the redundancy factor,

Calculating diaphragm forces,

Validating conformance with the 25% rule for moment frames in dual systems, and

Scaling the results of modal response spectrum or linear response history analysis.

18.1 Overview of the ELF Procedure Some form of the ELF procedure has been available in codes and standards since the mid 1950s. The basic components of the procedure are that the total lateral force acting on the structure depends on the site seismicity, the total weight of the structure, the structural system, and the system’s period of vibration. In addition, the procedure distributes the total lateral force along the height of the structure in conformance with an assumed ﬁrst mode shape pattern and, with some adjustment, for higher mode effects. The procedure was developed for two-dimensional (2D) analysis (no signiﬁcant torsional response) and is in general applicable to systems with a relatively uniform distribution of mass and stiffness along the height. Table 12.6-1 disallows ELF in the higher seismic design categories where any of these basic assumptions are violated. In ASCE 7-16, the design base shear V is given by V = CsW

(12.8-1)

where Cs is the seismic response coefﬁcient, and W is the effective seismic weight. Cs is determined from one of the three following equations, depending on the period of vibration of the system: the constant acceleration region applicable for 0 < T < Ts S C s = RDS

(12.8-2)

the constant velocity region applicable for Ts ≤ T ≤ TL CS =

S D1 T IRe

or the constant displacement region applicable for T > TL

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(12.8-3)

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Description and Use of the Equivalent Lateral Force Procedure

CS =

S D1 T L T 2 IRe

(12.8-4)

Equation (12.8-4) will rarely be used for buildings as the minimum value of TL is 4 s, and the vast majority of building have periods less than 4 s. In addition, for buildings in the SDC D through F, a period of 4.0 s would be greater than 3.5 Ts, and hence ELF would not be allowed for ﬁnal design (Table 12.6-1). The standard provides two expressions for the minimum value of Cs: C s = 0.044S DS I e ≥ 0.01

(12.8-5)

which is applicable where S1 < 0.6g, and Cs =

0.5S 1 ðIRe Þ

(12.8-6)

which is applicable where S1 ≥ 0.6g. Equation (12.8-5) is applicable to buildings that are located more than approximately 10 km from the active fault (far-fault ground motions). The minimum value of CS = 0.01 will control where SDS ≤ 0.227/Ie. Equation (12.8-6) is used for buildings sited closer than approximately 10 km from the active fault (near-fault ground motions). A more precise deﬁnition of near-fault motions is provided in Section 11.4.1. Equations (12.8-2) through (12.8-5) represent three zones of the inelastic design acceleration spectrum and are plotted in Figure G18-1 for a system located in a

Figure G18-1. Inelastic design acceleration spectrum for region of moderate seismicity.

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region of moderate seismicity with SDS = 0.5g, SD1 = 0.2g, Ie = 1.0, R = 6, Cd = 5, and TL = 4.0 s. A horizontal line representing the minimum Cs of 0.044SDSIe is also shown. The minimum value of Cs [Equation (12.8-5)] would control for periods greater than TMF = 22.7Ts/R = 1.51 s. Note that TMF is the period at which the far-fault minimum value of Cs controls and is not included in ASCE 7. Figure G18-2 is an inelastic design displacement spectrum, wherein the ordinate for each period value is Cs multiplied by the acceleration of gravity (386.4 in./s2) times T 2/4π2 times Cd/Ie. Note that the displacement for periods greater than TL is constant and is based on accelerations computed using Equation (12.8-4) (not using Cs = 0.044SDSIe). This is allowed by exception in Section 12.8.6.1. The acceleration spectrum in Figure G18-3 was developed for a region of high seismicity where Ss = 1.5g, S1 = 0.60g, and Fa = Fv = 1.0 (Site Class B with velocity measurements not made) producing design accelerations SDS = 1.0g and SD1 = 0.4g. As before Ie = 1.0, R = 6, and Cd = 5. Here, the minimum value of CS is given by Equation (12.8-6) and controls when T is greater than TMN = 1.33 Fv. Note that TMN is the period at which the near-fault minimum value of Cs controls and is not included in ASCE 7. The corresponding inelastic displacement spectrum is provided in Figure G18-4, which shows that for periods greater than 1.33 s the displacement increases exponentially with period. This is because Equation (12.8-6) is considered as part of the response spectrum. The term V = CSW produces the design base shear, which can be different in the two orthogonal directions owing to possible differences in the structural system in the two directions. It is now necessary to distribute this shear along the height of the structure, and this is accomplished using Equations (12.8-11) and (12.8-12). Equation (12.8-12) is based on a single empirical mode shape, with 100% of the

Figure G18-2. Inelastic design displacement spectrum for region of moderate seismicity.

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Figure G18-3. Inelastic design acceleration spectrum for region of high seismicity.

Figure G18-4. Inelastic design acceleration spectrum for region of high seismicity. effective seismic weight distributed to this mode. Figure G18-5 shows a multistory system of total height hn. The height from the base to level x is hx, and this level has a weight wx. With the roof displacement δroof known, the deﬂection at any level is given by δx =

hkx δroof hkn

(G18-1)

where k is dependent on the period of vibration T. For T less than 0.5 s, k = 1.0, and for periods greater than 2.5 s, k = 2.0. For intermediate periods, k = 0.5T + 0.75.

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Roof

wx g

2 2 x

wx hxk

Roof

ghnk

Deﬂected Shape given by:

hn hx

hxk hnk

Roof

Deflected Shape

Ineral Forces

Figure G18-5. Basis of the vertical force distribution in ELF analysis. The term k is intended to account for higher mode effects. The restriction on using ELF analysis for buildings with periods greater than 3.5 Ts in SDC D through F (Table 12.6-1) is because for such systems the single empirical mode shape is unable to accurately represent higher mode effects. A modal response spectrum or a linear or nonlinear response history analysis is required for these systems. Given the displacement at a given level x, the total acceleration can be estimated as ω2δx, (ω is the circular frequency of vibration = 2π/T) and by substituting Equation (G18-1) for the deﬂection, the story inertial force at level x is 2 w ω δroof (G18-2) V x = x ω2 δx = wx hkx g ghk The total inertial force is 2 X ω δroof X Vi = wi hki = V k gh n i i

(G18-3)

and the ratio of the story force to the inertial force is Fx w hk = P x xk V wi h i

(G18-4)

Equation (12.8-11) of the standard is produced by multiplying both sides of Equation (G18-4) by V: w hk V x = P x x k V = C vx V wi hi

(G18-5)

The accuracy of the ELF procedure is directly related to the accuracy of the assumed deﬂected shape, and this shape is valid only for relatively uniform mass and stiffness along the height, and for predominantly 2D behavior (minimal system torsion).

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Description and Use of the Equivalent Lateral Force Procedure

18.2 Use of the ELF Procedure for Purposes Other than Final Design Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

Assessment of System Irregularities A torsional irregularity occurs when the lateral forces, applied at a 5% eccentricity, results in story drifts at the edge of the building that are in the range of 1.2 to 1.4 times the average story drift (Type 1a horizontal irregularity) or greater than 1.4 times the average story drift (Type 1b horizontal irregularity). The lateral forces applied to the system must be determined using the ELF procedure (the standard provides no other option), and a separate assessment of the presence of the irregularity must be made for positive and negative eccentricity, positive and negative directions of load, and in each of two orthogonal directions. Clearly a 3D analysis must be used for each required loading. If a torsional irregularity occurs for one or more of these loadings, the system is torsionally irregular, and in accordance with Table 12.6-1 the ELF procedure is not allowed for final design in SDC D through F. Where accidental torsion is required in analysis (Section 12.8.4.2), the torsional amplification factors Ax would also be determined using an ELF analysis. A soft story irregularity exists if the story stiffness of a lower story is significantly less than the stiffness in the story above. The determination of story stiffness should not be based on the ELF loading as explained in Chapter 11 of this guide as well as FAQ A1. However, the exception in Section 12.3.2.2 allows the presence of the soft story irregularity (or weight irregularity) to be determined from story drifts, and these drifts would be based on an ELF analysis of the system. The presence of a soft story or weight irregularity prohibits the use of ELF in final design for SDC D through F.

Application of Accidental Torsion As mentioned previously, accidental torsion must be included in the analysis used to determine if a torsional irregularity exists. If Type 1b horizontal irregularity (extreme torsion) is present in SDC B buildings, or a Type 1a or 1b horizontal irregularity (torsion or extreme torsion) exists in SDC C through F, accidental torsion must be included in the analysis. In SDC B and C, the ELF procedure is allowed when torsional irregularities exist, and the accidental torsion is applied by applying the lateral loads at an eccentricity of 0.05Ax times the building dimension orthogonal to the direction of load, or by applying the appropriate lateral load without eccentricity and adding a concentrated torque at the center of mass. For torsionally irregular systems in SDC D through F, the ELF procedure is not allowed for buildings with more than two stories, and either the modal response spectrum method or the response history method must be used. For the response history methods, accidental torsion must be included by use of a physical mass offset. In modal response spectrum analysis, a physical mass offset may be used, but it is more common to apply the accidental torsion by use

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154

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of static torques as previously described for the ELF method. See Chapter 20 of this guide for additional discussion on the application of accidental torsion.

Stability Ratios Section 12.8.7 presents the requirements for including P-delta effects in the analysis. Such effects must be included in ELF analysis or MRS analysis if the stability ratio, θ, computed using Equation (12.8-16) is greater than 0.10 and less than or equal to θmax [Equation (12.8-17)] at any story of the building. (P-delta effects must be included in linear and nonlinear response history analysis.) The center-of-mass story drift Δ and the story shear Vx in Equation (12.8-16) are typically determined from an ELF analysis without accidental torsion. An alternate approach for determining the stability ratio is discussed in FAQ A5, but this also requires the determination of drifts using the ELF procedure. See Chapter 19 of this guide for a more detailed discussion on computing drifts and including P-delta effects in the analysis. For torsionally irregular systems in SDC C, D, E, or F, Section 12.8.6 of the standard requires that drifts Δ be checked at the edge of the building. According to Section 12.7, these same drifts should be used to check the stability in accordance with Equation (12.8-16). This approach seems to be irrational and extremely conservative, because 100% of the P load is being applied at the edge of the building to assess system stability. As shown in FEMA P2012 (FEMA 2018), however, checking the stability coefﬁcient in the manner described previously is essential to providing safety against collapse under the maximum considered ground motions.

Redundancy Factor Section 12.3.4 provides procedures for determining the redundancy factor ρ. For structures in SDC D through F, it is likely that the methodology outlined in Table 12.3-3 will be used, which requires that the inﬂuence of removing individual components of the structure on the computed lateral strength or on the system torsional irregularity be assessed. The structural analysis used to assess the consequence of removing the component is most efﬁciently performed using the ELF procedure. The analysis used to determine if there is an excessive reduction in strength or to determine if an extreme irregularity exists would use a 5% center-of-mass eccentricity.

Diaphragm Forces Section 12.10.1.1, and speciﬁcally Equation (12.10-1), provides the traditional procedure for determining diaphragm forces in buildings. In Equation (12.10-1) the force quantity Fi is the equivalent lateral story force determined from Equations (12.8-11) and (12.8-12). Section 12.10.3 of ASCE 7-16 provides an alternate method to determine diaphragm forces, and this does not require the use of the ELF procedure.

Seismic Loads

Description and Use of the Equivalent Lateral Force Procedure

25% Rule in Dual Systems Moment resisting frames that are part of a dual system are required to have the capacity to resist not less than 25% of the seismic design forces. The standard does not make it clear how this requirement is to be checked. In one scenario the entire system is analyzed, and it is shown that the moment frame carries at least 25% of the base shear. A second option, which seems to be most often used, separates the moment frame(s) from the system and analyzes them using lateral forces 25% of the ELF forces determined for the combined system. In the second case, a drift analysis need not be performed for the separately analyzed moment frames. However, the elements of the moment frame must have sufﬁcient strength to resist the 25% loading. See guide Chapter 7 and FAQ A14 for additional discussion related to the 25% strength requirement in dual systems.

Scaling Results of Modal Response Spectrum and Linear Response History Analysis Sections 12.9.1.4.1 and 12.9.1.4.2 discuss the scaling of the member forces and the drifts obtained from modal response spectrum analysis. Forces must be scaled such that the base shear determined from the modal response spectrum analysis is not less than the ELF base shear determined from Equation (12.8-1). Displacements must also be scaled if Equation (12.8-6) controls the design base shear. A similar requirement is imposed in Section 12.9.2.5 for the linear response history analysis procedure.

Seismic Loads

155

19 Drift and P-delta Effects

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

There are no changes to ASCE 7-16 relative to ASCE 7-10 that affect drift and P-delta effects.

In this chapter, the drift for a 9-story building is calculated in accordance with Section 12.8.6 and then checked against the acceptance criteria provided in Section 12.12 and speciﬁcally in Table 12.12-1. P-delta effects are then reviewed in accordance with Section 12.8.7. The building is analyzed using the equivalent lateral force method, but only those aspects of the analysis that are pertinent to drift and P-delta are presented in detail. Drift is an important issue in seismic design, and is addressed in Sections 12.8.6, 12.8.7, and 12.12 of the standard. The determination of story drift is explained in Section 12.8.6, and the inﬂuence of P-delta effects on the computation of story drift and seismic design forces is covered in Section 12.8.7. Limits on story drift and other related criteria, such as building separation, are provided in Section 12.12. Figure 12.8-2 of the standard explains the concept of story drift, Δx, which is the difference in inelastic displacement between two adjacent levels of the structure: Δx = δ x − δ x − 1

(G19-1)

where δx is the inelastic story displacement at level x, and δx−1 is the inelastic story displacement at the level below level x. The inelastic story displacement is

157

Seismic Loads

158

Seismic Loads

computed in accordance with Equation (12.8-15) as δx =

C d δxe Ie

(12.8-15)

where Cd = Deflection amplification factor (provided in Table 12.2-1), Ie = Importance factor (Table 1.5-2), and δxe = Elastic displacement computed at level x. Section C12.8.6 of commentary provides background on the development of Equation (12.8-15). Section 12.8.6 explains that δxe should be computed at the center of mass of levels at the top and bottom of the story under consideration, or using the center of mass at the upper story and the projection of that point on the lower story if the centers of mass of the two levels do not align vertically. Further, it is noted that for systems that are torsionally irregular in SDC C through F (and which will require the application of accidental torsion in accordance with 12.8-4), the deflections used to compute story drift shall be determined at the edges of the building. These deflections will be significantly larger than those at the center of mass, and this is a significant penalty for torsional irregularity. This penalty is compounded for buildings comprising solely moment frames (in the direction of response), as Section 12.12.1.1 stipulates that the allowable drifts for such systems are divided by the redundancy factor ρ, which will be 1.3 for some systems. Two additional issues related to computing drift are related to Sections 12.8.6.1 and 12.8.6.2. In the first of these sections it is noted that where the design base shear is controlled by Equation (12.8-5), a set of reduced lateral forces based on Equation (12.8-3) may be used to compute drift. However, if Equation (12.8-6) controls the design base shear, the lateral forces based on Equation (12.8-6) shall be used to determine story drift. See Chapter 18 of this guide, and specifically discussion related to Figures G18-1 to G18-4 for additional background on these provisions. Regarding Section 12.8.6.2, it is allowed to use the computed period of vibration (e.g., from an eigenvalue analysis) to determine a separate set of lateral forces for the purpose of computing drift. For buildings with CuTa greater than Ts, the computed period will likely be significantly greater than CuTa, and the drifts will be considerably reduced. See Table G17-4 and related discussion for specific examples of computed period relative to CuTa. Section 12.7.3 of the standard, “Structural Modeling,” states that “a mathematical model of the structure shall be constructed for the purpose of determining member forces and structure displacements resulting from applied loads and any imposed displacements and P-delta effects.” Although modern analysis software easily accommodates direct inclusion of P-delta effects in analysis, it is still common to exclude such effects in the analysis, and use the ad hoc

Seismic Loads

159

Drift and P-delta Effects

procedure of Section 12.8-7 to determine if such effects are important (0.1 < θ ≤ θmax), or excessive (θ > θmax), and where it is necessary to modify the results to account for such effects. The ﬁrst step in a P-delta analysis is to compute the story stability index, θ, for each story and for each direction of response. There are two approaches to compute θ: 1.

Use standard Equation (12.8-16), where the deﬂections Δ are computed using an ELF analysis without P-delta effects, are based on lateral forces that include Ie [see Equations (12.8-2) through (12.8-6)], and for which the story drift is computed using Equation (12.8-15). As noted in the commentary, the terms Cd and Ie in Equation (12.8-6) cancel the same terms in Equation (12.8-15). The force Px is the total gravity force in the story under consideration and is based on unfactored dead loads and unfactored fully reduced live loads. For torsionally irregular buildings in SDC C, D, E, and F, drift must be computed at the edge of the building. See the P-delta discussion in Chapter 18 of this guide for commentary on this requirement.

Perform an ELF analysis with and without P-delta effects. The story stability ratio is then determined as Equation (G19-2):

θ=1−

Δ0 Δf

(G19-2)

where Δ0 is the story drift computed without P-delta effects, and Δf is the drift computed with P-delta effects. The lateral and gravity forces used to compute drift would be the same as those used in Equation (12.8-16). See FAQ A5 for additional details on this methodology. It is a bit ironic to use analysis with and without P-delta to determine if P-delta effects are required. If the software used has the capability to include such effects automatically, it would be more logical to include these effects. However, even if P-delta effects can be included in the analysis, it is necessary to determine the stability ratios to ensure that they are not greater than θmax at any story. The last paragraph of Section 12.8-7 provides an alternate method to determine θ, if the term Δ in Equation (12.8-16) is based on analysis with P-delta effects. If the stability ratio in all stories is less than 0.1, P-delta effects may be ignored. If the stability ratio is greater than 0.1 and less than θmax in any story, and if P-delta effects were not included in the analysis, all member forces and displacements must be multiplied by 1/(1−θ) for the story under consideration. On the other hand, if P-delta effects were included in the analysis, forces and drifts determined in the analysis can be used without modiﬁcation. A few points about Equation (12.8-17) should be considered. The provisions allow β to be taken as 1.0, but this is conservative. The term β is effectively the inverse of the story overstrength, and the overstrength is usually considerably greater than 1. Thus, if it is found that θ is greater than θmax for any story with β = 1 it is worthwhile to make an estimate of overstrength and compute a rational value of β.

Seismic Loads

160

Seismic Loads

For cases in which Cd is greater than 5.0 and β = 1, θmax is less than 0.1. For example, for a special steel moment frame Cd = 5.5 and θmax = 0.5/(1 × 5.5) = 0.0909. Thus, in this case, for any story with a computed θ > between 0.0909 and 1.0, the provision is stating that P-delta effects need not be included (θ < 0.10), but also that the structure is likely unstable and needs to be redesigned (θ > θmax), which is contradictory. It is not explicitly stated, but θmax need not be taken as less than 0.1. Where P-delta effects are included in the mathematical model, it is important that the inﬂuence of 100% of the gravity load is captured, and that the spatial distribution of gravity load is realistically replicated. The use of so-called leaning columns is discouraged, and instead every vertical element that resists gravity load should be represented in the model, even if the column or wall is not part of the lateral load resisting system. It must be emphasized, however, that columns and walls that are not part of the lateral load resisting system should be assigned such that their lateral stiffness is zero.

19.1 Example Building The seismic force–resisting structural system for the example building is a structural steel moment-resisting space frame placed at the perimeter. Each perimeter frame has five bays, each 30 ft wide. There is one 12 ft deep basem*nt level, an 18 ft high first story, and eight additional upper stories, each with a height of 13 ft. The building has no horizontal or vertical structural irregularities. The total height of the structure above grade is 122 ft. The building is located in Seattle, Washington, on Site Class C soils. An elevation of one of the perimeter frames is shown in Figure G19-1. The beam sizes are the same for each bay across a level, and the column size is the same for all columns in a given story. Doubler plates are used in interior columns only. Table G19-1 provides the live load weights, the dead load weights, and the total weights for each level and the entire building. Live loads, needed for the P-delta analysis, are based on a reduced live load of 20 psf acting over the full floor. This estimate is sufficient for the purposes of this example or for a preliminary design but developing more accurate values for a final design is advisable. The seismic weights at each level are equal to the given dead load weights. In this example, the lateral loads used to compute drift are determined in two ways. In the first case, loads are based on the upper limit period of vibration, T = CuTa, computed in accordance with Section 12.8.2. In the second case, lateral loads are computed using the period of vibration determined from a rigorous (finite-element) analysis of the system. This period is referred to as Tcomputed in this example. The second case is used to illustrate the potential benefit of Section 12.8.6.2, which allows Tcomputed to be used to determine the lateral loads that are applied to the structure for the purpose of computing drift.

Seismic Loads

161

Drift and P-delta Effects

Figure G19-1. Frame used for drift analysis. Table G19-1. Building Dimensions and Weights Story x

Height (in.)

WLive (kips)

WDead (kips)

WTotal (kips)

9 8 7 6 5 4 3 2 1

156 156 156 156 156 156 156 156 216

450 450 450 450 450 450 450 450 450

2,250 2,325 2,325 2,325 2,325 2,325 2,325 2,325 2,475

2,700 2,775 2,775 2,775 2,775 2,775 2,775 2,775 2,925

The design spectral accelerations for the Site Class C location are as follows: SS = 1.25g S1 = 0.5g

Fa = 1.2 Fv = 1.5

SDS = 1.17g SD1 = 0.50g

The risk category for the building is III, the importance factor Ie is 1.25, and the SDC is D. Using Table 12.2-1, the response modification coefficient, R, is 8 for the special steel moment frame, and the deflection amplification factor, Cd, is 5.5. There is no height limit for special moment frames.

Seismic Loads

162

Seismic Loads

The effective seismic weight of the entire building, W, is 21,000 kips. The approximate fundamental period of the building is computed using Equation (12.8-7), with hn = 122 ft and coefficients Ct = 0.028 and x = 0.8 from Table 12.8-2 as follows: T a = C t hxn = 0.028 × 1220.8 = 1.31 s The height used in this computation (122 ft) is based on the assumption at grade level that the structure is laterally restrained at the grade level (as shown by a pin support in Figure G19-1). Using Table 12.8-1, the coefficient for the upper limit on period, Cu, is 1.4; thus, the period T used for determining base shear and lateral loads is T = C u T a = 1.4 × 1.31 = 1.83 s However, the upper limit on period may be used only if a computed period based on a properly substantiated structural analysis is available. The analytical periods were computed using centerline analysis, which approximately accounts for deformations in the panel zones of the beam–column joints but does not explicitly include the stiffening effect of the doubler plates. The inclusion of panel zone flexibility is required in Section 12.7.3. Section 12.7.3 also requires that the analytical model includes P-delta effects, but this is somewhat at odds with the requirements of Section 12.8.6, and specifically Equation (12.8-16), which uses drift quantities Δ that come from an analysis that does not include P-delta effects. The application of Equation (12.8-16) to results from an analysis that includes P-delta effects would be including such effects twice. This problem is recognized in the last paragraph of Section 12.8.7 and is discussed later in this example. The computer analysis resulted in Tcomputed = 2.95 s for the model that did not explicitly include P-delta effects. When P-delta effects were explicitly included, the period increased to 3.11 s. This 5% increase in period represents approximately a 10% reduction in lateral stiffness when P-delta effects are included. The computed period is significantly greater than the adjusted period T = CuTa, and this difference is of some concern. Because of this concern, the computer model was thoroughly checked, and no errors were found. However, differences between the empirical and the computed period, with the computed period greater than the empirical period, are not unusual in moment frame analysis. As shown later in this example, however, periods that are significantly greater than the CuTa upper limit may be an indicator that the building is too flexible.

Drift Computations Based on T = CuTa = 1.83 s The design seismic base shear based on the upper limit for period of vibration is computed by V = CsW

Seismic Loads

(12.8-1)

163

Drift and P-delta Effects

Table G19-2. Drift Analysis Using T = CuTa without P-delta Effects Story x

Fx (kips)

δxe (in.)

Δxe (in.)

Δx = CdΔxe/Ie (in.)

Limit (in.)

Ratio 5/6

Okay?

9 8 7 6 5 4 3 2 1

216.5 185.4 150.1 117.8 88.8 63.0 41.0 22.9 9.9

6.721 6.222 5.576 4.824 4.038 3.230 2.411 1.599 0.844

0.499 0.646 0.752 0.786 0.809 0.818 0.813 0.755 0.844

2.195 2.843 3.308 3.458 3.559 3.600 3.575 3.323 3.712

2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 3.24

0.938 1.215 1.414 1.478 1.521 1.538 1.528 1.420 1.146

OK NG NG NG NG NG NG NG NG

Note: NG = No Good (unacceptable).

Equation 12.8-3 controls the value of Cs. Using T = CuTa = 1.83 s, then Cs =

S D1 0.5 = 0.0426 = TðR=I e Þ 1.83 × ð8=1.25Þ

Using W = 21,000 kips for the entire building, then V = C s W = 0.0426 × 21,000 = 895 kips The ELF story forces for the full building (not a single frame) are shown in Column 2 of Table G19-2. These forces were computed according to Equations (12.8-11) and (12.8-12), with the exponent k = 1.665 for T = 1.83 s. Application of these forces to the building resulted in the story displacements δxe shown in the third column of the table. See Equation (12.8-15) and Figure 12.8-2 of ASCE 7 for a description of symbols used in computing drift. Story drifts (the displacement at the top of a story minus the displacement at the bottom of the same story) are shown in Column 4 of Table G19-2. The designlevel story drifts, Δx, computed according to Equation (12.8-15), are shown in Column 5. These drifts are based on Cd = 5.5 and Ie= 1.25. According to Table 12.12-1 and Section 12.12.1, the story drift limits for this Risk Category III building are 0.015/ρ times the story height where ρ is the redundancy factor, which is equal to 1.0 for this highly redundant conﬁguration. These limiting story drift values are shown in Column 6 of Table G19-2. The ratio of the design-level drift to the drift limit is provided in Column 7. The limits are exceeded (ratios greater than 1.0) at all stories except for Story 9. In Story 4, the computed drift is 1.538 times the speciﬁed limit.

Drift Computations Based on T = Tcomputed = 2.95 s The calculations are now repeated for the same structure analyzed with lateral forces consistent with the computed period of 2.95 s, which is the period computed when P-delta effects are not explicitly included in the analysis.

Seismic Loads

164

Seismic Loads

Table G19-3. Drift Analysis Using T=Tcomputed without P-delta Effects Story x

Fx (kips)

δxe (in.)

Δxe (in.)

Δx = CdΔxe/Ie (in.)

Limit (in.)

Ratio 5/6

Okay?

9 8 7 6 5 4 3 2 1

148.9 122.9 95.3 71.3 50.7 33.6 20.0 9.9 3.5

4.337 3.999 3.556 3.067 2.554 2.032 1.511 0.998 0.526

0.338 0.434 0.498 0.514 0.522 0.521 0.513 0.473 0.526

1.486 1.908 2.191 2.260 2.295 2.294 2.255 2.080 2.312

2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 3.24

0.635 0.815 0.936 0.966 0.981 0.980 0.964 0.889 0.714

OK OK OK OK OK OK OK OK OK

The seismic coefﬁcient Cs for T = 2.95 s is Cs =

S D1 0.5 = 0.0265 = TðR=I e Þ 2.95 × ð8=1.25Þ

Using W = 21,000 kips for the entire building, then V = C s W = 0.0265 × 21,000 = 556 kips The results of the drift analysis are presented in Table G19-3. The exponent k for computing the distribution (Section 12.8-3) of lateral forces is 2.0 in this case. The drifts have reduced substantially and do not exceed the limiting values at any level. In this case, using the computed period when calculating drifts appears to provide a signiﬁcant advantage. However, a drift analysis is not complete without performing a P-delta check. This check is performed in the following section for the case where Tcomputed = 2.95 s is used to determine the story forces used in drift analysis.

19.2 P-delta Effects The P-delta check is carried out in accordance with Section 12.8.7. In the P-delta check, the stability ratio is computed for each story, in accordance with Equation (12.8-16) as θ=

P x ΔI e V x hsx C d

(12.8-16)

where Px = Total vertical design gravity load at level x, Δ = Story drift at level x and is based on center of mass story displacements computed using Equation (12.8-15), Ie = Seismic importance factor, Vx = Total design shear at level x and is based on Cs computed using Equation (12.8-3) and thus includes the importance factor as a multiplier,

Seismic Loads

165

Drift and P-delta Effects

hsx = Story height, and Cd = Deflection amplifier from Table 12.2-1. The results of the P-delta analysis are shown in Table G19-4, in which Column 3 provides the accumulated story gravity forces, P, in each story of the building. The gravity forces are unfactored, in accordance with the definition of Px in Section 12.8.7. The shears in Column 4 of Table G19-4 are the accumulated story shears, whereas the story drifts in Column 5 of Table G19-4 are the same as those in Column 5 of Table G19-3. The calculated stability ratios are in Column 6 of Table G19-4, where the maximum value of 0.121 occurs at level 2. The limiting value of θ is given by Equation (12.8-17) as follows: θmax =

0.5 βC d

(12.8-17)

where β is the ratio of shear demand to shear capacity of the story, which in essence is the inverse of the story overstrength. If β is taken as 1.0, θmax is 0.5/5.5 = 0.091 and is the same for all stories. Table G19-4 shows that the ratio of 0.091 is exceeded at Stories 1 through 5. Without further analysis, the building would be deemed to be noncompliant with the stability requirements and would have to be redesigned. However, the redesign can be avoided if the story overstrengths can be shown to be greater than the ratio values shown in Column 8 of Table G19-4. For example, the required overstrength for Story 2 is 1.330. The computed overstrength is likely significantly greater than 1.330 for Story 2 because of the strong column–weak beam rules that are built into the various design specifications, such as the Seismic Provisions for Structural Steel Buildings (AISC 2016b). As shown later in the example, the computed overstrengths for the structure are more than sufficient to satisfy the stability requirements (θ < θmax) for this structure. However, the influence of P-delta

Table G19-4. Stability Analysis Using T = Tcomputed and Results from Table G19-3

Story x 9 8 7 6 5 4 3 2 1

Height (in.)

Ptotal (k)

Vstory (k)

Δx (in.)

θmax

Ratio Okay?

156 156 156 156 156 156 156 156 216

2,700 5,475 8,250 11,025 13,800 16,575 19,450 22,125 25,050

148.9 271.8 367.1 438.4 489.1 522.7 542.7 552.6 556.1

1.486 1.908 2.191 2.260 2.295 2.294 2.255 2.080 2.312

0.039 0.056 0.072 0.082 0.094 0.106 0.118 0.121 0.110

0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091

0.429 0.615 0.791 0.901 1.033 1.165 1.296 1.330 1.208

Note: NG = No Good (unacceptable).

Seismic Loads

OK OK OK OK NG NG NG NG NG

Required Overstrength = 1/β 1.0 1.0 1.0 1.0 1.033 1.165 1.296 1.330 1.208

166

Seismic Loads

Table G19-5. P-delta–Adjusted Drifts from Table G19-3

Story x 9 8 7 6 5 4 3 2 1

Δx = CdΔxe/Ie (in.)

Δx/(1−θ)

Limit (in.)

Ratio 4/5

Okay?

1.486 1.908 2.191 2.260 2.295 2.294 2.255 2.080 2.312

0.039 0.056 0.072 0.082 0.094 0.106 0.118 0.121 0.110

1.546 2.021 2.361 2.461 2.533 2.566 2.523 2.366 2.569

2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 3.24

0.661 0.864 1.009 1.052 1.082 1.096 1.078 1.011 0.793

OK OK NG NG NG NG NG NG OK

Note: NG = No Good (unacceptable).

effects on story drift must still be investigated because the computed θ values are greater than 0.10 at most stories. As stipulated in Section 12.8.7, the drifts adjusted for P-delta effects are determined by multiplying the drifts computed without P-delta by the quantity 1/(1−θ). Table G19-5 shows the P-delta adjusted story drifts. The drifts shown in Column 2 of Table G19-5 are the same as those shown in Column 5 of Table G19-3. Column 4 of Table G19-5 presents the ampliﬁed drifts, which exceed the drift limit at Stories 2 through 7. It is of some interest to perform one additional set of drift calculations for the system analyzed with P-delta effects explicitly included. As mentioned previously, the period of vibration for this case is 3.11 s. Using this period, the base shear is computed as follows: Cs =

S D1 0.5 = 0.0251 = TðR=I e Þ 3.11 × ð8=1.25Þ

V = C s W = 0.0251 × 21,000 = 527 kips Table G19-6 shows the resulting drift analysis, where the lateral forces in Column 2 are based on V = 527 kips and k = 2.0. The allowable drift ratios at a few levels are marginally greater than the limits, and thus the drift is not acceptable. The main reason for the difference between the drifts in Tables G19-5 and G19-6 is that the values in Table G19-6 are based on a reduced lateral load of 527 kips (using a computed period of 3.11 s) versus 556 kips (using a computed period of 2.95 s).

19.3 Back-Calculation of Stability Ratios when P-delta Effects are Included in Analysis Many structural analysis programs provide the option to directly include P-delta effects. If an analysis is run with and without P-delta effects, the story stability

Seismic Loads

167

Drift and P-delta Effects

Table G19-6. Drift Analysis of Building in Figure G19-1 Using T = Tcomputed with P-delta Effects Story x

Fx (kips)

δxe (in.)

Δxe (in.)

Δx = CdΔxe/Ie (in.)

Limit (in.)

Ratio 7/8

Okay?

9 8 7 6 5 4 3 2 1

141.2 116.6 90.4 67.6 48.1 31.9 19.0 9.4 3.4

4.535 4.196 3.758 3.247 2.715 2.168 1.616 1.068 0.561

0.339 0.439 0.510 0.532 0.547 0.552 0.548 0.507 0.561

1.491 1.932 2.244 2.341 2.407 2.429 2.411 2.231 2.468

2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 3.24

0.637 0.826 0.958 1.000 1.028 1.065 1.030 0.953 0.762

OK OK OK OK NG NG NG OK OK

Note: NG = No Good (unacceptable).

ratios may be estimated from the results of the two analyses. Although the approach may be used for three-dimensional analysis in theory, the most straightforward use is for two-dimensional analysis. This approach is demonstrated next. This method is based on the following equation: Δf =

Δ0 1−

PΔ0 VH

Δ0 1−θ

(G19-3)

where Δf = Story drift from the analysis including P-delta effects, Δ0 = Drift in the same story for the analysis without P-delta effects, P = Vertical design load in the story [the same as that used in Equation (12.8-16)], V = Seismic story shear [the same as that used in Equation (12.8-16)], and H = Story height (using the same length units as those used for drift). The story drifts must be computed from the same lateral loads that produce the story shears, and the story shears must be the same for each analysis. A rearrangement of terms in Equation (G19-3) produces the simple relationship shown earlier as Equation (G19-2) and repeated as follows for convenience. θ=1−

Δ0 Δf

This is demonstrated through the use of data provided in Table G19-7. Column 2 of this table provides the story drifts from Table G19-3, and Column 3 provides the drifts calculated using the same loading and model, except that P-delta effects are included. The stability ratios shown in Column 4 of Table G19-7 were computed using these drifts and Equation (G19-2). As may be seen, the ratios are very similar to those computed using Equation (12.8-16).

Seismic Loads

168

Seismic Loads

Table G19-7. Stability Ratios Back-calculated from Analysis Including P-Delta Effects

Story 9 8 7 6 5 4 3 2 1

Δ0 (in.)

Δf (in.)

0.338 0.434 0.498 0.514 0.522 0.521 0.513 0.473 0.526

0.357 0.463 0.538 0.561 0.576 0.582 0.577 0.534 0.592

0.053 0.062 0.074 0.084 0.097 0.105 0.111 0.114 0.111

19.4 Computation of Actual Story Overstrength As shown previously in the example, the computed stability ratios θ exceed the maximum allowable value θmax at several levels of the structure. However, the maximum allowable stability ratios were based on β values of 1.0 for each story. Given that β represents the design strength of a story divided by the actual strength, the inverse of β is in fact a measure of overstrength, which is deﬁned as the ratio of actual strength to design strength. To ﬁnd the value of overstrength (1/β) required to satisfy Equation (12.8-17), the following formula is useful: 1 C d θcomputed = β 0.5

(G19-4)

where θcomputed is the value determined from Equation (12.8-16). For example, using Story 2 from Table G19-4 where θcomputed = 0.121, then 1 5.5 × 0.121 = = 1.33 β 0.5 This quantity is exactly equal to the ratio shown in Column 8 for Story 2 in Table G19-4; in fact, these ratios can be used in lieu of Equation (G19-3). However, a value of 1/β less than 1.0 would not be used, the minimum reasonable value of 1/β is 1.0. Given this, the required values of 1/β required to satisfy Equation (12.8-17) are shown in Column 10 of Table G19-4. Unfortunately, the calculation of actual story strengths is not straightforward and typically requires a series of nonlinear static analyses. A simpliﬁed method for estimating story strengths is provided in Section C3 of the commentary to the Seismic Provisions for Structural Steel Buildings (AISC 2005). If the structure has been designed in accordance with the strong column–weak beam design rules, the plastic story strength may be estimated from the following (AISC 2005): P 2 nj= 1 M pGj (C3-2) V yi = H

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Table G19-8. Story Overstrength Requirements Using Beam Mechanism

Story 9 8 7 6 5 4 3 2 1

θμαξ

Required overstrength

Vy (kips)

Vdemand (kips)

Vdemand/(1 – θ) (kips)

Ratio 5/7

0.039 0.056 0.072 0.082 0.094 0.106 0.118 0.121 0.110

0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091 0.091

1 1 1 1 1.033 1.165 1.296 1.330 1.208

461 461 641 641 814 814 897 897 691

108 201 276 335 379 411 431 443 447

113 213 297 365 418 459 488 504 502

4.08 2.29 2.16 1.75 1.94 1.77 1.83 1.77 1.38

where MpGj = Plastic moment capacity of the girder in bay j, n = Number of bays, and H = Story height under consideration. Using the section sizes shown in Figure G19-1 and assuming a yield stress of 50 kips/in.2 for steel, the story strengths for one frame are computed as shown in Column 5 of Table G19-8. Column 6 lists the strength demands, which are based on the story force values in Column 2 of Table G19-2 but divided by 2.0 to represent a single frame. Before calculating the true overstrength, the values in Column 6 of Table G19-8 must be divided by the quantity (1 – θ), as required by Section 12.8.7. The ratio of the computed capacity to the strength demand is shown in Column 8 of Table G19-8. Clearly, the ratios all exceed the required ratios (1/β values) shown in Column 4 of Table G19-8. Hence, the structure satisfies the stability requirements of ASCE 7-16 and satisfies the drift requirements when an explicit P-delta analysis is used to compute drifts. Drifts are not satisfied for the structure when the drifts computed without P-delta effects are amplified by the quantity 1/(1 – θ). The AISC formula [Equation (C3-2)] does not work for braced frames, dual systems, or any other type of structure except a moment frame. Calculating story strengths for general structural systems is not straightforward and may not even be possible without a detailed nonlinear static pushover analysis. For this reason (and several reasons not discussed here), future versions of ASCE 7 are likely to abandon Equation (12.8-17) in favor of requiring the designer to demonstrate stability through the use of a nonlinear static pushover analysis.

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20 Accidental Torsion and Ampliﬁcation of Accidental Torsion

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • • • •

Accidental torsion should be considered in Seismic Design Category B only if there is an extreme torsional irregularity. Accidental torsion should be considered in Seismic Design Categories C, D, E, and F only if there is a torsional irregularity or an extreme torsional irregularity. Three-dimensional analysis is required when the modal response spectrum, linear response history, or nonlinear response history methods of analysis are used. When linear or nonlinear response history analysis is used and accidental torsion is required, it must be implemented by physically moving the center of mass. In Supplement 2 to ASCE 7-16, it is no longer allowed to use a mass offset to account for accidental torsion when modal response spectrum analysis is used, and where there is an extreme torsional irregularity. The issues that led to this important change are addressed at the end of this chapter.

This chapter considers several issues related to torsional loading. Included are torsional irregularities, accidental torsion, torsional ampliﬁcation, and application of accidental torsion to structures analyzed using the equivalent lateral force, modal response spectrum, and linear response history analysis

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procedures. Systems with rigid and semirigid diaphragms are considered. Accidental torsion need not be considered for systems with flexible diaphragms. Figure G20-1 is a plan view of a 5-story reinforced concrete shear wall building. The first story is 12 ft 4 in. tall, and the upper stories are each 11 ft 4 in. tall. The building, located in central Missouri, houses various business offices and is classified as Risk Category II. The following design spectral accelerations have been determined for the site: S DS = 0.45 g S D1 = 0.19 g Tables 11.6-1 and 11.6-2 indicate that the seismic design category is C. Table 12.2-1 allows the use of an ordinary reinforced concrete shear wall, with the following design parameters: R=5 C d = 4.5 Ω0 = 2.5 For this analysis, all walls are assumed to be 10 in. thick and constructed with 4,000 lb/in.2 normal weight concrete. Walls A, B, and C have a length of 22 ft, and Walls D, E, F, G, H, and I have a length of 16 ft. Floor and roof diaphragms are assumed to be 6.0 in. thick solid slabs, constructed with 4,000 lb/in.2 normal weight reinforced concrete. The period of vibration is estimated from Equation (12.8-7). Using hn = 12.33 + 4(11.33) = 57.7 ft and coefficients Ct = 0.02 and x = 0.75 from Table 12.8-2, then T = T a = C t hxn = 0.02 × 57.70.75 = 0.42 s

Figure G20-1. Plan of reinforced concrete shear wall building. Note: C.M. = center of mass.

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This period is used for analysis (in lieu of CuTa) because an analytical period (from a computer program) is not available. However, assessment of torsional irregularity and torsional ampliﬁcation is not strongly period dependent. Lateral forces are computed using the equivalent lateral force method. Using the ground motion parameters given in the aforementioned, TS = SD1/SDS = 0.19/0.45 = 0.42, which by coincidence is equal to T = 0.42 s, so Equations (12.8-2) and (12.8-3) produce the same base shear. Using a total seismic weight of the building of 9,225 kips, the base shear is determined from Equation (12.8-2) as follows: S 0.45 C s = DS = = 0.090 R Ie

5.0 1.0

V = C s W = 0.090ð9,225Þ = 830 kips Equivalent lateral forces are computed in accordance with Section 12.8.3, with k = 1.0. The results of the calculation are provided in Table G20-1. Because of the plan shape (Figure G20-1), the structure has a reentrant corner irregularity. Hence, according to Section 12.3.1.2, the diaphragm may not be classified as rigid and must be analyzed as semirigid although the behavior will be essentially rigid owing to the 6 in. thick slabs. By the requirement of Sections 12.8.4.1, inherent torsion must be included, but accidental torsion must only be included if there is a Type 1a or Type 1b horizontal (torsional) irregularity. A 3D analysis is required for the structure, because the in-plane deformations of the semirigid diaphragm must be included (see Section 12.7.3) and this cannot be reasonably done without a 3D analytical model. There is no need to compute separately the effects of inherent torsion because such effects are automatically included in a 3D analysis. A 3D analysis is also needed to determine if a torsional irregularity exists and if it is necessary to compute the accidental torsion amplification factors. For this example, such an analysis was run using a 3D finite-element analysis program, wherein the walls were modeled as membrane elements. Membrane elements were used in lieu of shell elements because excluding the out-of-plane stiffness of the walls was desirable for simplicity. The use of membrane elements

Table G20-1. Equivalent Lateral Forces Level

H (ft)

h (ft)

W (kip)

Whk

Whk/total

F (kips)

5 4 3 2 1 Total

11.33 11.33 11.33 11.33 12.33 57.65

57.66 46.33 35.00 23.66 12.33 —

1,820 1,845 1,845 1,845 1,870 9,225

104,941 85,479 64,575 43,653 23,057 321,705

0.326 0.266 0.201 0.136 0.070 1.00

271 221 167 113 58 830

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automatically includes in-plane axial, flexural, and shear deformation in the walls. Uncracked properties were used because the main purpose of the analysis is to determine the elastic deformations in the system and to determine the distribution of the forces in the walls. Although cracking affects the absolute magnitude of displacements, it does not affect the ratio of the displacements at the edge of the building to the displacement at the center of the building, as long as the same stiffness reduction factors are used to represent cracking in each wall. Similarly, cracking does not affect the distribution of forces if all walls are cracked to the same degree. (This discussion is based on flexural properties and flexural cracking. For shear wall systems, the effect of shear deformations and shear cracking should also be considered because these effects can have a significant influence on the distribution of forces in the system.) To determine the possible presence of a torsional irregularity, the concrete diaphragms were modeled with 6.0 in. thick membrane elements. The concrete was assumed to be uncracked. Membrane elements were used in lieu of shell elements to avoid unintentional frame action that would be developed by bending (out-of-plane deformations) in the diaphragm. The analysis is carried out only for forces acting in the north–south direction. Three load conditions are applied, one without accidental eccentricity, one with the lateral force applied east of the center of mass, and the other with the forces applied west of the center of mass. The location of the center of mass is shown in Figure G20-2. As required by Section 12.8.4.2, the lateral forces are applied at an eccentricity of 0.05 times the length of the building perpendicular to the direction of loads.

Figure G20-2. Plan shown with loading and monitoring locations. Note: C.M. = center of mass.

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Accidental Torsion and Ampliﬁcation of Accidental Torsion

Thus, the eccentricity is 0.05(210) = 10.5 ft when the lateral loads are applied in the north–south direction. Although the diaphragm is classified as semirigid, its behavior is essentially rigid, allowing the lateral load and accidental torsion to be applied through the use of two loading points, shown as F1 and F2 in Figure G20-2. [The loads could also be applied as a single concentrated force (lateral load) plus moment applied about the vertical axis (accidental torsion). These loads would be applied at a single node at the center of mass.] The forces caused by the lateral load without torsion are based on simple beam reactions for a beam with a span of 30 ft [Figure G20-3(a)]. The accidental torsional component of load is also applied as two concentrated forces [Figure G20-3(b)]. The total load is simply the lateral load, plus or minus the torsional load [Figure G20-3(c and d)]. To determine if a torsional irregularity exists (Table 12.3-1), story drifts (not displacements) are monitored at the extreme edges of the building under a loading that consists of the design lateral forces and (plus or minus) accidental torsion. If the maximum drift at the edge of any story exceeds 1.2 times the average of the drifts at the two edges of the story, a torsional irregularity exists. If the maximum drift exceeds 1.4 times the average, an extreme irregularity exists. In this example, the computed displacements were used without the deflection amplifier Cd because the Cd term cancels out when computing the ratio of drifts.

