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Seismic Loads
Seismic Loads
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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
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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
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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
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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
20
1
2 3 4 5
Seismic Loads
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Contents
Preface
xi
Abbreviations and Symbols
xv
Table of Conversion Factors
xvii
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
9
2.2
Examples
11
Chapter 6
1
2
5
7
9
Determining Ground Motion Parameters
3.1
Examples
3.2
Using the ASCE 7 Hazard Tool
17
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
27
28
28
31
33
Developing an Elastic Response Spectrum
5.1
1
35
Development of an Elastic Vertical Response Spectrum
39
Importance Factor and Seismic Design Category
6.1
Seismic Importance Factor Ie
6.2
Seismic Design Category
43
v
Seismic Loads
41
41
vi
Contents
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Chapter 7
Selection of Structural Systems
47
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
50
50
52
54
55
7.6 Steel Frame Systems Not Specifically Detailed for Seismic
Resistance 55
7.7
Chapter 8
Alternate and Nonconforming Systems
56
Combinations of Lateral Load Resisting Systems
57
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
62
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
67
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
75
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)
83
10.5
Nonparallel System Irregularity (Type 5)
85
10.6
Consequences of Horizontal Irregularities
85
Vertical Structural Irregularities
75
80
81
87
11.1
Soft Story (Stiffness) Irregularities (Types 1a and 1b)
11.2
Weight (Mass) Irregularity (Type 2)
11.3
Vertical Geometric Irregularity (Type 3)
87
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
Seismic Loads
97
72
vii
Contents
Chapter 12
Redundancy Factor
99
Chapter 13
Load Combinations
105
13.1
Basic Load Combinations
106
13.2 Special Seismic Load Combinations, Including the Overstrength
Factor 111
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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
Seismic Loads
168
viii
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
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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
249
24.2
Elastic Base Shear Comparisons
251
Chapter 25 Nonlinear Response History Analysis
261
25.1
Development Process
25.2
Overview of the ASCE 7-16 Chapter 16 Provisions
Seismic Loads
263
264
ix
Contents
Chapter 26 Diaphragms and Collectors
269
Nonstructural Components
277
Chapter 27
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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
314
Chapter 30 Frequently Asked Questions
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
Seismic Loads
351
347
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Seismic Loads
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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,
xi
Seismic Loads
xii
Preface
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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
Seismic Loads
xiii
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.
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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
advancedstructures@gmail.com, 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
xv
Seismic Loads
xvi
Abbreviations and Symbols
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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
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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
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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).
1
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2
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
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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,
2.
Seismic risk was changed from quasi-deterministic (seismic zones and zone factors)
to probabilistic,
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4
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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
4.
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.
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Table G1-1. Updates to Various Codes and Standards Documents
Code or standard
Year of published updates
ANSI A58.1
ASCE 7
SEAOC Blue Book
UBC
1945, 1955, 1972, 1982
1988, 1993, 1995, 1998, 2002, 2005, 2010, 2016
1959, 1966, 1973, 1974, 1988, 1996, 1999
1927, 1935, 1937, and every 3 years thereafter, concluding
in 1997
1985, 1988, 1991, 1994, 1997, 2003, 2010, 2015
2000, 2003, 2006, 2009, 2012, 2015, 2018
NEHRP provisions
IBC
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.
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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;
2.
Review and ballot proposed changes to the previous edition of ASCE 7 prepared by
external users;
3.
Review changes being developed for the NEHRP provisions, and based on them,
create ballot change proposals to ASCE 7 for potential incorporation;
4.
Review the proposed changes to other standards (e.g., ACI–318, AISC 341), and
based on these, propose changes to ASCE 7;
5.
Review other source documents (e.g., the latest version of IBC) and, based on the
results, propose changes to ASCE 7;
6.
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
7.
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
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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
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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 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.
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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
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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.
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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
17
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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.
2.
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.
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.
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.
5.
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.
6.
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.
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19
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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
SS ≤ 0.25
SS = 0.50
SS = 0.75
SS = 1.0
SS = 1.25
SS ≥ 1.5
A
B (w/ m)
B (w/o m)
C
D (investigated)
D (default)
E
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
F
See
11.4.8
See
11.4.8
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
0.8
0.9
1.0
1.2
1.0
1.2
See
11.4.8
See
11.4.8
Site class
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 (w/ m)
B (w/o m)
C
D (investigated)
D (default)
E
F
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
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.
