NIST Technical Note 1863-3 

Assessment of 

First Generation 

Performance-Based 

Seismic Design 

Methods for 

New Steel Buildings 

Volume 3: 

Eccentrically Braced 

Frames 

John L. Harris III 

Matthew S. Speicher 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-3 
NIST Technical Note 1863-3 

Assessment of First Generation PerformanceBased Seismic Design Methods 

for New Steel Buildings 

Volume 3: Eccentrically Braced Frames 

John L. Harris III 

Matthew S. Speicher 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-3 

February 2015 

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie May, Acting Under Secretary of Commerce for Standards 

and Technology and Acting Director 
Disclaimers 

Certain commercial software, equipment, instruments, or materials may have been used in the preparation 

of information contributing to this report. Identification in this report is not intended to imply 

recommendation or endorsement by NIST, nor is it intended to imply that such software, equipment, 

instruments, or materials are necessarily the best available for the purpose. 

NIST policy is to use the International System of Units (metric units) in all its publications. In this report, 

however, information is presented in U.S. Customary Units (inch-pound), as this is the preferred system of 

units in the U.S. earthquake engineering industry. 

National Institute of Standards and Technology Technical Note 1863-3 

Natl. Inst. Stand. Technol. Tech Note 1863-3, 279 pages (February 2015) 

CODEN: NTNOEF 

This publication is available free for charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-3 

 

Preface 

In June 2008, the National Earthquake Hazards Reduction Program (NEHRP) sponsored a PerformanceBased Seismic Design (PBSD) workshop for leading practitioners and researchers from around the United 

States to develop a comprehensive list of research needs to foster full development and implementation of 

PBSD. From this workshop, the Building Seismic Safety Council (BSSC) reported a prioritized list of key 

PBSD research and implementation needs in NIST GCR 09-917-2: Research Required to Support Full 

Implementation of Performance-Based Seismic Design (NIST 2009a). The highest priority need identified 

in this report was to “benchmark” current PBSD methodologies (e.g., ASCE/SEI 41-06: Seismic 

Rehabilitation of Existing Buildings (ASCE 2006)—hereafter referred to as ASCE 41) with code procedures 

for design of new buildings. Two observations from the report were that among workshop participants (1) 

ASCE 41 procedures are perceived to be overly conservative and (2) existing PBSD methods are not 

accepted by practitioners as providing a uniform level of confidence. A supporting reason for these two 

observations was that no systematic effort had been undertaken to benchmark structural performance as 

determined using ASCE 41 procedures, together with widely accepted procedures for designing new 

buildings using ASCE/SEI 7-10: Minimum Design Loads for Buildings and Other Structures (ASCE 

2010)—hereafter referred to as ASCE 7. 

Work was initiated at the National Institute of Standards and Technology (NIST) to support this priority 

study under the Assessment of Design Methods in Existing PBSD Standards Project. This task was 

conducted by the Earthquake Risk Reduction in Buildings and Infrastructure group, the research division 

of the NEHRP Office at NIST. This research involves problem-focused studies in PBSD assessing the 

applicability and accuracy of implementing first-generation PBSD analysis methods now used for 

evaluating existing buildings in the performance-based design of new buildings. The current study focuses 

on buildings with lateral systems utilizing structural steel frames. This project evaluates the results of the 

studies and identifies changes to current model building codes and standards provisions that will encourage 

more universal use of PBSD. The volume of data required to illustrate the results and conclusions 

necessitated three separate reports, as follows: 

 Volume 1: Special Moment Frames 

 Volume 2: Special Concentrically Braced Frames 

 Volume 3: Eccentrically Braced Frames (this report) 

A fourth report, Volume 4: Buckling Restrained Braced Frames, is under development. 

A peer review panel (PRP) was engaged under a contract with the NEHRP Consultants Joint Venture 

(NCJV)—www.nehrp-consultants.org. The PRP was tasked to complement the NIST project by providing, 

where needed, individual subject matter expert guidance to improve the technical detail and outcome of the 

project; provide technical support on specific topics on seismic hazard analysis, ground motion scaling for 

iii 
 

   

   

           

varying return periods, nonlinear dynamic analysis, structural behavior and design of building structures; 

and provide peer review services. The review panel for this project was structured as follows: 

NCJV

Jon Heintz

Ayse Hortacsu

Project Review Panel

William Holmes, Chair

Robert Hanson

Peter Somers

Nicolas Luco

Robert Pekelnicky

Concentrically Braced

FramePanel

Rafael Sabelli

Stephen Mahin

Eccentrically Braced

FramePanel

James Malley

Charles Roeder

Moment FramePanel

Thomas Sabol

Michael Engelhardt

Jon Heintz (Program Manager) 

Applied Technology Council 

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

Michael Engelhardt 

The University of Texas at Austin 

Dept. of Civil, Arch. and Environ. Eng. 