(a) Lateral Load Only

(b) Torsion Only

(d) Lateral - Torsion

Figure G20-3. Loading values applied to building.

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For determining the torsional amplification factor, the story displacements (not drifts) are used. An amplification factor, Ax, is then computed for each story. This factor is determined using Equation (12.8-14) as follows: δmax 2 Ax = (12.8-14) 1.2δavg where δmax is the maximum deflection at the edge of the story, and δavg is the average deflection at the two edges. The two points at which the deflections were monitored are designated as δ1 and δ2 in Figure G20-2. Inherent torsion must be included in the analysis, which is automatically accomplished when a 3D analysis is performed. Separating out the inherent torsion is not needed, however, because it is never used independently. Nevertheless, applying the lateral loads without accidental torsion and observing the resulting deflection patterns is worthwhile. These deflections indicate the location of the center of rigidity relative to the center of mass. Accidental torsion loadings that rotate the floor plates in the same direction as the rotation resulting from inherent torsion clearly control when determining if torsional irregularities occur and when computing amplification factors. To determine the displacements in the system under lateral load only, the forces listed in Column 7 of Table G20-1 were applied as shown in Figure G20-3(a). The results of the analysis are presented in Table G20-2. The rotational measurement, θ, is the rotation about the vertical axis, which is counterclockwise positive. The deflections at point δ2 at any level are always greater than those at δ1, causing the building to twist counterclockwise, which is a positive rotation. This situation indicates that the center of mass lies east of the center of rigidity, which is to the right in Figure G20-2. Clearly, lateral loads plus torsion results in greater twisting in the positive direction. The results in Table G20-3 indicate an increasing rotation when the torsion is applied in the positive direction. The twisting causes an extreme torsional irregularity. A given irregularity type needs to occur only at one story for the whole building to be classified as having that irregularity. Given the presence of an extreme torsional irregularity, accidental torsion must be included in the analysis.

Table G20-2. Displacements for Building under Lateral Force without Torsion Level 5 4 3 2 1

δ1 (in.)

δ2 (in.)

θ (radians)

0.463 0.341 0.224 0.120 0.042

0.754 0.555 0.364 0.196 0.068

1.15 × 10−04 8.50 × 10−05 5.56 × 10−05 2.98 × 10−05 1.04 × 10−05

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Table G20-3. Results for Lateral plus Accidental Torsion: Irregularity Check Level (δ) Story (Δ)

δ1 (in.)

δ2 (in.)

Δ1 (in.)

Δ2 (in.)

Δavg (in.)

Δmax/Δavg

Torsional irregularity

5 4 3 2 1

0.304 0.224 0.147 0.079 0.027

0.929 0.684 0.449 0.241 0.084

0.080 0.077 0.068 0.052 0.027

0.245 0.235 0.208 0.157 0.084

0.163 0.156 0.138 0.104 0.056

1.508 1.510 1.505 1.507 1.506

Extreme Extreme Extreme Extreme Extreme

Table G20-4. Results for Lateral plus Accidental Torsion: Ampliﬁcation Factors Level (δ) 5 4 3 2 1

δ1 (in.)

δ2 (in.)

δavg (in.)

δmax/δavg

0.304 0.224 0.147 0.079 0.027

0.929 0.684 0.499 0.241 0.084

0.617 0.454 0.298 0.160 0.056

1.508 1.507 1.507 1.507 1.506

1.578 1.578 1.577 1.577 1.576

Table G20-5. Results for Lateral minus Accidental Torsion: Irregularity Check Level (δ) Story (Δ)

δ1 (in.)

δ2 (in.)

Δ1 (in.)

Δ2 (in.)

Δavg (in.)

Δmax/Δavg

Torsional irregularity

5 4 3 2 1

0.623 0.458 0.301 0.162 0.056

0.579 0.426 0.280 0.150 0.052

0.165 0.157 0.139 0.106 0.056

0.153 0.146 0.130 0.098 0.052

0.159 0.152 0.135 0.102 0.054

1.038 1.036 1.033 1.039 1.037

None None None None None

Table G20-4 shows the computation of the torsional ampliﬁcation factor at each level. In this case, the values are virtually the same all the way up the building because the walls continue the full height of the building. When the accidental torsion is applied in the opposite direction, it offsets the inherent torsion and the irregularity disappears. These results are provided in Tables G20-5 and G20-6. In addition, the computed ampliﬁcation factors are less than 1.0, so the minimum factor of 1.0 is applied. The following points are worthy of discussion: 1.

When determining torsional amplification, it is not necessary to iterate by analyzing the system with the amplified accidental torsion, determining a new amplification

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Table G20-6. Results for Lateral minus Accidental Torsion: Ampliﬁcation Factors

Level (δ) 5 4 3 2 1

δ1 (in.)

δ2 (in.)

δavg (in.)

δmax /δavg

0.623 0.458 0.301 0.162 0.056

0.579 0.426 0.280 0.150 0.052

0.601 0.442 0.291 0.156 0.054

1.037 1.036 1.036 1.038 1.037

1.0 1.0 1.0 1.0 1.0

Note: Minimum Ax = 1.0.

factor, analyzing again, and so on. A single analysis using the 5% accidental eccentricity determines ampliﬁcation factors. 2.

When assessing torsional regularity or torsional ampliﬁcation, applying the accidental torsion simultaneously in the two orthogonal directions is not necessary.

When assessing torsional irregularity or torsional ampliﬁcation, it is not necessary to apply orthogonal loading (see Section 12.5 of the standard).

20.1 Application of Accidental Torsion in Systems with Relatively Flexible Semirigid Diaphragms Previously, this example noted that the floor and roof diaphragms were modeled with 6.0 in. thick membrane elements. Although the diaphragm is classified as semirigid, it will behave like a rigid diaphragm. In some structures, a diaphragm that is classified as semirigid may behave more like a flexible diaphragm. In such cases the lateral forces should not be applied as shown in Figure G20-2. Instead, these forces should be distributed throughout the diaphragm in some reasonable manner. A possible distributed loading for the structure analyzed in this example is shown in Figure G20-4, in which the lateral force at a level is applied on the basis of nodal forces, where the sum of the individual nodal forces is equal to the total load applied at the level. Nodal forces are based on a tributary area (mass) basis. Accidental torsion is applied by a series of moments applied in the plane of the diaphragm. Shell, not membrane, elements would be required for such an analysis, and the element formulation used in the finiteelement analysis program must be able to accommodate drilling degrees of freedom (nodal moments applied about an axis normal to the plane of the diaphragm). If applying moments directly to the nodes is not possible, the torsion may be applied by modifying the lateral forces that are applied to each node. However, indiscriminate use of ELF analysis with semirigid diaphragms is not appropriate. This is particularly true when the diaphragm tends to be more flexible than rigid or when the diaphragm has a highly irregular shape [e.g., the diaphragms with large openings in Chapter 10 (Figure G10-6)]. In such circ*mstances it may be necessary to use a refined mesh, particularly in

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Accidental Torsion and Ampliﬁcation of Accidental Torsion

Figure G20-4. Direct and torsional loading for a system with a semirigid diaphragm. locations where stresses are to be recovered. A trial-and-error procedure is often required to determine the correct level of mesh reﬁnement.

20.2 Application of Accidental Torsion and Torsional Ampliﬁcation in Modal Response Spectrum and Linear Response History Analysis Where the modal response spectrum procedure of Section 12.9.1 is utilized and accidental torsion is required, the accidental torsion may be accounted for in one of two ways: 1.

By performing a separate static analysis with accidental torsions applied at each level, and directly adding the results to those obtained using the response spectrum analysis. In this case no adjustments are made to the center of mass of the individual diaphragms.

By adjusting the diaphragm mass distribution such that the center of mass is moved ±5% of the building dimension perpendicular to the direction of applied lateral load.

When the linear response history procedure is used, the only option for accommodating accidental torsion is to relocate the center of mass

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(See Section 12.9.2.2.2). This is necessary for preserving the signs of displacement and force results. The disadvantage of the second approach is that moving the center of mass affects the modal properties (mode shapes and frequencies) of the system, and this may complicate the formation of load combinations because such combinations must be made from separate analytical models. Some software available for dynamic analysis automatically adjusts the mass distribution to accommodate the required mass eccentricity and simpliﬁes the load combinations among different runs. An advantage of the second approach is that torsional ampliﬁcation need not be included (Ax = 1.0) (see Sections 12.9.1.5 and 12.9.2.2.2).

Procedure for Shifting Center of Mass Supplement 2 of ASCE 7-16 restricts the use of mass offsets in modal response spectrum analysis to systems that do not have an extreme torsional irregularity. No such restrictions are placed on linear or nonlinear response history analysis. See the discussion at the end of this chapter for background on this issue. When accidental torsion is allowed to be used by modeling a mass offset, it is necessary to shift the mass in the X-direction without affecting the Y-direction, and vice versa. The following procedure provides the required results by dividing the diaphragm into four regions and then determining mass modiﬁers that provide the desired offsets. The procedure is summarized as follows: 1.

Divide each ﬂoor plate into four regions as shown in Figure G20-5.

Name these regions A, B, C, D as shown.

Compute the mass and center of mass for each region, where the center of mass is oriented relative to a given origin. One can alternately work with weights.

Figure G20-5. Diaphragm mass divided into four quadrants.

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Using the same origin, compute the total mass and the center of mass for the full plate.

Establish coefﬁcients αA, αB, αC, αD, such that the center of mass is moved in the desired direction.

The procedure utilizes the following equations: αA M A + αB M B + αC M C + αD M D = M total

(G20-1a)

αA M A X¯ A + αB M B X¯ B + αC M C X¯ X + αD M D X¯ D = ðX¯ total + eXÞM total

(G20-1b)

αA M A Y¯ A + αB M B Y¯ B + αC M C Y¯ Y + αD M D Y¯ D = ðY¯ total + eY ÞM total

(G20-1c)

In Equation (G20-1a) the total mass is unchanged, and in Equations (G20-1b) and (G20-1c) the desired mass offset is determined. If one is determining the desired offset eX, set eY to zero. If one is determining the desired eY, set eX to zero. Note however that there are three equations and four unknowns, which means that there are an inﬁnite number of solutions. To resolve this issue, a fourth equation can be written that establishes a relationship between two of the alpha terms. The suggested rules for doing this are as follows: 1.

If it is desired to move the mass in the + or − X-direction, set αA = αC, or αB = αD.

If it is desired to move the mass in the + or − Y-direction, set αA = αB, or αC = αD.

This produces the same result as if the ﬂoor plate was divided into only three segments, in which case a unique solution can be found. The added equation produces a system of equations. For example, if it is desired to ﬁnd the positive Y offset with αA = αB, Equation (G20-2) is applicable. 2

MA 6 M A X¯ A 6 4 M A Y¯ A 1

MB M B X¯ B M B Y¯ B −1

MC M C X¯ C M C Y¯ C 0

9 38 9 8 MD αA > M total > > > > > > > < = < = ¯ total M total M D X¯ D 7 α X B 7 (G20-2) = M D Y¯ D 5> αC > ðY¯ total + eY ÞM total > > > > > > : ; : ; 0 αD 0

Example The floor plate shown in Figure G20-6 has dimensions shown, and a uniform interior weight of 0.1 ksf. Perimeter-cladding weights parallel to the x-direction are 1.0 klf, and perimeter-cladding weights parallel to the y-direction are 1.5 klf. (Here we work with weight instead of masses simply for convenience). The structure is divided into four quadrants, A, B, C, and D. Weight and center of weight distributions are as shown in Table G20-7. The floor-plate weight modifiers were computed in Excel, with the results presented in Figure G20-7 for the desired 5% mass offsets in the +X, −X, +Y and −Y directions. As may be observed the desired offsets are obtained in the given direction without affecting the center of weight in the perpendicular direction.

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Figure G20-6. Floor plate dimensions, weights, and subplate designations.

Table G20-7. Properties of Subplate Weights Subplate A B C D Total

Weight (k)

X¯ (ft.)

Y¯ (ft.)

525 525 562.50 300.00 191.25

34.143 117.857 35.000 110.937 68.873

78.571 78.571 20.833 34.757 54.657

(a) Positive 7.5 ft. X direction Shift

(b) Negative 7.5 ft. X direction Shift

(d) Negative 5.0 ft. Y direction Shift

Figure G20-7. Mass adjustment factors and revised centers of mass.

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Accidental Torsion and Ampliﬁcation of Accidental Torsion

A very signiﬁcant mass redistribution is required to obtain a 5% accidental eccentricity. It is highly unlikely that this level of uncertainty in the mass distribution will occur in a real building. However, there are other uncertainties that contribute to the 5% mass offset used in the standard. These include uncertainties in locating the center of rigidity, the likelihood of nonuniform yielding in the lateral systems (which causes a migration of center of rigidity), and the possibility of torsional components of ground motion.

Background on ASCE 7- Supplement 2 Prohibition of Mass Offset in MRS Analysis In the ATC 123 Project (FEMA 2018), the horizontal and vertical system irregularities discussed standard Section 12.3.2 were studied in some detail, and several recommendations were made for modifying the requirements that trigger the irregularity, or in some cases, eliminating the irregularity altogether. When studying torsional irregularities, it was found that designs using MRS analysis together with the mass offset method of applying accidental torsion could result in unsafe designs relative to designs that used ELF or MRS analysis with a statically applied accidental torsion. Figure G20-8, taken directly from Appendix A of FEMA P-2012 (FEMA 2018), illustrates the issue. Here, systems were designed using MRS analysis with a static torsion applied with a force offset of 0.05Ax times the building dimension perpendicular to the loading (the baseline condition), and redesigned using MRS analysis with accidental torsion applied using a mass offset of 0.05 times the perpendicular building dimension. The vertical axis is the ratio of adjusted collapse margin ratios (ACMR) for the two systems, computed in accordance with FEMA P-695 (FEMA 2009). The horizontal axis is the torsional irregularity factor, which is equal to the displacement of the edge of the building relative to the displacement at the center of the building when lateral forces are applied at a 5% eccentricity. An extreme torsional irregularity occurs where the TIF is greater than about 1.42. In Figure G20-8 colored curves are provided for each

Figure G20-8. Results from the FEMA P-2012 report regarding use of mass offset versus static torsion. Source: FEMA (2018).

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of three different plan aspect ratios in rectangular buildings. The lateral load resisting systems were placed symmetrically about the center of the building. If the ratio of the ACMRs is less than 1.0, the system designed using a mass offset is unsafe relative to the system designed using static torsion. Using the median response minus one standard deviation, this occurred only for systems that had extreme torsional irregularities, or worse. Interestingly, systems with TIFs less than 1.4 are safer using a 5% mass offset than they are using a static torsion. More detail on this issue is presented in DeBock et al. (2019).

Seismic Loads

21 Equivalent Lateral Force Analysis

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • •

Ground motion parameters SS, S1, Fa, and Fv are different because of the development of new hazard maps and changes in the site factor coefﬁcients. Accidental torsion need not be included in the analysis if the structure is in SDC D through F and there is no torsional irregularity.

In this chapter, the eight-story steel frame described in Appendix B is analyzed using the equivalent lateral force procedure. Included in the analysis are preliminary issues such as determination of the presence of structural regularities, diaphragm flexibility, and the redundancy factor. Story drifts are computed and compared to specified limits, with P-delta effects explicitly included in the analysis. Seismic forces for several elements are computed and tabulated for comparison with results obtained using the modal response spectrum and the linear response history methods of analysis. This comparison of results is presented in Chapter 24 of this guide. A second example of a five-story building is provided to demonstrate the twostage ELF analysis procedure that is provided in Section 12.3.2 of the standard. This structure is analyzed using both the two-stage procedure and the traditional ELF procedure, and the results are compared and discussed.

185

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21.1 8-Story Building The 8-story building analyzed in this chapter is described in detail in Appendix B of this guide. Analysis is performed using ETABS, developed by Computers and Structures (CSI 2018). A plan and elevation of the building is provided in Figure G21-1, and an image of the ETABS 3D model is shown in Figure G21-2.

Structural System A detailed discussion of the evolution of the structural system is presented in Appendix B. For loads in the east–west direction, the system is a special steel moment-resisting frame (System C1 in Table 12.2-1). Two perimeter frames are

Figure G21-1. Plan and elevation of the 8-story building.

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187

Equivalent Lateral Force Analysis

Figure G21-2. 3D ETABS model of the 8-story building. provided, and these frames utilize the four interior bays (Grid lines B through F) of frames on Grids 1 and 4. The base conditions of the columns can play an important role in modeling moment frame systems. In this case, because of the presence of a basem*nt wall, it is assumed that the perimeter columns are ﬁxed at the base as they are intended to be embedded into the wall (using pilasters if required), and this will help signiﬁcantly with the stiffness of the system. Columns not on the perimeter that extend into the basem*nt are assumed to have pinned bases. System parameters for the frames are as follows: Special steel moment frame∶

R=8

Ω0 = 3.0

C d = 5.5

In the north–south direction, the system is a dual special moment frame/special concentrically braced frame (system D2 in Table 12.2-1). The braced frames are located in the center bay of Grid lines B, C, E, and F. The moment-resisting frames utilize all three bays aligned along Grid lines A and G. System parameters are as follows: Dual system∶ R = 7

Ω0 = 2.5

C d = 5.5

As noted in Appendix B, the special moment frames in the dual system, acting independently, have been proportioned to have the capacity to resist at least 25% of the base shear in the north–south direction. Both systems satisfy the height limitation requirements of Table 12.2-1. The member sizes used in the analysis are shown in Figures GB-8 through GB-11. The structural system is essentially symmetric in each direction of response, with the only deviation resulting from the skewed arrangements of diaphragm openings.

Ground Motion Parameters The ground motion parameters for the Site Class C location near Raleigh Hills, Oregon, are described in Appendix B of this guide and are summarized as follows:

Seismic Loads

188

Seismic Loads

S S = 0.893g S 1 = 0.405g T L = 16 s

F a = 1.2 S MS = 1.072g S DS = 0.715g F v = 1.5 S M1 = 0.607g S D1 = 0.405g

In addition, TS = SD1/SDS = 0.405/0.715 = 0.566 s.

Seismic Design Category and Importance Factor The building is designated as Risk Category III on the basis of current and future use. Because of this, it is determined that the seismic importance factor Ie = 1.25 (Table 1.5-2) and that the structure is in SCD D (Tables 11.6-1 and 11.6-2).

Story Weights The story weights for the building are determined from the system geometry and loading described in Appendix B and are presented in Table G21-1. These weights include only dead load contributions from the structural weight, ceiling and mechanical systems, rooﬁng, partitions, and cladding. The total system weight W = 14,018 kips. This represents a system density of approximately 8.7 pcf for the above-grade portion of the building.

Seismic Base Shear The seismic base shear, V, is determined in accordance with Section 12.8. For loading in the east–west direction, the system is a special moment-resisting frame. Using from Table 12.8-2 Ct = 0.028, x = 0.8, and hn = 102.5 ft, then T a = C t hxn = 0.028ð102.5Þ0.8 = 1.137 s In anticipation of the computed (eigenvalue) period’s being greater than CuTa, the base shear is based on T = CuTa as For S D1 = 0.405g, C u = 1.4, and T = C u T a = 1.4ð1.137Þ = 1:592 s

Table G21-1. Story Weights for 8-Story Building

Level Roof and parapet 8 7 6 5 4 3 2 Total

Contribution from horizontal surfaces (kip)

Contribution from vertical surfaces (kip)

Total (kip)

1,604 1,494 1,494 1,494 1,494 1,494 1,494 1,494 12,062

280 236 236 236 236 236 236 260 1,956

1,884 1,730 1,730 1,730 1,730 1,730 1,730 1,754 14,018

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189

Equivalent Lateral Force Analysis

Because this period is greater than Ts and less than TL, the design base shear is computed using Equations (12.8-1) and (12.8-3) V = CsW Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

Cs =

S D1 0.405 = 0.0398 = TðR=I e Þ 1.592ð8=1.25Þ

but in accordance with Equation (12.8-5), Cs shall not be less than C s = 0.044S DS I e = 0.044ð0.715Þð1.25Þ = 0.0393 Equation (12.8-3) controls, giving V = 0.0398(14,018) = 558 kips in the east–west (moment frame) direction. For loading in the north–south direction, the system is a dual special momentresisting frame/special concentrically braced frame. From Table 12.8-2, Ct = 0.020, x = 0.75, and hn = 102.5 ft, then T a = C t hxn = 0.020ð102.5Þ0.75 = 0.644 s In anticipation of the computed (eigenvalue) period being greater than CuTa, the base shear is based on T = CuTa For S D1 = 0.405g, C u = 1.4, and T = C u T a = 1.4ð0:644Þ = 0.902 s Because this period is greater than Ts and less than TL, the design base shear is based on Equations (12.8-1) and (12.8-3) V = CsW Cs =

S D1 0.405 = 0.0802 = TðR=I e Þ 0.902ð7=1.25Þ

This value controls over Equation (12.8-5) (Cs = 0.0393), giving V = 0.0802 (14,018) = 1,124 kips in the north–south (dual system) direction. This design base shear is approximately 2.0 times that in the east–west direction, with the main difference being caused by the different periods of vibration in the two directions. The base shears of 558 kips in the east–west direction and 1,124 kips in the north–south direction will be the basis for scaling forces determined from the modal response spectrum and linear response history analyses.

Preliminary Lateral Forces Lateral forces and story torques are needed to check for the presence of several of the horizontal and vertical irregularities and to compute the redundancy factor. These forces are provided in Tables G21-2 and G21-3 for forces in the east–west and the north–south directions, respectively. The torques are based on an accidental eccentricity of 0.05 times the building dimension perpendicular to the direction of loading.

Seismic Loads

190

Seismic Loads

Table G21-2. Lateral Forces in the East–West (Moment Frame) Direction Level

w (k)

h (ft)

hn (ft)

Whnk

Whnk/sum

F (k)

T (ft-k)

R 8 7 6 5 4 3 2 Sum

1,884 1,730 1,730 1,730 1,730 1,730 1,730 1,754 14,018

12.5 12.5 12.5 12.5 12.5 12.5 12.5 15.0 102.5

102.5 90.0 77.5 65.0 52.5 40.0 27.5 15 —

2.42 × 106 1.82 × 106 1.44 × 106 1.10 × 106 9.08 × 105 6.22 × 105 2.91 × 105 1.15 × 105 8.71 × 106

0.278 0.209 0.165 0.126 0.104 0.071 0.033 0.013 1.0

154.7 116.2 92.2 70.3 58.1 39.8 18.6 7.4 557.3

657.6 493.9 392.0 298.6 247.1 169.2 79.0 31.4

Note: k = 1.546. Eccentricity for determining T = 0.05(85) = 4.25 ft.

Table G21-3. Lateral Forces in the North–South (Dual System) Direction Level

w (k)

h (ft)

hn (ft)

Whnk

Whnk/sum

F (k)

T (ft-k)

R 8 7 6 5 4 3 2 Sum

1,884 1,730 1,730 1,730 1,730 1,730 1,730 1,754 14,018

12.5 12.5 12.5 12.5 12.5 12.5 12.5 15.0 102.5

102.5 90.0 77.5 65.0 52.5 40.0 27.5 15 —

4.90 × 105 3.85 × 105 3.22 × 105 2.60 × 105 2.25 × 105 1.67 × 105 9.26 × 104 4.53 × 104 1.99 × 106

0.247 0.194 0.162 0.131 0.113 0.084 0.047 0.023 1.0

277.2 217.7 181.9 147.3 127.1 94.7 52.4 25.7 1,124

2564.0 2014.0 1683.0 1362.0 1176.0 876.0 484.9 237.3

Note: k = 1.201. Eccentricity for determining T = 0.05(185) = 9.25 ft.

Preliminary Mathematical Model For the purpose of determining if the structural system has horizontal and vertical irregularities, a preliminary analytical model is needed. The features of the model are as follows: 1.

The system is modeled in 3D (as needed to determine if a torsional irregularity exists).

Moment-resisting frames are modeled using centerline dimensions, which approximately accounts for panel zone deformations.

Floor and roof diaphragms are modeled as inﬁnitely rigid in-plane and with zero stiffness out-of-plane. Final analysis may require the use of a semirigid diaphragm.

All the gravity columns and beams that are not part of the lateral system were explicitly included in the analysis. These elements are modeled such that they do not contribute to lateral stiffness. Their main purpose is to accommodate the inclusion of P-delta effects. There are only four of these columns (B-2, B-3, F-2, and F-3).

Seismic Loads

191

Equivalent Lateral Force Analysis

P-delta effects are ignored in the analysis used to determine the presence of irregularities but are included in the analysis used to determine ﬁnal drift estimates and member forces.

Regularity Checks A review of Table 12.3-1 shows that the structure does not have horizontal irregularities of Types 2, 3, 4, or 5. It is clear that a torsional irregularity will not occur for east–west loading because the torsional eccentricity is low owing to the narrow 85 ft building width. For north–south loading, the building has significant width (185 ft), and a significant portion of the lateral stiffness is not on the perimeter. It is possible that a torsional irregularity exists for loading in the north–south direction, and it is necessary to analyze the structure in this direction using the lateral forces and the story torsions provided in Table G21-3. In this table drifts come from the elastic analysis, do not include P-delta effects, and have not been adjusted by the factor Cd/Ie. The Cd/Ie factors are not needed because they will cancel out when the ratios of drifts are computed. Table G21-4 provides the results of the analysis, which shows that the system is torsionally regular under this loading although it is close to the margin of where it will become torsionally irregular (maximum drift divided by average drift greater than 1.2). Regarding the vertical irregularities described in Table 12.3-2, a structural analysis is required to determine whether stiffness irregularities (Types 1a and 1b) exist. Such an analysis (not shown herein) indicated that there are no soft story irregularities for either direction of loading. Vertical irregularity Types 2 through 4 do not exist by inspection. The structural system is designed such that lower Stories 1 through 7 have equal or greater strength than the structure directly above, thus assuring that a weak story irregularity (Type 5a or 5b) does not exist. Note that in conformance with the requirements of Table 12.6-1, the ELF procedure is allowed for final design of this building.

Table G21-4. Drifts for Assessing Torsional Irregularity for North– South Loading

Level

δavg (in.)

Δavg (in.)

δmax (in.)

Δmax (in.)

Δmax/Δavg

Result

R 8 7 6 5 4 3 2

13.22 11.31 9.23 7.18 5.33 3.55 2.24 1.05

1.91 2.08 2.05 1.85 1.78 1.31 1.19 1.05

15.22 13.03 10.62 8.26 6.12 4.07 2.57 1.21

2.19 2.41 2.36 2.14 2.05 1.5 1.36 1.21

1.15 1.16 1.15 1.16 1.15 1.15 1.14 1.15

Torsionally Regular Torsionally Regular Torsionally Regular Torsionally Regular Torsionally Regular Torsionally Regular Torsionally Regular Torsionally Regular

Note: Story drift Δ is in story below level indicated.

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Seismic Loads

Diaphragm Flexibility Section 12.3 provides requirements for determination of diaphragm flexibility. The evaluation of this structure would result in the allowable usage of the rigid diaphragm conditions. Although not specifically stated in the standard, it is advisable to use semirigid diaphragms when analyzing dual systems because diaphragm flexibility affects the interaction between the moment-resisting frames and the braced frames. For that reason, the model of this structure will include a semirigid diaphragm.

Redundancy None of the conditions speciﬁed in Section 12.3.4.1 apply, so the redundancy factor cannot be automatically set to 1.0. The system does not have an extreme torsional irregularity; thus it is possible that the redundancy factor can be set to 1.0 using the tests “a” and “b” stipulated in Section 12.3.4.2. Although the system strictly conforms to the requirements of test “b” by having at least two bays of seismic force resisting framing on each side of the perimeter, most of the lateral load capacity in the north–south direction is resisted by the braced frames. Therefore, it seems prudent to apply test “a” to this system. It is clear by inspection that there will not be a 33% reduction in strength by removing a single element or connection of the lateral system. Removing a single element or connection did not create an extreme torsional irregularity, thus the redundancy factor ρ can be set to 1.0 in each direction of response. Results are shown in Tables G21-5a and G21-5b for two different element removal scenarios.

Direction of Loading Requirements Direction of loading requirements are speciﬁed in Section 12.5.4 for systems in Seismic Design Category D. For the structure analyzed, there is no direct interaction between the framing systems in the two orthogonal directions, thus the system can be analyzed independently in each direction. However, to provide consistency with the linear response history procedure (see Chapter 23 of this

Table G21-5a. Drifts for Assessing Redundancy for North–South Loading: Brace in Frame F Removed

Level

δavg (in.)

Δavg (in.)

δmax (in.)

Δmax (in.)

Δmax/Δavg

R 8 7 6 5 4 3 2

9.23 7.90 6.44 5.02 3.74 2.51 1.62 0.79

1.34 1.45 1.43 1.28 1.23 0.90 0.82 0.79

11.35 9.74 7.97 6.24 4.68 3.19 2.10 1.08

1.61 1.77 1.73 1.56 1.49 1.09 1.02 1.08

1.20 1.22 1.21 1.22 1.21 1.21 1.24 1.36

Note: Story drift Δ is in story below level indicated.

Seismic Loads

Result

Not extremely torsionally irregular

193

Equivalent Lateral Force Analysis

Table G21-5b. Drifts for Assessing Redundancy for North–South Loading: Beam in Frame G Removed

Level

δD (in.)

ΔD (in.)

δG (in.)

ΔG (in.)

Δmax/Δavg (in.)

R 8 7 6 5 4 3 2

9.23 7.89 6.44 5.01 3.73 2.50 1.60 0.76

1.34 1.46 1.43 1.28 1.23 0.90 0.84 0.76

11.33 9.71 7.92 6.18 4.61 3.11 2.02 0.98

1.62 1.79 1.74 1.58 1.50 1.09 1.04 0.98

1.21 1.22 1.22 1.23 1.22 1.21 1.24 1.28

Result

Not extremely torsionally irregular

Note: Story drift Δ is in story below level indicated.

guide), the structure is analyzed with 100% of the lateral load in one direction, with 30% of the load applied simultaneously in the orthogonal direction.

Drift and P-delta Effects Drifts are determined in accordance with Section 12.8.6. However, before the drifts are computed and compared to the limits speciﬁed in Section 12.12, it is necessary to determine if P-delta effects need to be included or if such effects are considered to be excessive. This is done in accordance with Section 12.8.7 and Equations (12.8-16) and (12.8-17). For the purpose of this analysis, the lateral forces provided in Tables G21-2 and G21-3 are used and are applied without accidental torsion. Drifts are checked at the center of mass of the ﬂoor plates. The vertical design load Px in Equation (12.8-16) is taken as full dead load plus 50% of live load. Results of the stability analysis are shown in Tables G21-6a and G21-6b for loads acting in the east–west and north–south directions, respectively. In both directions the stability limit (see calculation below each table) is 0.0909. Note

Table G21-6a. Stability Check for East–West Loading

Story 8 7 6 5 4 3 2 1

H (in.)

PD (kip)

PL (kip)

PTOT (kip)

Px (kip)

Vx (k)

Δ (in.)

1/(β)required

150 150 150 150 150 150 150 180

1,884 1,730 1,730 1,730 1,730 1,730 1,730 1,754

126 377 377 377 377 377 377 377

2,010 2,107 2,107 2,107 2,107 2,107 2,107 2,127

2,010 4,034 6,051 8,068 10,058 12,102 14,119 16,246

116.0 198.8 260.6 304.6 339.2 360.7 369.0 371.6

1.66 2.11 2.11 2.16 2.25 2.20 2.10 1.74

0.044 0.065 0.074 0.087 0.101 0.112 0.122 0.096

NA NA NA NA 1.11 1.23 1.34 1.06

Note: Stability limit = 0.5β/Cd = 0.5(1)/5.5 = 0.0909. Bold indicated θ is greater than θmax.

Seismic Loads

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Seismic Loads

Table G21-6b. Stability Check for North–South Loading

Story 8 7 6 5 4 3 2 1

H (in.)

PD (kip)

PL (kip)

PTOT (kip)

Px (kip)

Vx (kip)

Δ (in.)

1/(β)REQD

150 150 150 150 150 150 150 180

1,884 1,730 1,730 1,730 1,730 1,730 1,730 1,754

126 377 377 377 377 377 377 377

2,010 2,107 2,107 2,107 2,107 2,107 2,107 2,127

2,010 4,034 6,051 8,068 10,058 12,102 14,119 16,246

200.1 352.7 476.0 571.9 652.4 709.2 737.3 749.3

1.56 1.70 1.66 1.50 1.43 1.05 0.94 0.86

0.024 0.029 0.032 0.032 0.033 0.027 0.027 0.024

NA NA NA NA NA NA NA NA

Note: Stability limit = 0.5 β/Cd = 0.5(1)/5.5 = 0.0909.

that this is based on β = 1.0, which is very conservative. The last column in each table indicates the value of (1/β) that would be required to make θmax greater than the story stability ratio, which allows the structure to be designed as is, including P-delta effects. Note that (1/β) is the required overstrength of the story, and as seen, these values are in the range of 1.06 to 1.34. It is expected that the actual story overstrength exceeds these values, but these computations are not included in the example. See FAQ A2 for suggested methods of determining story overstrength. It is required to include P-delta effects in the analysis (or make postanalysis adjustments) because θ is greater than 0.10 in several instances in the moment frame direction. The structure was reanalyzed with P-delta effects explicitly included. Note that the drifts are determined at the edge of the building in accordance with Section 12.8.6. (This is not explicitly required for this structure because there is no torsional irregularity. However, because no accidental torsion is included, the drifts at the edge are essentially the same as at the center of mass.) Section 12.8.6.2 allows the story drifts to be based on lateral forces that are based on the computed period of vibration (using a rational analysis). These periods are presented in Table G22-1 and are summarized as follows: T computed in the north−south direction = 1:421 s

ðC u T a = 0:902 sÞ

T computed in the east−west direction = 2.718 s

ðC u T a = 1.592 sÞ

The deformations computed using the forces based on Tcomputed in each direction, respectively, including the effects of P-delta are shown in Tables G12-7a and G12-7b. In these tables, the drifts in the east–west direction are shown to exceed the allowable drift limits at the fourth and fifth floors. In addition, this same structure will be analyzed using modal response spectrum and linear response history, and the drifts will be verified in those analyses, which are more accurate than the ELF method. For the north–south direction, the drifts at all floors are less than the applicable limits.

Seismic Loads

195

Equivalent Lateral Force Analysis

Table G21-7a. Frame Line 1 Drifts for East–West Loading

Level R 8 7 6 5 4 3 2

δE-W (in.)

δE-W (with P-δ) (in.)

δx (in.)

Δ (in.)

Δ Limit (in.)

Ratio

3.24 2.91 2.49 2.06 1.63 1.17 0.73 0.32

3.71 3.35 2.89 2.41 1.91 1.39 0.87 0.38

16.32 14.74 12.72 10.60 8.40 6.12 3.83 1.67

1.58 2.02 2.11 2.20 2.29 2.29 2.16 1.67

2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.70

0.70 0.90 0.94 0.98 1.02 1.02 0.96 0.62

Notes: T = Tcomputed and P-Delta included. Story drift Δ is in story below level indicated. Bold indicates drift limit was exceeded.

Table G21-7b. Frame Line A Drifts for North–South Loading Level R 8 7 6 5 4 3 2

δN-S (in.)

δN-S (with P-δ) (in.)

δx (in.)

Δ (in.)

Δ Limit (in.)

Ratio

1.99 1.70 1.38 1.07 0.79 0.53 0.33 0.15

2.06 1.76 1.43 1.11 0.82 0.54 0.34 0.16

9.06 7.74 6.29 4.88 3.61 2.38 1.50 0.70

1.3 1.5 1.4 1.3 1.2 0.9 0.8 0.7

2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.70

0.59 0.65 0.63 0.57 0.55 0.39 0.35 0.28

Notes: T = Tcomputed and P-Delta included. Story Δ drift is in story below level indicated.

Selected Seismic Member Forces Seismic forces for selected members are presented in Tables G21-8 through G21-10 for analysis with P-delta effects, and in Tables G21-11 through G21-13 for analysis without P-delta effects. In each case the forces (axial force, bending moment, and shear) are based on the lateral loads of Tables G21-2 and G21-3. P-Delta effects are included in the analysis by using the geometric stiffness based on full dead load and 50% of live load. As may be seen, P-delta effects were not particularly signiﬁcant for the north–south direction of the structure (dual system). However, in the east–west direction, signiﬁcant impacts result from the inclusion of P-delta, which is consistent with the stability ratios shown in Table G21-6a.

Effects of Orthogonal Loading Although it is not required for this structure, the effect of orthogonal loading as required in Section 12.5.3.1a is used to evaluate the effects of loading two directions simultaneously with one direction scaled to 30%. The results of select column forces at the level above grade are shown in Tables G21-14a and G21-14b. What should be noted is that the weak axis moments in some

Seismic Loads

196

Seismic Loads

Table G21-8. Forces in the Moment Frame on Grid Line 1 under East–West Load Including P-Delta

Beams Supports level quantity R 8 7 6 5 4 3 2

Bay D1–E1

Columns

Bay E1–F1

M (in-k)

V (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

833 2,119 2,903 4,018 4,634 5,004 5,363 4,627

4.8 12.3 16.9 23.4 27.0 29.1 31.2 26.9

871 2,317 3,092 4,319 5,071 5,471 5,939 5,275

4.9 12.9 17.5 24.3 28.5 30.8 33.4 29.5

0.1 0.7 1.3 2.2 3.7 5.5 7.7 10.3

1,627 2,250 3,806 4,499 4,996 5,846 6,203 6,812

22.0 32.9 49.7 59.1 66.0 73.3 75.1 55.9

4.9 17.8 35.2 59.6 88.1 118.9 152.3 181.8

719 1,230 1,943 2,335 2,693 3,222 3,497 5,426

10.6 18.6 25.1 30.8 35.1 38.6 39.8 38.8

Table G21-9. Forces in the Moment Frame on Grid Line A under North–South Load Including P-Delta Beams

Columns

Bay A2–A3

Bay A3–A4

Support level

M (in-k)

V (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

R 8 7 6 5 4 3 2

463 728 836 1,207 1,716 2,519 3,662 3,280

4.1 6.4 7.5 10.8 15.3 22.6 32.9 29.5

396 581 641 934 1,427 2,141 3,304 3,019

2.2 3.3 3.7 5.3 8.0 12.1 18.6 16.8

1.9 5.0 8.8 14.2 21.4 31.9 46.3 59.0

708 540 1,198 1,426 2,141 3,550 3,802 3,664

10.2 7.5 14.0 15.6 25.3 40.7 48.5 34.1

2.2 5.5 9.1 14.5 22.5 34.5 53.1 69.9

336 245 565 618 1,141 1,688 1,844 2,112

4.5 3.3 6.1 6.2 12.6 17.9 23.3 18.4

cases are greater than the strong axis moments. The largest weak axis moment increases are for the east–west loading as the larger deformations result in larger weak axis moments in the columns oriented with their strong axis in the north– south direction (A-1, A-2, and B-2).

Effects of Accidental Torsion Because this system is torsionally regular, strength design and drift checks are not required to include accidental torsion. However, this structure is very close to the torsional irregularity limit in the north–south direction and many structures do have torsional irregularities, so this is an important aspect of seismic analysis. To see the effects of accidental torsion, Table G21-15 shows the drift

Seismic Loads

197

Equivalent Lateral Force Analysis

Table G21-10. Forces in CBF on Grid Lines B and C under North– South Loads Including P-Delta

Frame B Support level R 8 7 6 5 4 3 2 1

Frame C

Diagonals P (k)

Columns P (k)

Diagonals P (k)

Columns P (k)

51.3 106.7 135.6 188.0 182.3 197.7 165.9 213.1 4.4

40.1 40.1 228.1 228.1 516.1 516.1 799.3 799.3 976.4

41.0 80.4 104.2 129.0 131.3 157.8 166.7 192.1 3.1

32.1 32.1 175.5 175.5 378.3 378.3 631.0 630.9 780.1

Table G21-11. Forces in the Moment Frame on Grid Line 1 under East–West Load Not Including P-Delta Beams Bay D1–E1

Columns

Bay E1–F1

Supports level quantity

M (in-k)

V (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

R 8 7 6 5 4 3 2

775 1,951 2,615 3,558 4,022 4,255 4,522 3,913

4.5 11.3 15.2 20.7 23.4 24.8 26.3 22.7

815 2,138 2,788 3,826 4,399 4,568 5,022 4,457

4.6 11.9 15.7 21.6 24.7 26.3 28.1 24.9

0.1 0.7 1.2 2.0 3.4 4.8 6.6 8.8

1,535 2,074 3,442 3,980 4,320 4,958 5,192 5,872

20.9 30.8 45.7 53.5 59.0 64.5 65.8 50.4

4.6 16.5 32.2 53.8 78.5 104.7 132.8 157.8

692 1,133 1,775 2,086 2,341 2,738 2,915 4,697

10.3 17.8 23.7 28.7 32.4 35.1 36.1 35.8

results in the north–south direction. The first three columns show the progression of different effects. The first column represents the linear-elastic (first-order) displacements. The second column includes the second-order effects (P-delta), which are not very significant for this direction of the structure. The third column shows the combined effect of P-delta and accidental torsion. In all cases, the drifts are still below the allowable limit. Clearly in this case, the accidental torsion has a greater impact than P-delta effects. The accidental torsion effects shown do not include the amplification that would be required for any structure that is torsionally irregular. The amplification is based on the initial calculation for torsional irregularity and ranges from 1 to 3. The amplification only applies to the accidental torsional moments. Two other consequences of the accidental torsion on this structure are related to the allowed analysis procedure and the diaphragm modeling. If the structure is

Seismic Loads

198

Seismic Loads

Table G21-12. Forces in the Moment Frame on Grid Line A under North–South Load Not Including P-Delta

Beams

Columns

Bay A2–A3

Bay A3–A4

Support level

M (in-k)

V (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

P (k)

M (in-k)

V (k)

R 8 7 6 5 4 3 2

448 703 805 1,163 1,652 2,430 3,539 3,174

4.0 6.2 7.2 10.4 14.7 21.8 31.8 28.5

384 560 618 899 1,374 2,065 3,192 2,920

2.1 3.2 3.5 5.1 7.7 11.7 17.9 16.3

1.8] 4.9 8.5 13.7 20.7 30.9 44.8 57.1

683 523 1,154 1,378 2,063 3,433 3,670 3,568

10.1 7.7 14.1 15.8 25.4 40.2 47.8 34.0

2.1 5.3 8.8 14.0 21.7 33.4 51.3 67.5

325 236 546 598 1,099 1,634 1,780 2,060

4.5 3.6 6.4 6.6 12.9 18.0 23.2 18.5

Table G21-13. Forces in CBF on Grid Lines B and C under North– South Loads Not Including P-Delta Frame B Support level R 8 7 6 5 4 3 2 1

Frame C

Diagonals P (k)

Columns P (k)

Diagonals P (k)

Columns P (k)

50.0 103.2 130.5 180.9 175.1 191.0 160.4 207.9 4.3

39.0 39.0 220.1 220.1 496.9 496.6 770.4 770.4 942.4

40.0 77.8 100.2 124.1 126.0 152.7 160.9 186.9 3.0

31.3 31.3 169.5 169.5 364.0 364.0 608.1 608.1 753.2

torsionally irregular, the rigid diaphragm idealization would not be allowed, requiring semirigid diaphragm models. In addition, a structure having a horizontal irregularity would need to be analyzed with either modal response spectrum or linear response history because the ELF method is not allowed in this case.

21.2 Two-Stage ELF Procedure According to Section 12.2.3.2 Section 12.2.3.2 allows the use of a two-stage equivalent lateral force analysis for structures that have a ﬂexible upper portion over a rigid lower portion, provided the following two criteria are met:

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Equivalent Lateral Force Analysis

Table G21-14a. Forces in Selected Columns from Unidirectional Loading Including P-Delta

East–west load

Member A-1 A-2 B-1 B-2

North–south load

Axial force (k)

Strong axis moment (in-k)

Weak axis moment (in-k)

Axial force (k)

Strong axis moment (in-k)

Weak axis moment (in-k)

0.0 0.0 182 0

3 3 5,429 1

1,529 2,414 0 1,200

70.0 59.0 0.1 799.3

2,114 3,665 79 1,007

38 13 625 18

Table G21-14b. Forces in Selected Columns Combined for Orthogonal Load Effects Including P-Delta 1.0 East–west load + 0.3 north–south load

0.3 East–west load + 1.0 north–south load

Member

Axial force (k)

Strong axis moment (in-k)

Weak axis moment (in-k)

Axial force (k)

Strong axis moment (in-k)

Weak axis moment (in-k)

A-1 A-2 B-1 B-2

21.0 17.7 182.1 239.7

637 1,097 5,406 301

1,518 2,410 187 1,195

70.0 59.0 54.7 799.3

2,116 3,664 1,549 1,007

421 710 624 342

Table G21-15. Frame Line G Drifts in the North–South Direction

Level R 8 7 6 5 4 3 2

δN-S (linear) (in.)

δN-S (with P-δ) (in.)

δN-S (with P-δ and AT) (in.)

δx (in.)

Δ (in.)

Δ Limit (in.)

Ratio

1.99 1.70 1.38 1.07 0.79 0.53 0.33 0.15

2.06 1.76 1.43 1.11 0.82 0.54 0.34 0.16

2.51 2.14 1.74 1.35 0.99 0.65 0.41 0.19

11.04 9.42 7.66 5.94 4.36 2.86 1.80 0.84

1.6 1.8 1.7 1.6 1.5 1.1 1.0 0.8

2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.7

0.72 0.78 0.76 0.70 0.66 0.47 0.43 0.31

Notes: T = Tcomputed, P-delta and accidental torsion (AT) included. Story drift Δ is in story below level indicated.