* See requirements for site-specific ground motions in Section 11.4.8. Values of Fv shall be used
only for calculation of Ts.
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Seismic Loads
0.8
0.9
1.0
1.3
1.6
1.6
2.4
See 11.4.8
A
B (w/ m)
B (w/o m)
C
D (investigated)
D (default)
E
F
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.
PGA ≤ 0.1
Site class
Table G3-3. Site Coefficients FPGA
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20
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21
Determining Ground Motion Parameters
Tables G3-1 and G3-2 reflect modifications made in Supplement 1 of ASCE 7-16,
effective December 12, 2018.
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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.
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22
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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.
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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
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24
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.
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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.
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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
27
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28
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Table G4-1. Site Classification
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Site class
vs ( ft/s)
A. Hard rock
B. Rock
C. Very dense soil and soft rock
D. Stiff soil
E. 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
<600
<15
<1,000
Any profile with more than 10 ft of soil that has the
following characteristics:
• Plasticity index PI > 20,
• Moisture content w ≥ 40%, and
• Undrained shear strength su < 500 lb/ft2.
See Section 20.3.1.
Source: Table 20.3-1 of ASCE 7-16.
experience and judgment, which are beyond the scope of this example. Proper
use of shear wave velocity data requires consulting with an experienced
professional.
4.1 Gathering Data
To classify a site, the proper subsurface profile and necessary data need to be
obtained. According to Section 20.1:
•
•
•
Site soil shall be classified based on the upper 100 ft (30 m) of the site profile.
In absence of data to a depth of 100 ft, soil properties, based on known
geological conditions, are permitted to be estimated by the registered design
professional preparing the soil investigation.
Where soil properties are not known in sufficient detail, Site Class D, subject
to the requirements of Section 11.4.4, shall be used unless Site Class E or F
soils are determined to be present.
where site class criteria are based on soil properties [Plasticity Index (PI), w, su],
the values are to be determined by laboratory tests as specified: Atterberg Limits
(ASTM D4318) (ASTM 2000b), moisture content (ASTM D2216) (ASTM 1998),
and undrained shear strength (ASTM D2166) (ASTM 2000a) or ASTM D2850
(ASTM 2003).
4.2 Site Class Determination
In general, movement through the procedure can be broken into three steps as
follows. A flowchart summarizing the steps is given in Figure G4-1.
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Site Class Procedure for Seismic Design
Figure G4-1. Site class determination flowchart.
Step 1: Check Site Class F (Section 20.3.1)
If any of the following conditions are met, the site shall be classified as Site
Class F:
1.
Soils vulnerable to potential failure or collapse under seismic loading, such as
liquefiable soils (see Section 20.3.1 for possible exceptions), quick or highly sensitive clays, and collapsible or weakly cemented soils;
2.
Peat and/or highly organic clays [H > 10 ft (3 m)];
3.
Very high plasticity clays [H > 25 ft (7.6 m) with PI > 75] (see Section 20.3.1 for
possible exceptions); or
4.
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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30
Seismic Loads
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.
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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),
2.
PI > 20,
3.
w ≥ 40%, and
4.
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
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Site Class Procedure for Seismic Design
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•
•
•
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:
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32
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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:
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Site Class Procedure for Seismic Design
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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
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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)],
35
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36
Seismic Loads
2.
Constant acceleration portion between T = T0 and T = TS (Sa = SDS),
3.
Descending constant velocity region between T = TS and T = TL [Equation (11.4-6)],
and
4.
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
37
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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
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38
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
39
Developing an Elastic Response Spectrum
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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
Fa
Fv
SDS (g)
SD1 (g)
TS (s)
A
B
C
D
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
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40
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
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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
41
Seismic Loads
(12.8-2)
42
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:
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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
43
Importance Factor and Seismic Design Category
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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
Seismic design category
SS
S1
SDS
SD1
Risk Category II
Risk Category IV
0.42
0.42
0.13
0.13
0.280
0.409
0.087
0.203
B
D
C
D
Seismic Loads
44
Seismic Loads
Table G6-2. Determination of Seismic Design Category for Site in
Concord, California
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Ground motion parameters (g)
Seismic design category
Site class
SS
S1
SDS
SD1
Risk Category II
Risk Category IV
B
D
1.74
1.74
0.60
0.60
1.16
1.16
0.40
0.68
D
D
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)]
45
Importance Factor and Seismic Design Category
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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)
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46
Seismic Loads
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Seismic Design Category Exception for Buildings with Short Periods
Under certain circumstances, 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
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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
47
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48
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
49
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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).