301 East Dean Keeton St., Stop C1747 

Austin, TX 78712 

William Holmes (PRP Chair) 

Rutherford + Chekene 

55 Second Street, Suite 600 

San Francisco, California 94105 

Stephen Mahin 

University of California, Berkeley 

Dept. of Civil and Environ. Eng. 

777 Davis Hall 

Berkeley, California 94720 

Ayse Hortacsu (Project Manager) 

Applied Technology Council 

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

Robert Hanson 

University of Michigan, Emeritus 

5885 Dunabbey Loop 

Dublin, Ohio 43017 

Nicolas Luco 

U.S. Geological Survey 

Box 25046 – DFC – MS 966 

Denver, Colorado 80225 

James Malley 

Degenkolb Engineers 

235 Montgomery St., Suite 500 

San Francisco, California 94104 

iv 
Robert Pekelnicky Charles Roeder 

Degenkolb Engineers University of Washington
 

235 Montgomery St., Suite 500 Dept. of Civil and Environ. Eng.
 

San Francisco, California 94104 Box 352700 

Seattle, WA 98195 

Rafael Sabelli Thomas Sabol 

Walter P. Moore Englekirk Institutional
 

595 Market St., Suite 2130 2116 Arlington Ave.
 

San Francisco, California 94105 Los Angeles, California 90018
 

Peter Somers 

Magnusson Klemencic Associates
 

1301 Fifth Ave., Suite 3200
 

Seattle, WA 98101 

The authors gratefully acknowledge the members of the PRP for their input and guidance during this project 

and in the preparation of report volumes 1-3. Further, the authors wish to thank Jon Heintz and Ayse 

Hortacsu at Applied Technology Council for management of Task Order 12. Special thanks are also 

extended to Jack Hayes (NEHRP Director), Steve McCabe (NEHRP Deputy Director), and Bob Pekelnicky 

for reviewing the final NIST reports. 

John L. Harris III 

Research Structural Engineer 

jay.harris@nist.gov 

Matthew S. Speicher 

Research Structural Engineer 

matthew.speicher@nist.gov 

National Institute of Standards and Technology 

Engineering Laboratory 

National Earthquake Hazards Reduction Program Office 

100 Bureau Dr., MS 8604 

Gaithersburg, MD 20899 

v 
 

vi 
Table of Contents 

Preface .............................................................................................................................................. iii
 

Table of Contents...................................................................................................................................... vii
 

List of Tables............................................................................................................................................ xiii
 

List of Figures ......................................................................................................................................... xvii
 

List of Abbreviations ............................................................................................................................. xxiv
 

Executive Summary .............................................................................................................................. xxvi
 

Chapter 1 Introduction ...................................................................................................................... 1-1
 

1.1 Project Motivation and Background ................................................................................ 1-3
 

1.2 Scope of Project .............................................................................................................. 1-5
 

Chapter 2 Overview and Design of Archetype Buildings ................................................................ 2-1
 

2.1 General Information ........................................................................................................ 2-1
 

2.2 Structural Design Loads .................................................................................................. 2-5
 

Load Combinations ............................................................................................ 2-5
 

Gravity Loads ..................................................................................................... 2-5
 

Environmental Loads ......................................................................................... 2-6
 

Earthquake Forces................................................................................. 2-6
 

Wind Forces .......................................................................................... 2-8
 

2.3 Structural Analysis and Mathematical Model ................................................................. 2-9
 

2.4	 SFRS Design ................................................................................................................. 2-12
 

SMF Design...................................................................................................... 2-12
 

EBF Design ...................................................................................................... 2-21
 

Chapter 3 Seismic Assessment ........................................................................................................... 3-1
 

3.1 Assessment Overview ..................................................................................................... 3-1
 

Seismic Hazard ................................................................................................... 3-3
 

General Analysis Requirements ......................................................................... 3-3
 

Analysis Procedures ........................................................................................... 3-5
 

Linear Analysis Procedures................................................................... 3-5
 

3.1.3.1.1	 Linear Static Procedure ............................................... 3-7
 

vii 
   

   

   

   

   

   

   

   

   