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•

The stiffness of the lower portion must be at least 10 times the stiffness of the upper portion, and The period of the entire structure shall not be greater than 1.1 times the period of the upper portion considered as a separate structure supported at the transition from the upper to the lower portion.

When the criteria are met, the upper portion is analyzed as a separate structure using the appropriate values of R and ρ for the upper portion, and the lower portion is designed as a separate structure using R and ρ for the lower portion. When analyzing the lower portion, the reactions from the upper portion must be applied as lateral loads at the top of the lower portion, and these reactions must be amplified by the ratio of the R/ρ of the upper portion to the R/ρ of the lower part of the lower portion. This amplification factor must not be less than 1.0. Also, although the upper portion can be analyzed with either ELF or modal response spectrum procedures, the bottom portion can only be analyzed with the ELF procedure. See question A16 of Chapter 30 of this guide for an explanation of why MRS analysis is not allowed for the lower portion. The procedure is illustrated for the structure shown in Figure G21-3. The base of the system is an ordinary precast shear wall (R = 3), and the upper portion is an ordinary concentrically braced steel frame (R = 3.25). The structure is assigned to SDC B and thus has ρ = 1 (Section 12.3.4.1). The seismic weights at each level are shown in Figure G21-3. The structure is situated on Site Class B soils, and SDS = 0.25g, and SD1 = 0.072g. Using these parameters TS = 0.072/0.25 = 0.288 s. The system was analyzed using SAP2000 (CSI 2019), wherein the precast walls were modeled with shell elements. The stiffness of the upper portion was determined by fixing it at its base (transition from the upper to the lower portion) and applying a 100 kip lateral load at the top. The displacement at the top was 0.607 in.; thus, the stiffness is approximately 100/0.607 = 165 kips/in. The stiffness of the lower portion was found by removing the upper portion and

Figure G21-3. Building with stiff base and ﬂexible upper portion.

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Equivalent Lateral Force Analysis

applying a 100 kip lateral force at the top of the lower portion. The displacement at the top of the lower portion was 0.0146 in., and the stiffness is 100/0.0146 = 6,872 kips/in. The ratio of the stiffness of the lower portion to the upper portion is 6,872/165 = 41.6, so the first criterion is met. The periods of vibration were computed as follows: T for the whole system = 0.396 s, and T for the upper system fixed at the transition from the upper to the lower portion = 0.367 s. The ratio of the period of the entire structure to the period of the upper portion = 0.396/0.367 = 1.079, so the second criterion is met. Because both criteria are met, the structure may be analyzed using the two-stage ELF method. The periods of vibration used to determine the period ratios must be determined using a rational analysis and not the approximate formulas provided by Section 12.8.2. In addition, the stiffness of a structure of several degrees of freedom does not have a unique definition. The approach used previously (wherein a 100 kip load was applied) is only one of several reasonable approaches that might be used. The equivalent lateral forces for the upper and lower portions of the structure are shown in Figure G21-4. The forces for the upper portion are determined using W = 450 kips, T = 0.367 s, and k = 1.0. The approximate formula for period (including the CuTa limit) is 1.7(0.02 × 450.75) = 0.591 s. This result is greater than the computed period (T = 0.367 s), so the computed period was used. For flexible upper portion: Cs = 0.072/(0.367 × 3.25) = 0.0604 > 0.044(0.25) = 0.011 W = 3(150) = 450 kips

Figure G21-4. Results of the two-stage ELF analysis.

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Table G21-16. Traditional ELF Analysis for 5-Story Building Level

H (ft)

W (kips)

R 5 4 3 2 Sum

15 15 15 15 15

75 60 45 30 15

150 150 150 500 500 1,450

Whk 11,250 9,000 6,750 15,000 7,500 49,500

Whk/sum

F (kips)

0.227 0.182 0.136 0.303 0.152 1.0

18.4 14.7 11.1 24.6 12.3 81.1

Figure G21-5. Lateral forces using regular ELF analysis. V = 0.0604(450) = 27.2 kips Using k = 1, F (from top) = 13.6, 9.1, 4.5 kips These values need to be multiplied by (3.25/3.0) = 1.083 before being transferred to the lower portion. For stiff lower portion: Cs = 0.25/(3.0) = 0.083 > 0.044(0.25) = 0.011 W = 2(500) = 1,000 kips V = 0.083(1,000) = 83 kips Using k = 1, F (from top) = 55.3, 27.7 kips When checking drift, the Cd values appropriate for the upper or lower portion should be used. The drift check is not shown herein. The analysis is now repeated for the system analyzed as a whole using ELF. Recall that T for the full system (using Tcomputed) is 0.396 s.

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Equivalent Lateral Force Analysis

Cs = 0.072/(0.396 × 3.25) = 0.0559 > 0.044(0.25) = 0.011 W = 3(150) + 2(500) =1,450 kips V = 0.0559(1,450) = 81.1 kips Using k = 1 F (from top) =18.4, 14.7, 11.1, 24.6, 12.3 kips (Table G21-13) These values for the upper three levels need to be multiplied by (3.25/3.0) = 1.083 before being transferred to the lower portion. Similarly, the forces 24.6 kips and 12.3 kips for the lower two levels need to be multiplied by 1.083, producing 26.6 kips and 13.3 kips at the second and ﬁrst levels above grade, respectively. The results for the ELF analysis of the full system are shown in Table G21-16 and Figure G21-5. Note that the lateral forces in the upper portion are signiﬁcantly greater than for the two-stage analysis. This is as expected because the whole point of the two-stage analysis is to compensate for the ELF method inappropriately drawing mass from the bottom of the system to the top.

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22 Modal Response Spectrum Analysis

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • •

•

Section 12.9 was renamed “Linear Dynamic Analysis,” and contains “Modal Response Spectrum Analysis” (Section 12.9.1) and “Linear Response History Analysis” (Section 12.9.2). Analysis must be performed in three dimensions. A sufﬁcient number of modes to capture 100% of the effective mass in each direction are required, relative to the minimum of 90% of the effective mass in ASCE 7-10. It is allowed to use rigid body modes to accommodate the 100% requirement. However, an exception allows the continued use of 90% effective mass as required in ASCE 7-10. The force results determined from the MRS analysis must be scaled such that the MRS base shear in each direction is not less than 100% of the ELF base shear. This is an increase over the 85% of ELF base shear scaling requirement in ASCE 7-10. If it is required to scale displacements, the basis of the scale factor is also increased from 85% to 100%.

In this chapter, the same 8-story building that was analyzed in Chapter 21 using the equivalent lateral force procedure is reanalyzed using the modal response spectrum procedure provided in Section 12.9.1 of the standard. Various steps in the analysis are described, and selected results are presented. In Chapter 24 of the guide, these results are compared to those obtained using the ELF and linear response history methods.

205

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206

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22.1 Overview The 8-story building analyzed in this example is described in detail in Appendix B, and the equivalent lateral force analysis for the building is presented in Chapter 21. For convenience, the plan and elevation of the building is repeated in Figure G22-1. The building is situated on Site Class C soils and is in Risk Category III. The importance factor Ie = 1.25. In the east–west direction, the structural system consists of four bays of special steel moment-resisting frames on Grid lines 1 and 4. In the north–south direction, a dual system is used, with special steel concentrically braced frames on Grid lines B, C, E, and F, and three bays of special steel moment frames on Grids A and G. The dual system has been proportioned such that the moment frames are capable of resisting at least 25% of the ELF base shear. The system parameters from Table 12.2-1 are as follows:

Figure G22-1. Plan and elevation of the 8-story building.

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Modal Response Spectrum Analysis

For the east–west direction: Special steel moment frames R = 8 For the north–south direction: Dual system R=7

Ω0 = 3.0

C d = 5.5

Ω0 = 2.5

C d = 5.5

The pertinent ground motion parameters are S DS = 0.715g S D1 = 0.405g T L = 16.0 s T s = SD1 =SDS = 0.566 s The ELF base shears were computed in Chapter 21, and are as follows: For the east–west direction V = 558 kips [controlled by Equation (12.8-3) using T = CuTa = 1.592 s] For the north–south direction V = 1,124 kips [controlled by Equation (12.5-3) using T = CuTa = 0.902 s] These shears will be used as the basis for scaling the member forces to 100% of the ELF base shear as required in Section 12.9.1.4.1. Scaling of drifts is not required because, as stipulated in Section 12.9.1.4.2, Equation (12.8-6) did not control the base shear in either direction. The beam, column, and brace sizes for the main lateral force resisting system are shown in Figures GB-8 through GB-11.

22.2 Response Spectrum Used for Analysis The 5% damped elastic response spectrum used for the MRS analysis was determined in accordance with Section 11.4.6 and is shown graphically in Figure G22-2. This elastic spectrum does not incorporate the terms R or Cd.

Figure G22-2. Response spectrum used for the MRS analysis.

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These factors are applied the to results of the MRS analysis in accordance with Section 12.9.1.2.

22.3 System Modeling As required in Section 12.9.1.8, the system is modeled in three dimensions. The diaphragms were modeled as semirigid, although the diaphragm could have been classified as rigid in accordance with Section 12.3.1.2. This was done because of the dual system, which causes a large transfer of forces through the diaphragms. P-delta effects were incorporated directly into the model using the full dead load and 50% of the live load. Accurate modeling of 3D P-delta effects required that all of the gravity columns be explicitly modeled. This was not a significant analysis burden because all of the columns except for those on grid intersections D-2 and D-3 are part of the lateral load resisting system, and only the tiers of columns on those grid intersections were added. These columns were modeled such that they resisted axial force only, and thereby do not resist lateral forces. As discussed in guide Chapter 21, the system is not torsionally irregular; thus, in accordance with Section 12.8.4.2, accidental torsion was not included in the analysis. However, drifts were recorded at the edge of the building and at the center of mass. Because the system has negligible inherent torsional response, the drifts at the edge of the building are nearly identical to the center of mass values. Orthogonal load effects were included in the analysis by combining 100% of the results in one direction with 30% of the results in the orthogonal direction. This combination, used also in the ELF analysis presented in Chapter 21, will have very little influence on the results and is not required by Section 12.5.4, because there are no components that simultaneously develop axial forces from both directions of loading. The orthogonal loading was included for consistency with the linear response history procedure that is presented in Chapter 23 of this guide. In addition, the influence of orthogonal loading was investigated by use of the ELF procedure in Chapter 21 of the guide.

22.4 Modal Properties The modal properties for the structure are shown in Table G22-1a for modeling without P-delta effects, and in Table G22-2b for modeling with P-delta effects. As expected, P-delta effects have a greater influence on the more flexible east– west response than on the north–south response. Also, it is observed that the computed first mode periods are significantly greater than calculated using CuTa. This issue is discussed in more length later in the chapter. Mode shapes for the first six modes are presented in Figure G22-3 for the system analyzed without P-delta effects. Shapes for the system modeled with P-delta effects are virtually identical.

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Modal Response Spectrum Analysis

Table G22-1a. Modal Properties Excluding P-delta Effects

Mode 1 2 3 4 5 6 7 8 9 10 11 12 18

Modal mass (%)

Accumulated modal mass (%)

Period (s)

E–W

N–S

Rotation

E–W

N–S

Rotation

2.718 1.420 1.301 0.964 0.537 0.389 0.381 0.346 0.245 0.209 0.198 0.184 0.115

0.7968 0 0 0.1122 0.0452 0 0 0.0218 0.0119 0 0 0.0669 0

0 0.7194 0.008 0 0 0.0078 0.1929 0 0 0.0004 0.0475 0 0.0093

0 0.0008 0.7168 0 0 0.1892 0.0075 0 0 0.0494 0.0004 0 0.0026

0.7968 0.7968 0.7968 0.9090 0.9542 0.9542 0.9542 0.9760 0.9879 0.9879 0.9879 0.9948 1.0000

0 0.7194 0.7202 0.7202 0.7202 0.7279 0.9208 0.9208 0.9208 0.9212 0.9687 0.9687 0.9954

0 0.0008 0.7176 0.7176 0.7176 0.9008 0.9142 0.9142 0.9142 0.9636 0.9643 0.9543 0.9824

Note: Bold indicates mode where 90% of mass is captured.

Table G22-1b. Modal Properties Including P-delta Effects

Mode 1 2 3 4 5 6 7 8 9 10 11 12 18

Modal mass (%)

Accumulated modal mass (%)

Period (s)

E–W

N–S

Rotation

E–W

N–S

Rotation

2.927 1.446 1.324 1.015 0.560 0.393 0.383 0.359 0.252 0.211 0.200 0.188 0.116

0. 8024 0 0 0.1082 0.0441 0 0 0.0215 0.0118 0 0 0.0068 0

0 0.7190 0.0008 0 0 0.0071 0.1942 0 0 0.0003 0.0474 0 0.0093

0 0.0008 0.7164 0 0 0.1906 0.0068 0 0 0.0494 0.0004 0 0.0025

0.8024 0.8024 0.8024 0.9107 0.9548 0.9548 0.9548 0.9763 0.9881 0.9881 0.9881 0.9949 1.0000

0 0.7190 0.7198 0.7198 0.7198 0.7269 0.9211 0.9211 0.9211 0.9215 0.9689 0.9689 0.9955

0 0.0008 0.7172 0.7172 0.7172 0.9077 0.9146 0.9146 0.9146 0.9639 0.9643 0.9643 0.9824

Note: Bold indicates mode where 90% of mass is captured.

22.5 Number of Modes to Include in the Analysis and Modal Combination Procedure Section 12.9.1.1 requires that sufﬁcient modes be included to capture 100% of the effective seismic mass. Where the number of modes that are required to capture this mass is excessive, it is allowed to capture the higher mode responses in a single “rigid body mode.” An exception allows for capturing only 90% of the

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Figure G22-3. Mode shapes for the ﬁrst six modes. effective mass, which was the requirement in ASCE 7-10. See question A18 in Chapter 30 of this guide for discussion on the use of rigid body modes. Tables G22-1 and G22-2 show that only seven modes are required to capture at least 90% of the translational mass. The use of 12 modes captures almost 100% of the mass in the east–west direction and 97% of the mass in the north–south direction. If the number of modes is increased to 18 (the last row in the tables), nearly 100% of the mass is included in each translational direction. The period associated with the 18th mode, approximately 0.115 s, is slightly greater than T0 = 0.2Ts = 0.113 s. Thus, as Figure G22-2 shows, all of the spectral ordinates used in the analysis are in the constant acceleration region or in the constant velocity portion of the spectrum. Based on these observations, it was decided to use 18 modes in the analysis. The response spectrum shown in Figure G22-2 shows dots that represent the spectral ordinates for east–west and north–south loading. Note that no dots are provided for torsional periods because there is no seismic input in torsion.

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Modal Response Spectrum Analysis

As allowed by Section 12.9.1.3, the individual modal responses were combined using the complete quadratic combination (CQC) method, with 5% damping speciﬁed in each mode.

22.6 Initial Scaling of Results (Determining Modal Response Parameters) Section 12.9.1.2 provides requirements for initial scaling of the results of the MRS analysis. This scaling is required because the MRS results are based on the elastic spectrum, which does not yet include the factors R, Cd, or Ie. To apply the scaling, all MRS results (forces and displacements) are multiplied by Ie/R. Next, the displacements, already multiplied by Ie/R, are multiplied by Cd/Ie. An alternative approach for displacements would be to simply take the displacements directly from the MRS analysis and multiply by the factor (Ie/R)(Cd/Ie) = Cd/R. Note that this scaling must be applied independently in each orthogonal direction where different R and Cd values are used in the different directions.

22.7 Analysis Results Section 12.9.1.4 provides the requirements for the scaling of MRS results for design. Recall that for ELF analysis, the period used to determine the design base shear is based on a period that is limited to CuTa. These periods are as follows for the system under consideration: For the east–west direction CuTa = 1.592 s For the north–south direction CuTa = 0.902 s The modal response spectrum analysis uses the periods determined from the eigenvalue analysis. These periods, from Table G22-1 (not including P-delta effects) are as follows: For the east–west direction Tcomputed = 2.718 s For the north–south direction Tcomputed = 1.420 s Thus, the east–west force results from the MRS analysis will be approximately 1.592/2.718 = 0.59 times the ELF values. The north–south forces from the MRS analysis will be approximately 0.902/1.420 = 0.64 times the ELF values. The purpose of the scaling requirements in Section 12.9.1.4.1 is to eliminate this discrepancy by scaling the results of the MRS analysis (already adjusted by R and Ie as appropriate) such that the base shear from the MRS and ELF analyses are identical. When the ELF base shear is controlled by Equation (12.8-5), Section 12.8.6.1 stipulates that lateral forces used for computing drift can be based on a new set

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of lateral forces based on Equations (12.8-1) and (12.8-3). [Note that Equation (12.8-3) is not directly mentioned, but this will almost certainly be the controlling equation in SDC C through F]. However, if Equation (12.8-6) controls the base shear, forces determined using that equation must be used to compute drift. The requirements in Section 12.9.1.4.2 for scaling MRS displacements [scale only if Equation (12.8-6) controls the base shear], provide consistency with Section 12.8.6.1. For this example, Equation (12.8-6) does not control the base shear, so scaling of displacements is not required. For cases in which Equation (12.8-6) does not control the base shear, it is important to note that the MRS displacements are computed using periods from the eigenvalue analysis, which as shown previously are signiﬁcantly greater than those determined using T = CuTa. An approximation of the ratio of stiffness of system based on CuTa to that using Tcomputed is given as K Cu T a T computed 2 ≈ (G22-1) K computed T Cu T a Using Equation (G22-1), the stiffness ratio in the east–west direction is (2.718/ 1.592)2 = 2.91, and the ratio in the north–south direction is (1.420/0.902)2 = 2.48. In the opinion of the authors, these stiffness ratios are very difﬁcult to justify. The problem is not with the CuTa period, which is based on a regression analysis from actual system measurements, but with Tcomputed which is based on an analytical model that includes only the main lateral structural system and does not include the out-of plane stiffness of the diaphragms (providing some composite behavior for all the beams), the gravity columns (which in this case are a minor contribution), or the nonstructural components. The structural analysis program ETABS provides the displacements at any desired location at each level of the building and provides the story drifts at the center of mass. Results for the analysis performed in the east–west direction are provided in Table G22-2a through G22-c. In Table G22-2a, east–west MRS displacements including P-delta effects are provided at each level of the building, aligned along Grid line 1. The values in Column 2 of Table G22-2a are the displacements taken directly from the analysis. In Column 3 these values have been multiplied by Cd/R, and these are the inelastic displacements. In modal response spectrum analysis, it is not technically correct to determine story drifts from the CQC displacements. Instead, the drifts should be determined for each mode, and then combined using CQC. However, it is instructive to determine drifts using the displacements, and these are shown in Column 4. The story drift ratios, shown in Column 5, are the story drifts divided by the story height. Column 6 shows the limiting story drift ratio as a fraction of the applicable story height, hsx. This is determined from Table 12.12-1 for Risk Category III buildings. As may be observed, the story drifts are less than the limiting value. In Table G22-2b, the story drifts determined for east–west loading, including P-delta effects, are provided. These are the CQC’d drifts determined at the center of mass. Column 2 of the table provides the elastic story drift ratios, and Column 3 gives these values multiplied by Cd/R. These values are not the same as

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Modal Response Spectrum Analysis

Table G22-2a. Frame Line 1 Displacements and Drifts for East–West Loading Including P-delta

Level R 8 7 6 5 4 3 2

Δelastic (in.)

Δelastic times (Cd/R) (in.)

Story drift* (in.)

Story drift ratio

Story drift ratio limit

15.70 14.34 12.64 10.85 8.87 6.66 4.32 1.96

10.79 9.86 8.69 7.46 6.10 4.58 2.97 1.35

0.935 1.169 1.231 1.361 1.519 1.609 1.623 1.348

0.0062 0.0078 0.0082 0.0091 0.0101 0.0107 0.0108 0.0075

0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150

* In story below indicated level.

Table G22-2b. Center of Mass Drifts for East–West Loading Including P-delta

Story 8 7 6 5 4 3 2 1

Elastic story drift ratio

Story drift ratio = elastic drift ratio times (Cd/R)

Story drift ratio limit

0.0124 0.0141 0.0137 0.0144 0.0156 0.0159 0.0159 0.011

0.0085 0.0097 0.0094 0.0099 0.0107 0.0109 0.0109 0.0076

0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150

Table G22-2c. Center of Mass Drifts for East–West Loading Not Including P-delta

Story 8 7 6 5 4 3 2 1

Elastic story drift ratio

Story drift ratio = elastic drift ratio times (Cd/R)

Story drift ratio limit

0.0124 0.0138 0.0132 0.0137 0.0144 0.0145 0.0144 0.0101

0.0085 0.0095 0.0091 0.0094 0.0099 0.0100 0.0099 0.0069

0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150

shown in Column 5 of Table G22-2a because of the technical incorrectness of the Table G22-2a story drift values. Regardless, all story drifts are less than the 0.015 hsx limit.

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Table G22-3a. Frame Line A Displacements and Drifts for N–S Loading Including P-delta

Level R 8 7 6 5 4 3 2

Δelastic (in.)

Δelastic times (Cd/R) (in.)

Story drift* (in.)

Story drift ratio

Story drift ratio limit

8.44 7.18 5.85 4.55 3.40 2.29 1.47 0.70

6.63 5.64 4.59 3.58 2.67 1.80 1.15 0.55

0.986 1.047 1.018 0.907 0.869 0.648 0.600 0.553

0.0066 0.0070 0.0068 0.0060 0.0058 0.0043 0.0040 0.0031

0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150

* In story below indicated level.

Table G22-3b. Center of Mass Drifts for N–S Loading Including P-delta

Story 8 7 6 5 4 3 2 1

Elastic story drift ratio

Story drift ratio = elastic drift ratio times (Cd/R)

Story drift ratio limit

0.00877 0.00929 0.00902 0.00791 0.00758 0.00564 0.00533 0.00391

0.0069 0.0073 0.0071 0.0062 0.0060 0.0044 0.0042 0.0031

0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150

Table G22-2c is similar to Table G22-2b, but the analysis did not include P-delta effects. Comparing the values in Column 4 of these tables shows that the drifts in the lower stories are inﬂuenced by P-delta effects. Tables G22-3 through G22-3c provide the results for the MRS analysis with loading in the north–south direction. Similar trends as occurred for east–west loading are apparent when comparing the various results. However, because of the increased stiffness of the braced frames, all displacements are well below the limiting values.

22.8 Determination of Force Results Before the element forces can be presented, it is necessary to determine the scale factors that are required to ensure that the MRS base shears in each direction are not less than ELF shears. Recall that the ELF base shears were

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Table G22-3c. Center of Mass Drifts for N–S Loading Not Including P-delta

Story 8 7 6 5 4 3 2 1

Elastic story drift ratio

Story drift ratio = elastic drift ratio times (Cd/R)

Story drift ratio limit

0.00862 0.00911 0.00884 0.00775 0.00742 0.00554 0.00523 0.00387

0.0068 0.0072 0.0069 0.0061 0.0058 0.0044 0.0041 0.0030

0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150

VELF-EW = 558 kips in the east–west (moment frame) direction VELF-NS = 1,124 kips in the north–south (dual system) direction Recall that these values include the R factors (8 and 7 in the east–west and north–south direction, respectively) and the importance factor Ie = 1.25. The base shears from the modal response spectrum analysis do not include R or Ie, and for the analysis that does not include P-delta effects the base shears were computed as VMRS-EW = 1,894 kips in the east–west (moment frame) direction VMRS-NS = 3,566 kips in the north–south (dual system) direction It is important to recognize that these shears are the total system shears and are signiﬁcantly greater than the shears carried by the elements of the designated lateral systems. For example, consider the east–west response, for which the lateral load resisting components are contained within bays B–C, C–D, D–E, and E–F on Grid lines 1 and 4. The sum of the column shears in the north–south direction for the frame in Grid line 1 is 745.5 kips, and for frames on Grid lines 1 and 4, the combined shear is 745.5 times two = 1,491 kips. This means that 1,894 − 1,491 = 403 kips, or approximately 21% of the total shear is resisted elsewhere. The source of this resistance is predominantly in weak-axis bending of the columns on Grid lines A and G. Note that this issue is further discussed in FAQ A19 in Chapter 30 of this guide. The standard does not strictly prohibit the frames on Grids A and G from resisting forces in the east–west direction. However, these columns should be designed for axial force and biaxial bending interaction, using 100% of the forces from the east–west analysis, and 30% of the forces from the north–south analysis. Of course, forces from 100% of the forces in the north–south direction combined with 30% of the forces in the east–west direction should be evaluated as well. The standard does not strictly require the orthogonal load combinations for this SDC D system because there are no components that develop axial load under simultaneous application of the east–west and north–south lateral loads.

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For the east–west direction, the MRS shear including R and Ie is 1.25(1,894)/ 8 = 296 kips, and the shear in the north–south direction is 1.25(3,556)/7 = 635 kips. Because these values are signiﬁcantly less than the ELF base shears, all force values from the MRS analysis must be scaled. If the results taken directly from the MRS analysis are used, the scale factors are as follows: SFEW = 558=1;894 = 0.2946 SFNS = 1;124=3;566 = 0.3152 Using these factors, the scaled MRS base shear in the east–west direction is 1,894(0.2946) = 558 kips, and in the north–south direction is 3,566(0.3152) = 1,124 kips. These are the desired values, so the scale factors have been determined correctly.

Table G22-4. Forces in the Moment Frame on Grid Line 1 under East–West Load Including P-delta Beams Bay D1–E1 Level R 8 7 6 5 4 3 2

Columns

Bay D1–E1

M (in.-k)

V (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

940 2,004 2,439 3,252 3,712 4,030 4,454 4,027

5.3 11.6 14.2 18.9 21.6 23.5 25.9 23.4

940 2,231 2,616 3,500 4,073 4,415 4,942 4,606

5.3 12.4 14.8 19.7 22.9 24.9 27.8 25.8

0.3 1.1 1.7 2.3 3.2 4.4 6.1 8.1

1,916 2,231 3,281 3,723 4,069 4,762 5,257 6,134

24.6 30.6 41.8 48.5 53.6 60.2 64.2 51.0

5.3 17.6 31.6 49.9 70.7 93.4 118.4 141.5

1,036 1,343 1,782 2,001 2,245 2,634 2,945 4,910

13.0 17.9 21.5 25.8 28.9 32.0 34.7 35.9

Table G22-5. Forces in the Moment Frame on Grid Line A under N–S Load Including P-delta Beams Bay A2–A3 Level R 8 7 6 5 4 3 2

Columns

Bay A3–A4

M (in.-k)

V (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

424 662 745 1,052 1,468 2,137 3,136 2,886

3.7 5.8 6.7 9.4 13.1 19.2 28.2 25.9

361 526 571 813 1,222 1,816 2,829 2,655

2.0 3.0 3.3 4.6 6.9 10.2 15.9 14.8

1.7 4.6 7.9 12.6 18.7 27.4 39.3 49.9

643 495 1,104 1,237 1,838 3,018 3,260 3,340

9.3 6.8 12.6 13.4 21.6 34.7 41.8 31.4

2.0 4.9 8.2 12.8 19.6 29.6 45.1 59.3

305 228 541 537 983 1,434 1,573 1,929

4.1 3.1 5.5 5.3 10.8 15.3 20.0 17.0

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Scaled member forces for analysis including P-delta effects are provided in Tables G22-4 through G22-6. Forces with analysis not including P-delta effects are provided in Tables G22-7 through G22-9. Comparing Tables G22-4 and G22-7, representing forces with and without P-delta effects in Frame 1 under east–west loading, it can be seen that the forces for the analysis with P-delta effects included are somewhat larger than those without. For example, for Bay D1–E1 of Level 6, the moments and shears including P-delta effects are 3,252 in.kips and 18.9 kips, respectively. For analysis without P-delta, the corresponding values are 3,107 in.-kips and 18.1 kips. This represents approximately a 5% increase where P-delta effects are included, relative to analysis without P-delta. As stated previously in the chapter, the columns at the lower levels of Frame A carry considerable weak-axis bending when loads are applied in the east–west direction. Similarly, columns in Frame 1 develop weak-axis moments when

Table G22-6. Axial Forces in CBF on Grid Lines B and C under N–S Load Including P-delta Frame B Story 8 7 6 5 4 3 2 1 B

Frame C

Diagonals P (k)

Columns P (k)

Diagonals P (k)

Columns P (k)

71 119 128 165 157 175 169 213 4.38

55.2 55.5 241.1 241.1 461.8 461.8 672.6 672.6 822.7

60 92 101 113 113 139 168 195 3.14

47.0 47.0 192.3 192.3 341.0 341.0 517.6 517.6 653.7

Table G22-7. Forces in the Moment Frame on Grid Line 1 under East–West Load Not Including P-delta Beams Bay D1–E1 Level R 8 7 6 5 4 3 2

Columns

Bay D1–E1

M (in.-k)

V (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

870 1,990 2,376 3,107 3,468 3,698 4,051 3,680

5.0 11.5 13.8 18.1 20.2 21.5 23.6 22.2

944 2,220 2,549 3,351 3,804 4,048 4,493 4,207

5.3 12.3 14.4 18.9 21.4 22.8 25.3 23.5

0.3 1.1 1.6 2.2 3.1 4.2 5.6 7.5

1,930 2,210 3,203 3,546 3,786 4,352 4,751 6,070

26.3 30.8 41.5 47.3 51.5 57.2 61.2 55.5

5.3 16.8 31.2 48.6 68.1 88.7 111.4 132.3

1,050 1,336 1,750 1,927 2,096 2,411 2,651 4,589

13.4 18.3 21.9 25.8 28.5 31.4 33.9 35.6

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Table G22-8. Forces in the Moment Frame on Grid Line A under N–S Load Not Including P-delta Beams

Bay A2–A3 Level

Columns

Bay A3–A4

M (in.-k)

V (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

P (k)

M (in.-k)

V (k)

416 651 734 1,033 1,437 2,095 3,083 2,841

3.7 5.7 6.5 9.2 12.8 18.8 27.5 25.5

356 514 560 798 1,195 1,782 2,776 2,610

2.0 2.9 3.2 4.5 6.7 10.1 15.6 14.5

1.7 4.5 7.8 12.4 18.4 26.9 38.6 49.1

632 488 1,086 1,214 1,800 2,965 3,200 3,306

9.4 7.1 13.0 13.8 22.0 34.7 41.9 31.7

2.0 4.9 8.0 12.6 19.2 29.0 44.2 58.2

300 225 530 532 965 1,411 1,547 1,914

4.2 3.3 5.9 5.8 11.2 15.6 20.3 17.3

R 8 7 6 5 4 3 2

Table G22-9. Forces in CBF on Grid Lines B and C under North–South Load Not Including P-delta Frame B Story

Frame C

Diagonals P (k)

Columns P (k)

Diagonals P (k)

Columns P (k)

70 117 125 161 154 172 166 210 4.38

54.8 54.8 237.3 237.0 452.0 452.0 659.4 659.4 807.2

60 91 99 111 111 137 165 192 3.13

46.6 46.6 189.1 189.1 333.8 333.5 515.7 515.7 641.4

8 7 6 5 4 3 2 1 B

Table G22-10a. Forces in Selected Columns from Unidirectional Elastic MRS Analysis Including P-delta E–W load

N–S load

Member

Axial force (k)

Strong axis moment (in.-k)

Weak axis moment (in.-k)

Axial force (k)

Strong axis moment (in.-k)

Weak axis moment (in.-k)

A-1 A-2 B-1 B-2

0 0 480.3 27.5

18 10 16,656 20,844

4,728 7,452 0 0

188 158 4.7 0.4

6,120 10,596 305 284

11 4 155 168

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Table G22-10b. Forces in Selected Columns from Unidirectional Elastic MRS Analysis Scaled to ELF Shear Including P-delta

E–W load (SF = 0.2946)

N–S load (SF = 0.3152)

Member

Axial force (k)

Strong axis moment (in.-k)

Weak axis moment (in.-k)

Axial force (k)

Strong axis moment (in.-k)

Weak axis moment (in.-k)

A-1 A-2 B-1 B-2

0.0 0.0 141.5 8.1

5 3 4,907 6,141

1,393 2,195 0 0

59.3 49.8 1.5 0.1

1,929 3,340 96 90

3 1 49 53

Note: SF = Scale Factor.

Table G22-10c. Forces in Selected Columns Combined for Orthogonal Load Effects Including P-delta 1.0 E–W load + 0.3 N–S load

0.3 E–W load + 1.0 N–S load

Member

Axial force (k)

Strong axis moment (in.-k)

Weak axis moment (in.-k)

Axial force (k)

Strong axis moment (in.-k)

Weak axis moment (in.-k)

A-1 A-2 B-1 B-2

17.8 14.9 141.9 8.1

584 1,005 4,936 6,168

1,394 2,196 15 16

59.3 49.8 43.9 2.6

1,931 3,341 1,568 1,932

421 660 49 53

loads are applied in the north–south direction. These columns must be designed to accommodate both strong axis and weak-axis moments. Although the standard does not require orthogonal loading for this structure, it is advised to combine the results from the east–west and north–south analyses using the 100%/30% combination stipulated in subparagraph a of Section 12.5.3.1. This approach was taken for this structure, with the results for four columns presented in Table G22-10a−c. Table G22-10a shows the unscaled results taken directly from the analysis, Table G22-10b applies the appropriate scale factors to these values, and Table G22-10c provides the combined responses. The weak-axis moments are shown to be signiﬁcant, and the 100%/30% combination forces the columns to be designed for a small but signiﬁcant amount of biaxial bending.

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23 Linear Response History Analysis

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • • • • •

Linear response history analysis was removed from Chapter 16 of ASCE 7-10 and moved to Section 12.9.2 of ASCE 7-16. The procedure provided in ASCE 7-16 is a complete revision of the ASCE 7-10 procedures. Although not speciﬁcally required, it is expected that the LRH analysis will be performed using modal superposition. It is required that the mathematical model be developed in three dimensions, that P-delta effects be explicitly included, and that orthogonal load effects be included. It is required to use not less than three sets of spectrally matched ground motions in the analysis. The number of modes to use in the analysis and the scaling of the force and displacement results are essentially the same as required for the ASCE 7-16 MRS analysis but note that the details have changed relative to ASCE 7-10.

In this chapter, the same 8-story building that was analyzed in Chapter 21 using the equivalent lateral force procedure, and in Chapter 22 using the modal response spectrum procedure, is reanalyzed using linear response history analysis. The LRH analysis requirements are provided in Section 12.9.2 of the standard. Various steps in the analysis are described, and selected results are presented. In Chapter 24 of the guide, these results are compared to those obtained using the ELF and MRS methods.

221

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23.1 Overview

The 8-story building analyzed in this example is described in detail in Appendix B. For convenience, the plan and elevation of the building is provided in Figure G23-1. The building is situated on Site Class C soils and is assigned Risk Category III. The importance factor Ie is 1.25. In the east–west direction the structural system consists of four bays of special steel moment-resisting frames on

Figure G23-1. Plan and elevation of eight-story building.

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Grid lines 1 and 4. In the north–south direction a dual system is used, with special steel concentrically braced frames on Grid lines B, C, E, and F, and three bays of special steel moment frames on Grid lines A and G. The dual system has been proportioned such that the moment frames are capable of resisting at least 25% of the ELF base shear. The system parameters from Table 12.2-1 are as follows: For the east–west direction: Special steel moment frames R = 8

Ω0 = 3.0

C d = 5.5

For the north–south direction: Dual system

Ω0 = 2.5

C d = 5.5

R=7

Preliminary calculations indicate that the system is not torsionally irregular, thus accidental torsion need not be included in the analysis. The redundancy factor ρ has been determined as 1.0. See Appendix B and Chapter 21 of this guide for details. The pertinent ground motion parameters are the following: S DS = 0.715g S D1 = 0.405g T L = 16.0 s T s = SD1 =SDS = 0.566 s The ELF base shears were computed in Chapter 21 and are as follows: For the east–west direction V = 558 kips [controlled by Equation (12.8-3) using T = CuTa = 1.592 s] For the north–south direction V = 1,124 kips [controlled by Equation (12.5-3) using T = CuTa = 0.902 s] These shears were used as the basis for scaling the member forces to 100% of the ELF base shear as required in Section 12.9.2.5. Scaling of drifts was not required because, as stipulated in the exception in Section 12.9.2.5.4, Equation (12.8-6) did not control the design base shear in either direction. The beam, column, and brace sizes for the main lateral force resisting system are shown in Figures GB-8 through GB-11.

23.2 Response Spectrum Used for Analysis The 5% damped elastic response spectrum used for the LRH analysis is the same as used for MRS analysis and is shown graphically in Figure G23-2. This spectrum was used as the target for spectrum matching as described subsequently in this chapter. Note that this elastic spectrum does not incorporate the terms Ie, R, or Cd. These factors are applied to the results of the LRH analysis in accordance with Section 12.9.2.5.

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Figure G23-2. Response spectrum used for MRS analysis.

23.3 System Modeling As required in Section 12.9.2.2, the system is modeled in three-dimensions. The diaphragms were modeled as semirigid, although it could have been classiﬁed as rigid in accordance with Section 12.3.1.2. This was done because of the dual system, which causes a large transfer of forces through the diaphragms. P-delta effects are required in LRH analysis according to Section 12.9.2.2.1 of the standard and were incorporated directly into the model using the full dead load and 50% of the live load. Accurate modeling of 3D P-delta effects required that all of the gravity columns be explicitly modeled. This was not a signiﬁcant analysis burden because all of the columns except for those on grid intersections D-2 and D-3 were part of the lateral load resisting system, and only the tiers of columns on those grid intersections were added. These gravity columns were modeled such that they resisted axial force only, and thereby do not resist lateral forces. Orthogonal load effects were included, as required by Section 12.9.2.5.4, by direct addition of the scaled response histories in the two orthogonal directions. In accordance with Section 12.9.2.5.4, design values are taken as the envelope of the values obtained from the three ground motions. (Note that Section 12.5.3.1 of the standard indicates that a 100% in one direction, 30% in orthogonal direction combination may be used for LRH analysis. This is an error, and 100% of the north–south component and 100% of the east–west component should be applied in the orthogonal directions.) A damping ratio of 5% of critical damping was used for each mode included in the analysis. This is consistent with the damping used to develop the target spectrum.

23.4 Modal Properties The modal properties for the LRH analysis are the same as for the MRS analysis, and these properties are summarized in Chapter 22 of this guide. Table G22-1a provides the results for modeling without P-delta effects, and in Table G22-2b

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for modeling with P-delta effects. As expected, P-delta effects have a greater influence on the more flexible east–west response than on the north–south response. Also, it is observed that the computed first mode periods are significantly greater than calculated using CuTa. This issue is discussed in Chapter 22. Mode shapes for the first six modes are presented in Figure G22-3 for the system analyzed without P-delta effects. Shapes for the system modeled with P-delta effects are virtually identical.

23.5 Number of Modes to Include in the Analysis and Modal Combination Procedure Section 12.9.2.2.4 refers to 12.9.1.1, which requires that sufﬁcient modes be included to capture 100% of the effective seismic mass. When the number of modes required to capture this mass is excessive, it is allowed to capture the higher mode responses in a single “rigid body mode.” An exception allows for capturing only 90% of the effective mass, which was the requirement in ASCE 7-10. See question A18 in Chapter 30 of this guide for discussion on the use of rigid body modes. As described in Chapter 22, it was decided to use 18 modes in the MRS analysis, because these are sufﬁcient to capture nearly 100% of the mass in each translational direction. The same number of modes is used in the LRH analysis.

23.6 Ground Motion Selection and Modification Section 12.9.2.3 requires that not less than three pairs (orthogonal horizontal components) of spectrally matched ground motions be used in the analysis. These can be derived from actual events or can be artificially generated. The spectral matching procedure begins with an unmodified seed record and then alters the record such that the response spectrum for the modified record closely matches the target spectrum over a specified range of periods. There are a variety of matching procedures that can be used, but the most common one uses wavelets. In this chapter, a specific implementation of this approach, incorporated into the computer program RspMatch (Abrahamson 1992, Al Atik and Abrahamson 2010) was used. RspMatch is executed within a convenient graphic user interface developed by Jayamon and Charney (2015). This interface allows three records to be imported from an available database of records, and then both components of each ground motion are matched to the target spectrum. When nonlinear response history analysis is used, it is very important that the ground motions selected for the analysis are strongly representative of the geological and seismological conditions at the site. Specific requirements are provided in Section 16.2.2. The requirements for ground motion selection for LRH analysis, provided in Section 12.9.2 3, are less detailed than for nonlinear analysis because spectrum matching tends to reduce record-to-record variability found in natural records, and because the influence of record-to-record variability on linear response is significantly less that the influence on nonlinear inelastic response. For linear analysis it is likely that a single pair of spectrally matched

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orthogonal components would sufﬁce. However, the standard requires that three sets of records be used to account for the small dependency of response on record-to-record variability. Although local geology and seismology are not particularly important in linear analysis, it valuable to understand the seismicity at the site. To this end a seismic deaggregation of the seismic hazard at the site was performed using the USGS Hazard Tool (USGS n.d.). The deaggregation is accessed as shown in Figures G23-3 and G23-4. The main result of the deaggregation is a three-dimensional graph as presented in Figure G23-5. This graph, developed for the site’s latitude and longitude (latitude 45.4974, longitude −122.7559) shows how various factors feed into the development of the peak ground acceleration (T = 0 s) ordinate of the uniform hazard spectrum for a return period of 2,475 years. Similar plots are available for other spectral periods and for other return periods. Each vertical bar in the deaggregation plot represents the percent contribution of one source to the hazard at the site. The color scale on the vertical bars is a representation of uncertainty (epsilon). The horizontal axes provide the moment magnitude (MW) of the event and the distance from the event to the site in kilometers.

Figure G23-3. Form for inputting ground motion parameters in the USGS Hazard Tool.

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Figure G23-4. Accessing the deaggregation tool.

Figure G23-5. Result for deaggregation of site using peak ground accelerations and 2,475-year return period. The graph indicates that there are several sources capable of generating events with magnitude in the range of 6.5 to 7.5 that occur at distances less than 10 km from the site. These events would be considered as near-field motions using the definition provided in Section 11.4.1 of the standard. These events would be associated with rupture of local faults. The other major contributor to the site is one very large magnitude event (approximately magnitude 9) at a distance of about 85 km from the site. This event is likely associated with a subduction earthquake at the Juan de Fuca Plate/North American Plate boundary. For the purpose of this analysis, the ground motions were selected from the FEMA P-695 (FEMA 2009) far-field record set. A preliminary set of six records was selected, with details shown in Table G23-1. The P-695 record numbers are shown in the first column of the table. The record sequence numbers in the table refer to the identifier in the PEER NGA database (Chiou et al. 2008). This database contains thousands of ground motion record sets. For each set the three orthogonal components (two horizontal and one vertical) can be downloaded for use in the analysis. The spectral matching routine used in this analysis can read these records directly. The computer program used to perform the

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Table G23-1. Summary of Ground Motions Considered for Analysis

FEMA P-695 record number 4 7 10 15 20 22

Event

Year

PEER NGA sequence number

Hector Mine, USA Kobe, Japan Kocaeli, Turkey Manjil, Iran Chi-Chi, Tiawan Fruili, Italy

1999

1787

7.1

Strike-slip

26.5

0.34

1995

1111

6.9

Strike-slip

8.7

0.51

1999

1148

7.5

Strike-slip

57.3

0.22

1990

1633

7.4

Strike-slip

40.4

0.51

1999

1485

7.6

Thrust

77.5

0.51

1976

125

6.5

Thrust

20.2

0.35

Magnitude Mechanism

Distance PGA (km) (g)

Source: FEMA (2009) ﬁrst column, Chiou et al. (2008) third column.

Table G23-2. Original, Unmatched Ground Motions Used in Analysis

Record name A B C

Event

File name for File name for Component component X (E–W) Y (N–S)

Hector Mine, HEC090 USA Kobe, SHI090 Japan Kocaeli, DZC180 Turkey

Time step (s)

Number of points in Duration record (s)

HEC180

0.01

4,531

45.31

SHI000

0.01

4,100

41.00

DZC270

0.005

5,440

27.20

analysis [(ETABS, version 17) (CSI 2018)] has the capability to perform spectral matching. From this initial set the three records shown in Table G23-2 were selected for the modal response history analysis. This table lists additional information useful in the spectral matching. For the purpose of this example, these earthquakes will be referred to as A, B, and C as shown in the ﬁrst column of Table G23-2. In the remainder of this chapter the ground motions and responses will be designated as follows: • • • •

AX: for ground motion A in the x (east–west) direction, AY: for ground motion A in the y (north–south) direction, BX: for ground motion B in the x (east–west) direction, BY: for ground motion B in the y (north–south) direction,

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• •

CX: for ground motion C in the x (east–west) direction, and CY: for ground motion C in the y (north–south) direction.