2.
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).
3.
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
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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,
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B
B
B
B
N
N
N
N
N
N
North
B
B
B=Bearing Wall
B
B
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
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B
B
B
B
N
N
B
B
N
N
North
B
B
B=Bearing Wall
B
B
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
B
N
N
N
N
N
N
B
B
B=Bearing Wall
B
B
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
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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.
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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.
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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.
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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.
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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
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Special R/C Moment Frame
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Special R/C Shear Wall
N
Building 1
Building 2
Building 3
Building 4
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.
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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
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R=8
Ω0 = 3
Cd = 5.5
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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
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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
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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
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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.
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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).
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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.
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Combinations of Lateral Load Resisting Systems
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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.
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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.
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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.
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Diaphragm Flexibility
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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.
A
B
C
D
12 ft
(a) Plan
11 ft (typ)
18 ft
44 ft
44 ft
44 ft
(b) Elevation
Figure G9-1. Three-bay concrete structure analyzed for diaphragm
flexibility.
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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:
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Diaphragm Flexibility
The ratio of the maximum to the average displacement is
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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.
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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)
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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.
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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.
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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.
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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 + B
(G10-3)
L
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
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(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.
2.
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.
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Horizontal Structural Irregularities
Figure G10-3. Effect of wall placement on torsional irregularity.
3.
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.
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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
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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
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(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.
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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
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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.
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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 circumstances 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).
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•
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.
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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.
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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.
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Vertical Structural Irregularities
The period of vibration of the structure is estimated (from Section 12.8.2) as
T = CuT a
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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
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Table G11-1. Development of Lateral Loads for Structure with Tall
First Story
Story
H (ft)
h (ft)
w (kips)
whk
whk/total
F (kips)
6
5
4
3
2
1
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
H (ft)
h (ft)
w (kips)
whk
whk/total
F (kips)
6
5
4
3
2
1
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.
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Table G11-4. Drift-Based Soft-Story Check for Structure with Tall
Second Story
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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 circumstances 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,
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Figure G11-3. Computing stiffness for Story i.
Table G11-5. Stiffness-Based Soft Story Analysis for Structure
with Soft Second Story
Story
Δ (in.)
K (kips/in.)
Kn/Kn+1
Kn/Avg Kn+1
6
5
4
3
2
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
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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.
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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
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Vertical Structural Irregularities
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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.
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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.
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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.
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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).
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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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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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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
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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,
2.
Elastic behavior with one wall removed,
3.
Inelastic behavior analysis with all walls in place, and
4.
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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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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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.
2.
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.
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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).
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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
circumstance 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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•
•
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
(c) Lateral East
(d) Lateral West
Figure G13-1. Basic load combinations for simple frame.
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Load Combinations
(a) Heavy Gravity + Lateral East
(b) Heavy Gravity + Lateral West
(c) Light Gravity + Lateral East
(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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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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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 circumstances 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.
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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.
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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),
2.
Modal response spectrum (MRS) analysis (Section 12.9.1),
3.
Linear response history (LRH) analysis (Section 12.9.2), and
4.
Nonlinear response history (NRH) analysis (Chapter 16).
Under certain (very limited) circumstances, 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 circumstances, 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.
2.
ELF analysis is permitted for all structures in SDC B and C.
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3.
4.
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.
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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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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.
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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).
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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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Structural Modeling Requirements
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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)
a
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.
b
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,
2.
Use a scissors model, or
3.
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
(c) Krawinkler
(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).
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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.
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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)
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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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Effective Seismic Weight (Mass)
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.
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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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Effective Seismic Weight (Mass)
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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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Seismic Loads
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).
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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 basements, 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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Period of Vibration
Figure G17-1. Periods of vibration for different systems.
a sloped site or when there are one or more basement 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 basement. 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 basement. 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 basement 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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138
Seismic Loads
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 basement 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 basement
slab. Thus, a height from the midlevel of the basement 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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Period of Vibration
Table G17-1. Summary of Period Values to Be Used in Calculations.
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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:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
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
Fi
(kip)
δi
(in.)
Wi
(kip)
δiFi
(kip-in.)