3.1.3.1.2 Linear Dynamic Procedure .......................................... 3-8
 

Nonlinear Analysis Procedures ............................................................. 3-8
 

3.1.3.2.1 Nonlinear Static Procedure........................................ 3-10
 

3.1.3.2.2 Nonlinear Dynamic Procedure .................................. 3-13
 

Acceptance Criteria .......................................................................................... 3-14
 

Linear Procedures................................................................................ 3-15
 

3.1.4.1.1 Calculating Component Assessment Results ............ 3-15
 

Nonlinear Procedures .......................................................................... 3-16
 

3.1.4.2.1 Calculating Component Assessment Results ............ 3-17
 

3.2 Eccentrically Braced Frame .......................................................................................... 3-19
 

Assessment Methodology................................................................................. 3-19
 

Linear Procedures................................................................................ 3-19
 

Nonlinear Procedures .......................................................................... 3-31
 

Seismic Assessment Results ............................................................................. 3-45
 

Four-Story Eccentrically Braced Frame .............................................. 3-46
 

3.2.2.1.1 Linear Static Procedure ............................................. 3-46
 

3.2.2.1.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-46
 

3.2.2.1.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-47
 

3.2.2.1.2 Linear Dynamic Procedure ........................................ 3-49
 

3.2.2.1.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-49
 

3.2.2.1.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-50
 

3.2.2.1.3 Nonlinear Static Procedure........................................ 3-52
 

3.2.2.1.4 Nonlinear Dynamic Procedure .................................. 3-56
 

Eight-Story Eccentric Braced Frame ................................................... 3-62
 

3.2.2.2.1 Linear Static Procedure ............................................. 3-62
 

3.2.2.2.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-62
 

3.2.2.2.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-65
 

3.2.2.2.2 Linear Dynamic Procedure ........................................ 3-67
 

3.2.2.2.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-67
 

3.2.2.2.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-69
 

3.2.2.2.3 Nonlinear Static Procedure........................................ 3-71
 

3.2.2.2.4 Nonlinear Dynamic Procedure .................................. 3-76
 

Sixteen-Story Eccentrically Braced Frame ......................................... 3-82
 

3.2.2.3.1 Linear Static Procedure ............................................. 3-82
 

3.2.2.3.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-82
 

viii 
   

   

   

3.2.2.3.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) ............. 3-86
 

3.2.2.3.2	 Linear Dynamic Procedure ....................................... 3-89
 

3.2.2.3.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-89
 

3.2.2.3.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) ............. 3-92
 

3.2.2.3.3	 Nonlinear Static Procedure ....................................... 3-95
 

3.2.2.3.4 Nonlinear Dynamic Procedure ................................ 3-101
 

Seismic Assessment Discussion ..................................................................... 3-108
 

Linear Procedures.............................................................................. 3-108
 

3.2.3.1.1	 Link Beams ............................................................. 3-108
 

3.2.3.1.2	 Member Cross-section Strength (flexural hinge) and 

Global Strength (member stability) ......................... 3-110
 

3.2.3.1.3 Summary ................................................................. 3-113
 

Nonlinear Procedures ........................................................................ 3-115
 

3.2.3.2.1	 Link Beams ............................................................. 3-115
 

3.2.3.2.2	 Member Cross-section Strength (flexural hinge) and 

Global Strength (member stability) ......................... 3-116
 

3.2.3.2.3 Summary ................................................................. 3-118
 

Comparison between Linear and Nonlinear Assessment Results ..... 3-119
 

Chapter 4 Summary, Conclusions, and Recommendations............................................................ 4-1
 

4.1 Summary of Project Work ............................................................................................... 4-1
 

4.2 Assumptions and Limitations of this Study..................................................................... 4-3
 

4.3 Conclusions and Observations ........................................................................................ 4-5
 

ASCE 41............................................................................................................. 4-5
 

General .................................................................................................. 4-5
 

Eccentrically Braced Frame .................................................................. 4-6
 

4.4 Recommendations for Future Research........................................................................... 4-7
 

ASCE 41............................................................................................................. 4-7
 

General .................................................................................................. 4-7
 

Eccentrically Braced Frames ................................................................. 4-8
 

ASCE 7............................................................................................................... 4-8
 

AISC 341 / 360 / 358.......................................................................................... 4-9
 

Eccentrically Braced Frames ................................................................. 4-9
 

Appendix A Ground Motions for Response History Analysis .......................................................... A-1
 

A.1 Ground Motion Record Set ............................................................................................ A-1
 