Table G23-3 provides additional information for each ground motion. The original (unmatched) ground acceleration histories are shown in Figures G23-6 through G23-8 for earthquakes A, B, and C, respectively. Also shown for each record is the x-direction acceleration plotted versus the y-direction acceleration. In each case it can be seen that the x and y ground acceleration directions are not highly correlated, meaning that the ground shaking is not dominant in one compass direction. Response spectra that have been amplitude scaled to the target spectra at the period CuTa, and at Tcomputed for the x-direction motions are shown in Figures G23-9 and G23-10, respectively. Here, the individual ground accelerations for earthquakes A, B, and C had all of their acceleration values multiplied by the same constant (unique to that ground motion) such that the modified ground motion spectral ordinate exactly matched the target spectrum ordinate at the indicated period. The plots for the y-direction are presented in Figures G23-11 and G23-12. From the both the x and y spectra, and for matching at periods CuTa or Tcomputed, the lower periods (higher modes) show significant variation in the ordinates of the modified and the target spectra. This will lead to significant differences in response among the three ground motions used. This difference is undesirable and is minimized by use of spectral matching. For spectral matching, the standard requires that the matching period range is 0.8 Tlower to 1.2 Tupper, where Tlower is the period at which 90% of the effective mass is captured, and Tupper is the fundamental mode of the fundamental period in the direction of response. For east–west response, the fundamental period is 2.927 s, and the period at which 90% of the mass is captured is 1.015 s. Thus, the matching range would be 0.812 to 3.51 s. For the north–south response the fundamental period is 1.446 s, and the 90% of the mass is captures at a period of 0.383 s. This produces a matching range of 0.306 to 1.735 s. Although not specifically stated in the standard, it is acceptable to match over a broader period range. Because

Table G23-3. Characteristics of Matched Ground Motions

Component

Time step (s)

Number of points in record

Duration (s)

Maximum acceleration (g)

Minimum acceleration (g)

X Y

0.01 0.01

4,594 4,594

45.94 45.94

0.287 0.255

−0.292 −0.324

X Y

0.01 0.01

4,096 4,096

40.96 40.96

0.202 0.288

−0.316 −0.262

X Y

0.005 0.005

5,823 5,823

29.11 29.11

0.243 0.263

−0.383 −0.289

Record Name

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Figure G23-6. Ground motion acceleration histories for original (unmatched) Earthquake A: (a) x-direction ground acceleration; (b) y-direction ground acceleration; and (c) x- versus y-direction ground acceleration. 18 modes are used in the analysis, and the period for the 18th mode is 0.116 s, a period range of 0.116 to 3.51 s encompasses the entire range of response in both the east–west and north–south directions. For the actual spectral matching, a period range of 0.110 to 3.50 s was used. The lower value of 0.110 s is slightly less than T0 = 0.2Ts which is where the constant acceleration region of the target spectrum begins. The three matched ground motion spectra, the average of the matched spectra, the target spectrum, and bounds of ± 10% of the target spectrum are shown for the x (east–west) direction in Figure G23-13. The same information for the y (north–south) direction is provided in Figure G23-14. Although a few points on the individual matched spectra fall outside the ± 10% envelops, the average of the matched spectra falls within the envelope for the full matching range. Thus, the matching meets the criteria provided in Section 12.9.2.3.1.

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Linear Response History Analysis

Figure G23-7. Ground motion acceleration histories for original (unmatched) Earthquake B: (a) x-direction ground acceleration; (b) y-direction ground acceleration; and (c) x- versus y-direction ground acceleration.

Before continuing with the analysis, it is important to note that the RspMatch program may add a short amount of time of near-zero acceleration to the beginning of the matched record, and this duration may be different for the two components of a given earthquake. To make sure that the ground motions remained synchronized, 63 time steps of zero acceleration were added at the beginning of the x-direction component of Ground motion A, and 386 time steps of zero acceleration were added at the beginning of the y-component of ground motion C. For the example under consideration, the following time adjustments were made by RspMatch: Ground motion A 0 time steps added in the x-direction 63 time steps added in the y-direction

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Figure G23-8. Ground motion acceleration histories for original (unmatched) Earthquake C: (a) x-direction ground acceleration; (b) y-direction ground acceleration; and (c) x- versus y-direction ground acceleration. Ground motion B 0 time steps added in the x-direction 0 time steps added in the y-direction Ground motion C 386 time steps added in the x-direction 0 time steps added in the y-direction Ground motion histories for earthquakes A, B, and C are presented in Figures G23-15 through G23-17, respectively. For each case it can be seen that the random character of ground shaking has been retained, and there is a

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Linear Response History Analysis

Figure G23-9. E–W ground motion spectra and target spectra scaled at CuTa.

Figure G23-10. E–W ground motion spectra and target spectra scaled as computed.

general lack of correlation between the x and y components. See Figures G23-6 through G23-8 for similar diagrams for the original, unmatched records. Analyses were run separately for each ground motion in each direction of response, and analysis was run with and without P-delta effects. (Note that although P-delta effects represent nonlinear phenomena, running the x- and y-directions separately and adding the results is appropriate because the P-delta effects were based on a constant linearized geometric stiffness. Had the geometric stiffness been updated on a step-by-step basis during the response history analysis, the x- and y-directions would need to be run simultaneously.) As described subsequently, the x and y results for each ground motion were combined by direct addition after the appropriate scaling factors were obtained.

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Figure G23-11. E–W ground motion spectra and target spectra scaled at CuTa.

Figure G23-12. E–W ground motion spectra and target spectra scaled at CuTa. The total duration of analysis for each ground motion was 40 s, with results stored at a time increment of 0.05 s. This is sufﬁcient resolution to accurately capture the peak responses.

23.7 Analysis Results Center of mass story drift ratios are shown in Table G23-4a and b for east–west and north–south loading, respectively. P-delta effects were included in the analysis. The tabulated values include the Cd/R modiﬁcation factors. In accordance with Section 12.9.2.5.4, the displacement results did not need to be scaled because Equation (12.8-6) did not control the design base shear in either direction. Values for the analysis run without P-delta effects are provided in

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Linear Response History Analysis

Figure G23-13. E–W matched ground motion spectra and target spectra for x (E–W) loading.

Figure G23-14. E–W matched ground motion spectra and target spectra for y (N–S) loading. Table G23-5a and b. Each of the tables shows the minimum (most negative) and maximum (most positive) value determined for each story and for each ground motion. Envelope values are shown in the last two columns of the table, with the peak absolute value shown in bold text. For analysis that includes P-delta effects, envelope values peak at about 0.0127 in the east–west direction and 0.0071 in the north–south direction. In both cases these drifts are less than the limit of 0.0150 for buildings in Risk Category III. Values for analysis that do not include P-delta effects are somewhat less, peaking at 0.0122 in the east–west direction and 0.0068 in the north–south direction.

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(a)

(b)

(c)

Figure G23-15. Ground acceleration histories for spectrally matched Earthquake A: (a) x-direction ground acceleration; (b) y-direction ground acceleration; and (c) x- versus y-direction ground acceleration. Based on these results, the inclusion of P-delta effects increased drifts by 4.7% in the east–west direction and 4.4% in the north–south direction. Base shears determined from all analyses, with and without P-delta effects, are provided in Table G23-6. Minimum and maximum values are provided, as well as envelope values (maximum absolute value), and averages. These shears come directly from the analysis, and do not yet include R or Ie. The shears developed for east–west loading are signiﬁcantly smaller for Ground motion A than for motions B and C. There is usually greater consistency in results for the north– south direction response, although the results for Ground motion C are somewhat less than for motions A and B. These differences in each direction are more than would be expected from a simple inspection of the spectrally matched response spectra (Figures G23-13 and G23-14). The last row of Table G23-6 shows the base shears determined from the response spectrum analysis (see Chapter 22 of this guide for details). For the

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(a)

(b)

(c)

Figure G23-16. Ground acceleration histories for spectrally matched Earthquake B: (a) x-direction ground acceleration; (b) y-direction ground acceleration; and (c) x- versus y-direction ground acceleration. east–west direction response, the envelope LRH values are nearly the same (within 3% of each other) as obtained from MRS analysis. However, for the north–south direction response, the envelope LRH values are significantly greater (by about 15%) than obtained from MRS analysis. A more detailed comparison of results obtained using ELF, MRS, and LRH analysis is provided in Chapter 24 of this guide. One final point regarding Table G23-6 is that the base shears including P-delta effects are usually less than those determined including such effects. This is somewhat counterintuitive because the drifts including P-delta are larger than those without. This issue comes up again in this chapter in relation to determining member forces. Section 12.9.2.5 provides requirements for modification of the response history results for design. As already discussed, the drift results did not require scaling.

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(a)

(b)

(c)

Figure G23-17. Ground acceleration histories for spectrally matched Earthquake C: (a) x-direction ground acceleration; (b) y-direction ground acceleration; and (c) x- versus y-direction ground acceleration. Table G23-4a. Center of Mass Story Drift Ratios for E–W Loading Including P-delta Ground motion A

Ground motion B

Ground motion C

Envelope

Story

Min

Max

Min

Max

Min

Max

Min

Max

8 7 6 5 4 3 2 1 Limit

−0.0066 −0.0081 −0.0082 −0.0084 −0.0084 −0.0080 −0.0080 −0.0056 −0.0150

0.0089 0.0114 0.0117 0.0116 0.0113 0.0100 0.0087 0.0058 0.0150

−0.0096 −0.0116 −0.0109 −0.0102 −0.0094 −0.0095 −0.0103 −0.0073 −0.0150

0.0087 0.0101 0.0089 0.0089 0.0113 0.0122 0.0118 0.0077 0.0150

−0.0122 −0.0119 −0.0119 −0.0127 −0.0125 −0.0118 −0.0103 −0.0072 −0.0150

0.0109 0.0113 0.0116 0.0119 0.0117 0.0106 0.0100 0.0071 0.0150

−0.0122 −0.0119 −0.0119 −0.0127 −0.0125 −0.0118 −0.0103 −0.0073 −0.0150

0.0109 0.0114 0.0117 0.0119 0.0117 0.0122 0.0118 0.0077 0.0150

Note: Bold font = peak absolute value.

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Table G23-4b. Center of Mass Story Drift Ratios for N–S Loading Including P-delta

Ground motion A

Ground motion B

Ground motion C

Envelope

Story

Min

Max

Min

Max

Min

Max

Min

Max

8 7 6 5 4 3 2 1 Limit

−0.0060 −0.0060 −0.0058 −0.0047 −0.0046 −0.0038 −0.0038 −0.0027 −0.0150

0.0055 0.0056 0.0054 0.0046 0.0048 0.0041 0.0040 0.0029 0.0150

−0.0061 −0.0060 −0.0057 −0.0052 −0.0051 −0.0039 −0.0038 −0.0027 −0.0150

0.0070 0.0071 0.0068 0.0053 0.0048 0.0035 0.0035 0.0026 0.0150

−0.0065 −0.0067 −0.0066 −0.0055 −0.0051 −0.0038 −0.0037 −0.0026 −0.0150

0.0057 0.0055 0.0052 0.0041 0.0039 0.0031 0.0029 0.0024 0.0150

−0.0065 −0.0067 −0.0056 −0.0055 −0.0051 −0.0039 −0.0038 −0.0027 −0.0150

0.0070 0.0071 0.0068 0.0053 0.0048 0.0041 0.0040 0.0029 0.0150

Note: Bold font = peak absolute value.

Table G23-5a. Center of Mass Story Drift Ratios for E–W Loading Not Including P-delta Ground motion A

Ground motion B

Ground motion C

Envelope

Story

Min

Max

Min

Max

Min

Max

Min

Max

8 7 6 5 4 3 2 1 Limit

−0.0072 −0.0082 −0.0071 −0.0075 −0.0077 −0.0075 −0.0070 −0.0052 −0.0150

0.0082 0.0103 0.0101 0.0102 0.0100 0.0091 0.0082 0.0054 0.0150

−0.0099 −0.0122 −0.0115 −0.0108 −0.0101 −0.0087 −0.0090 −0.0064 −0.0150

0.0090 0.0107 0.0095 0.0083 0.0084 0.0097 0.0098 0.0068 0.0150

−0.0122 −0.0122 −0.0102 −0.0109 −0.0107 −0.0105 −0.0095 −0.0064 −0.0150

0.0114 0.0119 0.0096 0.0097 0.0098 0.0089 0.0092 0.0066 0.0150

−0.0122 −0.0122 −0.0115 −0.0109 −0.0107 −0.0105 −0.0095 −0.0064 −0.0150

0.0114 0.0119 0.0101 0.0102 0.0100 0.0097 0.0098 0.0068 0.0150

Note: Bold font = peak absolute value.

For determination of member forces, scaling is required and is done in two steps. First, the elastic base shear determined from the analysis in each direction, VEX and VEY, is multiplied by Ie and divided R to obtain the inelastic forces. The inelastic forces are designated as VIX and VIY. For this analysis Ie = 1.25, and R is 8.0 and 7.0 for the east–west and north–south direction of response, respectively. The next step is to determine the base shear scale factors, ηX and ηY for each ground motion and for each direction of response. These factors are determined as follows: ηX =

VX ≥ 1.0 V IX

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(12.9-3)

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Table G23-5b. Center of Mass Story Drift Ratios for N–S Loading Not Including P-delta

Ground motion A

Ground motion B

Ground motion C

Envelope

Story

Min

Max

Min

Max

Min

Max

Min

Max

8 7 6 5 4 3 2 1 Limit

−0.0058 −0.0058 −0.0056 −0.0047 −0.0046 −0.0040 −0.0039 −0.0028 −0.0150

0.0055 0.0055 0.0054 0.0045 0.0045 0.0039 0.0038 0.0027 0.0150

−0.0057 −0.0056 −0.0054 −0.0049 −0.0048 −0.0038 −0.0037 −0.0027 −0.0150

0.0068 0.0068 0.0065 0.0052 0.0047 0.0036 0.0036 0.0027 0.0150

−0.0064 −0.0065 −0.0064 −0.0053 −0.0049 −0.0038 −0.0037 −0.0026 −0.0150

0.0057 0.0055 0.0051 0.0041 0.0040 0.0032 0.0031 0.0022 0.0150

−0.0064 −0.0065 −0.0064 −0.0053 −0.0049 −0.0040 −0.0039 −0.0028 −0.0150

0.0068 0.0068 0.0065 0.0052 0.0047 0.0039 0.0038 0.0027 0.0150

Note: Bold font = peak absolute value.

Table G23-6. Base Shears from All Analyses, With and Without P-delta E–W direction Ground motion

N–S direction

With P-delta (kips)

Without P-delta (kips)

With P-delta (kips)

Without P-delta (kips)

Min Max

−1,355 1,324

−1,382 1,457

−4,104 3,894

−3,994 4,053

Min Max

−1,725 1,715

−1,835 1,729

−3,904 3,912

−4,057 4,003

Min Max

−1,688 1,750

−1,813 1,800

−3,849 3,598

−3,683 3,665

Envelope Average MRS analysis

1,750 1,593 1,767

1,835 1,669 1,894

4,104 3,877 3,530

4,057 3,909 3,566

ηY =

VY ≥ 1.0 V IY

(12.9-4)

The values VX and VY are the design base shears used in the ELF analysis and were determined in Chapter 21 of this guide as 558 kips in the east–west direction, and 1,124 kips in the north–south direction. Table G23-7 shows the computation of the scale factors, which range from 2.07 to 2.67 in the east–west direction and 1.57 to 1.69 in the north–south direction. The factors are based on the average of the minimum and maximum result for each analysis, with P-delta effects included. For example, the elastic shear VEX of 1,339 kips for Ground motion A in Table G23-7 is equal to (1,355+1,324)/2. Note that these scale factors are applied to the LRH results than have been multiplied by Ie/R.

Seismic Loads

VEX (E–W) VEY (N–S)

Note: Using ASCE 7 procedure.

VEY (N–S) VEY (N–S)

VEX (E–W) VEY (N–S)

Designation

Ground motion

1,719 3,723

1,720 3,908

1,339 3,999

Shear (kips)

Elastic response history analysis

VIX (E–W) VIY (N–S)

VIY (N–S) VIX (E–W)

VIX (E–W) VIY (N–S)

Designation

269 665

269 698

209 714

Shear (kips)

Inelastic response history analysis

Table G23-7. Scale Factors for Determining Member Forces

558 1,124

Shear (kips)

ELF analysis Scale factors

ηX = 558/269 = 2.07 ηY = 1,124/665 = 1.69

ηX = 558/269 = 2.07 ηY = 1,124/698 = 1.61

ηX = 558/209 = 2.67 ηY = 1,124/714 = 1.57

Linear Response History Analysis

241

242

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Table G23-8. Scale Factors for Determining Member Forces (Alternate Procedure)

Ground motion A B C

Direction

MRH base shear (kips)

ELF base shear (kips)

Scale factor

E–W N–S E–W N–S E–W N–S

1,339 3,999 1,720 3,908 1,719 3,723

558 1,124 558 1,124 558 1,124

558/1,339 = 0.417 1,124/3,999 = 0.281 558/1,720 = 0.324 1,124/3,908 = 0.288 558/1,719 = 0.325 1,124/3,723 = 0.302

It is often convenient to determine scale factors in one step by simply dividing the ELF base shear by the elastic response history shear determine for the same direction of response. These results are shown in Table G23-8. The equivalence of the approaches can be seen by using 2.67(209) = 558 kips or using 1,339(0.417) = 558 kips. This one-step approach was used to determine the member forces for each analysis. Before presenting the ﬁnal scaled member forces, it is of some interest to review the unscaled elastic beam and column forces to indicate the level of scatter in results obtained from Ground motions A, B, and C that were tightly matched to the same target spectrum. Also of interest is the difference between results obtained with and without P-delta effects. This is done by use of Tables G23-8 through G23-12. The ﬁrst two tables present beam shears (Table G23-9) and column shears (Table G23-10) in the special moment frame on Grid line 1 for loading in the east–west direction. Tables G23-11 and G23-12 present the beam and column shears for the special moment frame on Grid line A loaded in the north–south direction. For each beam or column in each table, the minimum (smallest negative) and maximum (largest positive) force values are reported. Results with and without P-delta effects are presented in each part of each table. The following general observations are made: 1.

Ground motions B and C appear to be more demanding than Ground motion A for computing response in the east–west direction, whereas the responses are very similar for all three motions applied in the north–south direction.

P-delta effects appear to be more signiﬁcant for loading in the east–west direction than for the north–south direction. This is expected, because the building is signiﬁcantly stiffer in the north–south direction owing to the presence of the braced frames.

The difference between results with and without P-delta effects is more apparent in the lower stories. In fact, for some of the upper stories, the results without P-delta included in the analysis are slightly larger than for the analysis that includes such effects.

For loading in the east–west direction, Table G23-10 indicates that there is a significant reduction in shear in the first-story column relative to the second story. This is a result of the influence of the fixed-base columns on Grid lines A and G resisting shear in their weak axes. This reduction in shear becomes smaller along the

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Table G23-9. Elastic Beam Shears in the Moment Frame on Grid Line 1 under E–W Load (a) Ground motion A Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

Including P-delta effects Bay D1–E1 (kips) Level R 8 7 6 5 4 3 2

Not including P-delta effects

Bay E1–F1 (kips)

Bay D1–E1 (kips)

Bay E1–EF (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−13.1 −31.1 −41.5 −55.3 −60.0 −60.0 −64.5 −58.4

17.6 44.1 59.2 77.8 81.8 78.2 74.4 62.4

−14.1 −33.2 −43.1 −57.8 −63.4 −63.3 −69.3 −64.5

18.1 46.7 61.6 81.3 86.6 82.6 79.4 68.6

−14.3 −33.8 −38.2 −48.6 −54.2 −56.3 −58.3 −53.2

16.1 40.3 52.1 67.9 72.1 70.1 69.5 58.5

−15.0 −36.3 −39.9 −50.8 −57.4 −59.6 −62.4 −58.8

16.6 42.7 54.2 70.9 76.2 74.0 74.3 64.1

(b) Ground motion B Including P-delta effects Bay D1–E1 (kips) Level R 8 7 6 5 4 3 2

Not including P-delta effects

Bay E1–F1 (kips)

Bay D1–E1 (kips)

Bay E1–EF (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−19.0 −46.3 −57.3 −70.6 −70.2 −64.8 −80.3 −76.3

17.3 41.1 47.9 55.8 71.7 87.3 97.5 83.7

−20.1 −49.3 −68.8 −73.8 −74.1 −69.0 −86.6 −84.3

18.1 44.0 50.0 58.0 76.1 93.0 105.0 92.1

−19.6 −48.2 −60.3 −74.6 −74.6 −78.8 −71.7 −66.8

17.8 43.0 51.2 59.2 56.4 67.4 78.9 71.8

−20.3 −51.2 −62.8 −78.0 −78.9 −72.6 −77.4 −73.7

18.5 46.0 53.8 62.0 59.4 71.9 85.0 79.1

Not including P-delta effects

Bay E1–F1 (kips)

Bay D1–E1 (kips)

Bay E1–EF (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−24.6 −52.8 −58.0 −82.5 −90.2 −87.4 −89.5 −74.2

21.9 48.8 58.0 78.3 84.5 82.2 81.0 74.1

−25.9 −56.7 −60.3 −86.5 −95.8 −93.2 −96.3 −81.9

23.0 29.4 60.3 81.9 89.5 87.0 86.7 81.8

−24.6 −52.9 −54.7 −70.3 −77.7 −77.0 −81.0 −67.3

22.9 51.0 52.5 63.1 69.6 68.7 73.2 68.7

−25.9 −56.9 −56.9 −73.7 −82.6 −82.1 −87.2 −74.2

24.1 51.0 52.5 63.1 69.6 68.7 73.2 68.7

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Table G23-10. Elastic Column Shears in the Moment Frame on Grid Line 1 under E–W Load (a) Ground motion A Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

Including P-delta effects Column E1 (kips) Story 8 7 6 5 4 3 2 1

Not including P-delta effects

Column F1 (kips)

Column E1 (kips)

Column F1 (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−67.2 −83.7 −121.8 −137.5 −142.2 −148.0 −161.7 −129.7

81.8 119.4 174.4 191.6 191.0 182.8 174.4 133.3

−37.3 −47.9 −62.2 −72.3 −76.1 −78.5 −86.6 −91.1

40.1 68.7 89.5 101.1 102.2 95.4 92.7 93.4

75.9 110.9 154.7 173.1 175.7 174.3 171.5 126.4

−70.0 −91.4 −108.9 −127.6 −135.8 −145.5 −150.8 −128.5

−36.6 −54.4 −57.2 −69.2 −74.9 −79.7 −83.5 −92.7

40.4 64.8 80.9 93.8 96.8 94.6 94.1 89.3

(b) Ground motion B Including P-delta effects Column E1 (kips) Story 8 7 6 5 4 3 2 1

Not including P-delta effects

Column F1 (kips)

Column E1 (kips)

Column F1 (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−95.2 −123.3 −163.9 −167.8 −159.0 −179.1 −210.2 −168.2

82.6 108.1 133.1 146.1 192.7 231.0 237.8 173.3

−51.8 −71.4 −84.2 −88.3 −85.0 −95.5 −113.3 = 118.2

41.9 63.0 68.9 76.7 104.2 123.5 127.2 120.2

−94.6 −137.1 −177.4 −183.9 −176.5 −171.5 −192.8 −154.2

85.1 117.7 148.2 139.9 149.3 191.6 207.7 163.6

43.3 69.9 78.5 75.5 83.0 106.3 115.4 117.3

−51.8 −77.3 −93.2 −99.7 −97.0 −94.9 −107.3 −110.6

Not including P-delta effects

Column F1 (kips)

Column E1 (kips)

Column F1 (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−122.1 −126.1 −180.3 −212.9 −214.3 −225.0 −206.3 −169.3

107.4 121.9 173.1 196.9 199.6 196.6 202.7 164.9

−65.5 −73.2 −93.7 −113.9 −116.0 −122.8 −110.1 −119.7

56.8 72.4 88.9 104.4 107.1 103.5 108.9 116.0

−123.8 −134.1 −154.9 −190.3 −191.3 −210.7 −200.1 −158.0

114.6 134.2 150.2 166.2 175.7 171.0 195.0 161.3

−67.0 −79.8 −81.9 −105.0 −106.5 −118.0 −110.9 −114.2

61.5 80.4 80.1 92.6 100.1 93.0 107.9 115.8

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Table G23-11. Elastic Beam Shears in the Moment Frame on Grid Line A under N–S Load (a) Ground motion A Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

Including P-delta effects Bay A2–A3 (kips)

Not including P-delta effects

Bay A3–A4 (kips)

Bay A2–A3 (kips)

Bay A3–A4 (kips)

Level

Min

Max

Min

Max

Min

Max

Min

Max

R 8 7 6 5 4 3 2

−11.6 −17.9 −19.9 −26.6 −36.9 −57.6 −88.7 −85.0

10.9 17.0 19.0 25.6 38.0 62.1 97.0 92.7

−6.2 −9.1 −9.8 −13.2 −19.4 −30.7 −49.8 −48.3

5.9 8.6 9.3 12.7 20.0 33.1 54.4 52.7

−11.3 −17.4 −19.3 −26.2 −37.4 −58.8 −92.1 −88.1

10.9 16.9 18.9 25.6 36.4 58.8 91.8 87.8

−60 −8.8 −9.5 −13.0 −19.6 −31.2 −51.7 −50.0

5.8 8.6 9.3 12.7 19.1 31.3 51.5 49.9

(b) Ground motion B Including P-delta effects Bay A2–A3 (kips)

Not including P-delta effects

Bay A3–A4 (kips)

Bay A2–A3 (kips)

Bay A3–A4 (kips)

Level

Min

Max

Min

Max

Min

Max

Min

Max

R 8 7 6 5 4 3 2

−12.1 −18.4 −20.0 −27.9 −41.0 −60.8 −91.4 −87.1

13.7 21.2 23.7 31.3 39.6 54.7 82.7 81.6

−6.5 −9.3 −9.8 −13.8 −21.6 −32.5 −51.3 −49.5

7.3 10.7 11.6 15.5 20.8 29.1 46.3 46.3

−11.3 −17.2 −18.6 −26.2 −39.2 −58.3 −89.1 −85.0

13.3 20.6 22.9 30.1 39.1 55.1 85.2 83.7

−6.1 −8.7 −9.1 −13.0 −20.6 −31.1 −50.0 −48.3

7.1 10.4 11.2 14.9 20.5 29.4 47.8 47.5

Not including P-delta effects

Bay A3–A4 (kips)

Bay A2–A3 (kips)

Bay A3–A4 (kips)

Level

Min

Max

Min

Max

Min

Max

Min

Max

R 8 7 6 5 4 3 2

−12.7 −19.9 −22.8 −31.4 −41.6 −58.4 −88.3 −83.2

11.1 16.8 18.1 23.5 31.0 46.2 70.0 71.3

−6.8 −10.2 −11.2 −15.5 −21.9 −31.2 −49.6 −47.3

5.9 8.5 8.9 11.6 16.3 24.6 39.2 40.4

−12.4 −19.4 −22.1 −30.4 −40.2 −57.6 −87.8 −82.7

11.1 16.8 18.0 23.5 32.2 47.6 73.1 68.2

−6.7 −9.8 −10.8 −15.0 −21.1 −30.8 −49.4 −47.0

5.9 8.5 8.8 11.6 16.9 25.4 41.0 38.8

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Table G23-12. Elastic Column Shears in the Moment Frame on Grid Line A under N–S Load (a) Ground motion A Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

Including P-delta effects Column A3 (kips) Story 8 7 6 5 4 3 2 1

Not including P-delta effects

Column A4 (kips)

Column A3 (kips)

Column A4 (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−29.2 −20.7 −38.4 −38.1 −61.7 −108.0 −133.1 −105.3

27.3 20.0 36.5 39.0 63.5 118.1 145.4 114.6

−13.0 −9.2 −17.1 −15.6 −30.6 −48.1 −63.5 −57.1

12.1 9.0 16.3 16.1 31.4 52.5 69.4 62.1

−28.9 −21.6 −39.1 −40.7 −64.9 −114.8 −140.8 −111.7

27.9 21.1 38.0 39.5 63.1 114.3 140.3 111.5

−13.1 −14.0 −18.1 −17.3 −32.9 −51.9 −67.9 −61.6

12.6 9.8 17.4 16.9 31.9 51.6 67.6 61.0

(b) Ground motion B Including P-delta effects Column A3 (kips) Story 8 7 6 5 4 3 2 1

Not including P-delta effects

Column A4 (kips)

Column A3 (kips)

Column F1 (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−30.3 −21.0 −38.0 −43.2 −68.1 −111.1 −137.1 −106.7

34.2 24.8 45.7 40.5 65.0 99.8 125.2 103.5

−13.6 −9.4 −16.9 −17.8 −33.9 −49.3 −65.5 −58.0

15.2 11.1 20.5 15.8 32.7 44.6 59.6 56.3

−29.1 −20.9 −37.4 −43.5 −67.8 −110.8 −136.3 −107.9

34.0 35.6 46.5 42.3 66.8 105.2 131.4 108.6

−13.3 −9.7 −17.0 −21.5 −34.4 −50.0 −65.7 −59.2

15.3 11.9 21.5 17.3 34.2 47.6 63.2 59.5

Not including P-delta effects

Column A4 (kips)

Column A3 (kips)

Column A4 (kips)

Min

Max

Min

Max

Min

Max

Min

Max

−31.7 −23.5 −43.7 −42.4 −68.6 −107.9 −131.7 −101.3

28.0 19.2 34.7 32.6 51.7 86.1 104.4 96.7

−14.1 −10.5 −19.4 −16.5 −34.6 −47.8 −62.9 −54.9

12.6 8.5 15.6 13.5 25.8 38.5 49.9 52.9

−31.8 024.5 −44.5 −43.4 −68.9 −109.8 −133.6 −103.4

28.6 20.2 36.1 35.7 55.8 92.1 111.0 92.9

−14.3 −11.2 −20.4 −17.7 −35.3 −49.4 −64.5 −56.5

10.0 9.4 16.7 15.3 28.4 41.7 53.6 50.9

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Linear Response History Analysis

Table G23-13. Envelope Scaled Column Shears in Column E1 under E–W Loads Ground motion A

Ground motion B

Ground motion C

Story Min (kips) Max (kips) Min (kips) Max (kips) Min (kips) Max 8 7 6 5 4 3 2 1

−28.0 −34.9 −50.8 −57.3 −59.4 −61.7 −67.4 −54.1

−30.8 −39.9 −53.1 −54.4 −51.5 −58.0 −68.1 −54.5

34.1 49.8 72.7 79.9 79.6 76.2 72.7 55.6

26.8 35.0 43.1 47.3 62.4 74.8 77.0 55.8

−39.7 −41.0 −58.6 −69.2 −69.6 −73.1 −67.0 −55.0

34.9 39.6 56.3 64.0 64.9 64.0 65.9 53.6

Envelope (kips) 39.7 49.8 72.7 79.9 79.6 76.2 77.0 55.8

Note: Results include P-delta effects.

Table G23-14. Summary of Scaled Beam and Column Shears in Moment Frames Beam shears (kips)

Column shears (kips)

E–W loading N–S loading E–W loading Beam level or column Bay Bay Bay Bay Column Column supporting D1–E1 E1–F1 A2–A3 A3–A4 E1 F1 R 8 7 6 5 4 3 2

8.0 18.4 24.7 32.4 34.1 32.6 31.6 27.1

8.4 20.6 25.7 33.9 36.1 34.4 36.1 35.2

4.8 7.5 8.3 11.1 15.8 25.9 40.4 38.7

2.6 3.8 4.1 5.5 8.3 17.5 22.7 22.0

39.7 49.8 72.7 79.9 79.6 76.2 77.0 55.8

21.3 28.6 37.3 42.2 42.6 40.0 41.2 38.9

N–S loading Column Column A3 A4 9.8 7.1 13.2 12.8 20.7 33.2 40.9 32.2

4.4 3.2 5.9 5.1 10.5 14.8 19.5 17.5

Note: Results include P-delta effects.

height as the influence of the fixed base becomes less important. A similar but less significant reduction in first-story column shear occurs for the loading in the north– south direction. Here, the influence of the weak axis stiffness of the columns of the frames on Grid lines 1 and 4 is reduced as a result of the dominant stiffness of the braced frame.

Table G23-13 illustrates the methodology for determining the envelope shear forces in the beams of the special moment frame on Grid line 1. Here, the elastic column shears from Table G23-11 are multiplied by Ie/R = 1.25/8 and then scaled by the value 2.67 provided in Table G23-7. Alternately, the elastic column shears from Table G23-11 could be multiplied by the factor 0.417 from Table G23-8. The envelope value shown in the last column of Table G23-13 is the maximum of the absolute values of all scaled values in the row.

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Table G23-15. Summary of Scaled Column Axial Forces in Moment Frames Column axial forces (kips)

E–W loading Story 8 7 6 5 4 3 2 1

N–S loading

Column E1

Column F1

Column A3

Column A4

0.4 1.7 2.4 4.1 5.7 7.5 9.5 11.8

8.4 26.9 52.6 86.6 122.6 157.1 190.0 216.5

1.8 4.8 8.3 13.0 19.0 26.6 37.1 46.4

2.1 5.2 8.5 13.2 19.8 28.7 42.3 55.2

Note: Results include P-delta effects.

Table G23-16. Summary of Scaled Axial Forces in Braced Frames under N–S Loading Column axial forces (kips) Frame B Story 8 7 6 5 4 3 2 1 B

Frame C

Column

Brace

Column

Brace

62.2 62.2 280.8 280.8 497.1 497.1 639.3 639.3 772.8

79.8 139.1 141.3 174.3 160.1 180.7 179.3 222.6 5.2

52.4 52.4 226.7 226.7 374.2 374.2 463.6 493.8 618.5

67.1 109.4 114.8 121.1 120.7 144.2 162.4 206.6 3.3

Tables G23-14 through G23-16 provide a summary of the scaled member forces for all analyses. P-delta effects are included in all cases. These results are compared with those from ELF and MRS analysis in Chapter 24 of this guide. One of the advantages of LRH analysis over MRS analysis is the ability to obtain the acceleration histories of each ﬂoor of the building. See Chapter 27 of this guide for an illustration of this procedure for the same 8-story structure analyzed in this chapter.

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24 Comparison of Computed Response Using ELF, MRS, and LRH Analysis

This chapter compares a selection of the results computed using equivalent lateral force analysis, modal response spectrum analysis, and linear response history analysis. A detailed description of the building analyzed is provided in Appendix B. Results are provided for ELF, MRS, and LRH analysis in Chapters 21, 22, and 23, respectively. All results shown in this chapter are for analyses performed including P-delta effects.

24.1 Inelastic Story Drift Comparisons Story drift ratios from the three analysis procedures are provided in Table G24-1 and in Figures G24-1 and G24-2 for the system loaded in the east–west and north–south directions, respectively. In each case, the drift ratios include the required scaling of Cd/Ie and include P-delta effects. The story drift ratio limit for each direction of response is 0.015, which is in accordance with Table 12.12-1 for “all other structures” in Risk Category III. For loading in the east–west direction, where resistance is provided exclusively by special steel moment frames, Figure G24-1 indicates that there is considerable scatter in the results, with the ELF method producing the largest story drift ratios in all stories, except for the uppermost story. Drifts from the LRH analysis are consistently larger than those from MRS analysis, except at the lowest story. With the exception of two stories where the ELF story drift ratios slightly exceed the limiting value of 0.015, all drifts fall within acceptable values.

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Table G24-1. Story Drift Comparisons E–W Loading (kips)

Level R 8 7 6 5 4 3 2

N–S Loading (kips)

ELF

MRS

LRH

ELF

MRS

LRH

0.0105 0.0135 0.0141 0.0147 0.0153 0.0153 0.0144 0.0093

0.0085 0.0094 0.0097 0.0099 0.0107 0.0109 0.0109 0.0076

0.0122 0.0119 0.0119 0.0127 0.0125 0.0122 0.0118 0.0077

0.0087 0.0100 0.0093 0.0087 0.0080 0.0060 0.0053 0.0039

0.0068 0.0072 0.0069 0.0061 0.0058 0.0044 0.0041 0.0030

0.007 0.0071 0.0068 0.0055 0.0051 0.0041 0.004 0.0029

Figure G24-1. Comparison of story drifts for east–west.

Figure G24-2. Comparison of story drifts for north–south. Figure G24-2 shows the story drifts for loading in the north–south direction, where resistance is provided by a dual braced frame–moment frame system. This system is quite stiff as indicated by the relatively small story drift ratios. As with the east–west response, the drifts arising from ELF analysis are

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Comparison of Computed Response Using ELF, MRS, and LRH Analysis

considerably larger than from MRS or LRH analysis. Figure G24-2 also shows that drifts from the MRS and LRH procedures are very similar along the full height of the building. Because of the stiffness of the system, none of the story drift ratios in Figure G24-2 exceed the limiting value of 0.015. In fact, the building should be considered as excessively stiff in this direction, and a revised design should be considered.

24.2 Elastic Base Shear Comparisons It is of some interest to compare the elastic base shears developed for each method of analysis wherein the shears are based on analysis of the actual system, not using the empirical period limit CuTa. These periods developed in Chapter 22 of the guide are summarized as follows: For east–west loading: Tcomputed without P-delta = 2.718 s Tcomputed with P-delta = 2.927 s For north–south loading: Tcomputed without P-delta = 1.420 s Tcomputed with P-delta = 1.446 s For the ELF method, the elastic base shear (not including Ie and R) is computed as V elastic = W

S D1 T computed

where SD1 = 0.405 and W = 14,018 kip. For the MRS and LRH methods, the base shears come directly from the analysis, which is determined from the spectrum (or ground motions matched to the spectrum) provided in Figure G22-2. The base shears from all three analysis methods are summarized in Table G24-2. For the LRH method, results are provided using envelope (maximum absolute values of positive or negative response values among all analyses) or average (average of absolute values of positive or negative response values among all analyses). The table indicates considerable scatter in the computed base shears for the different methods of analysis. Comparisons of envelopes of scaled inelastic component forces are provided for the three methods of analysis in Tables G24-3 through G24-10 and in Figures G24-3 through G23-18. Tables G24-3 through G24-5 are for the special moment frame on Grid line 1 under east–west loading and provide beam shears, column shears, and column axial forces. Tables G24-6 through G24-8 provide beam shears, column shears, and column axial forces for the moment frame in Grid line A under north–south loading. Finally,

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Tables G24-9 and G24-10 summarize the column axial forces and the brace axial forces for Frames B and C under north–south loading.

There is considerable scatter in the results even though the base shears have been normalized for each method of analysis.

Table G24-2. Elastic Base Shears Computed Using ELF, MRS, and LRH Analysis Computed base shear (kips) Loading direction E–W N–S

P-delta effects

Period (s)

ELF

MRS

LRH envelope

LRH average

Not included Included Not included Included

2.718 2.927 1.420 1.446

2,089 1,940 3,998 3,926

1,894 1,767 3,566 3,530

1,835 1,750 4,057 4,104

1,669 1,593 3,909 3,877

Table G24-3. Envelope of Scaled Inelastic Beam Shears for E–W Loading Bay D1–E1 beam shear (kips)

Bay E1–F1 beam shear (kips)

Level

ELF

MRS

LRH

ELF

MRS

LRH

R 8 7 6 5 4 3 2

4.8 12.3 16.9 23.4 27.0 29.1 31.2 26.9

5.3 11.6 14.2 18.9 21.6 23.5 25.9 23.4

8.0 18.4 24.7 32.4 34.1 32.6 31.6 27.1

4.9 12.9 17.5 24.3 28.5 30.8 33.4 29.5

5.3 12.4 14.8 19.7 22.9 24.9 27.8 25.8

8.4 20.6 25.7 33.9 36.1 34.4 36.1 35.2

Table G24-4. Envelope of Scaled Inelastic Column Shears for E–W Loading Column E1 (kips)

Column F1 (kips)

Story

ELF

MRS

LRH

ELF

MRS

LRH

8 7 6 5 4 3 2 1

22.0 32.9 49.7 59.1 66.0 73.3 75.1 55.9

24.6 30.6 41.8 48.5 53.6 60.2 64.2 51

39.7 49.8 72.7 79.9 79.6 76.2 77.0 55.8

10.6 18.6 25.1 30.8 35.1 38.6 39.8 38.8

13.3 17.9 21.5 25.8 28.9 32 34.7 35.9

21.3 28.6 37.3 42.2 42.6 40.0 41.2 38.9

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Comparison of Computed Response Using ELF, MRS, and LRH Analysis

Table G24-5. Envelope of Scaled Inelastic Column Axial Forces for E–W Loading

Column E1 (kips)

Column F1 (kips)

Story

ELF

MRS

LRH

ELF

MRS

LRH

8 7 6 5 4 3 2 1

0.1 0.7 1.3 2.2 3.7 5.5 7.7 10.3

0.3 1.1 1.7 2.3 3.2 4.4 6.1 8.1

0.4 1.7 2.4 4.1 5.7 7.5 9.5 11.8

4.9 17.8 35.2 59.6 88.1 118.9 152.3 181.1

5.3 17.6 31.6 49.9 70.7 93.4 118.4 141.5

8.4 26.9 52.6 86.6 122.6 157.1 190.0 216.5

Table G24-6. Envelope of Scaled Inelastic Beam Shears for N–S Loading Bay A3–A4 beam shear (kips)

Bay A4–A5 beam shear (kips)

Level

ELF

MRS

LRH

ELF

MRS

LRH

R 8 7 6 5 4 3 2

4.1 6.4 7.5 10.8 15.3 22.6 32.9 29.5

3.7 5.8 6.7 9.4 13.1 19.2 28.2 25.9

4.8 7.5 8.3 11.1 15.8 25.9 40.4 38.7

2.2 3.3 3.7 5.3 8.0 12.1 18.6 16.8

2 3 3.3 4.6 6.9 10.2 15.9 14.8

2.6 3.8 4.1 5.5 8.3 17.5 22.7 22.0

Table G24-7. Envelope of Scaled Inelastic Column Shears for N–S Loading Column A3 (kips)

Column A4 (kips)

Story

ELF

MRS

LRH

ELF

MRS

LRH

8 7 6 5 4 3 2 1

10.2 7.5 14.0 15.6 25.3 40.7 48.5 34.1

9.3 6.9 12.6 13.4 21.6 34.7 41.8 31.4

9.8 7.1 13.2 12.8 20.7 33.2 40.9 32.2

4.5 3.3 6.1 6.2 12.6 17.9 23.3 18.4

4.1 3.1 5.5 5.3 10.8 15.3 20.0 17.0

4.4 3.2 5.9 5.1 10.5 14.8 19.5 17.5

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Table G24-8. Envelope of Scaled Inelastic Column Axial Forces for N–S Loading

Column A3 (kips)

Column A4 (kips)

Story

ELF

MRS

LRH

ELF

MRS

LRH

8 7 6 5 4 3 2 1

1.9 5.0 8.8 14.2 21.4 31.9 46.3 59.0

1.7 4.6 7.9 12.6 18.7 27.4 39.3 49.9

1.8 4.8 8.3 13.0 19.0 26.6 37.1 46.4

2.2 5.5 9.1 14.5 22.5 34.5 53.1 69.9

2 4.9 8.2 12.8 19.6 29.6 45.1 59.3

2.1 5.2 8.5 13.2 19.8 28.7 42.3 55.2

Table G24-9. Envelope of Scaled Inelastic Braced Frame Column Axial Forces for N–S Loading Frame B (kips)

Frame C (kips)

Story

ELF

MRS

LRH

ELF

MRS

LRH

8 7 6 5 4 3 2 1 B

40.1 40.1 228.1 228.1 516.1 516.1 799.3 799.3 976.4

55.2 55.2 241.1 241.1 461.8 461.8 672.6 672.6 822.7

62.2 62.2 280.8 280.8 497.1 497.1 639.3 639.3 772.8

32.1 32.1 175.7 175.5 378.3 378.3 631.0 630.9 780.1

47 47 192.3 192.3 341 341 517.6 517.6 653.7

52.4 52.4 226.7 226.7 374.2 374.2 463.6 493.8 618.5

Table G24-10. Envelope of Scaled Inelastic Braced Frame Brace Axial Forces for N–S Loading Frame B (kips)

Frame C (kips)

Story

ELF

MRS

LRH

ELF

MRS

LRH

8 7 6 5 4 3 2 1 B

51.3 106.7 135.6 188.0 182.3 197.7 165.9 213.1 4.4

71 119 128 165 157 175 169 213 4.4

79.8 139.1 141.3 174.3 160.1 180.7 179.3 222.6 5.2

41.0 80.4 104.2 129.0 131.3 157.8 166.7 192.1 3.1

60.0 92.0 101.0 113.0 113.0 139.0 168.0 195.0 3.1

67.1 109.4 114.8 121.1 120.7 144.2 162.4 206.6 3.3

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Comparison of Computed Response Using ELF, MRS, and LRH Analysis

Figure G24-3. Envelope of scaled inelastic beam shears in Bay D1–E1 for east–west loading.

Figure G24-4. Envelope of scaled inelastic beam shears in Bay E1–F1 for east–west loading.

Figure G24-5. Envelope of scaled inelastic Column E1 shears for east–west loading.

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256

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Figure G24-6. Envelope of scaled inelastic Column F1 shears for east–west loading.

Figure G24-7. Envelope of scaled inelastic Column F1 axial forces for east–west loading.

Figure G24-8. Envelope of scaled inelastic Column F1 axial forces for east–west loading.

Seismic Loads

Comparison of Computed Response Using ELF, MRS, and LRH Analysis

Figure G24-9. Envelope of scaled inelastic beam shears in Bay A3–A4 for north–south loading.

Figure G24-10. Envelope of scaled inelastic beam shears in Bay A4–A5 for north–south loading.

Figure G24-11. Envelope of scaled inelastic Column A3 shears for north–south loading.

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Figure G24-12. Envelope of scaled inelastic Column A4 shears for north–south loading.

Figure G24-13. Envelope of scaled inelastic Column A3 axial forces for north–south loading.

Figure G24-14. Envelope of scaled inelastic Column A4 axial forces for north–south loading.

Seismic Loads

Comparison of Computed Response Using ELF, MRS, and LRH Analysis

Figure G24-15. Envelope of scaled inelastic Frame B column axial forces for north–south loading.

Figure G24-16. Envelope of scaled inelastic Frame C column axial forces for north–south loading.

Figure G24-17. Envelope of scaled inelastic Frame B brace axial forces for north–south loading.

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260 Seismic Loads

Figure G24-18. Envelope of scaled inelastic Frame C brace axial forces for north–south loading.

Seismic Loads

25 Nonlinear Response History Analysis

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • •

Chapter 16 was completely revised and contains requirements for nonlinear response history analysis. Procedures for linear response history analysis were also fully revised and are contained in Section 12.9.2.

This chapter briefly describes the completely revised procedure for nonlinear response history (NRH) analysis that is included in Chapter 16 of the standard. Although no examples for nonlinear analysis are included in this chapter of the guide, a variety of resources for performing nonlinear analysis are provided. One of these resources contains a detailed example analysis of a high-rise building. During a design-level seismic event, most building structures experience significant nonlinear response. The nonlinearity is caused by inelastic behavior in the critical regions of the main lateral load resisting system and by significant changes in system geometry. Explicit consideration of these nonlinear behaviors has been possible for decades, but it has not been practical to do so until very recently as a result of advances in computational power and disc storage capacity. Also important to the advancement of nonlinear analysis is the availability of commercial nonlinear analysis software and a number of guidelines for performing the analysis and for evaluating the acceptability of the computed performance.