Σδi2Wi
(kip-in.2)
6
5
4
3
2
1
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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Period of Vibration
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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 circumstances. 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
1
3
5
7
100 ft
2
4
6
8
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
hn
CW
Ta (s)
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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Period of Vibration
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.
Seismic Loads
Seismic Loads
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
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Period of Vibration
145
146
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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,
2.
Determining the presence of certain horizontal or vertical irregularities,
3.
Computing the torsional amplification factors,
4.
Application of accidental torsion,
5.
Computing P-delta stability ratios,
6.
Determining the redundancy factor,
7.
Calculating diaphragm forces,
8.
Validating conformance with the 25% rule for moment frames in dual systems, and
9.
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)
Ie
the constant velocity region applicable for Ts ≤ T ≤ TL
CS =
S D1
T IRe
or the constant displacement region applicable for T > TL
Seismic Loads
(12.8-3)
149
Description and Use of the Equivalent Lateral Force Procedure
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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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151
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Description and Use of the Equivalent Lateral Force Procedure
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.
Seismic Loads
152
Seismic Loads
Roof
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wx
Vx
x
Vx
wx
g
2
2
x
wx hxk
Roof
ghnk
Deflected Shape
given by:
hn hx
x
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)
i
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)
i
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).
Seismic Loads
Description and Use of the Equivalent Lateral Force Procedure
18.2 Use of the ELF Procedure for Purposes
Other than Final Design
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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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Seismic Loads
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.
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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
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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.
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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
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158
Seismic Loads
computed in accordance with Equation (12.8-15) as
δx =
C d δxe
Ie
(12.8-15)
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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
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Drift and P-delta Effects
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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.
2.
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
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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
basement 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.
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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.
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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)
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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.
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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,
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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, θ max 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.)
θ
θ max
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
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Story x
9
8
7
6
5
4
3
2
1
Δx = CdΔxe/Ie (in.)
θ
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
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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
0
1 − PΔ
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
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Table G19-7. Stability Ratios Back-calculated from Analysis
Including P-Delta Effects
Story
Δ0 (in.)
Δf (in.)
θ
9
8
7
6
5
4
3
2
1
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
Seismic Loads
169
Drift and P-delta Effects
Table G19-8. Story Overstrength Requirements Using Beam
Mechanism
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Story
9
8
7
6
5
4
3
2
1
θ
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.
Seismic Loads
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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
171
Seismic Loads
172
Seismic Loads
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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.
Seismic Loads
173
Accidental Torsion and Amplification of Accidental Torsion
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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
Seismic Loads
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174
Seismic Loads
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.
Seismic Loads
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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
(c) Lateral + Torsion
(d) Lateral - Torsion
Figure G20-3. Loading values applied to building.
Seismic Loads
175
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176
Seismic Loads
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
δ1 (in.)
δ2 (in.)
θ (radians)
5
4
3
2
1
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
Seismic Loads
177
Accidental Torsion and Amplification of Accidental Torsion
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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)
δ1 (in.)
δ2 (in.)
δavg (in.)
δmax/δavg
Ax
5
4
3
2
1
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)
δ1 (in.)
δ2 (in.)
δavg (in.)
δmax /δavg
Ax
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
0.601
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.
3.
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
circumstances 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.
2.
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.
2.
Name these regions A, B, C, D as shown.
3.
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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Accidental Torsion and Amplification of Accidental Torsion
4.
Using the same origin, compute the total mass and the center of mass for the full
plate.
5.
Establish coefficients αA, αB, αC, αD, such that the center of mass is moved in the
desired direction.
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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 X̄ A + αB M B X̄ B + αC M C X̄ X + αD M D X̄ D = ðX̄ total + eXÞM total
(G20-1b)
αA M A Ȳ A + αB M B Ȳ B + αC M C Ȳ Y + αD M D Ȳ D = ðȲ 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.
2.
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 X̄ A
4 M A Ȳ A
1
MB
M B X̄ B
M B Ȳ B
−1
MC
M C X̄ C
M C Ȳ C
0
9
38 9 8
M D > αA > >
M total
>
< = <
=
M D X̄ D 7 αB
X̄ total M total
=
(G20-2)
M D Ȳ D 5> αC > > ðȲ 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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182
Seismic Loads
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)
X̄ (ft.)
Ȳ (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
(c) Positive 5.0 ft. Y 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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184
Seismic Loads
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).
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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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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 basement 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 basement 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:
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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
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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
Seismic Loads
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
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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.
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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).
2.
Moment-resisting frames are modeled using centerline dimensions, which approximately accounts for panel zone deformations.
3.
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.
4.
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).
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Equivalent Lateral Force Analysis
5.
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.
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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.
Seismic Loads
192
Seismic Loads
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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
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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
H
(in.)
PD
(kip)
PL
(kip)
PTOT
(kip)
Px
(kip)
Vx
(k)
Δ
(in.)
θ
1/(β)required
8
7
6
5
4
3
2
1
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
194
Seismic Loads
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Table G21-6b. Stability Check for North–South Loading
Story
H
(in.)
PD
(kip)
PL
(kip)
PTOT
(kip)
Px
(kip)
Vx
(kip)
Δ
(in.)
θ
1/(β)REQD
8
7
6
5
4
3
2
1
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
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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
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Beams
Columns
Supports
level
quantity
Bay D1–E1
Bay E1–F1
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)
R
8
7
6
5
4
3
2
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
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
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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
Columns
Supports
level
quantity
Bay D1–E1
Bay E1–F1
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)
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
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Beams
Columns
Bay A2–A3
Bay A3–A4
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
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East–west load
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
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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•
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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.
Seismic Loads
201
Equivalent Lateral Force Analysis
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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)
H (ft)
W (kips)
Whk
Whk/sum
F (kips)
R
5
4
3
2
Sum
15
15
15
15
15
75
60
45
30
15
150
150
150
500
500
1,450
11,250
9,000
6,750
15,000
7,500
49,500
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
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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
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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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Seismic Loads
These factors are applied the to results of the MRS analysis in accordance
with Section 12.9.1.2.
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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
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Table G22-1a. Modal Properties Excluding P-delta Effects
Modal mass (%)
Accumulated modal mass (%)
Mode
Period
(s)
E–W
N–S
Rotation
E–W
N–S
Rotation
1
2
3
4
5
6
7
8
9
10
11
12
18
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
Modal mass (%)
Accumulated modal mass (%)
Mode
Period
(s)
E–W
N–S
Rotation
E–W
N–S
Rotation
1
2
3
4
5
6
7
8
9
10
11
12
18
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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210
Seismic Loads
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
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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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212
Seismic Loads
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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Table G22-2a. Frame Line 1 Displacements and Drifts for
East–West Loading Including P-delta
Level
Δelastic
(in.)
Δelastic times (Cd/R)
(in.)
Story drift*
(in.)
Story drift
ratio
Story drift
ratio limit
R
8
7
6
5
4
3
2
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
Δelastic
(in.)
Δelastic times
(Cd/R) (in.)
Story drift*
(in.)
Story drift
ratio
Story drift
ratio limit
R
8
7
6
5
4
3
2
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
Seismic Loads
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Modal Response Spectrum Analysis
Table G22-3c. Center of Mass Drifts for N–S Loading Not Including
P-delta
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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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216
Seismic 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
Columns
Bay D1–E1
Bay D1–E1
E1
F1
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
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
Columns
Bay A2–A3
Bay A3–A4
A3
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
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
Seismic Loads
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217
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Modal Response Spectrum Analysis
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
Columns
Bay D1–E1
Bay D1–E1
E1
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
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
Seismic Loads
F1
218
Seismic Loads
Table G22-8. Forces in the Moment Frame on Grid Line A under
N–S Load Not Including P-delta
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Beams
Columns
Bay A2–A3
Bay A3–A4
A3
A4
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
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
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
Seismic Loads
219
Modal Response Spectrum Analysis
Table G22-10b. Forces in Selected Columns from Unidirectional
Elastic MRS Analysis Scaled to ELF Shear Including P-delta
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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.
Seismic Loads
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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
Seismic Loads
222
Seismic Loads
23.1 Overview
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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.
Seismic Loads
223
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Linear Response History Analysis
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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Linear Response History Analysis
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
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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.
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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)
A
X
Y
0.01
0.01
4,594
4,594
45.94
45.94
0.287
0.255
−0.292
−0.324
B
X
Y
0.01
0.01
4,096
4,096
40.96
40.96
0.202
0.288
−0.316
−0.262
C
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
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
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
Envelope
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
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
Envelope
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
Seismic Loads
(12.9-3)
240
Seismic Loads
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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
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
Envelope
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)
A
Min
Max
−1,355
1,324
−1,382
1,457
−4,104
3,894
−3,994
4,053
B
Min
Max
−1,725
1,715
−1,835
1,729
−3,904
3,912
−4,057
4,003
C
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
Seismic Loads
VEX (E–W)
VEY (N–S)
C
Note: Using ASCE 7 procedure.