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Before describing the NRH analysis procedures, it must be noted that nonlinear analysis is considerably more time-consuming than are the “traditional” linear procedures provided in Chapter 12 of the standard. There are two principal reasons for the time-consuming nature. First, the analytical models must be much more detailed because of the requirement to represent the system in three dimensions, to capture the expected degradation in component stiffness and strength that is associated with multiple cycles of reverse inelastic deformation, and to account for destabilizing P-delta effects. Second, the response history analysis under each ground motion can take several hours and produce gigabytes of data. The standard requires that a minimum of 11 pairs of orthogonal components of ground motions be used, and where accidental torsion is required, the number of separate analyses would need to increase by a factor of 4. In addition, the use of site-specific target spectra can increase the number of required runs. Thus, although a linear response history analysis of a complex building may take a few seconds or minutes, the nonlinear analysis of the same system may require hours or days to complete. Fortunately, the availability of multicore systems and cloud computing can reduce the computational time significantly. An additional factor in nonlinear analysis is the high level of expertise necessary to develop the mathematical model, select and modify ground motions, validate the results, and evaluate the system performance in terms of the stated acceptance criteria. In many cases the required skills fall outside the expertise of any individual. Concepts needed for performing the analysis are not taught in undergraduate courses. A minimum of a master’s degree is needed with courses in structural dynamics; finite-element analysis; earthquake engineering; and steel, concrete, masonry, and/or timber design. More advanced courses such as nonlinear structural analysis, seismology, and geotechnical earthquake engineering are typically available only in a doctoral level program. Research experiences performed at the master’s and doctoral levels are also valuable. Even when such training, expertise, and experience is available within a firm, the standard mandates that the design/analysis process be carefully documented, that the Authority Having Jurisdiction be continually involved, and that all aspects of the procedure be reviewed by a highly qualified, independent, thirdparty individual or firm (Section 16.5, “Design Review”). Given the challenges, there are clear advantages to nonlinear analysis. The first of these is that the procedure provides much better estimates of expected system response than that which can be provided by a linear analysis. However, this in itself cannot justify the use of the nonlinear procedure. Other more realistic motivations include the following: •

•

Overcome speciﬁed height limits. The height limits in Table 12.2-1 severely limit the applicability of “bearing wall and building frame” systems such as braced frames and shear walls, for which the height limit in higher SDCs is 100 to 160 ft (potentially increased in accordance with Section 12.2.5.4). Use of alternate systems, elements, and connections. Systems not listed in Table 12.2-1 may be used if approved by the Authority Having Jurisdiction and if the analysis and design of the system is externally reviewed in

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Nonlinear Response History Analysis

•

• •

•

accordance with Section 16.5 (see Section 12.2.1.1 for system requirements and 12.2.1.2 for requirements for elements and connections). Provide improved estimates of design forces (e.g., accumulated BRB forces delivered to columns) for some systems. In general, a nonlinear analysis will produce lower axial forces in columns of braced frames than that determined from an upper bound analysis in which it is assumed that all braces deliver their peak inelastic forces into the columns simultaneously. Avoid penalties caused by a lack of redundancy. For some systems, design penalties can occur because of a lack of redundancy (requiring ρ = 1.3). Where nonlinear analysis is used, the redundancy factor can be taken as 1.0. Avoid component design penalties where the design must be based on load combinations that include the overstrength factor Ω0. Where nonlinear analysis is used in accordance with Chapter 16, the overstrength factor can be taken as 1.0 in all situations. This is attributable to improved estimates of component demand when nonlinear analysis is used and to the strict deformation and force-based acceptance criteria speciﬁed in Section 16.4. Increased overall drift limits. Where nonlinear analysis is used, drift limits may be taken as 2.0 times the values speciﬁed in Table 12.12-1. Given that nonlinear analysis is carried out at the MCER level ground motions and Table 12.12-1 is tied to design-level motions, the effective increase in the drift limit is equal to 2.0 × (2/3) = 1.33 (Section 11.4.5). Performance-based design. Although performance-based design is not yet fully embraced in ASCE 7-16, the analysis procedures described in Chapter 16 of ASCE 7 are utilized in ASCE 41-17 (ASCE 2017b) and in greater detail in the FEMA P-58 (FEMA 2012) procedure.

The preceding alternatives are allowed via the use of Sections 1.3.1.3 and 11.1.4. Although nonlinear analysis is often used for systems with seismic isolation (Chapter 17) and/or passive energy devices (Chapter 18), the analysis requirements are different from those speciﬁed in Chapter 16.

25.1 Development Process The nonlinear analysis provisions in Chapter 16 were adapted from similar provisions developed for the 2015 NEHRP Recommended Provisions (FEMA 2015a, b). The work to develop the NEHRP NRH procedures was carried out by Issue Team 4, which included nearly 30 participants from professional practice, academia, and government agencies. The Chapter 16 commentary of the 2015 NEHRP Provisions provides a detailed technical background of the new code requirements, and this background is further detailed in a series of four Earthquake Spectra articles (Haselton et al. 2017a, b; Zimmerman et al. 2017; Jarrett et al. 2017). A special task committee of the ASCCE 7-16 Seismic Subcommittee used the NEHRP procedures as a starting point, and through a deliberative process made several changes that were approved by the full Seismic Subcommittee and by the main committee.

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The Chapter 16 provisions for NRH analysis have the following subsections: 16.1 16.2 16.3 16.4 16.5 16.6

General Requirements Ground Motions Modeling and Analysis Analysis Results and Acceptance Criteria Design Review Consensus Standards and other Referenced Documents

The first five of these subsections are briefly described next.

General Requirements Section 16.1 provides the general requirements for the nonlinear analysis. Key to this section is the requirement that the structure analyzed (to the extent possible) be designed initially using the elastic analysis procedures specified in Chapter 12. However, in anticipation of an analysis that explicitly accounts for inelastic response, some important requirements in the chapter are waived. For example, the redundancy factor, ρ, can be taken as 1.0, load combinations including the overstrength factor, Ω0, are not required, and amplification of accidental torsion is not required (even when accidental torsion and torsional amplification is required for design with ELF or MRS analysis). Also provided in Section 16.1 are detailed requirements for documentation of the analysis and design process.

Ground Motions It is required to use not less than 11 pairs of recorded or simulated ground motions that have characteristics consistent with general tectonic regime, magnitude, and fault distances for the site. Ground motions must be modified to provide a ground shaking intensity consistent with the MCER level events. Modification may be performed by use of amplitude scaling, or by spectral matching. In both cases the modification is relative to a target response spectrum, which can be either the basic ASCE 7 spectrum (Sections 11.4.7 and 11.4.8) or a site-specific target spectrum (sometimes called a conditional mean or scenario spectrum). Although a scenario spectrum may provide a more realistic demand over the range of structural frequencies that are excited during an earthquake, special expertise is required and there is an added cost for developing the spectra. In addition, there is a requirement that at least two target spectra be used in each direction of response, and this, at a minimum, doubles the number of ground motions required for the analysis.

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In amplitude scaling, all of the ground accelerations in both horizontal components of the ground motion are multiplied by the same factor, and a maximum direction spectrum is developed. Over a specified range of periods, the average ordinate of the maximum direction spectrum for the 11 ground motions shall not fall below 90% of the target spectrum (see FAQ A15 in Chapter 30 of this guide for an overview of the procedure used to develop a maximum direction spectrum). When spectrum matching is used, the ground motion is modified by use of a procedure that produces a ground motion spectrum that has a shape very similar to the target spectrum. The average of the maximum direction spectra from the matched records must equal or exceed 110% of the ordinate of the target spectrum over the same range of periods used in amplitude scaling. It is noted that the spectral matching approach is more stringent than the amplitude scaling approach because of reasons cited in the commentary. In addition, “unacceptable responses” are allowed for 1 in 11 ground motions for Risk Category I and II buildings where amplitude scaling is used but are prohibited where spectral matching is used. The two horizontal components of the modified ground motions must be applied simultaneously in orthogonal directions. Section 16.2.4 provides requirements for application of horizontal motions. Application of vertical components may be required in some circ*mstances, as specified in Section 16.1.3. Significant background on the requirement for ground motion selection and modification in the 2015 NEHRP provisions and in ASCE 7-16 may be found in Haselton et al. (2017a). A more general background is given in NIST (2011). Specific examples are available in Zimmerman et al. (2017), and in the set of examples provided in FEMA P-1051 (FEMA 2016). There are several sources for obtaining ground motion records from actual events. Among the most complete collections is the database provided by the Pacific Engineering Earthquake Research Center (PEER).

Modeling Section 16.3 provides detailed requirements for mathematical modeling. In all cases the system must be modeled in three dimensions, ground motions must be simultaneously applied at full value in the two orthogonal directions, inelastic behavior must be explicitly included, and second-order effects (P-delta effects) must be captured. It is very important to note that the mathematical model must be able to predict system collapse. This is because of the requirement that the global acceptance criteria allow no more than one “unacceptable response,” which includes a simulated collapse. In some cases, it can be extremely challenging to adequately capture collapse. Modeling of elements expected to respond in an inelastic manner, called deformation-controlled elements in the standard, must be able to track cyclic degradation in stiffness and strength, and in some cases complete loss of capacity (no residual strength). Modeled behavior must be consistent with available test results, or where applicable, with the requirement of ASCE 41-17 (ASCE 2017b). However, that ASCE 41 provides basic “backbone” behavior, but does not specify

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requirements for cyclic loss of strength and stiffness wherein the losses become more severe during the response. In many cases it is also important to capture interactive effects, such as axial-force bending-moment interaction. Finally, for systems in which diaphragm flexibility or inelastic behavior is expected to be important to the response, such effects should be modeled explicitly. Gravity loads must be applied to the mathematical model before the dynamic analysis is performed. Levels of gravity load are specified in Section 16.3.2. The gravity loading also serves to initialize the required P-delta effects. It is essential that bidirectional lateral and system-wide torsional P-delta effects are realistically captured. This usually requires a spatial distribution of “geometric stiffness” throughout the structure. Accidental torsion must be included where required in Section 16.3.4. This must be implemented by a physical offset of the center of mass. See Chapter 20 of this guide for a procedure for modification of diaphragm mass distribution to provide the required offset where this is not automatically accommodated by the software. Note that the accidental torsion must be applied with four 5% offsets (plus and minus in each direction, without amplification), even where the triggering torsional irregularity occurs only for one of the four eccentricities. This requirement multiplies by four the number of required response history analysis cases, which is a significant incentive for proportioning the system such that the accidental torsion requirement is not triggered. System-level damping is usually modeled using linear viscous damping. Two approaches are in general use: Rayleigh damping and modal damping. Use of Rayleigh damping has the tendency to provide spurious viscous damping forces in inelastic components (Charney 2008) and should be used with caution. In most cases the spurious forces can be minimized by not assigning any stiffness proportional damping to inelastic components (Zareian and Medina 2010). Modal damping tends to avoid these problems (Chopra and McKenna 2016). Specific requirements are not provided in Chapter 16 for foundation modeling. The reader is referred to NIST (2012) for recommended procedures for foundation modeling where it is expected that foundation–soil–structure interaction is significant. Additional general sources of information for modeling inelastic response are provided in NIST (2017). Specific requirements for modeling structural steel and reinforced concrete systems will be provided in future publications.

Acceptance Criteria Acceptance criteria provide the limits for acceptable response for the global system (Section 16.4.1) and for the structural components (Section 16.4.2). Component requirements are further divided into force-controlled and deformation-controlled actions, and elements of the gravity system. Global acceptance criteria evaluate unacceptable responses and story drift. An unacceptable response (Section 16.4.1.1) occurs where (1) the solution fails to

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Nonlinear Response History Analysis

converge, (2) predicted demands on deformation-controlled elements exceed the valid range of modeling, (3) predicted demands on critical or ordinary forcecontrolled elements exceed element capacity, or (4) predicted demands on elements that are not specifically modeled (e.g., gravity systems) exceed the ability of these elements to sustain their vertical loads. Although not specifically stated, a system collapse would also be an unacceptable response because this would certainly cause the development of deformations or forces that exceed the capacities for the preceding items (2) through (4). This, theoretically, implies that models must be able to capture collapse, which is a significant hurdle in the development of the mathematical model. Unacceptable responses are allowed for only one in 11 ground motions for Risk Category I and II systems and for which spectral matching was not used. It is believed that allowing one in 11 unacceptable collapses for the MCER level ground motions is consistent with allowing a 10% probability of collapse for the same risk category systems subjected to the same level of ground motions. Story drift limits are two times the tabulated values in Table 12.12-1. For masonry shear wall structures the limits of Table 12.2-1 applicable to masonry structures shall not apply and these structures shall instead comply with the limits for “other structures.” The factor of two is partially because the nonlinear analysis is run at MCER rather than DE motions (a factor of approximately 1.5) and because Cd is usually less than R (a factor of R/Cd). It is important to note that drifts are measured at the edges of the building, even if the system is torsionally regular. Element acceptance criteria is provided for deformation and for force-controlled components. Deformation-controlled components are those for which significant deformation capacity is provided through special detailing. These elements are modeled with the nonlinear characteristics described previously. Forcecontrolled elements are those elements that have very limited ductility and which can be modeled using linear properties. The commentary provides examples of force-controlled and deformation-controlled elements, for example • •

Force-controlled components: shear in reinforced concrete and axial forces in diaphragm collectors; and Deformation-controlled components: ﬂexure in reinforced beams, columns, and walls; and axial yielding in buckling restrained braces.

The force and deformation limits are based on the criticality of the components in the prevention of collapse where the degree of criticality is “noncritical,” “ordinary,” or “critical.” Specific definitions are not provided in the standard or in the commentary. However, a critical element would be one in which loss of capacity could cause a partial collapse of a significant portion of the structure or of the entire structure.

Analysis Review Analysis performed under the requirements of Chapter 16 must be peer reviewed by an independent ﬁrm or individual. Requirements for the review, as well as for the qualiﬁcations of the reviewers, are provided in Section 16.5.

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Analysis Validation

It is virtually impossible to assess the accuracy of a nonlinear dynamic analysis. However, conﬁdence may be obtained in the results by performing the analysis in such a manner that nonlinearities and other complex behaviors are introduced in a systematic manner. The following steps are suggested: •

• •

•

Linear static and dynamic analyses should be performed before the nonlinear analysis is attempted. This analysis should be run with and without P-delta effects. The inﬂuence of P-delta effects on the computed modal properties should be evaluated. Mode shapes should be reviewed and animated for all important modes. A free vibration analysis of the elastic model should be performed to show that the damping (computed log decrement) is as expected. A nonlinear static pushover analysis should be performed under bidirectional loading and including accidental torsion (even if not required for the dynamic analysis). This analysis should be run with and without P-delta effects. Trial nonlinear dynamic analyses of the structure should be performed for a subset of ground motions, with and without P-delta effects. If available in the software used, an energy balance should be plotted to demonstrate that the input energy is precisely balanced by the system energy.

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26 Diaphragms and Collectors

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

An entirely new approach was introduced in Section 12.10.3 for determining diaphragm forces in precast concrete buildings. This method is mandatory for such buildings in SDC C through F and may be used in lieu of the traditional method which is retained in Section 12.10.1

This chapter discusses Section 12.10 of ASCE 7, which covers the computation of in-plane ﬂoor diaphragm forces, including collector and chord elements. Diaphragm forces caused by both inertial and system effects are included. ASCE 7-16 has introduced a new alternative diaphragm design methodology and it is discussed herein. The structure considered in this example is a 6-story ofﬁce building located near Memphis, Tennessee. The pertinent information for the building and the building site are as follows: Site Class = B (measured) SS = 0.6g S1 = 0.2g Fa = 1.0 Fv = 1.0 SDS = (2/3) SS × Fa= 0.400g SD1 = (2/3) S1 × Fv= 0.133g Risk Category = II Importance Factor Ie = 1.0 Seismic Design Category = C

(Table 11.4-1) (Table 11.4-2) [Equations (11.4-1) and (11.4-3)] [Equations (11.4-2) and (11.4-4)] (Table 1.5-1) (Table 1.5-2) (Tables 11.6-1 and 11.6-2)

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Figure G26-1. Typical ﬂoor plan of a 6-story building. A plan view of the structural system for the building is shown in Figure G26-1. Intermediate steel moment frames resist all of the forces in the east–west direction, and a dual intermediate moment frame–special concentrically braced frame system is used in the north–south direction. The lowest story has a height of 15 ft, and the upper stories each have a height of 12.5 ft. The total seismic weight of the system W is 7,500 kips. This example considers loads acting in the north–south direction only. The design values for the dual system are determined from Table 12.2-1 and are summarized as follows: R=6 Ω0 = 2.5 Cd = 5.0 Height limit = None The period of vibration from structural analysis is 0.73 s. This period controls over the upper limit period T = CuTa, which is 0.85 s for this structure. The seismic response coefﬁcient is taken as the larger of the values computed from Equations (12.8-3) and (12.8-5) as Cs =

S D1 0.133 = 0.0304 = TðR=I e Þ 0.73ð6=1Þ

C s = 0.044S DS I e = 0.044ð0.40Þð1Þ = 0.0176 > 0.01 The design base shear [Equation (12.8-1)] is V = C s W = 0.0304ð7,500Þ = 228 kips

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The ﬂoor deck consists of a 4.5 in. concrete slab over metal deck. This slab must resist both inertial forces and forces developed because of shear transfer between the lateral force–resisting elements. Also considered in the analysis are the collector elements (drag struts) and diaphragm chords. These elements are shown in Figure G26-1. The elements shown as diaphragm chord elements act as collector elements when seismic forces act in the east–west direction. The inertial forces at a given level x are computed in accordance with Section 12.10.1.1 and Equation (12.10-1) as n X

F px =

i=x n X

Fi wpx = qpx wpx

(12.10-1)

i=x

where Fi = Lateral force applied to level I which is derived from Equations (12.8-11) and (12.8-12), wi = Weight at level i, wpx = Weight of the diaphragm (or portion thereof) at level x, and n = Number of levels. The term qpx is not explicitly used in ASCE 7, but it is a convenient parameter to determine. The force Fpx that is obtained from Equation (12.10-1) shall not be less than 0.2SDSIewpx [Equation (12.10-2)] but need not exceed 0.4SDSIewpx [Equation (12.10-3)]. The results of the analysis for the coefficient qpx is provided in Table G26-1. The minimum value given by 0.2SDSIe controls at each level. By observing Table G26-1, to calculate the diaphragm forces, the forces applied to the vertical lateral system (Fx from Section 12.8.3) must first be calculated. Forces at each level from Section 12.8.3 are different from the diaphragm forces from Section 12.10.1.1. The reason for this is described subsequently. Section 12.8.3 takes the base shear, V, and distributes it vertically to each floor level. The forces at each level in Figure G26-2 form a triangular shape (or a slightly curved shape for longer period structures). The resulting deflections mimic the first mode shape and include 100% of the mass. This is a conservative and necessary approach for the design of the lateral force–resisting system that exists in the vertical plane. Figure G26-2(a and b) show that the story shears increase from top story to bottom story. However, the influences of higher modes must also be considered. At higher modes, the deflected shape is more akin to an S-shaped curve, with accelerations and forces at one floor occurring in the opposite direction of the floor above and below. Although the higher modes will not produce higher story shears when compared to the forces of Section 12.8.3, the higher modes will produce locally higher forces within the horizontal diaphragm. Section 12.10.1.1 produces the forces caused by the higher mode effects. Other provisions within Section 12.10

Seismic Loads

1,150 1,250 1,250 1,250 1,250 1,250 7,400

wx (kips)

77.5 65 52.5 40 27.5 15

hx (kips) 146,984 131,313 103,487 76,420 50,323 25,601 534,128

wxhkx 0.28 0.25 0.19 0.14 0.09 0.05 1.00

wxhkx/Σ 62.7 56.1 44.2 32.6 21.5 10.9 228.0

Fx (kips) 0.055 0.045 0.035 0.026 0.017 0.009

qx Fx/wx 62.7 118.8 163.0 195.6 217.1 228.0

ΣFi (kips) 1150 2400 3650 4900 6150 7400

ΣWi (kips)

0.055 0.049 0.045 0.040 0.035 0.031

qpx ΣFi/ΣWi

62.7 61.9 55.8 49.9 44.1 38.5

Fpx (kips)

92 100 100 100 100 100

Fpx min (kips)

184 200 200 200 200 200

Fpx max (kips)

Section 12.10.1.1 Forces applied to horizontal diaphragm qmin = 0.08, qmax=0.160

Note: qmin = 0.2SDSIe = 0.2(0.40)1.0 = 0.080 ; qmax = 0.4SDSIe = 0.4(0.40)1.0 = 0.160 ; T = 0.73 s; k = 1.115 interpolated from Section 12.8.3; and base shear V = 228 kips.

6 5 4 3 2 1 Sum

Level

Section 12.8.3 Forces at each level applied to lateral system in the vertical plane

Table G26-1. Diaphragm Forces for a 6-Story Building

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Figure G26-2. First mode and higher mode effects in diaphragms: (a) top; and (b) bottom. are intended to assure that these diaphragm forces have an appropriate and adequate load path through the diaphragm, chords, and collectors, and connect to the seismic force–resisting system that exists in the vertical plane. On the basis of the preceding calculations, each level of the diaphragm must be designed for a force of 0.08 times the seismic weight at the level of interest. For the ﬁfth level, for example, the total diaphragm force is 0.08(1,250) = 100.0 kips. From a structural analysis perspective, the most accurate way to determine the stresses and forces in the various components of the diaphragm would be to model the diaphragm with shell or membrane elements and distribute the 100 kip force to the individual nodes of the element on a “tributary mass” basis. Thus, the diaphragm would be modeled as semirigid, although Section 12.3.1.2 would deﬁne this diaphragm as rigid. Other analysis approaches are also available, including the linear collector method, the distributed collector method, and the strut and tie modeling method. Sabelli et al. (2009) provides a description of these methods. Additional comments regarding the analysis and design of the diaphragm components are as follows:

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Discontinuities in the lateral load–resisting elements above and below the diaphragm cause forces to be transferred between the lateral load–resisting elements and impose in-plane forces in the diaphragm. These forces must be added to the forces developed from the diaphragm forces Fpx that have been determined with Equation (12.10-1). In accordance with Section 12.3.4.1(7) elements resisting the transfer forces must be designed with the redundancy factor ρ that has been determined for the structural system, but the forces caused by the application of Fpx alone may be designed with a redundancy factor of 1.0. Section 12.10.1.1 requires that the transfer force be increased by the overstrength factor of Section 12.4.3.

In SDC C and above, collector elements must be designed using the overstrength factor Ω0 that has been assigned to the structural system resisting forces in the direction of Fpx.

Special care has to be taken to produce realistic diaphragm, collector, and chord forces when the diaphragm is modeled as rigid in a three-dimensional structural analysis.

Recovering diaphragm forces from a modal response spectrum analysis is not straightforward. It is reasonable to use the approach outlined in Section 12.10 to determine diaphragm forces, even when MRS has been used for the analysis of the lateral load–resisting system. However, as mentioned in Point 1, the total diaphragm forces must include the transfer forces, if present, and these forces must be recovered from the MRS analysis.

ASCE 7-16 has introduced a new Section 12.10.3, “Alternative Design Provisions for Diaphragms, Including Chords and Collectors.” It is mandatory for precast concrete diaphragms in SDC C, D, E, and F. The method is allowed as an alternative method for precast concrete diaphragms in SDC B, cast-in-place concrete diaphragms, and wood-sheathed diaphragms supported by wood diaphragm framing. New deﬁnitions may be found in Section 11.2 for terms such as ﬂexure-controlled diaphragm, shear-controlled diaphragm, and diaphragm transfer forces. The methodology introduces the following precast concrete diaphragm design option categories: • • •

Basic design option (BDO), which targets elastic diaphragm flexural response in the design earthquake, and MCER earthquake, Elastic design option (EDO), which targets elastic diaphragm flexural response in the design earthquake and inelastic response MCER earthquake, and Reduced design option (RDO), which targets inelastic diaphragm flexural response in the design earthquake and inelastic response MCER earthquake.

For BDO, EDO, and RDO the response in shear is expected to be elastic for both the design earthquake and the MCER earthquake. See commentary Section C12.10.3.5 for additional discussion. New symbols are defined in Section 11.3 and include variables such as diaphragm design acceleration coefficients Cp0, Cpi, Cpn, Cpx, and Cs2.; RS = diaphragm design force reduction factor (Table 12.10-1); Γm1, Γm2 = first

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and higher modal contribution factors, respectively, and a few other new symbols specific to this method. Additional provisions may be found in Chapter 14; of particular interest are Sections 14.2.4, 14.2.4.2, and 14.2.4.4. The reason for this new method is that there was concern that the level of diaphragm design force from Section 12.10 may not ensure that diaphragms have sufficient strength and ductility to mobilize the inelastic behavior of vertical elements of the seismic force–resisting system. The provisions of Section 12.10.3 consider both the significantly greater forces observed in near-elastic diaphragms and the anticipated overstrength and deformation capacity of diaphragms, resulting in an improved distribution of diaphragm strength over the height of buildings and among buildings with different types of seismic force–resisting systems.

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27 Nonstructural Components

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: • • • • • • •

Table 13.5-1 has been modified substantially. Egress stairs (Section 13.5.10) are included as well as changes to Ω0, Section 13.1.4 has modifications to the exemptions, Section 13.3.1.4 has new provisions for dynamic analysis and floor response spectra, and Section 13.3.3 discusses component period, Section 13.5.3 has new provisions for exterior nonstructural wall elements and connections, Section 13.5.6.2.2 has new provisions for acoustic tile and lay-in panel ceilings, Section 13.6.7 has revisions for distribution systems: piping and tubing systems, and Various other minor modifications.

Chapter 13 of the standard provides seismic design requirements for nonstructural components. In this chapter, the focus is on the use of the empirical method (Section 13.3.1.1) for calculation of seismic forces on a variety of architectural components and mechanical/electrical components that are attached to a 4-story reinforced concrete frame in San Francisco, California. Also illustrated is the development and use of a ﬂoor response spectrum (Section 13.3.1.4) for an 8-story steel frame building located near Memphis, Tennessee. During an earthquake, a typical building will experience horizontal ground acceleration. If the structure is rigid (inﬁnite lateral stiffness), there will be no

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Figure G27-1. States of acceleration in a building with nonstructural components. lateral deformation at the floor and roof levels of the structure, and the attachment points of all nonstructural components will have the same acceleration as the base of the structure as shown in Figure G27-1(a). If the building is flexible laterally, each level will accelerate relative to the base of the structure; as shown in Figure G27-1(b), the acceleration at each level of the building is equal to the ground acceleration plus deformational acceleration relative to the base (i.e., its attachment point). This total floor or roof acceleration is what the nonstructural component feels at its base. If the nonstructural component is rigid, it will develop a seismic inertial force equal to its weight times the total floor or roof acceleration. If the component is flexible, as depicted in Figure G27-1(c), it will develop an additional acceleration, and now the component inertial force is the weight times the total (ground + structure + component) acceleration felt by the component. Although these accelerations add, they may have different signs (positive or negative), and it is unlikely that all three components of acceleration will reach their peak at the same time. ASCE 7-16 provides two basic methods to compute the component accelerations. The first method, provided in Section 13.3.1.1, is empirical and is very simple to apply. The second method, provided in Section 13.3.1.4, requires some form of a dynamic analysis that ranges from computing modal properties only to performing a linear or nonlinear response history analysis. The empirical procedure uses Equation (13.3-1) to determine the component force Fp as 0.4ap S DS z Fp = (13.3-1) 1 + 2 Wp RP h Ip

and is subject to the limits F p < 1.6S DS I P W P

(13.3-2)

F p > 0.3S DS I P W P

(13.3-3)

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Equation (13.3-1) is a version of Newton’s second law, F = ma, that is, force equals mass (the weight of the component, Wp) times acceleration in g units. The product of factors Downloaded from ascelibrary.org by UNIVERSITY OF NEW SOUTH WALES on 04/18/20. Copyright ASCE. For personal use only; all rights reserved.

0.4S DS ap

z 1+2 h

represents the total acceleration at the center of mass of the component. The component force used for design is the product of this acceleration and the component weight, divided by the quantity (Rp/Ie). The value 0.4SDS is an approximation of the peak ground acceleration, ap is a component amplification factor determined from Tables 13.5-1 (architectural components) or 13.6-1 (mechanical/electrical components), and the term in parenthesis amplifies the acceleration from 1.0 at the base of the building (z = 0) to 3.0 at the roof of the building (z = h). The value of ap ranges from 1.0 for a rigid component to 2.5 for a flexible component. Rp, also obtained from Tables 13.5-1 or 13.6-1, is the component response modification coefficient, which is a measure of the ductility and overstrength inherent in the component. This is much the same as R for a building’s lateral system. Tables 13.5-1 and 13.6-1 also contain overstrength factors that are used for anchorage to concrete or masonry. Ip is the importance factor of the component; Ip is derived from Section 13.1.3 and is either 1.0 or 1.5 depending on functionality for life safety purposes after an earthquake or release of toxic materials. Although a building may have a seismic importance factor Ie of 1.0, 1.25, or 1.50, Ip is independent of Ie and fully dependent on Section 13.1.3. So, it is possible to have an Ip = 1.5 component in a building with Ie = 1.0. It is also possible to have an Ip = 1.0 component in a building with Ie =1.25. In the dynamic approach, the component force is computed as ai ap W p F p = R Ax

(13.3-4)

where the term ai is the total (ground plus relative) acceleration computed by dynamic analysis at level i, using R = 1.0. The upper and lower limits given by Equations (13.3-2) and (13.3-3) are applicable. Section 13.3.1.4.1 provides a variation of the dynamic analysis approach wherein a floor response spectrum is developed at each level of the structure. The floor (or roof) spectrum is similar to a ground motion response spectrum with the primary differences being (1) that the spectrum is developed by using the total floor acceleration (ground acceleration plus relative acceleration at the given level), and (2) that the damping used to develop the floor spectra may be different from that used to compute the relative floor acceleration. The component acceleration is equal to the floor’s (or roof’s) spectral acceleration determined at the component’s period of vibration, Tp. The component period can be

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Figure G27-2. Floor spectrum concept. provided by the component manufacturer or by using Equation (13.3-11) as follows: sffiffiffiffiffiffiffiffiffi Wp (13.3-11) T p = 2π K pg The component force Fp is then determined using Equation (13.3-4) with ai coming from the appropriate spectrum and with ap taken as 1.0 (because the component’s flexibility is now included in the development of the floor spectrum). Figure G27-2 illustrates the floor spectrum concept, and an example is provided subsequently in this chapter. Section 13.3.1.4.2 of the standard provides an alternate floor response spectra approach. In the author’s opinion, the method is technically incorrect and should not be used because the modal participation factor pix given in Equation (13.3-5) depends on the method used to normalize the mode shapes, and this fact has not been considered.

27.1 Example of Empirical Method for 4-Story Reinforced Concrete Building In this example the design forces on a variety of architectural and electrical components are determined using the empirical method provided in Section 13.3.1.1 (horizontal forces) and 13.3.1.2 (vertical forces). The structure containing the components is a 4-story reinforced concrete special moment frame sited on Site Class D soils in San Francisco, California. SDS for the site is 1.00g. Figure G27-3 illustrates the type and location of the components considered, and Figure G27-4 shows the egress stair system that is also considered in the example. Tables 13.5-1 and 13.6-1 were used to determine the values of ap, Rp, and Ω0. The tables have footnotes that describe overstrength, Ω0, as required for nonductile anchorage to concrete and masonry and (Table 13.6-1 only) factors for vibration isolator mounting (Fp × 2.0).

Seismic Loads

281

Nonstructural Components

Figure G27-3. Fp values for nonstructural components building elevation/cross section.

Figure G27-4. Building elevation/cross section for egress stairs. The building contains components labeled and described as follows: •

•

G1, G2, G3, G4, G5 = electrical generators. This is predominantly a rigid motor on a wide ﬂange skid beam with four anchor rods to the concrete ﬂoor below, one anchor at each corner, not mounted on vibration isolators. Wp = 1,000 lb. ○ Table 13.6-1: Generator, ap = 1, Rp = 2.5, Ω0 = 2. I1, I2, I3, I4, I5 = instrumentation cabinets. This is a cabinet with sheet metal walls and contains electrical modules fastened within. It is 7 ft tall and 1.5 ft (square) in plan dimension. ○ Table 13.6-1: instrumentation cabinet ap = 2.5, Rp = 6, Ω0 = 2.

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282

Seismic Loads

•

C1, C2, C3, C4, C5 = an 8 in. solid grouted masonry wall cantilevered about its base in a guardrail-like fence or parapet constitution, 5 ft tall, 83 psf × 2.4 ft long sections = 1,000 lb each. ○ Table 13.5-1: cantilever interior nonstructural walls, ap = 2.5, Rp = 2.5, Ω0 = 2. W1, W2, W3, W4 = concrete precast wall panels, 8 in. thick, 12 ft tall × 8.3 ft long = 10.0 kips, attached at four corners. ○ Table 13.5-1: exterior nonstructural wall elements: ○ Wall element, ap = 1, Rp = 2.5, Ω0 = NA, ○ Body of wall panel connectors, ap = 1, Rp = 2.5, Ω0 = NA, and ○ Fasteners of the connecting system, ap = 1.25, Rp = 1, Ω0 = 1.0.

See Section 13.5.3 for descriptions and further strength requirements, as well as accommodation for story drifts. •

S3A, S3B = egress stairs. Note that S3A is orthogonal to the plane of shaking, and S3B is in the plane of shaking. The stairs are prefabricated of structural steel and concrete. The top of the stair is attached the ﬂoor slab and this connection provides resistance in both the vertical and horizontal directions. The bottom of the stair has vertical support and horizontal slotted connections to allow movement parallel to the stair, but the slots prevent movement perpendicular to the stair. The stairs are 4 ft wide and weigh 10.0 kips each. ○ Table 13.5-1: Egress stairs not part of building seismic force-resisting system, ○ Stairway body, ap = 1, Rp = 2.5, Ω0 = 2, and ○ Fasteners and attachments for egress stairs, ap = 2.5, Rp = 2.5, Ω0 = 2.5.

Per (13.1.3), Ip = 1.0 for all previously mentioned components, except the egress stair, which has an Ip = 1.5. The height, z, is the point of attachment of the component with respect to the base of the structure. It is the location where acceleration is imparted into the component. For a wall panel spanning between two floors as shown herein, one may use the average height of the attachments. See commentary C13.3.1 for more specific advice and options. Notice that stair S3A uses z = 30 ft (average height of attachments), and stair S3B uses 36 ft. This is because horizontal accelerations are imparted to the stair at, and only at, the attachment at elevation 36 ft. Tables G27-1 and G27-2 and Figures G27-3 and G27-4 provide spreadsheets of calculations and graphics of loadings, respectively. The tabular values in bold govern. The cantilever element C1 is essentially a 5 ft tall masonry fence. Chapter 13 yielded Fp = 0.4Wp and Ω0 = 2. If it were 6 ft or greater in height, then ASCE 7 would trigger the classification of nonbuilding structure (Section 15.6.8 “Ground Supported Cantilever Walls or Fences”) and Table 15.4-2 yields R = 1.25, Ω0 = 2, Cd = 2.5. Section 15.4 is invoked, which in turn invokes the equations of Section 12.8. For the example location herein, this would yield a base shear of

Seismic Loads

1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 10,000 10,000 10,000 10,000 10,000 10,000

G1 G2 G3 G4 G5 C1 C2 C3 C4 C5 I1 I2 I3 I4 I5 W1 W2 W3 W4 W4 connector1,2,3 W4 fastener1,2,3

1.00 1.00 1.00 1.00 1.00 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 1.00 1.00 1.00 1.00 1.00 1.25

ap 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 6.00 6.00 6.00 6.00 6.00 2.50 2.50 2.50 2.50 2.50 1.00

Rp 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 NA NA NA NA NA 1.00

Ω0 0 12 24 36 48 0 12 24 36 48 0 12 24 36 48 6 18 30 42 42 42

z (ft) 1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0 1.25 1.75 2.25 2.75 2.75 2.75

(1+2z /h) 160 240 320 400 480 400 600 800 1,000 1,200 167 250 333 417 500 2,000 2,800 3,600 4,400 4,400 13,750

Fpa (lb) 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 16,000 16,000 16,000 16,000 16,000 16,000

Fp maxb (lb)

300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 3,000 3,000 3,000 3,000 3,000 3,000

Fp minc (lb)

Equation (13.3-1).

Equation (13.3-2).

Equation (13.3-3).

For all components SDS = 1.0g, Ip = 1.0, and h = 48 ft. Fastener and connector concept applies to W1, W2, W3, and W4. Body of panel and connectors per Section 13.5.3. Fasteners of the connecting system per Section 13.5.3. Tabular values are bold.

Note:

Wp (lb)

Component

Table G27-1. Forces on Components G, C, I, and W

Nonstructural Components

283

284

Seismic Loads

Table G27-2. Forces on Stair Components

Component S3A body S3A fasteners and attachments S3B body S3B fasteners and attachments

Wp (lb)

Ω0

z (ft) (1+2z/h)

Fpa (lb)

Fp maxb (lb)

Fp minc (lb)

10,000 1.00 2.50 2.00 10,000 2.5 2.50 2.50

30 30

2.25 2.25

5,400 24,000 4,500 13,500 24,000 4,500

10,000 1.00 2.50 2.00 10,000 2.5 2.50 2.50

24 36

2.50 2.50

6,000 24,000 4,500 15,000 24,000 4,500

Notes: For all components SDS = 1.0g, Ip = 1.5, and h = 48 ft. Tabular values are bold. Section 13.5.3. Tabular values are bold. a

Equation (13.3-1).

Equation (13.3-2).

Equation (13.3-3).

V = CsW

[Equation (12.8-1)]

Cs = S DS =ðR=I e Þ

[Equation (12.8-2)]

which results in V = SDS (W)/(R/Ie) = 1.0 W/(1.25/1.0) V = 0.8W In addition, a distributed mass cantilever structure should have its base shear distributed over its height in a triangular fashion, whereby the center of force is located at 2/3 the height, even though the center of gravity of the fence/wall is at midheight. This is invoked via ASCE 7 Sections 15.1.3 and 12.8.3. A detailed set of calculations is provided next for Instrumentation Panel I5. Figure G27-5 provides a graphical representation of the calculation results. Detailed calculations for Instrumentation Cabinet I5: F p = ½0.4 ðap Þ S DS W p =ðRp =Ip Þ × ½1 + 2z=h

(13.3-1)

Fp = [0.4 (2.5) (1.00) 1,000 lb/(6/1.0)] [1+2 (48 ft/48 ft)] Fp = 500 lb F p max = 1.6 S DS I p W p

(13.3-2)

Fp max = 1.6 (1.00) 1.0 (1,000 lb) = 1,600 lb

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285

Nonstructural Components

Figure G27-5. Instrumentation Cabinet I5. F p min = 0.3 S DS I p W p

(13.3-3)

Fp min = 0.3 (1.00) 1.0 (1,000 lb) = 300 lb Fp = 500 lb governs Ev = 0.2 SDS Wp = 0.2 (1.00) 1,000 lb = 200 lb Reactions: Per corner/anchor Vu = 500 lb/4 anchors = 125 lb horizontal D = 1,000 lb/4 anchors = 250 lb Ev = 200 lb/4 anchors = 50 lb Eh = 500 lb (3.5 ft)/[(1.5 ft) (2 anchors)] = 583 lb Downward: Combined per Section 2.3.6 Pu = 1.2D + Ev + Eh = 1.2(250 lb) + 50 lb + 583 lb Pu = 933 lb compression downward Uplift: combined per Section 2.3.6 Tu = 0.9D − Ev − Eh = 0.9(250 lb) − 50 lb − 583 lb Tu = −408 lb tension upward

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286

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Eh is deﬁned in Section 12.4.2.1 as Eh = ρQE where the redundancy factor, ρ = 1.0 per Section 13.3.1.1, and QE represents all of the forces caused by Fp. For concrete ACI 318 (ASCE 7 Section 13.4.2.1) or masonry TMS 402/ACI 530/ ASCE 5 (ASCE 7 Section 13.4.2.2) calculations that require Ω0 overstrength, load cases shall be combined per ASCE 7 Sections 2.3.6 and 12.4.3; thus Ω0 = 2 Emh = Ω0 (QE) = Ω0 (Fp) = (2.0) 584 lb Tu = 0.9D − Ev − Emh = 0.9(250 lb) − 50 lb – (2.0)583 lb Tu = −991 lb tension upward Vu = 125 lb Ω0 = 125 lb (2.0) = 250 lb When including overstrength, Ω0, the Ω0 factor is applied only to the horizontal seismic load effects (i.e., because of Fp) and is not applied to Ev nor to dead load, Wp. Section 13.3.1.1 states that Fp shall be applied in at least two orthogonal directions. However, in following through the load combinations of Section 2.3.6 and deﬁnition of Qe in Section 12.4.2.1 and 12.4.3.1, the reader is directed to 12.5.3 and 12.5.4 whereby orthogonal effects must be considered. Although the requirements of Section 12.5.4 only mention “column or wall,” 12.5.3.1a mentions “members and foundations,” and logic would dictate that it is appropriate to design anchors at the corners of the cabinet for 100% of the forces in one direction and 30% of the forces in the perpendicular direction. This only applies to the loads caused by horizontal seismic effects Fp. Thus, the forces in the corner anchor rod would be as described next. Including orthogonal effects of Section 12.5.4: Vu = 1.0(125 lb) + 0.30(125 lb) = 163 lb Tu = 0.9D − Ev – (1.0)Eh north−south – (0.3) Eh east−west Tu = 0.9(250 lb) – 50 lb – (1.0)583 lb – (0.3)583 lb Tu = –583 lb tension upward And where overstrength Ω0 is required: Vu = 1.0(2.0)125 lb + 0.3(2.0)125 lb = 325 lb Tu = 0.9D – Ev – Emh = 0.9(250 lb) – 50 lb – (1.0)(2.0)583 lb – (0.3)(2.0)583 lb Tu = –1,341 lb tension upward In summary, for Generator G5, design the anchor rods for Vu = 163 lb and Tu = 583 lb, or where overstrength Ω0 is required, use Vu = 325 lb and Tu = 1,341 lb. Common errors when implementing Fp include •

Applying Fp at the ﬂoor level and not at the center of gravity of the component, thus ignoring the overturning effects (upward and downward reactions) and applying horizontal shear to the anchorage only,

Seismic Loads

287

Nonstructural Components

• •

Ignoring the 100%/30% combination, and Ignoring Ω0 where required.

Such errors are especially dangerous when the erroneous analysis results in no net uplift, when actually signiﬁcant uplift forces need to be considered. In this example, errors could yield results of 0 to 409 lb net tension when actually 1,343 lb should be applied. Note that 1,345 lb tension for all four anchor rods may appear surprising high because the cabinet weight is only 1,000 lb.

27.2 Development and Use of Floor Response Spectra In this example, floor response spectra are developed for an 8-story special steel frame structure, the elevation of which is shown in Figure G27-6. The intended use of the building is for offices, thus the risk category is II and the seismic importance factor Ie = 1.0. Spectra are provided for the fourth and eighth (roof) level for shaking in the east–west direction using three recorded ground motions than have been amplitude scaled to match the design spectrum at the structures fundamental (first mode) period of vibration, 2.5 s. Periods in Modes 2 through 5 are 0.914, 0.509, 0.336, and 0.264 s, respectively. In the direction of loading, the system is torsionally regular so accidental torsion has not been included in the analysis, and Ax = 1.0. The MCER spectral accelerations are

Figure G27-6. Elevation of 8-story building analyzed.

Seismic Loads

288

Seismic Loads

SS = 0.75g S1 = 0.30g The building is on Site Class B soils with no measurements taken. For this situation, the second paragraph of Section 11.4.3 states that Fa = 1.0, and Fv = 1.0. Design-level ground motions are SDS = 0.75(1.0)(2/3) = 0.5g SD1 = 0.30 (1.0)(2/3) = 0.2g The target spectral acceleration at T = 2.5 s is SD1/T = 0.2/2.5 = 0.08g = 30.9 in/s2 The three ground motions used in the analysis are from southern California. Ground motion parameters, as well as the scale factor required to match the 2.5 s ordinate of the 5% damped ground motion spectra with the target spectrum are provided in Table G27-3. Figure G27-7 shows the 5% damped response spectra for the three scaled records, the average of the scaled records, and the design target.

Table G27-3. Ground Motion Parameters for Floor Spectrum Analysis

Earthquake San Fernando Imperial Valley Northridge

PEER NGA ID

Year

68 169 953

1971 1979 1994

Magnitude

Site Class

6.6 6.5 6.7

D D D

Fault type

Epicenter distance (km)

Scale factor

Thrust Strike-slip Thrust

39.5 33.7 13.3

0.967 0.464 0.456

Figure G27-7. Ground motion spectra and target design spectrum.

Seismic Loads

289

Nonstructural Components

Relative acceleration histories were computed at the fourth floor level and the roof and were then added to the appropriate ground acceleration history to provide the history of the total floor and roof accelerations. Floor spectra for 1%, 3%, and 5% damping were then computed using the total accelerations, and envelope spectra were determined. The resulting fourth floor spectra are shown in Figure G27-8, and the roof spectra are provided in Figure G27-9. The use of the floor spectra is demonstrated for an architectural component with Rp = 2.5 and Ip = 1.0. For use with the empirical approach, values of ap = 1 (rigid component) and ap = 2.5 (flexible component) are considered. In all cases, Wp is taken as 1,000 lb.