VEY (N–S)
VEY (N–S)
VEX (E–W)
VEY (N–S)
Designation
B
A
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
558
1,124
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
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Linear Response History Analysis
241
242
Seismic Loads
Table G23-8. Scale Factors for Determining Member Forces
(Alternate Procedure)
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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.
2.
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.
3.
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.
4.
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
Seismic Loads
243
Linear Response History Analysis
Table G23-9. Elastic Beam Shears in the Moment Frame on Grid
Line 1 under E–W Load
(a) Ground motion A
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Including P-delta effects
Not including P-delta effects
Bay D1–E1
(kips)
Bay E1–F1
(kips)
Bay D1–E1
(kips)
Bay E1–EF
(kips)
Level
Min
Max
Min
Max
Min
Max
Min
Max
R
8
7
6
5
4
3
2
−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
Not including P-delta effects
Bay D1–E1
(kips)
Bay E1–F1
(kips)
Bay D1–E1
(kips)
Bay E1–EF
(kips)
Level
Min
Max
Min
Max
Min
Max
Min
Max
R
8
7
6
5
4
3
2
−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
(c) Ground motion C
Including P-delta effects
Not including P-delta effects
Bay D1–E1
(kips)
Bay E1–F1
(kips)
Bay D1–E1
(kips)
Bay E1–EF
(kips)
Level
Min
Max
Min
Max
Min
Max
Min
Max
R
8
7
6
5
4
3
2
−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
Seismic Loads
244
Seismic Loads
Table G23-10. Elastic Column Shears in the Moment Frame on
Grid Line 1 under E–W Load
(a) Ground motion A
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Including P-delta effects
Not including P-delta effects
Column E1
(kips)
Column F1
(kips)
Column E1
(kips)
Column F1
(kips)
Story
Min
Max
Min
Max
Min
Max
Min
Max
8
7
6
5
4
3
2
1
−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
Not including P-delta effects
Column E1
(kips)
Column F1
(kips)
Column E1
(kips)
Column F1
(kips)
Story
Min
Max
Min
Max
Min
Max
Min
Max
8
7
6
5
4
3
2
1
−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
(c) Ground motion C
Including P-delta effects
Not including P-delta effects
Column E1
(kips)
Column F1
(kips)
Column E1
(kips)
Column F1
(kips)
Story
Min
Max
Min
Max
Min
Max
Min
Max
8
7
6
5
4
3
2
1
−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
Seismic Loads
245
Linear Response History Analysis
Table G23-11. Elastic Beam Shears in the Moment Frame on Grid
Line A under N–S Load
(a) Ground motion A
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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
(c) Ground motion C
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
−12.7
−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
Seismic Loads
246
Seismic Loads
Table G23-12. Elastic Column Shears in the Moment Frame on
Grid Line A under N–S Load
(a) Ground motion A
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Including P-delta effects
Not including P-delta effects
Column A3
(kips)
Column A4
(kips)
Column A3
(kips)
Column A4
(kips)
Story
Min
Max
Min
Max
Min
Max
Min
Max
8
7
6
5
4
3
2
1
−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
Not including P-delta effects
Column A3
(kips)
Column A4
(kips)
Column A3
(kips)
Column F1
(kips)
Story
Min
Max
Min
Max
Min
Max
Min
Max
8
7
6
5
4
3
2
1
−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
(c) Ground motion C
Including P-delta effects
Not including P-delta effects
Column A3
(kips)
Column A4
(kips)
Column A3
(kips)
Column A4
(kips)
Story
Min
Max
Min
Max
Min
Max
Min
Max
8
7
6
5
4
3
2
1
−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
Seismic Loads
247
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
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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.
Seismic Loads
248
Seismic Loads
Table G23-15. Summary of Scaled Column Axial Forces in Moment
Frames
Column axial forces (kips)
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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
Frame C
Story
Column
Brace
Column
Brace
8
7
6
5
4
3
2
1
B
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.
Seismic Loads
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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.
249
Seismic Loads
250
Seismic Loads
Table G24-1. Story Drift Comparisons
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E–W Loading (kips)
N–S Loading (kips)
Level
ELF
MRS
LRH
ELF
MRS
LRH
R
8
7
6
5
4
3
2
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
Seismic Loads
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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,
Seismic Loads
251
252
Seismic Loads
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.