Empirical Approach At Level 4, z/h = 52.5 ft/102.5 ft = 0.512 ft. For the rigid component Fp =

0.4ap S DS W p z 0.4ð1.0Þð0.5Þð1,000Þ 1 + 2 1 + 2ð0.512Þ = 162.4 lb = Rp 2.5 h Ip

1.0

For the ﬂexible component Fp =

0.4ap S DS W p z 0.4ð2.5Þð0.5Þð1,000Þ 1 + 2 1 + 2ð0.512Þ = 406.0 lb = Rp 2.5 h Ip

1.0

At the roof, z/h = 1.0. For the rigid component Fp =

0.4ap S DS W p z 0.4ð1.0Þð0.5Þð1,000Þ 1 + 2 = 1 + 2ð0.1.0Þ = 240.0 lb h ð2.5 Rp 1.0Þ Ip

For the ﬂexible component Fp =

0.4ap S DS W p z 0.4ð2.5Þð0.5Þð1,000Þ 1 + 2 1 + 2ð1.0Þ = 600.0 lb = Rp 2.5 h Ip

1.0

Lower limit: Fp = 0.3SDSIpWp = 0.3(0.5)(1.0)(1,000) = 150 lb Upper limit: Fp = 1.6SDSIpWp = 1.6(0.5)(1.0)(1,000) = 800 lb All values are between these limits, so the calculated values control. Using the ﬂoor spectra. the rigid system has Tp = 0.0. For the ﬂexible system. a component period Tp = 0.2 s is assumed.

Seismic Loads

290

Seismic Loads

(a)

(b)

(c)

Figure G27-8. Floor spectra for Level 4 of 8-story building: (a) 1% damping; (b) 3% damping; and (c) 5% damping.

Seismic Loads

291

Nonstructural Components

(a)

(b)

(c)

Figure G27-9. Floor spectra for roof level of 8-story building: (a) 1% damping; (b) 3% damping; and (c) 5% damping.

Seismic Loads

292

Seismic Loads

27.3 1% Damping

From Level 4 spectra: Level 4 Rigid: Flexible:

aiap = 93.1/386 = 0.241g aiap = 137.6/386 = 0.356g

Fp = 0.241(1,000)/(2.5/1.0) = 94.4 lb Fp = 0.356(1,000)/(2.5/1.0) = 142.4 lb

From roof spectra: Rigid: Flexible:

aiap = 146.3/386 = 0.379g aiap = 176.2/386 = 0. 456g

Fp = 0.379(1,000)/(2.5/1.0) = 151.6 lb Fp = 0.456(1,000)/(2.5/1.0) = 182.4 lb

For Level 4, the minimum value of Fp = 150 kip controls. For the roof level, the computed values of 151.6 kips for the rigid component and 182.4 kips for the flexible component control. In summary, the floor spectrum approach produced significantly lower values than the empirical method. In particular, it seems that for the 0.2 s period chosen, the dynamic magnifier ap = 2.5 seems excessive, as does the influence of the magnifier 1 + 2(z/h).

Seismic Loads

28 Nonbuilding Structures

Changes in ASCE 7-16 relative to ASCE 7-10 that affect this chapter: •

• • • • • • •

Section 15.1.3 allows use of 85% of base shear for modal analysis for certain nonbuilding structures such as stacks and wind turbines. For nonbuilding structures similar to buildings, this 85% was allowed in ASCE7-10 but eliminated in ASCE 7-16. The applicable modal analysis method for nonbuildings similar to buildings is found in Section 12.9.1. Section 15.1.4, “Nonbuildings Structures Sensitive to Vertical Ground Motions” has new provisions. This is applicable for tanks and vessels as well as horizontal cantilevers. Section 15.4.1, paragraph 5, allows relief from accidental torsion analysis in some specific situations. Section 15.4.9.4 has new requirements for post-installed anchors in concrete and masonry. Section 15.4.10.1 requires that shallow foundations be resistant to liquefiable conditions. Section 15.6.8 has new provisions for cantilever fences and walls. Section 15.7.6.1.2 has new provisions for sloshing of stored liquids. Various other minor modifications.

This chapter provides a set of examples that demonstrate the seismic force calculations for nonbuilding structures. Two examples are presented: a power station pipe rack structure supporting electrical fans and tanks, and a large equipment structure supported on a reinforced concrete mat. Nonbuilding structures are covered in Chapter 15 of the standard. Such structures are classiﬁed into two types: similar to buildings, and not similar to

293

Seismic Loads

294

Seismic Loads

buildings. Similar to buildings would include structures that have seismic force– resisting systems that are composed of braced frames and moment frames comparable to that which would be found in buildings (Table 12.2-1). Examples include a pipe rack, an unoccupied enclosure, or a building housing equipment. Nonbuilding structures not similar to buildings would include tanks on the ground, tanks on legs, silos, chimneys, trussed towers, cantilevered walls, and fences 6 ft and taller, and others. ASCE 7 Section 11.2 provides definitions for buildings and nonbuildings, and Section 11.1.3 allows the following: Buildings whose purpose is to enclose equipment or machinery and whose occupants are engaged in maintenance or monitoring of that equipment, machinery, or their associated processes shall be permitted to be classified as nonbuilding structures designed and detailed in accordance with Section 15.5 of this standard. For nonbuildings similar to buildings, Table 15.4.1 provides R, Ω0, and Cd values as well as the detailing requirements and system limitations. Often, nonbuilding structures cannot meet the detailing requirements specified by AISC 341 (AISC 2016b) or ACI 318 seismic Chapter 18 (ACI 2014). The following is a list of seismic detailing requirements that are often difficult to achieve in a nonbuilding structure: • • • • • •

Prequalified connections require field welding and weld testing, but stakeholders discourage the practice, especially welding on galvanized steel. Protected zones cause conflict with function of structure, for example, a pipe rack. Slenderness (kL/r) of brace minimums results in large connections in ordinary concentric braced frames. K bracing or knee bracing detailing is not allowed but is necessary for stakeholders. Strong column/weak beam proportioning is difficult to achieve. Large connections are required for long braces in lightweight structures.

To accommodate these situations, ASCE 7 allows nonbuilding structures to be designed without the seismic detailing of AISC 341 (seismic) and ACI Chapter 18 (seismic), provided that a very low R factor is used. This in essence is trading ductility for high elastic strength. For instance, Table 15.4-1 allows a steel structure to be detailed per AISC 360 (AISC 2015) (i.e., nonseismic) with R = 1.5 for braced frames and R = 1.0 for moment frames, even in SDC D, E, and F. An ordinary reinforced concrete moment frame may be designed with an R = 0.8 up to 50 ft tall and detailing per ACI Chapter 18 is not required. Section 15.4.1, Item 1, allows nonbuilding structures similar to buildings to use systems from Chapter 12, Table 12.2-1. Thus, a nonbuilding structure in SDC B and C may be designed without seismic detailing by selecting Table 12.2-1, H. “Steel Systems Not Speciﬁcally Detailed for Seismic Resistance”: R = 3, Ω0 = 3, Cd = 3, whereby the detailing required per Section 14.1 and Section 14.1.2.2.1 (exception) allows the use of AISC 360, and it need not be detailed per AISC 341.

Seismic Loads

295

Nonbuilding Structures

Although it is always wise to include seismic detailing where feasible, this brute strength, essentially elastic approach, of using a low R factor is often necessary and on occasion less expensive than other options for the wide variety of nonbuilding similar to building conﬁgurations and conditions.

28.1 Example 1: Pipe Rack This pipe rack is part of a power generating plant located approximately 3 mi south of the airport in Memphis, Tennessee. This power generating plant is not part of a public utility facility that would be classified as Risk Category IV, so therefore a review of ASCE 7 Table 1.5-1, as well as IBC 2018 Table 1604.5 (ICC 2017) classifies this power station as Risk Category III. A drawing of the structural system is given in Figures G28-1 through G28-3. The location of equipment is provided in Figure G28-3. This structure would classify as a nonbuilding structure similar to buildings for which specific requirements are provided in Section 15.5. Weights of structure and components: Allowance for piping (operating full), cable tray, other utilities at each level = 50 psf, Self-weight of structural steel and bar grating tributary to each level = 35 psf, Fin fan equipment units FF-1 and FF-2 = 12 kips each, and

Figure G28-1. Pipe rack structure.

Seismic Loads

296

Seismic Loads

Figure G28-2. Pipe rack structure: Typical framing plan.

Figure G28-3. Pipe rack structure: Elevation.

Tanks T1 and T2 on braced legs = 7 kips empty plus 25 kips liquid contents = 32 kips (each tank). Seismic force–resisting system: North–south: moment frames on Line 1 and 4, and East–west: concentric braced frames as shown in Figure G28-1. Bar grating at all levels with live load = 100 psf (dictated by owner, not Table 4-1). Determine site seismic parameters: From the ASCE 7 Hazard Tool (ASCE 2019) or Chapter 22, maps, and Chapter 11: Ss = 0.832, S1 = 0.291, Fa = 1.171, Fv = 1.818, SDS = 0.643, SD1 = 0.353, TS = SD1/ SD1 = 0.549 s; TL = 12 s (Figure 22-12), and

Seismic Loads

297

Nonbuilding Structures

Per Tables 11.6-1 and 11.6-2, SDC = D. Verify that exemptions do not apply from Sections 11.1.2 and 11.4.1.

Determine period of vibration: Procedures for computing the period, T, are provided in Section 15.4.4. T may be computed from 3D elastic computer analysis. The period T is a function of mass and stiffness [Equation (15.4-6)]. Therefore, the computer analysis must have the full seismic resisting system and the entire seismic weight. Having only the selfweight of the structural steel will yield erroneous results. The seismic weight should include the self-weight of structural steel, all permanent dead load, and all normal operating loads. Normal operating loads include the pipes and tanks full of contents (with no sloshing within tanks). From 3D computer analysis: North–south direction (moment frames): T = 0.87 s, and East–west direction (concentric braced frames): T = 0.26 s. Equations (12.8-7), (12.8-8), (12.8-9), and (12.8-10) shall not be used for determining the period of a nonbuilding structure. However, one may check 12.8.2 using Equation (12.8-7) and Table 12.8.2 (for the moment frame), whereby Ta = Cthnx = 0.28(49)0.8 = 0.88 s which is greater than 0.87 s, and therefore is acceptable. For the east–west direction, a similar computation provides Ta = 0.37 s. Determine analysis procedure allowed: Check for irregularities (Section 12.3): Horizontal (Tables 12.3-1) = None Vertical (Table 12.3-2) = Type 4 in-plane offset (Sections 12.3.3.3 and12.3.3.4). See Table G28-3 (drift), and Figures G28-4 and G28-5 (forces) and compare to the requirements of Table 12.3-2 1(a) and Section 12.3.2.2, Exception 1. Check T < 3.5 TS; 0.87 s < (3.5) 0.549 s; okay (Table 12.6-1). Therefore, the ELF procedure may be used and it is not necessary to use the MRS method or seismic response history procedure. Determine response modiﬁcation factor, R: See Section 15.1.3 and Table 15.4-1, “Steel Ordinary Concentrically Braced Frame,” with unlimited height, “Detailing” AISC 360, R = 1.5, Ω0 = 1, Cd = 1.5 (no height limit for SDC D); and “Steel Ordinary Moment Frame,” with unlimited height, “Detailing” AISC 360, R = 1, Ω0 = 1, Cd = 1.0. For this 49 ft tall pipe rack, Table 15.4-1 allows an R = 2.5 for the moment frame and R = 2.5 for the braced frame. However, detailing per AISC 341 is required.

Seismic Loads

298

Seismic Loads

Figure G28-4. Pipe rack structure: Story and diaphragm forces.

Figure G28-5. Pipe rack structure: Story and diaphragm forces.

Seismic Loads

299

Nonbuilding Structures

AISC 341 requires that columns and most member connections, including anchor rods, be designed for Ω0 = 2.5 forces and the beam–column connection shall be designed for the expected strength of the beam. Therefore, it is similar or less cost to use an R = 1 or 1.5 for this structure. The foundation will experience higher loading owing to a low R value. Resistance to uplift, sliding, and shear in piles (if any) may cause additional size and cost to foundations. Determine seismic importance factor, Ie: Per Table 1.5-2, Risk Category III yields a seismic importance factor Ie = 1.25. Determine base shear: Effective Seismic Weight, Section 12.7.2 Include dead load plus operating weight of equipment and tanks (full). W level 3 = (35 psf + 50 psf)(75 ft × 25 ft) + 12 kips {FF-1} + 12 kips {FF-2} = 183 kips, W level 2 = (35 psf + 50 psf)(75 ft × 25 ft) + 32 kips {T-1} = 191 kips, W level 1 = (35 psf + 50 psf)(75 ft × 25 ft) + 32 kips {T-2} = 191 kips, and W total = 565 kips (resulting in a system density of 7.69 pcf). Seismic base shear∶ V = C S W

(12.8.1)

North–south direction: C S = S DS =ðR=I e Þ = 0.643=ð1.0=1.25Þ = 0.804

(12.8-1)

C S = S D1 =½TðR=I e Þ = 0.353=½:87 sð1.0=1.25Þ = 0.507 need not exceed Equation (12.8.3) C S = 0.044 S DS I e = 0.044 ð0.643Þ ð1.25Þ = 0.0354

minimum [Equation (15.4-1)]

C S = 0.03

minimum [Equation (15.4-1)]

CS = 0.507 governs V = CS W = 0.507(565 kips) = 286 kips V = 286 kips north–south direction (moment frames) East–west direction: CS = SDS /(R/Ie) = 0.643/(1.5/1.25) = 0.536

[Equation 12.8-1]

CS = SD1/[T(R/Ie)] = 0.353/[0.26 s(1.5/1.25)] = 1.131 need not exceed Equation (12.8.3) CS = 0.044 SDS Ie = 0.044 (0.643) (1.25) = 0.0354

minimum [Equation (15.4-1)]

CS =0.03

minimum [Equation (15.4.-1)]

CS= 0.536 governs

Seismic Loads

300

Seismic Loads

V = CS W = 0.536(565 kips) = 303 kips V = 303 kips east–west direction (braced frames)

Accidental torsion: Section 15.4.1, Item 5: R < 3.5, no horizontal torsional irregularity, and so forth, 3D model; therefore, accidental torsion of 12.8.4.2 need not be included. Vertical distribution of force: The base shear, V, is distributed over the height of the structure per Section 12.8.3. In addition, diaphragms must be checked for the forces of Section 12.10.1. Table G28-1 is a spreadsheet which quantifies the forces. To verify your proper implementation of the summation equations, or for checking or programming spreadsheets, Equation (12.8-12) may be written as follows (when k =1.0): F3(roof) = (w3h3)V/(w1h1 + w2h2 + w3h3) F2 = (w2h2)V/(w1h1 + w2h2 + w3h3) F1 = (w1h1)V/(w1h1 + w2h2 + w3h3) and Equation (12.10-1) may be written as Fp3(roof) = [(F3(roof) /w3)] (w3) Fp2 = [(F2 + F3(roof))/(w3 + w2)] (w2) Fp1 = [(F1 + F2 + F3(roof))/(w3 + w2 + w1)] (w1) This is applicable to the 3-story pipe rack, in the east–west direction, where k = 1.0 (Table G28-1). When the exponent k is not 1.0, the exponent may be added to the first three equations, thus F3(roof) = (w3h3k)V/(w1h1k + w2h2k+ w3h3k) F2 = (w2h2k)V/(w1h1k + w2h2k+ w3h3k) F1 = (w1h1k)V/(w1h1k + w2h2k + w3h3k) This is applicable to the 3-story pipe rack, in the north–south direction, where k is not equal to 1.0 (Table G28-1). The definition of diaphragm in Section 11.2 includes bracing systems acting to transfer the lateral forces to the vertical resisting elements. Therefore, the horizontal trusses at each level in this pipe rack would be subject to the diaphragm provisions of Section 12.10. Section 12.10.1.1 provides values for diaphragm design (Table G28-1). The term q is used herein to represent the percent of seismic weight applied horizontally. The term q has a maximum value of 0.4SDSIe per Equation (12.10-3). This maximum pertains to Equation (12.10-1) and should not override the results of Equation (12.8-11). This is logical; however, it may be overlooked because

Seismic Loads

18422 13783 8661 40867

0.45 0.34 0.21 1.00

128.9 96.5 60.6 286.0

0.704 0.505 0.317

128.9 225.4 286.0

ΣFi (kips) 183 374 565

ΣWi (kip) 0.704 0.603 0.506

qpx ΣFi/Σwi 128.9 115.1 96.7

Fpx (kips) 29.5 30.8 30.8

q min = 0.161 Fpx min (kips)

58.9 61.5 61.5

q max = 0.322 Fpx max (kips)

Seismic Loads

183 191 191 565

Level

3 2 1 Sum =

49 37 25

hx (ft) 8967 7067 4775 20809

wxhxk 0.43 0.34 0.23 1.00

wxhxk/Σ

q max = 0.4 SDS Ie = 0.4(0.643) 1.25 = 0.322

130.6 102.9 69.5 303.0

Fx (kips)

Notes: q min = 0.2 SDS Ie = 0.2 (0.643) 1.25 = 0.161

wx (kips) 0.713 0.539 0.364

qx Fx 130.6 233.5 303.0

ΣFi (kips)

183 374 565

ΣWi (kips)

0.713 0.624 0.536

qpx ΣFi/Σwi

130.6 119.2 102.4

Fpx (kips)

29.5 30.8 30.8

q min = 0.161 Fpx min (kips)

58.9 61.5 61.5

q max = 0.322 Fpx max (kips)

East-West Direction T = 0.26 s; k = 1.0 interpolated from Section 12.8.3 Base Shear V = 303 kips Cs = 0.507

49 37 25

wxhxk/Σ

qx Fx

3 2 1 Sum =

wxhxk

Fx (kips)

183 191 191 565

Level

hx (ft)

wx (kip)

130.6 102.9 69.5

Controlling Fpx used (kips)

128.9 96.5 61.5

Controlling Fpx used (kips)

Table G28-1. North-South Direction T = 0.87 s; k = 1.185 interpolated from Section 12.8.3 Base Shear V = 286 kips Cs = 0.507

Nonbuilding Structures

301

302

Seismic Loads

Equation (12.8-11) usually does not exceed diaphragm force calculations, except for the lower ﬂoors when very low values of R are used.

See Figures G28-4 and G28-5 for graphic of forces at each level. Redundancy: Section 12.3.4.1 will require that the redundancy factor, ρ = 1.3 be used for the north–south direction as well as the east–west direction. An additional moment frame could be added at Grid line 3, which may eliminate the redundancy and allow ρ = 1.0 instead of ρ = 1.3, but only if an extreme horizontal torsional irregularity does not result, as described in Table 12.3-1. Check Drift: Calculation of drift is described in Sections 15.5.2.1 and 12.8.6. The force level used in analysis should include the Fx values shown in Figures G28-4 and G28-5. These are strength level forces. If allowable stress design is being used, one must verify the drift is being calculated based on strength level forces before any reduction for allowable stress design. Per Section 12.3.4.1, Item 2, redundancy should be equal to 1.0 for drift calculations, however, with the exception that moment frames are penalized for redundancy ρ on the allowable drift per Section 12.12.1.1 as (Δa/ρ). P-delta effects per Section 12.8.7 may be necessary to be included in the analysis. Accidental torsion need not apply to this structure per Section 15.4.1, Paragraph 2, Exception 1. δx = C d δxe =I e

[Equation (12.8-15)]

Cd = 1.5, Ie = 1.25 From elastic computer analysis, displacements are reported as shown in Table G28-3 as δxe. Drift Δ is calculated per Figure 12.8-2. Allowable drift Δa is as described in Section 12.12 per Table 12.12-1 and Δa = 0.020hx was deemed appropriate for this pipe rack. Section 12.12.1.1 requires that Δa be divided by ρ for moment frames. See Table G28-3a and b for drift checks. Avoid pounding between adjacent structures or adjacent pipe racks as described in Section 12.12.3. Load Combinations: See Sections 12.4 and 2.3.1; and Section 12.4.3 when Ω0 overstrength factor is required; Redundancy (Section 12.3.4.1) ρ = 1.3; Horizontal seismic load effect (Section 12.4.2.1) Eh = ρQE = 1.3QE;

Seismic Loads

303

Nonbuilding Structures

Table G28-2. Drift Moment Frame

Level

hx (ft)

Story height hsx (ft)

Elastic deﬂection δxe (in.)

Inelastic deﬂection δx (in.)

8.75

7.00

6.74

5.39

5.06

4.05

0.00

Inelastic drift Δ (in.)

Allowable drift Δa/ρ (in.)

Test OK/NG ?

1.61

2.20

1.34

2.20

4.05

4.61

Inelastic drift Δ (in.)

Allowable drift Δa (in.)

Test OK/NG ?

0.06

2.88

0.08

2.88

0.28

6.00

12 2

12 25

Notes: Cd = 1.0 Moment Frame ρ = 1.3 Ie = 1.25 Δa/ρ = 0.020hsx/ρ δx = Cdδxe/Ie

Table G28-3. Drift Braced Frame

Level

hx (ft)

Story height hsx (ft)

Elastic deﬂection δxe (in.)

Inelastic deﬂection δx (in.)

0.35

0.42

0.30

0.36

0.23

0.28

12 2

12 25

Notes: Cd = 1.5 Braced Frame Δa = 0.020hsx Ie = 1.25 δx = Cdδxe/Ie

Vertical seismic load effect (Section 12.4.2.2) Ev = 0.2SDSD= 0.2(0.643)D = 0.129D; and Orthogonal effects (Section 12.5.3) 100% − 30% is required for corner columns. Per Section 12.3.4.1 redundancy ρ is permitted to be equal to 1.0 for diaphragm force calculations as well as other areas as listed in Items 1 through 9. In Figure G28-5, collectors, and their connections (including the transfer forces across column at grid line 2) must be designed for overstrength Ω0 level seismic forces as described in Section 12.10.2.1. This is required for SDC C, D, E, and F. Discontinuous frames must be designed for overstrength Ω0 level seismic forces as described in Section 12.3.3.3. This is required for SDC B, C, D, E, and F. This

Seismic Loads

304

Seismic Loads

use of overstrength is independent of the detailing requirements of AISC and ACI. So even, when designing with R = 3 (Table 12.2-1 H, Steel systems not speciﬁcally detailed for seismic resistance, AISC 360) and R = 1 or 1.5 (Table 15.4-1, nonbuildings, AISC 360), it is still required to apply the overstrength Ω0 in the SDC mentioned. A reduction of applied bearing pressure on the foundation could be implemented per Section 12.13.4. This is helpful for the high foundation loads that occur with low R value designs. Tanks and equipment: The equipment consists of ﬁn fan air cooler units and tanks. Each item weighs less than 25% of the total structure weight, so Section 15.3.1 dictates that each item be treated as a component, and forces shall be generated from Chapter 13, with Rp and ap values per Section 13.1.6. F p = ½0.4ðap ÞS DS W p =ðRp =I p Þ × ½1 + 2z=h

[Equation (13.3-1)]

F p max = 1.6S DS I p W p

[Equation (13.3-2)]

F p min = 0.3S DS I p W p

[Equation (13.3-3)]

Section 13.1.6 for this example dictates that ap and Rp be taken from Table13.6-1, or if not listed, then from Table 15.4.2 with ap per footnote a of Table 13.6-1. This results in the following parameters: Fin fan FF-1, FF-2: Table 13.6-1, air cooler (fin fans) ap = 2.5, Rp = 3, Ω0 = 1.5; and Tank T-1, T-2: Table 15.4-2, elevated tank on symmetrically braced legs, R = 3, Ω0 = 2. Per Section 13.1.6 , R = Rp = 3, and ap = 2.5 per footnote a of Table 13.6-1. At power generating facilities, the importance factor, Ie = 1.25. When the component is less than 25%, and Chapter 13 is used, and Equation (13.3-1) (Fp) contains Ip. Ip is per Section 13.1.3 and is either 1.0 or 1.5. Section 13.1.3 would result in Ip = 1.0 at a power plant. However, components and equipment can be very large, complex, and massive, and even when the component is less than 25% of total, it would be reasonable to use Ip = Ie, which is 1.25. This approach is consistent with the power plant owner requirements and expectations that the facility shall be designed with an importance factor of 1.25, including large equipment containing significant structural frames. This example conservatively uses Ip = 1.25 for calculation of Fp. In Table G28-4, the resulting forces Fp = 9.6k (0.80 or 80% of the mass) for the fin fans and 21.5k (0.67) for Tank T-1 and 17.3k (0.54) for Tank T-2. These forces are to be used for the design of the component and its attachment to the diaphragm. The load Fp should be applied at the center of gravity of the equipment, and the reactions at the connection of the diaphragm should include the vertical forces caused by overturning. Ev forces should be combined as well as dead load/operating load per Section 2.3. These Fp forces are localized, such that the diaphragm design and vertical frame design is based not on Fp level

Seismic Loads

Sds

0.64 0.64 0.64 0.64

Component

Fin Fan FF-1 Fin Fan FF-2 Tank T-1 Tank T-2

Table G28-4. Fp

1.00 1.00 1.00 1.00

Ie, Ip 12,000 12,000 32,000 32,000

Wp (lb)

2315 2315 6173 6173

Eq. 13.3-3 Fp min (kips)

Nonbuilding Structures

305

Seismic Loads

306

Seismic Loads

forces, but rather the inertia forces calculated per Sections 12.8.3 and 12.10.1.1, whereby the weight of the equipment is included with all of the other weight that exists at a given level. For most buildings, the acceleration coefficient of Fp [Equation (13.3-1)] is usually much higher than the coefficient of the Fx [Equation (12.8-12)]. However, nonbuilding structures with very low R values and varying Ie and Ip values may produce a Fp coefficient lower than Fx. It would be prudent to use the higher acceleration value for the component design and its attachments and scale up the Fp value accordingly. If loads/reactions are provided from a vendor of the equipment, one should verify the ap, Rp, Ω0, and z (elevation) are appropriate for the item, and then design the attachments to the diaphragm for those forces. If these vendorsupplied loads/reactions are input into a computer model, then they should be scaled to the accelerations used for diaphragm design, and vertical system design, when designing those portions.

28.2 Example 2: Large Equipment Structures on a Pile Supported Mat In the design of multistory buildings, portions of footings and pile caps below grade are usually below the “base” and usually have very little weight when compared to the building superstructure; thus the weight of the footing or pile cap is often neglected in the generation of seismic base shear forces. Figure G28-6 depicts various industrial components on a thick pile supported mat. Because the mat is pile supported, the soil beneath the mat may settle away, especially if liquefaction conditions are present. Thus, resistance from sliding friction is unreliable and should not be considered. The base shear must be dissipated into the soil via a load path though horizontal shear in each pile. The shear force will be composed of not only the base shear of the superstructures, but also the shear attributed to the self-weight of the mat/pile cap. The force

Figure G28-6. Large equipment structures on a pile supported mat.

Seismic Loads

307

Nonbuilding Structures

from self-weight of the pile cap may be calculated using Section 15.4.2 as V = 0.3SDSWIe [Equation (15.4-5)].

Given: SDS = 0.9, SD1 = 0.34; Ie = 1.0, Ip = 1.0, SDC D Generator Set: Weight = W = 150 kips Rigid motor, generator and equipment on skid beam on grade Table 13.6-1, Generator: ap = 1, Rp = 2.5, Ω0 = 2 F p = ½0.4ðap ÞS DS W p =ðRp =I p Þ × ½1 + 2z=h

[Equation (13.3-1)]

F p = ½0.4ð1.0Þ 0.9 ð150kÞ=ð2.5=1Þ × ½1.0 = 21.6k F p max = 1.6S DS I p W p = 1.6ð0.9Þ1.0ð150kÞ = 216k

[Equation (13.3-2)]

F p min = 0.3S DS I p W p = 0.3ð0.9Þ1.0ð150kÞ = 41k

[Equation (13.3-3)]

Or alternatively, you could use Section 15.4.2, rigid structures: V = 0:30SDS WIe = 0.3ð0.9Þð150kÞ1.0 = 41k

[Equation (15.4-5)]

Note that Equation (15.4-5) and Equation (13.3-3) yield the same value. Use V = 41k for generator. Vendor-supplied equipment structure: Complex equipment supported by a steel braced frame that extends from the ground upward and through the housing to the top of the structure. The vendor has reported that the operating weight is 600 kips, and was designed with an R = 6, and Ω0 = 2, and special detailing of AISC 341 was included. The vendor provided a report of reactions at the base of each leg, in all directions, owing to dead, live, seismic and wind. The EOR will provide the anchorage to the concrete mat and apply Ω0 = 2.0 where appropriate. The EOR summed the horizontal reactions and veriﬁed that the sum was equal to V = CSW and CS = SDS/(R/Ie) [Equation (12.8-1) and (12.8-2)]. V = 0.9W/(6/1.0) = 0.15W = 0.15(600k) = 90 kips, and Use V = 90 kips for vendor-supplied equipment structure. Concrete barrier wall/fence: Wall cantilevers from base of mat.

Seismic Loads

308

Seismic Loads

Weight = W = 180 kips Table 15.4-2, ground supported cantilever wall or fence, detailing per Section 15.6.8 R = 1.25, Ω0 = 2, Cd = 2.5 V = CSW, CS = SDS/(R/Ie) [Equations (12.8-1) and (12.8-2)] V = 0.9W/(1.25/1.0) = 0.72 W = 0.72(189k) = 136k Use V = 136 kips for cantilevered wall/fence. Concrete mat/pile cap: Three ft thick concrete mat supported on 70 piles spaced approximately 6 ft on center each way. Weight = W = 3 ft thick × 50 ft × 50 ft (0.150 kcf) W = 1,125k Section 15.4.2, rigid nonbuilding structure V = 0.3WSDSIe = 0.3W(0.9)1.0 = 0.27W = 0.27(1,125k) = 304k Use V = 304 kips for concrete mat Pile shear: Total base shear to be resisted by piles; the total load may be conservatively added algebraically V to piles = 41k + 90k + 136k + 304k = 571k V per pile = 571k/70 piles = 8.15k/pile Alternatively, the ﬂexible structures will not be vibrating in phase with the other structures, so the shears may be combined probabilistically using SRSS. V to piles = [(41k +304k)2 + (90k)2 + (136k)2]0.5 = 382k V per pile = 382k/70 piles = 5.5 k/pile Check concrete capacity of pile for shear load. Check soil bearing strength and deﬂection into soil with an L-pile style analysis. Multiply V by 0.7 to convert to allowable stress level as appropriate.

Seismic Loads

29 Complete Seismic Load Analysis of Simple Building

This chapter demonstrates a complete seismic load analysis of a simple building. It is deliberately a small building for the purpose of maintaining simplicity and the resulting loads are small compared to capacities provided. The calculation format demonstrates an approach, especially commonplace in low seismic risk regions, where member sizes are ﬁrst selected for resistance to gravity and wind forces, as well as connection method and potential for future expansion, and then those members are checked against seismic forces. It is not intended to demonstrate that a very strong building is a conservative approach; on the contrary, many experienced earthquake engineers believe that using a highly ductile system (i.e., one with high R factors and associated ductile detailing) is the safer and more conservative approach. The primary purpose of this example is to provide, in essence, a ﬂowchart of tasks that the structural engineer can compare to when designing a larger building. Some sections of ASCE 7 do not apply to this simple building but are included in the sequence so that they are not missed when designing a different building. ASCE 7 section numbers are shown in parenthesis.

29.1 Simple Building Details Given: ASCE 7-16 (ASCE 2017a), AISC 360 (AISC 2015), ACI 318 (ACI 2014) Location: Hardeeville, South Carolina Use: Storage and ofﬁce without partitions. See Section 4.3.2 and 12.7.2(2) for partition load requirements), Risk Category II. Roof dead load = 70 psf

309

Seismic Loads

310

Seismic Loads

Roof live load = 20 psf, Ground and minimum Roof Snow Load = 20 psf Seismic force resisting system: Steel braced frame

Soil allowable net bearing pressure = 2,000 psf Materials: Concrete f′c = 4,000 psi; steel shapes and plates Grade 50; welding E70 electrode, bolts A325N, snug tight Owner and steel erector prefer double clip angle connections at beam ends where possible, so W10 columns were selected to accommodate. However, at braced frame lines, shear tabs were used to avoid prying action in double clip angles when subjected to beam axial collector loads. See Figures G29-1 through G29-3.

29.2 Seismic Design Determine SS and S1: Site Class D default per (11.4.2) From ASCE 7 Hazard Tool (ASCE 2019): SS = 0.31, S1 = 0.130, SDS = 0.356, SD1 = 0.198 Verify that exemptions do not apply: (11.1.2) and (11.4.1).

Figure G29-1. Simple building perspective.

Figure G29-2. Simple building elevation.

Seismic Loads

Complete Seismic Load Analysis of Simple Building

Figure G29-3. Simple building foundation plan.

Determine analysis procedure allowed: See (12.6) and (Table 12.6-1) Check 12.14, simplified method (okay, but not used in this example) Period (12.8.2.1): Ta = CT hnx ; CT = 0.02, x = 0.75; hn = 14 ft; Ta = 0.14 s T = Ta (12.8.2, last sentence); T = 0.14 s; TS = SDS/SD1 = 0.198/0.356 = 0.55 s TL = 8 s (Figure 22-14) Check for irregularities (12.3). Horizontal (Tables 12.3-1) = None (see accidental torsion check) Vertical (Table 12.3-2) = None Check T < 3.5TS; 0.14 s < (3.5) 0.55 s; okay (Table 12.6-1). Therefore, the ELF procedure may be used and it is not necessary to use the MRS method nor the seismic response history procedure. Determine response modification factor, R: Per Tables 11.6-1 and 11.6-2, SDC = C Seismic force resisting system: Braced frame per Table 12.2-1, H. Steel systems not specifically detailed for seismic resistance: R = 3, Ω0 = 3, Cd = 3, Detailing required per (14.1), and (14.1.2.2.1, Exception): Use AISC 360; it is unnecessary to detail per AISC 341, seismic (AISC 2016b). Determine seismic importance factor, Ie: See (11.5.1) and Table 1.5-2. Risk Category II, Ie = 1.0

Seismic Loads

311

312

Seismic Loads

Determine base shear: Effective seismic weight (12.7.2)

Roof = 70 psf dead load (20 × 20 ft) = 28.0 k Walls = Height tributary to roof = 14 ft/2 = 7 ft; perimeter of building = 80 ft Wall weight = 10 psf (7 × 80 ft) = 5.6 k W = Effective seismic weight = 28.0 k + 5.6 k = 33.6 k Seismic base shear: V = CsW [Equation (12.8.1)] CS = SDS/(R/Ie) = 0.356/(3/1.0) = 0.1187 [Equation (12.8-2)] CS = SD1/[T(R/Ie)] = 0.198/[0.14 (3/1.0)] = 0.471 need not exceed [Equation (12.8.3)] CS = 0.044 SDS Ie = 0.044(0.356)(1.0) = 0.0157 minimum [Equation (12.8-5)] CS = 0.01 [Equation (12.8-5)] minimum CS = 0.1187 governs V = CSW = 0.1187(33.6 k) = 4.0 k V = 4.0 k Vertical distribution of force (12.8.3) and diaphragm forces (12.10.1.1) yield same results for a 1-story structure: 100% of base shear V is distributed to roof, and this applies to diaphragm calculations as well as vertical bracing calculations.

29.3 Accidental Torsion ASCE 7-16 has a signiﬁcant change from ASCE 7-10 for accidental torsion requirements. For many buildings, accidental torsion forces are now only applied to verify if a horizontal torsional irregularity exists. If it does not exist, then the earthquake forces may be calculated without accidental torsion. See Section 12.8.4.2 for speciﬁcs. For this building, earthquake and accidental torsion forces are applied and the displacements at each corner are calculated. Mta = Mass displaced 5% per (12.8.4.2) Mta = 4.0 k (20 ft)(0.05) = 4.0 ft-kips Distribute Mta to all four braced frames in proportion to their relative rigidities and distance from center of rigidity/rotation. Reaction to each braced frame = 4.0 ft-kips/[(10 ft)(4 equal frames)] = 0.10 k per frame [Figure G29-4(a)]. Per Table 12.3-1, torsional irregularity check, the following formula may be created.

Seismic Loads

Complete Seismic Load Analysis of Simple Building

Figure G29-4. Seismic loading, reactions and displacements: (a) with accidental torsion; and (b) without accidental torsion. Torsional irregularity exists if drift at ends of building are as follows: Δ1 max > 1.2ðΔ1 max + Δ1 min Þ=2 0.015 in. < 1.2 (0.015+0.013)/2 = 0.0168 in. (okay, no torsional irregularity exists).

Seismic Loads

313

314

Seismic Loads

Because this is a relative displacement check, it does not matter if drift is calculated at the elastic or inelastic level. Because no torsional irregularity exists, per Section 12.8.4.2, third paragraph, accidental torsion moments need not be included when determining the seismic forces E in the design of the structure and in determination of the design story drifts. The applied loads, drift, and reactions may be calculated as shown in Figure G29-4(b). Load combinations: See (12.4), (2.3.6), and (12.4.3) when Ω0 overstrength factor is speciﬁcally required. Redundancy (12.3.4.1): ρ = 1.0 in SDC C Horizontal seismic load effect (12.4.2.1): Eh = ρQE = 1.0QE = QE Vertical seismic load effect (12.4.2.2): Ev = 0.2SDS = 0.2(0.356) = 0.0712 Orthogonal effects (12.5.3): 100%/30% corner columns: SDC C not required. Check drift: From elastic computer analysis, maximum roof displacement measured at the center of rigidity (excluding accidental torsion) is 0.014 in. Per (12.8.6): δxe = 0.014 in. δx = Cd(δxe)/Ie = 3.0(0.014 in.)/1.0 = 0.042 in. Drift = Δ1 = δx = 0.042 in. P-delta effects per (12.8.7) are inconsequential by inspection. Allowable drift (12.12) Table 12.12-1: Δa = 0.020hsx = 0.020(14 ft)(12 in./ft) = 3.36 in. 0.042 in. < 3.36 in., therefore okay.

29.4 Member and Connection Checks Figure G29-5(a and b) display roof framing plan forces with and without accidental torsion, respectively. Figure G29-6 displays elevation view forces without accidental torsion. The following checks will use the forces without accidental torsion for the aforementioned reasons. Diaphragm: Diaphragm forces are outlined in Section 12.10.1.1. wpx = 33.6 k F px = ½4:0 k=ð33:6 kÞ 33:6 k = 4:0 k

[Equation (12.10-1)]

F px min = 0:2S DS I e wpx = 0:2ð0:356Þð1:0Þ33:6 k = 2:39 k min [Equation (12.10-2)]

Seismic Loads

315

Complete Seismic Load Analysis of Simple Building

Figure G29-5. Roof framing plan with forces (a) with accidental torsion; and (b) without accidental torsion. F px max = 0:4S DS I e wpx = 0:4ð0:356Þð1:0Þ33:6 k = 4:78 k max [Equation (12.10-3)] The diagram forces from Equation (12.10-1) need not exceed Equation (12.10-3); however, Section 12.10.1.1 states that “Floor and roof diaphragms shall be designed to resist design forces from structural analysis, but shall not be less than Equation (12.10-1).” This infers that the diaphragm forces shall not be less than those caused by the base shear, V, Fx forces of Section 12.8, including accidental torsion Mta when applicable. Thus, v = Diaphragm shear = 2.0k/(20 ft) = 0.10 k/ft [Figure G29-5(b)]. Check concrete slab thickness and connection of diaphragm to collector beams for this ultimate strength level force.

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Figure G29-6. Frame elevation with forces shown without accidental torsion. Collector: Collector force requirements are outlined in Section 12.10.2.1. In essence this section requires that collectors be designed for the maximum of the following (paraphrasing): 1.

Forces Fx in diaphragm owing to base shear V, including accidental torsion Mta, and including Ω0, but excluding redundancy ρ [12.3.4.1(5)] (i.e., ρ = 1.0).

Forces Fpx in diaphragm owing to Equation (12.10-1) excluding accidental torsion Mta, including Ω0, and excluding redundancy ρ.

Forces Fpx max from Equation (12.10-2) excluding accidental torsion Mta, excluding Ω0,but including redundancy ρ.

For this example, however, accidental torsion Mta need not be included in the preceding determination for collectors (Section 12.8.4.2, third paragraph). W12 × 26: The preceding Item 1 governs as follows: v = Diaphragm shear (including accidental torsion) = 0.10 k/ft T = Tension (or compression force) = 0.10 k/ft(10 ft) = 1.0 k axial load in beam Dead load = 1.75 k down Live load = 0.50 k down Check beam end connection for the following ultimate strength level loads per Section 2.3.6 (6):

Seismic Loads

Complete Seismic Load Analysis of Simple Building

1:2D + E v + E h + 1:0L + 0:2S

[Load combination (LC) 6 in Section 2.3.6]

which per Equation (12.4-4a) and Equation (12.4-3) evolves to

ð1.2þ0.2S DS ÞD + ρQE + 1.0L + 0.2S and per (12.10.2.1) SDC C use load combinations with overstrength per [2.3.6 (6)]: 1:2D þ Ev + E mh + 1:0L + 0:2S

[LC 6 in Section 2.3.6, with overstrength]

which per Equation (12.4-4a) and Equation (12.4-7) evolves to (1.2 + 0.2SDS)D + Ω0QE + 1.0L + 0.2S (note that ρ is not included) [1.2+0.2(0.356)]1.75 k + 1.0(0.5 k) = 2.72 k vertical shear on connection Ω0QE = 3.0(1.0 k) = 3.0 k axial/horizontal load on connection Compare 2.72 k vertical and 3.0 k axial to capacity of (3) 3/4 in. diameter A325 N bolts per AISC ϕrn = 17.9 k per bolt and verify that all other limit states within connection do not govern. Note that although this is SDC = C, and R = 3 was used, ASCE 7 Section 12.10.2.1 requires use of Ω0 for collectors, independent of AISC requirements. Brace: E = 3.4 k Capacity of brace L = 17 ft (approximate/conservative) From AISC tables: L= 17 ft, ϕcPn = 56.1 k 3.4 kip < 56.1 k, therefore okay See Figure G29-7.

Figure G29-7. Collector beam and brace connection forces.

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Brace connection: E = 3.4 k

Capacity of 1/4 in. ﬁllet weld per AISC ϕRn = 0.8(0.6)70 ksi (0.707)(0.25 in.) = 5.56 k/in. Compare E = 3.4 k to weld capacity and check other limit states within the connection (e.g., gusset plate). This is a braced frame per Table 12.2-1 H. Steel systems not speciﬁcally detailed for seismic resistance, SDC C, and R = 3. AISC 360 is used and it is unnecessary to detail per AISC 341, seismic. Therefore, brace connections need not be designed for Ω0, nor full strength of the brace, as would be required in AISC 341 and SDC D, E, and F for higher R factor systems. Column: Axial loads dead load = 7.0 k; live load = 2.0 k; E = 2.8 k Section 2.3.6 (6)): 1.2D + Ev+ Eh + 1.0L + 0.2S Which per Equation (12.4-4a) and Equation (12.4-3) evolves to (1.2 + 0.2SDS)D + ρQE + 1.0L + 0.2S Pu = [1.2 + 0.2(0.356)]D + 1.0E + 1.0L + 0.2S Pu = 1.27(7.0 k) + 1.0(2.8) + 1.0(2.0) + 0.2(0.0) Pu = 13.7 k Per AISC tables L = 14 ft; W10 × 33 col; ϕcPn = 248 k 13.7k < 248 k, therefore okay. Column base connection: Uplift case governs by inspection Horizontal shear = 2.0 k Dead load = 2.4 k Seismic = 2.8 k Section 2.3.6 (7): 0:9D − Ev + E h

(LC 7 in Section 2.3.6)

which per Equation (12.4-4a) and Equation (12.4-3) evolves to (0.9 – 0.2SDS)D + ρQE Tu = [0.9–0.2(0.356)]D – 1.0E Tu = (0.829)2.4k – 1.0(2.8k) Tu = 0.82 k net uplift

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Complete Seismic Load Analysis of Simple Building

Vu = 2.0 k horizontal shear

Compare to anchor bolt ultimate capacities for combined tension and shear [See AISC Design Guide Number 1 (AISC 2006)]. See Figure G29-8. This is a braced frame per Table 12.2-1 H. Steel systems not speciﬁcally detailed for seismic resistance, SDC C, and R = 3. AISC 360 is used and it is unnecessary to detail per AISC 341, seismic. Therefore, anchor rods and related connections need not be designed for Ω0, nor full strength of the brace, as would be required in AISC 341 and SDC D, E, and F. Footing loads: Uplift: Verify weight of footing multiplied by 0.9 exceeds Tu = 0.89 k Tprovided = footing weight × (0.9) = 0.9(0.150 kcf)(3 × 3 × 2 ft) = 2.4 k 0.89 k < 2.4 k, therefore no net uplift, okay. Bearing pressure: New to ASCE 7-16, there is no need to include Ev in bearing pressure calculations. See Section 12.4.2.2 for speciﬁcs. Allowable net bearing pressure = 2,000 psf

Figure G29-8. Column base forces.

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Dead load = 7.0 k Live load = 2.0 k

Seismic = 2.8 k Convert seismic load to allowable strength level by multiplying by 0.7 permitted by allowable stress design load combinations Section 2.4.5(8) and (9). 1:0D + 0:7E v + 0:7Eh

(LC 8 in Section 2.3.6)

which per 12.4.2.2 Exception 2, Equation (12.4-4a), and Equation (12.4-3) evolves to 1.0D + 0.7ρQE P = [1.0D + 0.7(1.0)E] P = [1.0(7.0 k)] + 0.7(1.0)2.8 k P = 9.0 k and 1:0D + 0:525E v + 0:525E h + 0:75L + 0:75S

(LC 9 in Section 2.3.6)

which per 12.4.2.2 Exception 2, Equation (12.4-4a) and Equation (12.4-3) evolves to 1.0D + 0.525ρQe + 0.75L + 0.75S P = 1.0D + 0.525(1.0)E + 0.75L + 0.75S P = [1.0(7.0k)] + 0.525(1.0)2.8k + 0.75(2.0) + 0.75(0.0) P = 9.97 k P = 9.97 kip governs maximum downward Allowable Stress Design (ASD) Force on footing. fbearing = applied bearing pressure = 9.97 k/(3 × 3 ft) = 1.108 psf 1,108 psf < 2,000 psf, therefore 3 ft × 3 ft footing is okay. A reduction of applied bearing pressure could be implemented per (12.13.4) but was not used in this example.

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30 Frequently Asked Questions The following list of “Frequently Asked Questions” were developed by the authors or were provided by practicing engineers that use ASCE 7 on a regular basis. With few exceptions, the answers provided are made without reference to the material in the guide, thereby allowing this FAQ section to be a stand-alone reference. The questions are divided into three subcategories: General, Analysis, and Design.

I. Questions Covering General Issues G1. Are there any specific guidelines to meet the provisions of Section 1.4: General Structural Integrity? There are currently no specific requirements for achieving structural integrity in ASCE 7. However, it is expected that seismic detailing such as required in Seismic Design Categories B and above will provide continuity, redundancy, and ductility. Recent editions of IBC (ICC 2017) have requirements associated with structural integrity in Section 1615. These requirements are only specified for a limited number of cases, but could be used, voluntarily, for any building. It is not certain that the provisions of Section 1.4 will be met by following Section 1615, but the overall integrity of the building will be improved. Section 1.4 allows the use of the general structural integrity provisions of Section 1.4 in lieu of Chapter 12 requirements for design of buildings in SDC A.

321

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G2. Section 11.8.3, which is applicable in SDC D, E, and F, requires that the geotechnical report include “lateral pressures on basem*nt and retaining walls due to earthquake motions.” Does that mean these pressures can be taken as zero in SDC B and C? Lateral pressures attributable to ground shaking may be neglected in buildings assigned to SDC B and C. Forces and stresses induced by such pressures in buildings assigned to SDC D through F would be considered as part of the earthquake load E in the pertinent load combinations of Chapter 2. G3. Where do the R, Cd, and Ω0 values in Table 12.2-1 come from? All of the values that are currently in Table 12.2-1 are completely qualitative. They are based on engineering judgment and on experience gained from building behavior in past earthquakes. R and Cd values ﬁrst appeared in the ATC 3-06 report (ATC 1978), and only 21 sets values were provided. Over the years, additional systems were added, or existing systems were subdivided into several systems. In ASCE 7-16 Chapter 12, there are 85 sets of values. The term Ω0 ﬁrst appeared in ASCE 7-98. More recently, an analytical procedure has been developed to provide the R, Cd, and Ω0 values. This procedure, described in the FEMA P-695 (FEMA 2009) report, states that for a given class of system (such as a special steel moment frame), R should be set such that there is no more than a 10% probability that the building will collapse when subjected to the maximum considered earthquake (MCE) ground motion. In the procedure, a variety of archetypes of the system are designed assuming some trial R value, and each archetype is analyzed, using nonlinear dynamic response history procedures, for 44 preselected ground motions. The analysis is necessarily quite detailed to capture all anticipated nonlinear effects (yielding, P-delta effects). For each archetype and for each ground motion, the ground motion’s intensity is increased until the system collapses. The ground motion intensity at which half of the earthquakes cause collapse of the archetype is used to compute the collapse margin ratio for that archetype. Using that value and a variety of adjustments, including those for uncertainty, the probability of collapse can be computed. If no individual archetype has more than a 20% probability of collapse, and if the average probability of collapse for all archetypes is less than 10%, the system passes and the R value used for design is deemed appropriate. If the probabilities of collapse are excessive, the procedure is repeated with a smaller R value; and if the probabilities of collapse are too low (indicating an overly conservative design), the process is repeated with a larger R value. One then keeps adjusting the R value until the desired behavior is obtained. At that point, Cd is taken as equal to R. Ω0 is determined separately from a nonlinear static pushover analysis. The procedure as described is extremely time consuming owing to the necessity to design several archetypes and to run thousands of nonlinear response history analyses. NIST (2010) provides a number of example applications of the procedure. To date, none of the existing structural systems (those currently listed in Table 12.2-1 of ASCE 7-16) have been completely vetted by the procedure.

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G4. Is there not an inherent contradiction within ASCE 7 in that the effective seismic weight used in computing equivalent lateral forces is based on 25% of Live Load (LL) (for storage loads), whereas the gravity effects include at least 0.5LL (up to 1.0LL) for strength design? First, according to Section 12.7.2, the 25% LL requirement is the minimum for storage live loads. It is feasible, if not likely, that higher loads would be used. The reason that a lower LL is used for effective seismic weight than for gravity load is that the loads are (probably) not rigidly attached to the structure and would therefore not be subjected to the same lateral accelerations (and inertial forces) as the structure. In addition, the sliding movement of the storage load dissipates energy, increasing the effective damping in the system. The same inconsistency occurs with partition loads and snow loads, wherein the amount of load included in the effective seismic weight is less than that used for gravity load effects. G5. What’s with TL? The long-period transition period TL impacts the convective (sloshing) forces and seismic freeboard (wave height) in a tank. The convective period of the liquid mass can be 10 s or more on very large liqueﬁed natural gas storage tanks. Because TL is a variable ranging from 4 to 16 s, its value can really increase the convective forces and seismic freeboard. If TL is greater than the convective period, the forces and freeboard then vary by 1/T instead of 1/T 2 (J. G. Soules, personal communication, 2019). Seismic loads on tanks and vessels are covered in Section 15.7 of ASCE 7. In addition, tall buildings may have periods greater than TL, and it is interesting to explore the circ*mstances under which this might occur. This is done on the basis of the structural height hn at which a given TL is obtained. An expression for obtaining the height is provided as follows, where Cu is the upper limit period coefﬁcient (Table 12.8-1), and Ct and x are system-dependent period parameters (Table 12.8-2): T L 1=x hn = CuCt Table G30-1 provides structural heights for a variety of systems for which T = TL = 4 s, and Table G30-1b provides heights where T = TL = 6 s. For

Table G30-1a. Height (ft) of a Given System at Which CuTa = 4.0 s Cu

Steel moment frame

Concrete moment frame

EBF or BRB

Other nondual

Other dual

1.4 1.5 1.6 1.7

324 297 274 254

317 294 274 256

435 397 364 336

747 681 625 576

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Table G30-1b. Height (ft) of a Given System at Which CuTa = 6.0 s Cu

Steel moment frames

Concrete moment frames

EBF or BRB

Other nondual

Other dual

1.4 1.5 1.6 1.7

538 494 456 422

498 462 429 402

747 681 625 576

1,282 1,170 1,073 990

the moment frames, the heights are likely beyond the upper limit of practicality for such systems. For the eccentrically braced frame and buckling restrained braced frames, all height values are well above the height limits in regions of the United States where such systems would be used. For other nondual and other dual systems, the heights, where allowed, are representative of building in excess of about 50 stories. Thus, although it is possible in certain circ*mstances that systems will have CuTa in excess of TL = 4.0 s, it is an extremely rare occurrence.

II. Questions Covering Design Issues D1. Does the interconnection requirement of Section 12.1.3 apply across any section cut a designer might draw across a diaphragm? Section 12.1.3 provides requirements for a continuous load path and interconnection of all parts of the structure. These requirements would apply across any section cut through a diaphragm. In addition, the diaphragm must be analyzed and designed in accordance with Section 12.10. D2. Why are forces for columns supporting discontinuous braced frames amplified by the overstrength coefficient Ω0, but not columns in braced frames that are continuous? This requirement, from Section 12.3.3.3, applies only to structures with an inplane (Type 4 horizontal irregularity) or out-of-plane offset (Type 4 vertical irregularity) in the lateral load–resisting system. Experience from previous earthquakes has indicated that such irregularities impose extreme demands on the portion of the structure below the irregularity, and such irregularities have been identified as a significant contributor to the partial or complete collapse of structures during earthquakes. The amplification factor serves as a penalty, discouraging the use of such irregularities, and reducing the likelihood of severe damage or collapse if such irregularities exist. Although ASCE 7-16 does not specifically require overstrength, Ω0, for the aforementioned columns, material specifications such as AISC 341-16 most often require overstrength, Ω0, for columns of special, intermediate, and ordinary systems.

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D3. Why in earthquake engineering, is the P-Δ stability index θ required to be less than 0.5/(βCd)? This results in permitted P-Δ effects much less than that which is allowed in nonseismic design. Considering the fact that no failures have been reported owing to P-Δ during earthquake, why is such a strict criterion provided that often controls the design? The limit on the stability coefficient provides two effects. First, it protects buildings in low seismic hazard regions against the possibility of post-earthquake (residual deformation triggered) failure. Second, it provides a limit in the implied overstrength of a building. Regarding P-delta triggered failures, P-delta effects are usually more critical in buildings in low and moderate hazard areas (where buildings have relatively low lateral stiffness) than they are in high hazard areas (where the stiffness is relatively high). There is very limited knowledge on the likely performance of code compliant buildings in the lower hazard areas, but without some limit on the stability ratio, it is entirely possible that failures may occur because of dynamic instability. In fact, nonlinear analysis usually indicates failure in buildings owing to dynamic instability, which is exacerbated by P-delta effects. The term β in the stability coefficient is essentially the inverse of the overstrength of the story. When computed, the overstrength often exceeds 2.0. Thus, it may be beneficial to compute the β factor when it appears that the upper limit on θ is controlling. Unfortunately, computing the story overstrength is not straightforward (see FAQ A2). D4. How much eccentricity in EBFs is required for a Ct value of 0.03 and x = 0.75 for determination of the approximate period? Table 12.8-2 provides parameters Ct and x to be used in the determination of the approximate period, Ta. The parameters Ct = 0.03 and x = 0.75, applicable to eccentrically braced frames, may be used only if the frame is designed and detailed as an EBF in accordance with the requirements of AISC 341-16 (AISC 2016b). Theoretically, a frame with eccentric connections may be used as part of an R = 3 “steel system not specifically detailed for seismic resistance” (System Type H in Table 12.2-1). However, in this circ*mstance, there is nothing preventing the designer from using, for example, a 6 in. eccentricity, which would result in a frame stiffness closer to that of a concentrically braced frame than that of an eccentrically braced frame. It is for this reason (the lack of limits on the geometry of R = 3 EBFs) that the coefficients in Table 12.8-2 are limited to systems specifically designed as EBFs. D5. Table 12.2-1 provides design coefficients for cantilever column systems. The various coefficients (R, Cd, Ω0, height limit, and so forth) depend on the type of detailing used in the cantilever column system. All systems under this section are frames (which are made up of columns and beams). How can one apply frame detailing requirements to cantilever columns?

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The various material specifications provide a number of requirements for the framing systems that are designated in Part G of Table 12.2-1. For example, for columns in special reinforced concrete moment frames, ACI 318 (ACI 2014) places limits on material properties, cross-sectional dimensions, area of reinforcement, spacing of reinforcement, and location of splices. In addition, detailing requirements are provided for detailing and spacing of transverse reinforcement. These limitations and requirements would be applicable to cantilever systems with a “special reinforced concrete moment frame” as the designated seismic force–resisting system. Certain rules, such as strong column– weak beam requirements, are clearly not applicable to cantilever systems (which do not have beams). Section 11.2 defines cantilever systems as “a seismic force-resisting system in which lateral forces are resisted entirely by columns acting as cantilevers from the base.” Section 12.2.5.2 also places limitations on the axial load that can be carried by the cantilever system and requires that the foundation for such systems be designed with the applicable overstrength factor Ω0 (which is 1.25 for all cantilever systems constructed from steel or concrete.) Finally, cantilever column systems are subject to the redundancy requirements of Section 12.3.4.2. D6. I am designing a pedestrian bridge support (hammerhead) for which in the longitudinal direction, I can have frame action, but in the transverse direction, I have to cantilever the support. If the height of the structure is more than 35 ft, no system in Table 12.2-1 (under “Cantilever Column System”) would be allowed. Can I designate the described support as shear wall and use the R, Cd, Ω0, and height limit provided for shear wall? More importantly, why is there a difference in a cantilevered system and a shear wall system? If the support could be designed and detailed in accordance with all of the requirements for a wall, it would seem that a wall system could be used in the transverse direction. It would appear unlikely, however, that an element with a length to thickness ratio less than 4, for example, could be detailed to meet all the requirements of a wall. For special concrete moment frames, columns with a length to thickness ratio greater than 2.5 (1/0.4) are not allowed, and must thereby be designated as walls. The lower design values and height limitations for cantilever systems are a result of the usually poor performance of these systems. The poor performance (in comparison with walls) is related to low lateral stiffness and a lack of redundancy of cantilever systems. If the hammerhead is significant, the system may need to be classified as an Inverted Pendulum (12.2.5.3). D7. Why was 65 ft chosen as the height limit in Section 12.2.5.6? There is no specific reason other than the fact that 65 ft (five to six stories) is a reasonable delineator between low-rise and mid-rise or high-rise buildings.

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D8. An ice cream kiosk is built in the San Francisco Bay area, on a 25 × 25 ft plan, where the back wall is a concrete shear wall and the other three walls are open for glass/doors. The three open walls are designed as steel ordinary moment frames, detailed according to AISC 341. Based on Section 12.3 of ASCE 7, the roof diaphragm is neither flexible nor rigid, and a torsional irregularity exists. It appears that Section 12.7.3 calls for a 3D model and analysis; however, the provision seems to talk about vertical distribution and multistory buildings. I have a hard time to explain to the owner (and get paid) for anything beyond common 2D analysis. Is this provision really applicable and intended for 1-story structures, especially if it is as small as this job? Before answering the main question, it is noted that Sections 12.2.5.6 and 12.2.5.7 allow but place strict restrictions on the use of single-story ordinary moment frames in SDC D and above. Regarding the main question, it would appear that a 3D analysis would be required to obtain a reasonable distribution of forces in the system, and hence, the requirement of Section 12.7.3 should be followed. (Some kind of 3D analysis was already required to establish the fact that a torsional irregularity exists). It does not seem necessary, however, to model the roof diaphragm as semirigid (using a computer analysis with shell elements, for example). It is recommended that analyses be performed with both flexible and rigid diaphragm assumptions, and the kiosk be designed for the larger forces arising from the two analyses. D9. How is the overstrength factor Ω0 used? Are elements designed with Ω0 factor expected to remain elastic during an earthquake? The overstrength factor is used in load combinations in strength design (Section 2.3) and in load combinations in allowable stress design (Section 2.4). This factor, discussed in detail in Section 12.4.3.1 is applied only to certain elements, and never to the structure as a whole. Specific cases in ASCE 7 where the overstrength factor is used include the following: 1.

Design of elements supporting discontinuous wall or frames (Section 12.3.3.3). This Applies only to systems with horizontal irregularity Type 4 of Table 12.3-1, or vertical irregularity Type 4 of Table 12.3-2.

Design of collector elements in SDC C, D, E, or F (Section 12.10.2.1).

Foundations of cantilever columns systems (Section 12.2.5.2).

Batter piles, pile anchorage and pile splices (Sections 12.13.8.4, 12.13.8.5, 12.13.8.6).

The various material specifications may also require design with the overstrength factor. For example, Section 8.3 of the Seismic Provisions for Structural Steel (AISC 341-16) requires that the required axial and tensile column strength, in the absence of applied moment, shall be determined on the basis of the amplified seismic load, for which the amplified seismic load is defined as that load combination that includes the overstrength factor Ω0. There are numerous

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other cases in which the overstrength factor must be considered in steel design. ACI 318-14 also refers to the overstrength factor in ACI Chapter 18 (seismic) and ACI Chapter 17 (anchorage). For example, the overstrength factor is used in association with the design of elements of concrete diaphragms (see Section 18.12.7.5 of ACI 318-14). Elements designed with the overstrength factor will not necessarily remain elastic during an earthquake. However, it is expected that these elements will suffer less damage than elements not designed with the overstrength factor and will have a lower likelihood of failure. D10. A new hangar is needed near the San Diego airport to house Airbus A380–size aircrafts (W = 235 ft, H = 79 ft) and perform regular cleaning and maintenance jobs (Risk Category II). What kind of SFRS can be selected since none of the systems listed in the ASCE 7-16 Table 12.2-1 seem adequate. The height limits of 35 to 60 ft cannot be met. A steel Special Moment Frame is not an option at a 250 ft span because of AISC 341-16 limits on width-to-thickness and other proportioning requirements. Braced frames, truss moment frames, or any similar listed system falls short of this job’s requirements owing to height of constructability concerns. What seismic force resisting system should be used? The described structural system is quite special and falls outside the basic intent of the building systems described in Table 12.2-1. However, Section 12.2 states that “seismic force–resisting systems that are not contained in Table 12.2-1 are permitted if analytical and test data are submitted that establish the dynamic characteristics and demonstrate the lateral-force resistance and energy dissipation capacity to be equivalent to the structural systems listed in Table 12.2-1 for equivalent response modification factors R, system overstrength coefficient Ω0, and deflection amplifier Cd.” The same clause applies to systems that are described in Table 12.2-1 but violate the height limits. The demonstrative requirements for an intermediate moment frame, for example, could be met through advanced analysis approaches (e.g., nonlinear response history analysis) and through published test data. D11. Is a torsional irregularity load-direction dependent? In other words, can a building be torsionally irregular for loading in one direction, and not irregular for loading in the other direction? If the structure is torsionally irregular (or extremely irregular) because of loading only in one of the two orthogonal directions, the entire system is torsionally irregular and all of the consequences associated with the irregularity are triggered. Similarly, if the irregularity check indicates a torsional irregularity only in one story, the entire system is irregular. Consequences of the irregularity include: • •

Prohibits diaphragm as being classiﬁed rigid (Section 12.3.1.2), Redundancy factor ρ is elevated to 1.3 in both directions of response if the system has an extreme torsional irregularity (in either direction of load) or if

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•

an extreme torsional irregularity occurs when a lateral load–resisting component is removed (Section 12.3.4), Elimination of the equivalent force procedure in Seismic Design Categories D, E, and F (Table 12.6-1), and Requirement to check drift at the edges of the structure for both directions of loading (Section 12.8.6).

III. Questions Covering Structural Analysis Issues A1. How are story stiffnesses calculated when determining whether a vertical structural irregularity of Type 1a or 1b exists? Table 12.3-2 discusses the conditions under which a vertical structural irregularity exists. Stiffness irregularities (Types 1a and 1b) occur when the lateral stiffness of one story is less than a certain percentage of the lateral stiffness of the story above it (or less than a certain percentage of the average stiffness of the three stories above it). However, it is only necessary to determine if such irregularities exist for buildings in SDC D and above because there are no consequences of stiffness irregularities in buildings assigned to SDC C and lower. To address the issue of determining story stiffness, consider the structure shown in Figure G30-1. This structure is a one-bay moment-resisting frame. The column stiffness is the same at each level and the beam stiffness is the same at each level. Three different conﬁgurations were analyzed, with each system having a different beam-to-column stiffness ratio as follows: Beam-to-column stiffness ratio = 0.01: Beam-to-column stiffness ratio = 1.00: Beam-to-column stiffness ratio = 100:

Structure behaves like a cantilever column Structure behaves like a moment frame Structure behaves like a shear frame

For all systems the columns are ﬁxed at the base. Two different methods were used to determine the lateral stiffness of the story: •

•

Method 1: Load the structure with a unit lateral force at each level (all levels loaded simultaneously), compute the story drift at each level, and determine the stiffness at each story as the story shear divided by the story drift. Only one loading is required for this method. Method 2: Load the structure with a positive unit force at level i, and a negative unit force at level i−1, compute the story drift between the two loaded levels, and invert to obtain the stiffness of the story between levels i and i−1. Ten separate loadings are required for this method.

The results of the analysis are shown in Figure G30-2, in which Figure G30-2(a) is for the system with a beam-to-column stiffness ratio of 0.01. The two methods produce dramatically different story stiffness, and for each method the stiffness increases signiﬁcantly at the lowest level. This is particularly true when Method 2

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Figure G30-1. System and loading for determination of story stiffness. is used. This increase in stiffness at the lowest level is caused by the fixed support at the base. The change in stiffness along the height is caused by the support condition and to rigid body rotation in the upper floors, and not to any actual variation in the stiffness of the structural system. The results for the system with the beam-to-column stiffness ratio of 1.0 is presented in Figure G30-2(b). As previously, the results are dramatically different for the two methods of analysis, with Method 2 providing the larger story stiffness. For Method 1 there is a large variation in stiffness along the height, but for Method 2 there is a relatively uniform stiffness, except for the first level. The increase in stiffness at the first level is attributed to the fixed base condition. The results for the analysis of the system with relatively stiff beams are shown in Figure G30-2(c). In this case, the two methods give very similar results, with Method 2 producing a consistently greater stiffness than Method 1. Although there is some influence of the fixed base condition on the results, this is less significant that it was for the other two beam-to-column stiffness ratios. Method 2 appears to be producing better results than Method 1 because the story stiffness reported by Method 2 are more uniform (as would be expected

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Figure G30-2. Results of stiffness analysis of a 10-story building system: (a) beam-to-column stiffness ratio = 0.01; (b) beam-tocolumn stiffness ratio = 1.0; and (c) beam-to-column stiffness ratio = 100. for a structure with uniform properties along the height). The results of Method 1 are highly inﬂuenced by the accumulated rotations of the stories below the story of interest. For example, for the system with the lowest beam-to-column stiffness ratio, almost all the drift in the upper levels is caused by rigid body rotation.

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The basic conclusions from the analysis are as follows: 1.

Method 1 should not be used to determine story stiffness.

Method 2 is preferred, but the computed stiffnesses at the lower levels may be artificially high owing to the fixed boundary conditions, and the stiffness at the upper levels may be artificially low because of the presence of rigid body rotations. The method appears to be reliable for moment-resisting frames but may produce unrealistic estimates of story stiffness in systems that deform like a cantilever (e.g., tall slender shear walls and braced frames).

A2. How are story strengths calculated when determining if a vertical structural irregularity of Type 5a or 5b exists (vertical structural irregularities of types 5a and 5b in Table 12.3-2). It is, in fact, quite difficult if not impossible to calculate the strength of a story of a lateral load–resisting seismic system. The computed strength depends on the loading pattern, the location of yielding throughout the story, and the capacities of the elements that are yielding. The element capacities are a function of the materials used, the details of the cross section, and the forces that act on the section. For example, the flexural strength of a reinforced concrete shear wall is a function of the axial compressive force in the wall. Similarly, the flexural capacity of a steel or concrete column is a function of the axial force in the column. Shear capacities of concrete sections are also a function of the axial force in the section. It is possible to estimate the story capacities of some simple systems, such as shown in Figure G30-3(a), which is a braced frame system, and the story capacity can be based on the strength of the braces as follows: V u = ðF uC + F uT Þ cos ϕ

(G30-1)

where FuC and FuT are the compressive and tensile capacities of the braces, respectively, and ϕ is the angle shown in the ﬁgure. This capacity assumes that the columns do not yield axially and have a moment release (moment-free hinge) at the top and bottom of the story. If it is assumed that the columns also yield, the strength from a column mechanism [Figure G30-3(b); Equation (G30-2)] may be added to the strength obtained from Equation G30-1. For a moment-resisting system, such as shown in Figure G30-3(b), the story capacity may be based on a sway mechanism. This method is based on the assumption that plastic hinges form in the top and bottom of each column of a particular story. If the ﬂexural capacities of the columns are known, the story strength may be obtained as Vu =

X 2 ncols M h i = 1 uC,i

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(G30-2)

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where

h = Story height, ncols = Number of columns in the story, and MuC = Flexural capacity of the column hinges at the top and bottom of the columns (which may be a function of the axial force in the column). This type of mechanism might form in columns of ordinary and intermediate moment frames, but it is unlikely to occur in special moment frames because of strong column–weak beam design requirements. A second type of story capacity may be computed on the basis of the beam strengths. The mechanism for computing the story capacity is shown in Figure G30-3(c). This computed capacity is Vu =

nbays 1 X + − ½M + M uB,i h i = 1 uB,i

(G30-3)

where nbays = Number of bays, + M uB = Positive moment ﬂexural capacity at one end of the beam, − = Negative moment capacity at the other end of the beam, and M uB nbays = Number of bays.

(a) Brace Mechanism

. .

(b) Column Mechanism

Figure G30-3. Three mechanisms for computing story strength: (a) brace, (b) column, and (c) beam.

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However, a mechanism consisting of plastic hinges at each end of each beam in a single story is impossible (without loss of continuity in the columns above and below the level in question). Equations similar to Equations F2 and F3 are discussed in Part C3 of the Commentary on the Seismic Provisions for Structural Steel Buildings (AISC 2005). There is no straightforward way to compute the story shear capacity of a shear wall. Determination of the story capacity of combined systems and dual systems is also problematic. ASCE 7 has only two consequences when weak-story irregularities occur. The ﬁrst of these is given in Section 12.3.3.1, which prohibits structures in SDC E and F from having a Type 5a or 5b vertical irregularity, and structures in SDC D from having a Type 5b irregularity. The second consequence is given by Section 12.3.3.2, which states that buildings with vertical irregularity Type 5b be limited in height to 30 ft (with certain exceptions). Weak-story irregularities do not prohibit one from using the equivalent lateral force method of analysis, whereas soft story irregularities in SDC D and above buildings may prohibit the use of ELF. Aside from determining whether weak-story irregularity exists, story shear capacity may also be needed in association with computing the redundancy factor (Section 12.3.4) and for determining the limiting value of the stability coefﬁcient [Equation (12.8-17)]. A3. How is the redundancy factor ρ calculated for walls with h/w < 1.0? Section 12.3.4.2 states that the redundancy factor ρ must be taken as 1.3 for buildings in SDC D and above unless one or both of two conditions are met. One of these conditions is that “each story resisting more than 35% of the base shear in the direction of interest shall comply with Table 12.3-3.” The intent of Table 12.3-3 is that the engineer considers each lateral load–resisting element in each direction and performs the test associated with that element. For example, consider a system with two moment frames (A and B) and one braced frame (C) resisting loads in a given direction. Analysis would be performed with moment releases placed at each end of a given beam in moment Frame A, with Frames B and C intact. If the placement of the releases does not reduce the system strength by more than 33%, or cause an extreme torsional irregularity, the redundancy factor can be taken as 1.0. Theoretically, the test must be performed once for each beam in Frame A, then again for each beam in Frame B, and then again, for each diagonal in the braced frame. Fortunately, the strength check may often be avoided by inspection. However, the extreme torsion irregularity check may not be as easy to visualize. There is no requirement to remove walls that have a height-to-width ratio of less than 1.0. Thus, if the aforementioned structure had two moment frames and one wall with the wall having h/w less than 1, the wall would never need to be removed in the redundancy analysis. If the system consisted only of walls, with each wall having h/w less than 1, no walls would need to be removed, and the redundancy factor would default to 1.0. This would even be the case for a

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system with only one or two walls (with h/w less than 1) in a given direction. It would seem that such systems are not particularly redundant and should be designed with ρ = 1.3. It appears that this system has “fallen through the cracks” in the standard, resulting in a potentially unconservative design. A4. Are P-Δ effects calculated based on the initial elastic stiffness or are they analyzed at the design story drift? The stability coefficient θ computed by Equation (12.8-16) has two uses. First, it is used to determine if it is necessary to include P-delta effects in the analysis. If θ is less than or equal to 0.1, P-delta effects may be neglected, and if θ is greater than 0.1, such effects must be included. Secondly, when θ > 0.1, θ is used to amplify both the displacements and the member forces, where the amplification factor is given by 1/(1−θ). The stiffness used to calculate displacements in Equation (12.8-16) should be the same stiffness used to compute the period of vibration of the structure and to compute the design story drifts used in accordance with the allowable story drift of Table 12.12-1. The analytical model used to compute the stiffness should conform to the requirements of Section 12.7.3. These modeling requirements are consistent with a structure subjected to service level loads. A5. Is it necessary to check P-Δ effects (per Section 12.8.7) when such effects are automatically included in the structural analysis? When the P-delta analysis is performed by a computer, the displacements and story shears are automatically amplified, so there is no need to amplify these quantities using the ratio 1/(1−θ). However, it is necessary to determine if the maximum allowable value of θ, given by Equation (12.8-17), has been exceeded. To do this, it is necessary to recover the stability coefficient from the structural analysis. This coefficient can be recovered by performing the analysis with and without P-delta effects and by computing the story drifts from each analysis. If the story drift from the analysis without P-delta included is designated Δ0, and the story drift from the analysis with P-delta effects included is Δf, the story stability coefficient is given by θ=1−

Δ0 Δf

(G30-4)

If the computed value of θ for each level is less than 0.1, the analysis may be rerun with P-delta effects turned off. If θ is greater than θmax for any story the structure must be reproportioned. A6. Section 12.7.3 has requirements for structural modeling and requires that cracked section behavior be considered for concrete structures. Speciﬁcally, how does one include concrete cracking in the analytical model? The cracked properties of reinforced concrete are difﬁcult to determine because they depend on the type (axial, bending, shear) of action and the magnitude of

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the action. Expressions for determining cracked section properties may be found in a number of textbooks, including Park and Paulay (1975) and Paulay and Priestly (1992). Table 10-5 of ASCE 41-13 (ASCE 2017b) provides estimates of cracked section properties for beams, columns, walls, and slabs. Cracked properties are provided for sections under flexure, shear, and axial load. Flexural properties are as low as 50% of the gross property (e.g., for non-prestressed beams), but the axial and shear rigidities are not reduced to account for cracking. For axial, this is appropriate if the member is in compression. If for any reason the member is in net tension and the concrete stress exceeds the cracking stress (a rare condition), the axial rigidity should be reduced accordingly. For shear, ASCE 41-17 establishes a rigidity of 0.4EcAg, where Ec is Young’s modulus of the concrete, and Ag is the gross area. It is very important to note here that the 0.4 factor is not a reduction factor for cracking. Instead, it is the factor that converts Young’s modulus (E) to the shear modulus (G). It is recommended that analysts carefully consider the effect of shear cracking, because the reduction in section rigidity to shear cracking can exceed the reduction caused by flexure. This is particularly true for squat shear walls for link beams in coupled wall construction where the length-to-depth ratio of the coupling beams is less than about 4. A7. Section 12.7.3 has requirements for structural modeling and requires that deformations in the panel zone of steel frames be considered. Specifically, how does one include such deformations in the analytical model? Shear deformations in the panel zones of beam–column joints can be an important source of drift in steel moment frames, and for some systems, can be responsible for as much as 40% of the total drift (Charney 1990). The most effective way to include shear deformations is to explicitly model the beam– column joint using an assemblage of rigid links and rotational springs (Charney and Marshall 2006). Many modern computer programs provide this type of model. When such a model is not used, the next-best approach is to model the frame using centerline dimensions, meaning that the flexible length of the beam is equal to the span length between column centerlines. This type of model will overestimate flexural deformations in the panel zone and underestimate shear deformations in the panel zone. The errors are offsetting, so the net result is a reasonably accurate analysis. However, there are cases in which the centerline model is unconservative, meaning it will produce results that underpredict the deflections. Some programs allow the use of a rigid end zone, but this should not be used unless the panel zone is reinforced with doubler plates, and even in this case, only a portion of the panel zone dimensions should be considered rigid. A8. What is the approximate period of a dual system? Table 12.8-2 does not include dual systems (or other combined systems), so such systems automatically default to “other structural systems,” wherein the values

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for parameters Ct and x are 0.02 and 0.75, respectively. It would seem that these parameters would produce a somewhat low period for a dual system, but because the stiffness of such systems is likely dominated by the stiffer component (e.g., the shear wall in a frame-wall system), the degree of conservatism is probably not excessive. Also of concern is the determination of periods for combined systems such as those shown as Buildings C and D in Figure G8-2. In such situations the default parameters may be excessively conservative, but perhaps this is warranted as a penalty for using nontraditional (and not well understood) structural systems. If the periods for dual systems and combined systems are determined analytically (using a computer) the degree of conservatism that is associated with the use of the default parameters may be reduced by using the upper limit period, CuTa when appropriate. A9. Should drifts be calculated at the center of mass or at the diaphragm corners for comparison to drift limits? According to Section 12.8.6, drifts are deﬁned as the difference between the displacements at the centers of mass of adjacent stories. However, if the structure is assigned to Seismic Design Category C or higher and has a torsion irregularity or an extreme torsion irregularity, Section 12.8.6 requires that the drifts be computed as the difference between displacements at the edge of the story. A10. What is the purpose of the exponent k in Equation (12.8-12)? The exponent k accounts, in an approximate manner, for higher mode effects when distributing the design base shear along the height of the structure. For a structure with a uniform story height and story mass, k = 1 (for relatively short buildings with T less than or equal to 0.5 s) will produce a straight-line uppertriangular lateral-force pattern, and k = 2 (for relatively tall buildings for T greater than or equal to 2.5 s) will produce a parabolic force distribution with increasing slope at higher elevations. The limit on using the ELF method of analysis for SDC D, E, and F buildings with T > 3.5 Ts (Table 12.6-1) is based on calculations by Lopez and Cruz (1996) that show that the ELF method may be unconservative when T > 3.5 Ts. A11. When using the modal response spectrum method of analysis (Section 12.9), I lose all the signs of member forces owing to the SRSS or CQC combinations. Sometimes it is useful to know these signs (e.g., is the moment positive or negative?). Is there a way to recover the signs? In general, it is not possible to recover the signs. If maintaining the signs is important, it is recommended that the analyst consider using the linear response history analysis method that is described in Chapter 12 of ASCE 7-16. Probably the greatest challenge to using this approach is the selection and scaling of

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appropriate ground motions. An efficient methodology for performing such analysis (which adheres to the requirements of Chapter 12) is provided by Aswegan and Charney (2014). Key to this approach is the use of spectrum matched ground motions that are derived from natural ground motions. In the linear response history method, the maximum positive and negative force results are provided for each ground motion, and either the average or the envelope of these forces among all ground motions analyzed is used for design. In addition to retaining the signs, concurrent actions may be reported, meaning that the axial force present in a column when it reaches the peak moment is available for checking axial-force bending-moment interaction. The ELF procedure (Section 12.8) is often used for preliminary design and for determination of irregularities and thus can be used as a comparison tool to determine signage of modal response spectrum results. A12. How does one calculate diaphragm forces (shears, collector, and chord forces) when using modal response spectrum analysis? Section cuts above and below the floors can be used to calculate diaphragm forces associated with the vertical distribution of seismic forces determined from the MRS analysis. These forces would be applied in a static manner, similar to the forces computed using Equation (12.10-1). The minimum diaphragm force requirements of Section 12.10 still apply when MRS analysis is used. A more accurate distribution of diaphragm forces may be achieved from MRS analysis if the diaphragms are physically modeled using shell elements. In this case, the analyst must be able to define a cut through the diaphragm for which net forces (e.g., shear through the cut) are determined for each mode and then combined using SRSS or CQC (Section 12.9.1.3). A13. What is the most effective way to shift the center of mass as needed to accommodate accidental torsion in linear or nonlinear response history analysis? Some commercial software has procedures that automatically provide the required 5% mass eccentricities. If this cannot be done automatically, a convenient hand or spreadsheet procedure is presented in Chapter 20 of this guide. This procedure divides the diaphragm into four sections and then determines mass modifiers (multiplying factors) that maintain constant mass and provide the desired eccentricity in one direction without affecting the eccentricity on the other direction. For a rectangular diaphragm with uniform mass, 20% of the mass must be removed from one half of the diaphragm and moved to the other half to provide a 5% mass eccentricity. Although this kind of redistribution seems to indicate an unlikely level of uncertainty in mass distribution, it must be recognized that the 5% eccentricity includes uncertainty in mass and stiffness distribution, nonuniform distribution in loss of lateral stiffness as the lateral load–resisting systems yield, and torsional components of ground motion.

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A14. What type of analysis needs to be performed to satisfy the 25% rule for dual systems? (This question is referenced in Chapters 7 and 18 of this guide.) Section 12.5.1 of the standard states that for a dual system, the moment frame must be capable of resisting as least 25% of the of the design seismic forces, and that the total resistance must be provided by the combination of the moment frame and the shear wall or braced frame in proportion to their rigidities. What is not clear in this requirement is that the moment frame, acting independently of the shear wall or braced frame, must be capable of resisting not less than 25% of the lateral load. Thus, two separate analyses are required. The ﬁrst of these is the complete structural system subjected to the full lateral force, and the second is the moment frame modeled independently, with only 25% of the load applied. Presumably, each element of the lateral load–resisting systems would then be proportioned to resist the larger forces developed from the individual analyses. The 25% rule was developed during a time when virtually all structural analysis was performed in two dimensions, and equivalent lateral-force analysis was used. Today, most analysis is performed in three dimensions, and the modal response spectrum method is often required. Some recommendations for the 25% rule applied to current practice are as follows: 1.

The 25% analysis of the moment frames must be performed using the equivalent lateral force method. There is no rational approach to perform the analysis using modal response spectrum analysis.

In addition to the lateral loading, the moment frames must be designed to carry tributary gravity loads.

It is not necessary to include P-delta effects.

It is not necessary to perform drift checks.

It is not necessary to include accidental torsion.

It is necessary, if required for the direction of loading under consideration, to use load combinations that include the appropriate value of ρ computed for the full system and the appropriate overstrength factor Ω0 for moment frame components where required by Section 12.3.3.3.

For the analysis of the full system, the analysis shall be in conformance with the requirements of Section 12.6 and should include accidental torsion and P-delta effects where required. Further, it is recommended (but not explicitly required by the standard) that the diaphragms be modeled as semirigid because the computed forces in the moment frame and shear wall or braced frame components can be very sensitive to in-plane deformations in the diaphragm. It is of some interest that 25% loading requirement does not satisfy compatibility; thus, the forces developed in the independent analysis will be unrealistic and vastly different from those computed for the full system. Instead of using an elastic analysis under 25% of the lateral force, it would be more rational to

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perform a nonlinear static pushover analysis of the full system and verify that the moment frames provide 25% of the peak strength.

A15. What is a maximum direction spectrum and how is it computed? In Chapter 16, Sections 16.2.3.2 and 16.2.3.3, it is necessary to compute maximum direction spectra of ground motion component pairs. The algorithm described next provides the required spectra. Preliminary Steps: 1.

Create vector arrays of the ground motion acceleration histories. We refer to these vector arrays as X and Y. Each record has nApoints, and a digitization interval of dt. Units should be in length/s2.

Create a vector array of equally spaced periods at which the response spectrum ordinates are to be computed. We will refer to this array as T. It will have nTpoints at an interval of dT.

Selecting a damping ratio, xi.

Select an angle increment dA. We will rotate from Angle 0 to 180 in this increment.

Have on hand a solver (called Solveit below) that can compute the displacement history of a single degree of freedom elastic system.

The required Pseudo Code is given below. For i=1 to nTpoints T=T(i) w=2*pi/T XDir=Solveit(X,T,dt,xi) YDir=Solveit(Y,T,dt,xi) RSmax=0 For j=0,180,dA Ang=j*dA*pi/180 R=(Xdir*cos(Ang)+YDir*sin(Ang))*w*w Rmin=Abs(min(R)) Rmax=max(R) Rmax=max(Rmin,Rmax) RSmax=Rmax if Rmax > RSmax Next j Resp(i)=RSmax Next i When done, the X-coordinates (period values) will reside in T, and the spectral ordinates will reside in Resp. It is easy to extend the routine to supply also the envelope, geomean, or SRSS spectra. Examples of computed spectra are provided in Figure G30-4.

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Figure G30-4. Maximum direction (and other) spectra.

A17. Section 12.8.6.2 allows one to use the computed period of vibration to develop a separate set of lateral forces for the purpose of computing displacements. What is the basis for this? Chapter 12 of the standard provides the following two different periods of vibration that can be used in analysis: 1.

Equation (12.8-7) and Table 12.8-2: Ta = Cthnx. This is the lower-bound period computed from a regression analysis of measured periods of buildings subjected to low-level (much lower than design basis) shaking. The buildings from which data are obtained are usually located in high seismic hazard regions.

T = CuTa, described in Section 12.8.2. Cu is dependent on ground motion intensity, provided in Table 12.8-1. This equation can be used only if an analytical period (e.g., from eigenvalue analysis) is determined from an analytical model, and this period is greater than CuTa. For high seismic hazard regions, Cu = 1.4, and provides a period that is approximately equal to the average from the regression analysis. Larger values of Cu (up to 1.7) recognize the fact that buildings in low seismic hazard regions are usually more ﬂexible than those in high hazard regions.

Section 12.8.6.2 allows for determination of displacements that the computed period of vibration, called Tcomputed herein, may be used to calculate a set of lateral forces, and these forces may be used for the determination of displacements. Experience has shown that Tcomputed is often signiﬁcantly greater than Ta or CuTa. For example, the 8-story building discussed in guide Chapters 21 through 24 had the following periods:

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Table G30-2. Data Used to Generate Figures G30-4(a and b)

Period formula

Period value (s)

SDOF stiffness (kips/in.)

Ta CuTa Tcomputed

1.137 1.592 2.718

1,105 564 193

Base shear (kips)

Elastic displacement Fig. G30-5a (in.)

Elastic displacement Fig. G30-5b (in.)

616 440 257

0.557 0.780 1.330

3.18 2.27 1.33

In the special moment frame direction: Ta = 1.137 s

CuTa = 1.592 s

Tcomputed = 2.718 s (not including P-delta effects).

In the dual system direction (special CBF plus special moment frame): Ta = 0.644 s

CuTa = 0.902 s

Tcomputed = 1.421 s (not including P-delta effects).

Consider the response in the special moment frame direction. The system weight W = 14,000 kip, and the associated mass is 36.2 kip-s2/in., an estimate of the system stiffness (assume single-degree-of-freedom behavior) is provided in Column 3 of Table G30-2. Using R = 8 and SD1 = 0.40, the base shears and associated displacements can be determined as shown in Columns 4 and 5 of the same table. For example, the elastic displacement (not modiﬁed by Cd) for the system with T = CuTa = 440/564 = 0.780 in. These results are shown also in Figure G30-5. As shown, in terms of displacement, it is conservative to compute these using lateral forces consistent with the period Tcomputed. Consider next what would happen if the base lateral forces were determined using a given period formula, but the displacements were computed using these forces and the computer model with a period equal to Tcomputed. If this is done, the displacements provided in Column 6 of Table G30-2 would be determined. As shown, the displacements computed using the shear based on Ta, and the computer model based on Tcomputed, are signiﬁcantly greater that those (e.g., 3.18 in. versus 0.557 in.) for the case in which the shear is based on Ta and the displacements are based on this shear and the mathematical model that produced T = Tcomputed. Results given in Column 6 of Table G30-2 are illustrated graphically in Figure G30-5(b). However, an analytical model that represents the best estimate of the actual stiffness would have a period close to CuTa. This displacement, 0.78 in., is considerably less than 1.33 in., again demonstrating the fact that using the analytical model to determine Tcomputed, and basing lateral forces and displacements on this model, produces conservative results with respect to displacement. A18. Can you provide some background on “Rigid Body Modes” as described in Section 12.9.1.1?

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Figure G30-5. Influence on assumed period on computing system displacements: (a) base shear and displacement computed using the same period formula; and (b) base shear computed using given period but displacements based on Tcomputed. A significant change made in ASCE 7-16 was to require that in modal response spectrum analysis (or modal response history analysis) that a sufficient number of modes be used to capture 100% of the effective seismic mass. If standard mode shapes (i.e., eigenvectors) are used, this would require that all of the modes be included in the analysis, which is thought to be a computational burden for some systems. To avoid using all the modes, it is allowed to represent all modes with a period less than 0.05 s as a single rigid body mode, which has a period of 0.05 s. An exception in ASCE 7-16 allows the continued use of the

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ASCE 7-10 procedure, which requires a sufficient number of modes to capture only 90% of the mass. The theoretical basis for the use of rigid body modes is provided by Powell (1979), Alvarez and Benito (1992), Carr (1994), and Gupta (1990), and is not repeated here. However, the mathematical development presented by the cited authors is somewhat inconsistent with the language in ASCE 7-16. Recall the standard states in Section 12.9.1.1 that “it is permitted to represent all modes with periods less than 0.05 s with a single rigid body mode with a period of 0.05 s.” The inconsistency relative to the preceding is that (1) the residual mode is not really a representation of a rigid body, and (2) the period of the residual mode must be determined mathematically and is a function of the number of active modes to retain in the analysis. As a final note it is mentioned that the use of residual modes is usually not a benefit for building systems. For building structures, it is not a computational burden to specify a sufficient number of modes to capture, for example, 98% of the mass. For certain nonbuilding systems, such as pipe networks, there may be a significant benefit to using residual modes. Indeed, such systems were a primary motivating factor for developing the residual mode concept (Powell 1979, Gupta 1990). A19. Should I be concerned about the fact that where a 3D analysis is performed, a significant portion of the design base shear is resisted by elements in lateral load–resisting systems that are orthogonal to the intended system? (This question is referenced in Chapter 22 of this guide.) In the author’s opinion, this is a concern that is not currently addressed by the standard. Unless it can be demonstrated that the components of the orthogonal system have the same (or greater) ductility as the intended system, the forces in the indented system should be scaled up such that the base shear in the intended system is equal to the design base shear. If the ductility of the orthogonal system is less than that of the intended system, and if the orthogonal system has specified design values in Table 12.2-1, it might be reasonable to consider the main lateral load–resisting system and the orthogonal (unintended) system to be part of a combined system. See Section 12.2.3.3 for requirements.

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Appendix A Overview of Modal Response History and Modal Response Spectrum Analysis

The modal response spectrum and the linear response history procedures that are provided in Section 12.9 of the standard at first glance appear to be significantly different, but in fact they are quite similar. In this appendix each procedure is summarized, and then a brief comparison of the procedures is provided. The linear dynamic analysis procedures are provided in Section 12.9 of the standard, with modal response spectrum (MRS) procedures in Section 12.9.1 and linear response history (LRH) analysis in Section 12.9.2. In MRS analysis, the equations of motion are decoupled by use of the natural mode shapes, and the response in each mode is determined by use of a response spectrum. The modal responses are then statistically combined to produce displacement and component forces. Two approaches are available in LRH analysis. The first is similar to the MRS procedure, except that the decoupled equations are solved using response history analysis, and after the solution the modal responses are added together. In the second approach the equations are not uncoupled, and the fully coupled system is solved using response history analysis. This first approach, called modal response history (MRH) analysis, is covered in detail in this appendix because it is more computationally efficient and is more commonly used.

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The mathematical bases of the different methods are not described here. For further information see Chopra (2017).

A.1 Overview of the MRS Procedure The following steps are required for the MRS analysis procedure that is contained in Section 12.9.1 of the standard. Analysis without accidental torsion, P-delta effects, or orthogonal loading is provided ﬁrst, and is then amended to include these effects. 1.