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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
Seismic Loads
253
Comparison of Computed Response Using ELF, MRS, and LRH Analysis
Table G24-5. Envelope of Scaled Inelastic Column Axial Forces for
E–W Loading
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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
Seismic Loads
254
Seismic Loads
Table G24-8. Envelope of Scaled Inelastic Column Axial Forces for
N–S Loading
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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
Seismic Loads
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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.
Seismic Loads
255
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256
Seismic Loads
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.
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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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258
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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.
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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
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Figure G24-18. Envelope of scaled inelastic Frame C brace axial
forces for north–south loading.
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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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262
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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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•
•
•
•
•
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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25.2 Overview of the ASCE 7-16 Chapter 16
Provisions
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The Chapter 16 provisions for NRH analysis have the following subsections:
16.1 General Requirements
16.2 Ground Motions
16.3 Modeling and Analysis
16.4 Analysis Results and Acceptance Criteria
16.5 Design Review
16.6 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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Nonlinear Response History Analysis
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 circumstances, 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
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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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Diaphragms and Collectors
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 =n x
X
Fi
wpx = qpx wpx
(12.10-1)
wi
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
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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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Diaphragms and Collectors
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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274
Seismic Loads
1.
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.
2.
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.
3.
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.
4.
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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Diaphragms and Collectors
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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.
Seismic Loads
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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
277
Seismic Loads
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278
Seismic Loads
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
1 + 2 Wp
Fp = (13.3-1)
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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Nonstructural Components
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
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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)
p
Ip
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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280
Seismic Loads
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).
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281
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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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•
•
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
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).
a
b
c
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
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Nonstructural Components
283
284
Seismic Loads
Table G27-2. Forces on Stair Components
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Component
S3A body
S3A fasteners and
attachments
S3B body
S3B fasteners and
attachments
Wp
(lb)
ap
Rp
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).
b
Equation (13.3-2).
c
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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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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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,
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Nonstructural Components
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•
•
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.
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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
PEER
NGA
ID
Year
San Fernando
Imperial Valley
Northridge
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.
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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.
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290
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(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.
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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.
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292
Seismic Loads
27.3 1% Damping
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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).
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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
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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.
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Nonbuilding Structures
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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.
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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
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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.
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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.
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298
Seismic Loads
Figure G28-4. Pipe rack structure: Story and diaphragm forces.
Figure G28-5. Pipe rack structure: Story and diaphragm forces.
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299
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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
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300
Seismic Loads
V = CS W = 0.536(565 kips) = 303 kips
V = 303 kips east–west direction (braced frames)
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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
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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)
<– Forces applied to horizontal diapragm –>
<– Forces at each level applied to the lateral system in the
vertical plane –>
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
<– Section 12.10.1.1 Diaphragms –>
3
2
1
Sum =
wxhxk
Fx
(kips)
<– Section 12.8.3 –>
183
191
191
565
Level
hx
(ft)
<– Forces applied to horizontal diapragm –>
<– Forces at each level applied to the lateral system in the
vertical plane –>
wx
(kip)
<– Section 12.10.1.1 Diaphragms –>
<– Section 12.8.3 –>
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
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Nonbuilding Structures
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Equation (12.8-11) usually does not exceed diaphragm force calculations, except
for the lower floors when very low values of R are used.
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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;
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Nonbuilding Structures
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Table G28-2. Drift Moment Frame
Level
hx
(ft)
3
49
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
0.00
Inelastic
drift Δ
(in.)
Allowable
drift Δa/ρ
(in.)
Test
OK/NG ?
1.61
2.20
OK
1.34
2.20
OK
4.05
4.61
OK
Inelastic
drift Δ
(in.)
Allowable
drift Δa
(in.)
Test
OK/NG ?
0.06
2.88
OK
0.08
2.88
OK
0.28
6.00
OK
12
2
37
1
25
G
0
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)
3
49
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
37
1
25
G
0
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
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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)
<–Input
2.5
2.5
2.5
2.5
ap
3
3
3
3
Rp
1.5
1.5
2
2
Ωo
49
49
37
25
z (ft)
49
49
49
49
h (ft)
3.00
3.00
2.51
2.02
[1+2 z/h]
7716
7716
17217
13857
Eq. 13.3-1 Fp
(kips)
12346
12346
32922
32922
Eq. 13.3-2 Fp max
(kips)
Output–>
2315
2315
6173
6173
Eq. 13.3-3 Fp min
(kips)
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Nonbuilding Structures
305
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306
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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)].
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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
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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
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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
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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
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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
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312
Seismic Loads
Determine base shear:
Effective seismic weight (12.7.2)
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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
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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
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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
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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.
Seismic Loads
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316
Seismic Loads
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).
2.
Forces Fpx in diaphragm owing to Equation (12.10-1) excluding accidental torsion
Mta, including Ω0, and excluding redundancy ρ.
3.
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
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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
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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
Seismic Loads
Complete Seismic Load Analysis of Simple Building
Vu = 2.0 k horizontal shear
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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
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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.
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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 basement 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 circumstances 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
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
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 circumstances
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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Frequently Asked Questions
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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 circumstance, 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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Frequently Asked Questions
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.
2.
Design of collector elements in SDC C, D, E, or F (Section 12.10.2.1).
3.
Foundations of cantilever columns systems (Section 12.2.5.2).
4.
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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Frequently Asked Questions
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.
2.
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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Frequently Asked Questions
where
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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
1 X +
− ½M + M uB,i
h i = 1 uB,i
nbays
Vu =
(G30-3)
where
nbays = Number of bays,
+
M uB
= Positive moment flexural capacity at one end of the beam,
−
M uB
= Negative moment capacity at the other end of the beam, and
nbays = Number of bays.
(a) Brace Mechanism
.
.
.
.
.
.
(c) Beam 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.
2.
In addition to the lateral loading, the moment frames must be designed to carry
tributary gravity loads.
3.
It is not necessary to include P-delta effects.
4.
It is not necessary to perform drift checks.
5.
It is not necessary to include accidental torsion.
6.
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.
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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.
2.
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.
3.
Selecting a damping ratio, xi.
4.
Select an angle increment dA. We will rotate from Angle 0 to 180 in this increment.
5.
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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Frequently Asked Questions
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.
2.
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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Frequently Asked Questions
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.
345
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The mathematical bases of the different methods are not described here. For
further information see Chopra (2017).
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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),
2.
Compute shape, frequency, participation factor, and effective mass of each mode,
3.
Determine the minimum number of modes to include in the analysis (12.9.1.1),
4.
Develop elastic response spectrum (11.4.6 or 21.2),
5.
Compute elastic modal displacements and forces in each direction of response,
6.
Scale elastic modal responses to obtain approximate design-level inelastic modal
responses (12.9.1.2),
7.
Combine the inelastic modal responses to determine the full-system inelastic
response in each direction (12.9.1.3), and
8.
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
Seismic Loads
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.
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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),
2.
Compute shape, frequency, participation factor, and effective mass of each mode,
3.
Determine the minimum number of modes to include in the analysis (12.9.2.2.4),
4.
Develop three sets of spectrally matched ground motions (12.9.2.3.1),
5.
For each ground motion (applied independently in the x- or y-directions) compute
elastic modal displacements and force response histories,
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6.
Scale elastic response histories to obtain approximate design-level inelastic
response histories (12.9.2.5.1),
7.
Scale elastic response histories to obtain parity with the Equivalent Lateral Force
Method (12.9.2.5.2), and
8.
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
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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.)
2.
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.)
3.
Floor response spectra can be easily obtained to assess the performance of
nonstructural components.
4.
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 basement 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:
351
Seismic Loads
70 psf
15 psf
20 psf
10 psf
35 psf
60 psf
12 psf
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352
Seismic Loads
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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354
Seismic Loads
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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8-Story Steel Building Case Study Structure
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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356
Seismic Loads
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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8-Story Steel Building Case Study Structure
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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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8-Story Steel Building Case Study Structure
Table GB-1. Reference to Design Checks for an 8-Story Building
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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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Chopra, A. 2017. Dynamics of structures, 5th ed. New York: Pearson.
Chopra, A., and McKenna, F. 2016. “Modeling viscous damping in nonlinear
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CSI. 2019. SAP2000 version 21. Walnut Creek, CA: CSI.
DeBock, D., Hohener, C., and Valley, M. 2019. “Does accidental torsion prevent
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FEMA. 2009. Quantification of building seismic performance factors. FEMA
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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.
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Seismic Loads
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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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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
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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
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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
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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
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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
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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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