Develop a 3D mathematical model of system (12.9.1.8),

Compute shape, frequency, participation factor, and effective mass of each mode,

Determine the minimum number of modes to include in the analysis (12.9.1.1),

Develop elastic response spectrum (11.4.6 or 21.2),

Compute elastic modal displacements and forces in each direction of response,

Scale elastic modal responses to obtain approximate design-level inelastic modal responses (12.9.1.2),

Combine the inelastic modal responses to determine the full-system inelastic response in each direction (12.9.1.3), and

Scale full-system responses to obtain parity with the Equivalent Lateral Force Method (12.9.1.4).

Accommodating Accidental Torsion If accidental torsion is required (see Section 12.8.4.2), there are two possible approaches: A. Apply the accidental torsion (with ampliﬁcation if required by Section 12.8.4.3) as a static loading by use of the equivalent lateral force method. Combine the results with those obtained in Step 8. B. Accommodate accidental torsion, without ampliﬁcation, by use of a physical mass offset. Four offsets are required (+ and –5% eccentricity in each direction of response). In Supplement 2 of ASCE 7-16, the mass offset method is not allowed for MRS analysis where the building is in SDC C through F, and where an extreme torsional irregularity exists. The offset method is still permitted for linear and nonlinear response history analysis, regardless of the presence of a torsional irregularity. This issue is discussed in more detail in Chapter 20 of this guide. Where MRS analysis is used, and where there is a torsional irregularity, the modal analytics would be run without a mass offset, with the results scaled in accordance with Section 12.9.1.4 of the standard. To accommodate accidental torsion, the results of a separate static torsion analysis would be added to the results from the MRS analysis. The story torsions in the static analysis would be

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Overview of Modal Response History and Modal Response Spectrum Analysis

equal to the ELF story lateral force, times 0.05AxB, where Ax is the torsional ampliﬁcation actor, and B is the width of the building perpendicular to the direction of lateral forces.

Accommodating P-delta Effects Where P-delta effects are required (see Section 12.8.7) there are two possible approaches: A. Do not include P-delta effects directly in analysis, and adjust forces and displacements obtained in Step 8 by multiplying by 1/(1-θ). B. Include P-delta effects directly in the analysis. Where the system is in SDC C through F, and has a torsional irregularity, the stability ratio θ should be computed using displacements at the edge of the building. This is a signiﬁcant penalty for systems with extreme torsional irregularities.

Accommodating Direction of Loading Requirements Where it is required to combine responses in the two orthogonal directions (12.5) there are two possible approaches in response spectrum analysis: A. Combine 100% of the response in one direction with 30% of the response in the orthogonal direction. Accidental torsion need be included only in the 100% direction. B. Combine by use of the SRSS the responses in the two orthogonal directions. Accidental torsion need be included only in the 100% direction.

A.2 Overview of the Modal Response History Procedure The following steps are required for the response history procedure that is contained in Section 12.9.2 of the standard. It is assumed that the analysis is performed on the system as transformed to modal coordinates. Analysis without accidental torsion, P-delta effects, or orthogonal loading is provided ﬁrst, and is then amended to include these effects. 1.

Develop a 3D mathematical model of system (12.9.2.2),

Compute shape, frequency, participation factor, and effective mass of each mode,

Determine the minimum number of modes to include in the analysis (12.9.2.2.4),

Develop three sets of spectrally matched ground motions (12.9.2.3.1),

For each ground motion (applied independently in the x- or y-directions) compute elastic modal displacements and force response histories,

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Scale elastic response histories to obtain approximate design-level inelastic response histories (12.9.2.5.1),

Scale elastic response histories to obtain parity with the Equivalent Lateral Force Method (12.9.2.5.2), and

Envelope response histories to obtain system responses in each direction of response (12.0.2.5.3).

Accommodating Accidental Torsion If accidental torsion is required it must be accommodated by use of a physical mass offset. Ampliﬁcation of accidental torsion is not required (Section 12.9.2.2.2).

Accommodating P-delta Effects Where required by Section 12.8.7, P-delta effects must be included directly in the analysis (12.9.2.2.1).

Accommodating Orthogonal Loading Requirements Orthogonal load effects are included in the LRH procedure by use of the combined force response procedures in 12.9.2.5.3.

A.3 Uniﬁed Approach As noted previously, there are distinct similarities in the MRS and MRH procedures. However, there are choices of the methodology in applying accidental torsion, P-delta effects, and orthogonal loading in the MRS method. If the “B” method is used for accidental torsion, P-delta, or combining modal responses, the only signiﬁcant difference in the MRS and MRH approaches is how the individual modal responses are obtained (response spectrum of response history analysis) and how the modal combinations are obtained (CQC+SRSS or direct addition).

A.4 Direct Response History Analysis In the preceding description of the MRH procedure, the response histories were obtained on a modal basis and then combined to ﬁnd the full-system response. An alternate approach is to solve the full system of equations without transforming to modal coordinates. This approach, called “direct dynamic analysis,” is more time consuming and uses considerably more storage than the modal procedure. Because of the various assumptions made in the analysis there is no advantage of using direct analysis for linear systems.

A.5 Advantages of Response History Analysis Linear response history analysis is unquestionably more complex that MRS analysis. However, once the method is fully implemented into commercial

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Overview of Modal Response History and Modal Response Spectrum Analysis

software, the differences will be virtually transparent to the user. A few advantages of LRH are provided as follows: 1.

Signs are retained in the computed nodal displacements and forces. Thus, it is known whether a brace is in compression or tension and whether a moment is positive or negative. (All of the signs arising from MRS analysis are positive owing to the modal combinations.)

Interactive forces are available, such as the bending moment at the time of maximum axial force. (Interactive forces are lost in MRS analysis because the times of peak response are not available from the response spectrum.)

Floor response spectra can be easily obtained to assess the performance of nonstructural components.

The method provides some experience in linear response history analysis, and this will be advantageous when the analyst ﬁrst attempts the nonlinear methods presented in Chapter 16.

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Appendix B 8-Story Steel Building Case Study Structure

This appendix describes the characteristics of the 8-story structural steel building used as a case study in several chapters. The site is located in Raleigh Hills, Oregon, which is a suburb to the west of Portland (latitude 45.4975, longitude −122.7559). The building is used for medical offices and has normal use as a nonemergency surgical facility. In the event of an earthquake or other event it is anticipated that there could be some emergency medical care. Because of the potential for use in an emergency, it has been decided to classify the structure as Risk Category III which leads to a seismic importance factor, Ie, of 1.25 in accordance with ASCE 7-16 Table 1.5-2. The structure is an 8-story building with a first story height of 15 ft and the remaining story heights of 12.5 ft. A 5 ft tall roof parapet is present around the entire perimeter. In addition, the structure has a 15 ft basem*nt level with a solid concrete perimeter wall. The outside plan dimensions of the building are 185 × 85 ft. The gravity system is a structural steel framing system with composite floor system utilizing composite deck, concrete topping, and shear studs. Plan and elevation views of the structure are shown in Figures GB-1 and GB-2. The nonseismic loading for the structure is summarized as follows: • • • • • • •

Structural system (all ﬂoors): Ceiling and mechanical (Levels 2 through 8): Ceiling and mechanical (roof): Fixed partitions (Levels 2 through 8): Exterior surfaces (vertical surfaces excluding parapet): Parapet (vertical surfaces): Rooﬁng:

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70 psf 15 psf 20 psf 10 psf 35 psf 60 psf 12 psf

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Figure GB-1. Plan view of case study building.

Figure GB-2. Elevation view of case study building.

• • • •

Live load (client speciﬁed for Levels 2 through 8): Roof live load: Ground snow load: Wind velocity (does not control):

60 psf 20 psf 10 psf 115 mph

The geotechnical report indicates a Site Class C soil condition that has been determined through investigation. The seismic hazard information, taken from the ASCE 7 Hazard Tool and shown in Figure GB-3, is summarized as follows:

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8-Story Steel Building Case Study Structure

Figure GB-3. ASCE 7 hazard report for case study structure. • • •

SS = 0.893 g, Fa = 1.2, SMS = 1.072 g, SDS = 0.715 g; S1 = 0.405 g, Fv = 1.5, SM1 = 0.607 g, SD1 = 0.405 g; and TL = 16 s.

The seismic force resisting system is different in the two orthogonal directions. In the east–west direction, a perimeter steel special moment resisting frame (SMRF) (R = 8, Ω0 = 3, Cd = 5.5) is used. Seismic design and detailing for the structures lateral systems are in accordance with the Seismic Provisions for Structural Steel Buildings (AISC 2016b). For the special moment frame, the

Figure GB-4. Location of special moment-resisting frames.

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requirements of Prequaliﬁed Connections for Special and Intermediate Steel Moment Frames for Seismic Applications (AISC 2016a) must also be fulﬁlled. Only the beams between gridlines B and F are part of the moment frame. This was done because it is expected that Grid lines A and F may be part of the orthogonal direction lateral system. If the corner columns are part of both lateral systems, the orthogonal loading provisions for seismic design in ASCE 7-16 may be triggered. In addition, a moment frame connection in the weak direction of

Figure GB-5. Location of concentrically braced frames.

Figure GB-6. Elevation view of concentrically braced frames.

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Figure GB-7. Plan view of combined lateral system.

Figure GB-8. Elevation of SMRF in the east–west direction (Grid lines 1 and 4).

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the column would cause difficulties meeting the strong column weak beam criteria in AISC (2016b). Figure GB-4 shows the location of the SMRF in the east–west direction. The preliminary design in this direction resulted in a moment frame controlled by drift criteria based on forces calculated using the computed period of vibration, Tcomputed. (See Chapter 16 for an explanation of the use of Tcomputed for the drift check.) In the north–south direction, two different types of lateral systems are combined. The first is a special steel concentrically braced frame (SCBF) along Grid lines B, C, E, and F (R = 6, Ω0 = 2, Cd = 5). The location of the SCBFs are shown in Figure GB-5. An elevation of the concentric braces are shown in Figure GB-6. The two-story X configuration has been used to increase the stiffness (over a single diagonal), enhance redundancy, and avoid large unbalanced forces on the beams that occur for chevron configurations. Architectural requirements do not allow braces at the exterior elevation. The elimination of perimeter bracing substantially reduces the torsional rigidity of the structure and also requires an analysis of the structure with specific lateral elements removed to determine if the redundancy factor, ρ, can be 1.0. Because of the aspect ratio of the structure, the building is susceptible to torsional irregularities in the north–south direction caused by the lateral system being

Figure GB-9. Elevation of SMRF in the north–south direction (Grid lines A and G).

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toward the center of the building and the larger dimension of the structure in the east–west direction causing a larger accidental torsion. The preliminary design of the structure in the north–south direction with only the SCBF was completed, and the braces were sized for strength and checked for drift limits using lateral forces at Tcomputed. The lateral system with the SCBF only met drift and strength criteria, had a torsional irregularity [torsional irregularity factor (TIF) = 1.29], but did not meet requirements for the redundancy factor, ρ, to be 1.0. This would have required using ρ = 1.3. An addition to the lateral system was needed to provide supplemental torsional resistance to provide a system that met the redundancy requirements. This supplemental resistance was provided in the form of a SMRF at Grid lines A and G. The layout of the combined brace frame and moment frame system is shown in Figure GB-7. Initially the two systems together were considered a combination system (R = 6, Ω0 = 3, Cd = 5.5) for which the moment frame is designed for the force demand, based on the analytical model. In this case, the seismic performance factors were based on the worst case from the two systems (i.e., lowest R value and largest Ω0 and Cd). The moment frames were initially sized for strength. Design iterations were completed until the moment frame was stiff enough at all levels to eliminate the extreme torsional irregularity, with

Figure GB-10. Elevation of SCBF in the north–south direction (Grid lines B and F).

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one brace on Grid line B or F removed from the system in accordance with Table 12.3-3, which allowed for a redundancy factor ρ = 1. The other option for the combination of two lateral systems is a dual system with a special moment frame and special concentric braces (R = 7, Ω0 = 2.5, Cd = 5.5). In this case a higher R factor is allowed, which reduces the base shear in this direction. Another difference between the two is that for a dual system, the moment frame must have the capacity to resist 25% of the total base shear. This would typically require an additional step of ensuring the moment frame has sufficient capacity to resist 25% of the base shear on its own. In this case, the moment frame was sized for stiffness to eliminate the extreme torsional irregularity under the brace removal scenario. The result of this was a moment frame with sufficient capacity to resist 25% of the total base shear without any further modification. The stronger and stiffer perimeter moment frame had the added benefit of also eliminating the torsional irregularity in the system (TIF = 1.16). The design sections for the east–west special moment frame on Grid lines 1 and 4 are shown in Figure GB-8. The moment frame that is part of the dual system on Grid lines A and G is shown in Figure GB-9. The elevation for the braced frames for the dual system on Grid lines B and F are provided in

Figure GB-11. Elevation of SCBF in the north–south direction (Grid lines C and E).

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Table GB-1. Reference to Design Checks for an 8-Story Building

Chapter 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Item discussed Risk category Ground motion parameters Design response spectra Seismic design category and importance factor Structural systems Combination of systems Diaphragm ﬂexibility Horizontal structural irregularities Vertical structural irregularities Load combinations and direction of loading Analysis requirements Modeling requirements Effective seismic weight Period of vibration ELF preliminaries (development of lateral forces) Drift and P-delta Accidental torsion Determination of redundancy factor Complete ELF example Complete MRS example Complete linear LRH example Comparisons of ELF, MRS, LRH analysis Considerations for NRH analysis Diaphragm forces Nonstructural components (including ﬂoor spectra)

Figure GB-10. Figure GB-11 shows the elevation of the braced frames on Grid lines C and E. Only the relevant lateral resisting elements are shown. Various checks and calculations are shown and discussed for this 8-story structure in the main chapters of the guide. These items are presented at the end of the relevant chapter as summarized in Table GB-1.

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References Abrahamson, N. A. 1992. “Non-stationary spectral matching.” Seismol. Res. Lett. 63: 30. ACI (American Concrete Institute). 2014. Building code requirements for structural concrete. ACI 318. Farmington Hills, MI: ACI. AISC. 2005. Seismic provisions for structural steel buildings. ANSI/AISC 341. Chicago: AISC. AISC. 2006. Design guide 1: Base plate and anchor rod design. Chicago: AISC. AISC. 2015. Specification for structural steel buildings. ANSI/AISC 360. Chicago: AISC. AISC. 2016a. Prequalified connections for special and intermediate steel moment frames for seismic applications. ANSI/AISC 358. Chicago: AISC. AISC. 2016b. Seismic provisions for structural steel buildings. ANSI/AISC 341. Chicago: AISC. Al Atik, L., and Abrahamson, N. A. 2010. “An improved method for nonstationary spectral matching.” Earthquake Spectra 26 (3): 601–617. Alvarez, R., and Bento, J. J. 1992. “On the use of residual modes in modal analysis.” In Proc., 10th World Conf. in Earthquake Engineering, Madrid, Spain. ANSI (American National Standards Institute). 2012. Specifications for the design, testing, and utilization of industrial steel storage racks. ANSI MH16.1. New York: ANSI. ASCE. 2017a. Minimum design loads and associated criteria for buildings and other structures. ASCE 7. Reston, VA: ASCE. ASCE. 2017b. Seismic evaluation and retrofit of existing buildings. ASCE/SEI 41. Reston, VA: ASCE. ASCE. 2019. “ASCE 7 hazard tool.” Accessed December 23, 2019. https:// ASCE7hazardtool.online. ASTM. 1998. Standard test method for laboratory determination of water (moisture) content of soil and rock by mass. ASTM D2216. West Conshohocken, PA: ASTM. ASTM. 2000a. Standard test method for unconfined compressive strength of cohesive soils. ASTM D2166. West Conshohocken, PA: ASTM. ASTM. 2000b. Standard test methods for liquid limit, plastic limit, and plasticity index of soils. ASTM D4318. West Conshohocken, PA: ASTM. ASTM. 2003. Standard test method for unconsolidated-undrained triaxial compression test on cohesive soils. ASTM D2850. West Conshohocken, PA: ASTM. ASTM. 2004. Standard test method for penetration test and split-barrel sampling of soils. ASTM D1586. West Conshohocken, PA: ASTM.

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ASTM. 2011. Standard practice for classification of soils for engineering purposes: Unified soil classification system. ASTM D2487. West Conshohocken, PA: ASTM. Aswegan, K., and Charney, F. 2014. “A simple linear response history analysis procedure for building codes.” In Proc., 10th National Conf. on Earthquake Engineering, Anchorage, Alaska. Aswegan, K., Charney, F. A., and Jarrett, J. 2015. “Recommended procedures for damage-based serviceability design of steel buildings under wind loads.” Eng. J. 52 (1): 1–26. ATC (Applied Technology Council). 1978. Tentative provisions for the development of seismic regulations for new buildings. Rep. No. ATC 3-06. Redwood City, CA: ATC. ATC. n.d. “ATC hazard by location.” Accessed December 23, 2019. https:// hazards.atcouncil.org. AWC (American Wood Council). 2015. 2015 special design provisions for wind and seismic. Leesburg, VA: AWC. Carr, A. 1994. “Dynamic analysis of structures.” Bull. N. Z. Nat. Soc. Earthquake Eng. 27 (2): 129–146. Charney, F. A. 1990. “Sources of elastic deformation in laterally loaded frame and tube structures.” In Proc., Council on Tall Buildings and Urban Habitat (CTBUH) Conf. on Tall Buildings, Hong Kong. Charney, F. A. 2008. “Unintended consequences of modeling damping in structures.” J. Struct. Eng. 134 (4): 581–592. Charney, F. A., and Marshall, J. 2006. “A comparison of the Krawinkler and Scissors models for including beam-column joint deformations in the analysis of moment-resisting steel frames.” Eng. J. 43 (1): 31–48. Chiou, B., Darragh, R., Gregor, N., and Silva, W. 2008. “NGA project strongmotion database.” Earthquake Spectra 24 (1): 23–44. Chopra, A. 2017. Dynamics of structures, 5th ed. New York: Pearson. Chopra, A., and McKenna, F. 2016. “Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation.” Earthquake Eng. Struct. Dyn. 45: 193–211. CSI (Computers and Structures, Inc.). 2018. ETABS version 17. Walnut Creek, CA: CSI. CSI. 2019. SAP2000 version 21. Walnut Creek, CA: CSI. DeBock, D., Hohener, C., and Valley, M. 2019. “Does accidental torsion prevent collapse?” Structure, March, 14–17. FEMA. 2009. Quantification of building seismic performance factors. FEMA P-695. Washington, DC: FEMA. FEMA. 2012. Seismic performance assessment of buildings. FEMA P-58-1. Washington, DC: FEMA. FEMA. 2015a. 2015 NEHRP provisions volume I: Part 1 provisions, part 2 commentary. FEMA P-1050-1. Washington, DC: FEMA. FEMA. 2015b. 2015 NEHRP provisions volume II: Part 3 resource papers. FEMA P-1050-2. Washington, DC: FEMA. FEMA. 2016. NEHRP recommended seismic provisions: Design examples. FEMA P-1051. Washington, DC: FEMA. FEMA. 2018. Assessing seismic performance of buildings with configuration irregularities: Calibrating current standards and practices. FEMA P-2012. Washington, DC: FEMA.

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Ghosh, S. K., and Dowty, S. 2007. “Bearing wall systems vs building frame systems.” Struct. Eng. (February). Goel, R. K., and Chopra, A. K. 1998. “Period formulas for concrete shearwall buildings.” J. Struct. Eng. 124 (4): 426–433. Gupta, A. K. 1990. Response spectrum method in seismic analysis and design of structures. Boca Raton, FL: CRC Press. Harris, J. R. 1992. “An overview of seismic codes.” In Civil engineering practice, 27–48. Boston, MA: Boston Society of Civil Engineers. Haselton, C. B., Baker, J. W., Stewart, J. P., Whittaker, A. S., Luco, N., Fry, A., et al. 2017a. “Response history analysis for the design of new buildings in the NEHRP provisions and ASCE/SEI 7 standard: Part I—Overview and specification of ground motions.” Earthquake Spectra 33 (2): 373–395. Haselton, C. B., Fry, A., Hamburger, R. O., Baker, J. W., Luco, N., Elwood, K. J., et al. 2017b. “Response history analysis for the design of new buildings in the NEHRP provisions and ASCE/SEI 7 standard: Part II—Structural analysis procedures and acceptance criteria.” Earthquake Spectra 33 (2): 397–417. ICC (International Code Council). 2017. 2018 International building code. Country Club Hills, IL: ICC. Jarrett, J. A., Zimmerman, R. B., Charney, F. A., and Jalalian, A. 2017. “Response history analysis for the design of new buildings in the NEHRP provisions and ASCE/SEI 7 standard: Part IV—A study of assumptions.” Earthquake Spectra 33 (2): 449–468. Jayamon, J., and Charney, F. 2015. “Multiple ground motion response spectrum match tool for use in response history analysis.” In Proc., 2015 Structures Congress, Portland, Oregon. Liew, J. Y. 2001. “Inelastic analysis of steel frames with composite beams.” J. Struct. Eng. 127 (2): 194–202. Lopez, O. A., and Cruz, M. 1996. “Number of modes for the seismic design of buildings.” Earthquake Eng. Struct. Dyn. 25 (8): 837–856. NIST (National Institute of Standards and Technology). 2010. Evaluation of the FEMA P-695 methodology for quantification of building seismic performance factors. NIST GCR 10-917-8. Gaithersburg, MD: NIST. NIST. 2011. Selecting and scaling earthquake ground motions for performing response-history analysis. NIST GCR 11-917-15. Gaithersburg, MD: NIST. NIST. 2012. Soil structure interaction for building structures. Rep. No. GCR 12-917-21. Gaithersburg, MD: NIST. NIST. 2017. Guidelines for nonlinear structural analysis for design of buildings, Part I–general. NIST GCR 17-917-46v1. Gaithersburg, MD: NIST. Park, R., and Paulay, T. 1975. Reinforced concrete structures. Hoboken, NJ: Wiley Interscience. Paulay, T., and Priestly, M. 1992. Seismic design of reinforced concrete and masonry buildings. New York: Wiley. PEER (Pacific Earthquake Engineering Research Center). 2013. “PEER ground motion database.” Accessed December 23, 2019. https://ngawest2. berkeley.edu/. PEER. 2017. Guidelines for performance based design of tall buildings. Berkeley, CA: Univ. of California. Powell, G. H. 1979. “‘Missing mass’ correction in modal analysis of piping systems.” In Proc., Conf. in Seismic Response Analysis of Nuclear Power Plants, Berlin, Germany.

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Sabelli, R., Pottebaum, W., and Dean, B. 2009. “Diaphragms for seismic loading.” Accessed December 23, 2019.https://csengineermag.com/wp-content/uploads/ 2017/11/SE0109_Diaphragms-copy.pdf. Schaffhausen, R., and Wegmuller, A. 1977. “Multistory rigid frames with composite girders under gravity and lateral forces.” Eng. J. 14 (2): 68–77. SEAOC (Structural Engineers Association of California). 1999. Recommended lateral force requirements and commentary. Sacramento, CA: SEAOC. USGS. n.d. “Uniﬁed hazard tool.” Accessed December 23, 2019. https://earthquake. usgs.gov/hazards/interactive/. Zareian, F., and Medina, R. 2010. “A practical method for proper modeling of structural damping in inelastic plane structural systems.” Comput. Struct. 88 (1–2): 45–53. Zimmerman, R. B., J. W. Baker, J. D. Hooper, S. Bono, C. B. Haselton, A. Engel, et al. 2017. “Response history analysis for the design of new buildings in the NEHRP provisions and ASCE/SEI 7 standard: Part III—Example applications illustrating the recommended methodology.” Earthquake Spectra 33 (2): 419–447.

Additional Reference Not Cited in the Text FEMA. 2010. Earthquake resistant design concepts. FEMA P-749. Washington, DC: FEMA.

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Index

Page numbers followed by e, f, and t indicate equations, ﬁgures, and tables. acceptance criteria, nonlinear response history (NRH) analysis and, 262, 263, 265, 266–267 accidental torsion: equivalent lateral force (ELF), 153–154, 173, 173t, 196–198, 199t; FAQs, 338; ﬂexible semirigid diaphragm systems and, 70f, 73, 82f, 174f, 178–179, 179f; load combinations, 105, 108, 108f, 109–111, 109f, 110e; modal response history (MRH) analysis, 348; modal response spectrum and linear response history analysis, 179–181, 180f, 181e, 182f, 182t, 183–184, 183f, 218, 346–347; modeling for, 123; simple building load analysis, 312–314, 313f; in systems with semirigid diaphragms, 67–68, 70f, 72–73; torsional irregularities, 75–80, 76f, 77f, 85, 88, 171–178, 172f, 173t, 174f, 175f, 176t, 177t, 178t. See also load combinations ACT 123 Project, 183–184, 183f alternate and nonconforming systems, selection of, 56 amplitude scaling, NRH analysis and, 264–265 approximate fundamental period Ta, period of vibration, 135–141, 137f, 139e, 139t, 140t ASCE 7 hazard report, 8-story steel building, 352–353, 353f ASCE 7 Hazard Tool, 23–25, 24f, 25f

ASCE 7 section 12.3.1.3, diaphragm flexibility classification using, 69–72, 69f, 70f, 71f, 72f ASCE 7 Seismic Load Provisions, overview of: brief history of, 2–5, 5f, 5t; intent of, 1–2; significant changes to ASCE 7-16 from ASCE 7-10, 7; update process for, 5–7 back-calculation of stability ratios when P-delta effects are included, 9-story building, 159e, 164t, 166–167, 167e, 168t beam-column joint deformations in steel (and concrete) moment frames, modeling of, 122, 122f bearing wall systems: building frame systems differ from, 50, 51f; system selection, 50–52, 51f, 52f book warehouse. See 4-story book warehouse, effective seismic weight example buckling-restrained braces (BRBs), period of vibration, 136–137, 136f, 137f building frame systems, bearing wall systems differ from, 50, 51f cantilevered column systems, 55, 55f, 325–326 center line analysis, beam-column deformations, 122, 122f center of mass: accidental torsion and shifting of, 180–181, 180f, 181e, 182f, 182t, 183; FAQs, 338

365

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366

Index

collectors. See diaphragms and collectors column systems, cantilevered, 55, 55f, 325–326 combinations of systems. See lateral load resisting systems, combinations of component acceleration, nonstructural components, 278–279 computed response, using ELF, MRS, and LRH analysis, 249; elastic base shear comparisons, 251–252, 252t, 253t, 254t, 255f, 256f, 257f, 258f, 259f, 260f; inelastic story drift comparisons, 249–251, 250f, 250t computer programs, computing period with, 140–141 concentrically-braced frames, 8-story steel building, 354f concrete cracking, FAQs, 335–336 concrete moment frames, modeling of beam-column joint deformations, 122, 122f concrete shear walls, 4, 51f, 52f, 53, 54–55, 54f, 58, 69, 136, 141–142 concrete wall structures, computing Ta for, 141–143, 142f, 142t coupled wall systems, 54–55, 54f, 121 cracked section properties in reinforced concrete structures, modeling of, 121, 121t Ct value, 325 CuTa and Tcomputed, 48–49, 89, 115–117, 138–140, 145t, 146; FAQs, 323–324, 323t, 324t dead load, 4-story book warehouse effective seismic weight example, 128–131, 132f deformation, FAQs, 336 deformation-controlled elements, NRH analysis and, 265–267 design response spectrum, 27, 33, 35–36, 39t, 48 diaphragm discontinuity irregularity (Type 3), horizontal structures, 81–83, 82f, 83f diaphragm ﬂexibility: accidental torsion in systems with semirigid diaphragms, 67–68, 70f, 72–73; equivalent lateral force (ELF), 8-story building, 192; example classiﬁcation, using section 12.3.1.3, 69–72, 69f, 70f, 71f, 72f

diaphragm forces: ELF procedure and, 154; FAQs, 338 diaphragm modeling, 120 diaphragms and collectors, 269–275, 270f, 272f, 273f direction of loading requirements: equivalent lateral force (ELF), 8-story building, 189, 191, 192–193; ﬂoor response spectra, 287; modal response history (MRH) analysis, 347 discontinuity in lateral strength–weak story irregularity (Types 5a and 5b), vertical structural irregularities, 94–97, 95f, 96f drift and P-delta effects, equivalent lateral force (ELF), 8-story building, 190t, 193–194, 193t, 194t, 195t dual systems: ELF procedure and, 155; FAQs, 59f, 336–337; system selection, 52–53, 54f ductility demand, importance factor and, 42 ductility-based design, 1 effective seismic weight (mass), 125; FAQs, 323; 4-story book warehouse example, 125–133, 127f, 132t; low-rise industrial building example, 133–134, 133f, 134f; mass modeling, 123–124 8-story building, ﬂoor response spectra, 277, 279–280, 280f, 287– 289, 287f, 288f, 288t, 290f, 291f 8-story steel building: reference to design checks for, 359f; structural system, 351–359, 352f, 353f, 354f, 355f, 356f, 357f, 358f. See also equivalent lateral force (ELF), 8-story building; linear response history (LRH), 8-story building; modal response spectrum (MRS), 8-story building elastic and inelastic analysis, redundancy factor and, 101–104, 103f elastic base shear, computed response comparisons, 251–252, 252t, 253t, 254t, 255f, 256f, 257f, 258f, 259f, 260f elastic response spectrum, developing of, 35–49, 37f, 38f, 38t, 39t; horizontal acceleration spectrum,

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367

Index

35, 36–37, 37f; vertical response spectrum, 35, 36, 39–40, 39f elastic stiffness, FAQs, 335, 335e equivalent lateral force (ELF), 147–148; accidental torsion and, 173, 173t; diaphragm flexibility and, 73; period T used in, 137f, 138–139, 139t; procedure overview, 148–152, 149f, 150f, 151e, 151f, 152e, 152f; structural analysis procedures, 114–117; uses for other than final design, 153–155; vibration for combined systems and, 59f, 64. See also computed response, using ELF, MRS, and LRH analysis; equivalent lateral force (ELF), 5-story building; equivalent lateral force (ELF), 8-story building equivalent lateral force (ELF), 5-story building, 185, 198, 200–203, 200f, 201f, 202f, 202t equivalent lateral force (ELF), 8-story building, 185, 186; accidental torsion effects, 196–198, 199t; diaphragm flexibility, 192; direction of loading requirements, 192–193; drift and P-delta effects, 190t, 193–194, 193t, 194t, 195t; ground motion parameters, 187–188; orthogonal loading effects, 195–196, 199t; preliminary mathematical model, 190–191; primary lateral forces, 189, 190t; redundancy, 192, 192t, 193t; regularity checks, 190t, 191, 191t; seismic base shear, 188–189; seismic design and importance factor, 188; seismic member forces, 190t, 193t, 195, 196t, 197t, 198t; story weights, 188, 188t; structural system, 186–187, 355f, 356f, 357f, 358f exponent k, FAQs, 337 FEMA P-2012, 154, 183–184, 183f 5-story building, ELF procedure, 185, 198, 200–203, 200f, 201f, 202f, 202t flexible diaphragms. See diaphragm flexibility flexible semirigid diaphragm buildings, application of accidental torsion in, 70f, 73, 82f, 174f, 178–179, 179f

ﬂoor response spectra, 277, 279–280, 280f, 287–289, 287f, 288f, 288t, 290f, 291f force deformation plots, 42, 42f, 102, 102f, 103f foundation modeling, 124, 266 4-story book warehouse, effective seismic weight example: building description, 125–128, 127f; dead load, 128–131, 132t; snow loads, 132–133, 132f; storage live loads, 131–132, 132f 4-story reinforced concrete building, empirical method example, nonstructural components, 280–282, 281f, 283t, 284–287, 284t, 285f frame elements, modeling of shear deformation in, 120 frequently asked questions (FAQs): design issues, 324–329; general issues, 321–324; structural analysis issues, 329–344 ground motion: equivalent lateral force (ELF), 8-story building, 187–188; nonlinear response history analysis, 264–265 ground motion parameters, determining of, 17–18, 19t, 20t, 21; examples of, 21–23, 22f, 23f; using ASCE 7 Hazard Tool, 23–25, 24f, 25f hammerhead pedestrian bridge support, FAQs, 326 horizontal acceleration spectrum, developing of, 35, 36–37, 37f horizontal structural irregularities, 75; consequences of, 85–86; diaphragm discontinuity irregularity (Type 3), 81–83, 82f, 83f; nonparallel system irregularity (Type 5), 85, 85f; out-of-plane offset irregularity (Type 4), 83–84, 84f; reentrant corner irregularity (Type 2), 80–81, 80f; torsional irregularities (Types 1a and 1b), 75–80, 76f, 77e, 77f, 78f, 79f, 80f importance factor Ie: determination of, 41–43, 42e, 42f; purpose of, 42 inelastic analysis. See elastic and inelastic analysis; inelastic story drift

Seismic Loads

368

Index

inelastic story drift, computed response comparisons, 249–251, 250f, 250t in-plane discontinuity in vertical lateral force-resisting element irregularity (Type 4), 93–94, 94f

Krawinkler model, beam-column deformations, 122, 122f lateral load resisting systems, combinations of, 57–58, 58f, 59f; computing approximate periods of vibration for, 59f, 64; 8-story steel building, 355f; framing systems in same or different directions, 58–61, 58f; structural systems in vertical direction, 59f, 62–64; vertical combination when the lower section is stiff relative to upper portion, 65 linear response history (LRH) analysis, 345, 348–349; application of accidental torsion in, 179–181, 180f, 181e, 182f, 182t, 183–184, 183f, 218, 346–347; ELF procedure and, 155; structural analysis procedures, 114–117. See also computed response, using ELF, MRS, and LRH analysis; linear response history (LRH) analysis, 8-story building linear response history (LRH) analysis, 8-story building, 221; analysis results, 234–237, 235f, 238f, 238t, 239–240, 239t, 240t, 241t, 242, 242f, 243t, 244t, 245t, 246t, 247–248, 247t, 248t; ground motion selection and modiﬁcation, 225–234, 226f, 227f, 228t, 229t, 230f, 231f, 232f, 233f, 234f, 235f, 236f, 237f, 238f; modal properties, 209t, 210f, 224–225; overview, 222–223, 222f; response system used for analysis, 223, 224f; system modeling, 224 load combinations, 105–111, 108f, 109f, 110e, 111e low-rise industrial building example, effective seismic weight (mass), 133–134, 133f, 134f masonry and concrete wall structures, computing Ta for, 141–143, 142f, 142t

mass modeling. See effective structural weight (mass) mathematical modeling requirements, structure and, 119–124, 122f maximum considered earthquake (MCE), 1, 17, 43, 322 maximum direction spectrum, 265, 340, 341f modal response history (MRH) analysis, 73, 228, 228t, 343, 345, 347–348 modal response spectrum (MRS) analysis, 345; application of accidental torsion in, 179–181, 180f, 181e, 182f, 182t, 183–184, 183f; ELF procedure and, 154, 155; FAQs, 337–338; procedure overview, 345, 346–347; structural analysis procedures, 114–117. See also modal response spectrum (MRS), 8-story building modal response spectrum (MRS), 8-story building, 205; analysis results, 209t, 211–214, 212e, 214t, 215t, 216t; force results determination, 214–217, 216t, 217t, 219, 219t, 318t; initial scaling of results, 211; modal properties, 208, 209t, 210f; number of modes and modal combination procedure, 207f, 209–211, 209t; overview, 206–207, 206f, 355f, 356f, 357f, 358f; response system used for analysis, 207–208, 207f; system modeling, 208 9-story building: back-calculation of stability ratios when P-delta effects are included, 159e, 164t, 166–167, 167e, 168t; building description, 160–164, 161f, 161t, 163t, 164t; computation of actual story overstrength, 161f, 163t, 165t, 167e, 168–169, 168e, 169t; P-delta effects, 158–160, 159e, 164–166, 165t, 166t, 167t; story drift analysis, 145t, 149f, 150f, 151f, 157–158, 157e, 162–164, 163t, 164t nonbuilding structures, 293–295; pile support mat, equipment structures on, 306–308, 306f; pipe rack example, 295–297, 295f, 296f, 298f, 299–300, 301t, 302–304, 303t, 305t, 306

Seismic Loads

369

Index

nonconforming systems, selection of, 56 nonlinear response history (NRH) analysis, 124, 261; advantages of, 262–263; challenges of, 262; development process, 263; FAQs, 338; modeling and, 265–266; overview of provisions, 264–268; structural analysis procedures, 114–117 nonparallel system irregularity (Type 5), horizontal structures, 85, 85f nonstructural components, 277–280, 278f, 280f; ﬂoor response spectra, 277, 279–280, 280f, 287–289, 287f, 288f, 288t, 290f, 291f; 4-story reinforced concrete building example, 280–282, 281f, 283t, 284– 287, 284t, 285f; 1% damping, 292 orthogonal loading effects: equivalent lateral force (ELF), 8-story building, 195–196, 199t; modal response spectrum (MRS), 8-story building, 218 out-of-plane offset irregularity (Type 4), horizontal structures, 83–84, 84f overstrength factor, load combinations, 106–107, 111, 111e overstrength factor Ω0, FAQs, 324, 327–328 P-delta effects: ELF procedure and, 154; FAQs, 325, 335, 335e; modeling of, 124; MRH procedure, 348; MRS procedure and, 218, 347; 9-story building, 158–160, 159e, 164–166, 165t, 166t, 167t period of vibration, 135; approximate fundamental period Ta, 135–141, 137f, 139e, 139t, 140t; computing approximate periods of, for combined systems, 59f, 64; computing Ta for masonry and concrete shear wall structures, 141–143, 142f, 142t; differences between CuTa and Tcomputed, 145t, 146; FAQs, 341–342, 342t, 343f; for three-dimensional systems, 143–144, 144f pile support mat, equipment structures on, 306–308, 306f

pipe rack structures, 295–297, 295f, 296f, 298f, 299–300, 301t, 302–304, 303t, 305t, 306 preliminary mathematical model, equivalent lateral force (ELF), 8-story building, 190–191 primary lateral forces, equivalent lateral force (ELF), 8-story building, 189, 190t R, Cd, and Ω0 values, FAQs, 323–327 Rayleigh analysis, 139, 139e Rayleigh damping, 266 redundancy, equivalent lateral force (ELF), 8-story building, 192, 192t, 193t redundancy factor, 99–104, 101f, 102f, 103f, 154, 192t, 293t; FAQs, 334–335 reentrant corner irregularity (Type 2), horizontal structures, 80–81, 80f regularity checks, equivalent lateral force (ELF), 8-story building, 190t, 191, 191t reinforced concrete structures, modeling of cracked section properties, 121, 121t rigid body modes, 210, 225, 342–344 rigid diaphragms. See diaphragm ﬂexibility Risk Category I, 9, 14 Risk Category II, 11–12, 13, 15 Risk Category III, 10, 12–13, 14–15 Risk Category IV, 9, 11, 15 risk category selection, 9–11; examples of, 11–15 risk-targeted maximum considered earthquake (MCER), 17–18, 43, 263–264, 267, 274, 287–288 scissors model, beam-column deformations, 122, 122f seismic base shear, equivalent lateral force (ELF), 8-story building, 188–189 seismic design and importance factor, equivalent lateral force (ELF), 8-story building, 188 seismic design category (SDC), determination of, 43–46, 43t, 44t seismic load, complete analysis. See simple building, seismic load analysis of

Seismic Loads

370

Index

semirigid diaphragms. See diaphragm flexibility SFRS, FAQs, 328–329 shear wave velocity, 18–19, 19t, 22, 27–28, 30, 32 simple building, seismic load analysis of, 309; accidental torsion, 312–314, 313f; building details, 309–310, 310f, 311f; member and connection checks, 314–320, 315f, 316f, 317f, 319f; seismic design, 310–312 site class procedure, for seismic design, 27–28, 28t; comments on site classification, 33; data gathering, 28; site class determination, 28–31, 28t, 29f; site class example, 28t, 31–33, 32f, 33t site coefficient factor (Fa or Fv), 18–19, 19t, 20t, 27 6-story structure: horizontal structural irregularities, 76, 76, 79f; period of vibration, 136; vertical structural irregularities, 88. See also diaphragms and collectors snow loads: 4-story book warehouse effective seismic weight example, 132–133, 132f; load combinations, 106, 108 soft story (stiffness) irregularities (Types 1a and 1b), in vertical structures, 87–92, 88f, 90t, 91f, 91t, 92f, 92t special moment-resisting frames (SMRF): 8-story steel building, 353–354, 353f, 355f, 356–357, 356f; FAQs, 328 spectral acceleration response parameters, 17–18, 36, 37t, 39, 42, 43, 161, 172, 279–280, 287f, 288 stability ratios: ELF procedure and, 154; P-delta analysis, 159, 159e, 164–167, 164t, 167e, 168t stairs, 128, 131, 280, 281f, 282, 284t steel concentrically braced frames (SCBF), 8-story steel building, 356–357, 357f, 358f steel frame systems not specifically detailed for seismic resistance, system selection, 55 storage live loads, 4-story book warehouse effective seismic weight example, 131–132, 132f

story drift: ELF, MRS, and LRH analysis comparisons, 249–251, 250f, 250t; FAQs, 335, 335e, 337; 9-story building, 145t, 149f, 150f, 151f, 157–158, 157e, 162–164, 163t, 164t; vertical structural irregularities, 87–91, 93. See also drift and P-delta effects story overstrength calculation, 9-story building, 161f, 163t, 165t, 167e, 168–169, 168e, 169t story stiffness, FAQs, 329–332, 330f, 331f story weights, equivalent lateral force (ELF), 8-story building, 188, 188t structural analysis procedures, selection of, 113–117 structural configuration issues, system selection, 50, 79f structural framing, not part of lateral force resisting system, 123 structural integrity, FAQs, 321 structural modeling requirements. See mathematical modeling requirements structural systems, selection of, 47–50, 49f; alternate and nonconforming systems, 56; bearing wall systems, 50–52, 51f, 52f; cantilevered column systems, 55, 55f; coupled reinforced concrete shear wall systems, 54–55, 54f; dual systems, 52–53, 54f; steel frame systems not specifically detailed for seismic resistance, 55; structural configuration issues, 50, 79f 10-story systems, structure selection and, 49, 49f three-dimensional systems: FAQs, 344; periods of vibration for, 143–144, 144f TL, 322, 323t, 324t torsional irregularities (Types 1a and 1b), horizontal structures, 75–80, 76f, 77e, 77f, 78f, 79f, 80f torsional irregularity: accidental torsion, 171–178, 172f, 173t, 174f, 175f, 176t, 177t, 178t; ELF procedure and, 153; FAQs, 328–329; redundancy factor and, 100–101, 101f, 103

Seismic Loads

371

Index

torsional irregularity factor (TIF), 75–78, 75f, 77f, 182–184, 356, 357 TS compared to 3.5 TS, 115–117 25% rule: dual systems and, 53, 58, 61, 155, 187, 206, 223, 339–340, 358; FAQs, 339–340; live loads and, 3, 128, 131–132, 323 two-dimensional or three-dimensional modeling, 119–120 two-story systems, structure selection and, 49, 49f vertical direction systems, combinations of, 59f, 62–64 vertical geometric irregularity (Type 3), in vertical structures, 93, 93f vertical response spectrum, developing of, 35, 36, 39–40, 39f

vertical structural irregularities, 87; consequences of, 97; discontinuity in lateral strength–weak story irregularity (Types 5a and 5b), 94–97, 95f, 96f; FAQs, 332–334, 332e, 333e, 333f; in-plane discontinuity in vertical lateral force-resisting element irregularity (Type 4), 93–94, 94f; soft story (stiffness) irregularities (Types 1a and 1b), 87–92, 88f, 90t, 91f, 91t, 92f, 92t; vertical geometric irregularity (Type 3), 93, 93f; weight (mass) irregularity (Type 2), 92–93 vibration. See period of vibration weight (mass) irregularity (Type 2), in vertical structures, 92–93

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Seismic Loads

About the Authors Finley A. Charney, Ph.D., P.E., received his bachelor’s degree in civil engineering and his master’s degree in architectural engineering from the University of Texas at Austin. He earned his doctorate degree at the University of California at Berkeley. He is currently a professor of structural engineering at Virginia Tech in Blacksburg, Virginia, and serves as President of Advanced Structural Concepts, Inc., also in Blacksburg. His career is almost evenly divided between professional practice (20 years), and university teaching and research (19 years). He has published approximately 40 journal papers, 100 conference papers, and several book chapters, most of which are related to seismic analysis or design. He is the author of the two previous editions of this guide. Dr. Charney has also developed and taught a variety of continuing education courses for ASCE, FEMA, the US Army Corps of Engineers, and other organizations. He served on the ASCE 7 Seismic Subcommittee for the 2010, 2016, and 2022 editions. He is licensed in the state of Colorado. Thomas F. Heausler, P.E., S.E., received his bachelor’s and master’s degrees in civil/structural engineering from Tulane University in New Orleans, Louisiana. He has written numerous technical articles for Structure magazine and has spoken frequently at national conferences and webinars. He has performed as a grader for the NCEES National Structural Engineering 16-hour exam. He has taught structural analysis and earthquake engineering at the University of Missouri-Kansas City. Mr. Heausler provides senior review, guidance, mentoring, and design for challenging and complex structural engineering tasks by applying his 38 years of structural engineering experience. He served on the ASCE 7 Seismic Subcommittee for the 2010, 2016, and 2022 editions, and is licensed in 25 states, including structural licensure in California. Justin D. Marshall, Ph.D., P.E., received his bachelor’s and master’s degrees in civil engineering from Brigham Young University. He earned his doctorate degree at Virginia Tech. He is currently an associate professor of civil/structural engineering at Auburn University in Alabama. Dr. Marshall has several years of consulting experience and has completed research projects related to earthquake engineering funded by the National Science Foundation, the American Institute of Steel Construction, the Metal Building Manufacturers Association, and the Alabama Department of Transportation. He has participated in postearthquake reconnaissance trips to Port-au-Prince, Haiti (2010) and Christchurch, New Zealand (2011). He served on the ASCE 7 Seismic Subcommittee for the 2016 and 2022 editions and is the current chair of the ASCE/SEI Seismic Effects Committee.

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Seismic Loads Guide To The Seismic Load Provisions of ASCE 7-16 by Finley Allan Charney, Thomas F. Heausler, Justin D. Marshall - PDFCOFFEE.COM (2024)

References