A.2 Ground Motion Selection and Scaling ........................................................................... A-2
 

ix 
A.3	 Four-Story Archetype Building ...................................................................................... A-3
 

4-Story Eccentrically Braced Frame ................................................................. A-3
 

A.4	 Eight-Story Archetype Building ..................................................................................... A-6
 

8-Story Eccentrically Braced Frame ................................................................. A-6
 

A.5	 Sixteen-Story Archetype Building ................................................................................. A-9
 

16-Story Eccentrically Braced Frame ............................................................... A-9
 

A.6 FEMA P-695 Far-Field Record Set.............................................................................. A-12
 

Appendix B Supplemental Design Information and Design Examples ............................................ B-1
 

B.1 Horizontal Design Forces............................................................................................... B-1
 

Wind Forces ...................................................................................................... B-1
 

Seismic Forces ................................................................................................... B-3
 

Effective Seismic Weights and Story Gravity Forces .......................... B-3
 

Horizontal Seismic Forces, E-W Direction .......................................... B-4
 

B.1.2.2.1	 ME4 (Special Moment Frame) ................................... B-4
 

B.1.2.2.2	 ME8 (Special Moment Frame) ................................... B-7
 

B.1.2.2.3 ME16 (Special Moment Frame) ............................... B-10
 

Horizontal Seismic Forces, N-S Direction ......................................... B-13
 

B.1.2.3.1	 ME4 (Eccentrically Braced Frame).......................... B-13
 

B.1.2.3.2	 ME8 (Eccentrically Braced Frame).......................... B-15
 

B.1.2.3.3	 ME16 (Eccentrically Braced Frame)........................ B-18
 

B.2	 Horizontal and Vertical Irregularities........................................................................... B-21
 

Special Moment Frame ................................................................................... B-21
 

Eccentrically Braced Frame ............................................................................ B-23
 

B.3 SMF AISC Frame Stability (Effective Length Method) .............................................. B-25
 

B.4 Eccentrically Braced Frame Plastic Link Rotation....................................................... B-28
 

B.5 Example Design Calculations ...................................................................................... B-33
 

Eccentrically Braced Frame Example ............................................................. B-33
 

Member Selection .............................................................................. B-33
 

EBF Link Beam.................................................................................. B-34
 

B.5.1.2.1	 Shear Demand .......................................................... B-34
 

B.5.1.2.2	 Shear Strength .......................................................... B-34
 

B.5.1.2.3	 Strength Check ......................................................... B-34
 

B.5.1.2.4 Link Rotation Angle Verification ............................ B-34
 

EBF Brace .......................................................................................... B-35
 

x 
 

B.5.1.3.1 Axial and Flexure Demand .......................................B-35
 

B.5.1.3.2 Axial Strength ...........................................................B-35
 

B.5.1.3.3 Strength Check ..........................................................B-36
 

EBF Column........................................................................................B-36
 

B.5.1.4.1 Axial and Flexural Demand ......................................B-36
 

B.5.1.4.2 Axial Strength ...........................................................B-37
 

B.5.1.4.3 Strength Check ..........................................................B-37
 

Appendix C Example Assessment Calculations ................................................................................. C-1
 

C.1 Linear Assessment Examples ......................................................................................... C-1
 

EBF Link............................................................................................................C-1
 

Shear Demand .......................................................................................C-1
 

Shear Strength .......................................................................................C-1
 

Acceptance Criteria ...............................................................................C-2
 

Acceptance Criteria Check ....................................................................C-2
 

C.2 Nonlinear Assessment Examples ................................................................................... C-2
 

EBF Link............................................................................................................C-2
 

Deformation Demand ............................................................................C-3
 

Acceptance Criteria ...............................................................................C-3
 

Acceptance Criteria Check ....................................................................C-3
 

Appendix D References ........................................................................................................................ D-1
 

xi 
 

xii 
List of Tables 

Table 1-1. Comparison of Seismic Hazard and Associated Performance for ASCE 7 and ASCE 41 ..... 1-4
 

Table 1-2. Performance Comparison between IBC and ASCE 41 – (From IEBC Table 301.1.4.1) ....... 1-4
 

Table 2-1. Structural Characteristics of Archetype Buildings.................................................................. 2-1
 

Table 2-2. Design Gravity Loads ............................................................................................................. 2-6
 

Table 2-3. Spectral Response Acceleration Parameters ........................................................................... 2-7
 

Table 2-4. Seismic Analysis and Design Parameters, E-W ...................................................................... 2-8
 

Table 2-5. Seismic Analysis and Design Parameters, N-S ....................................................................... 2-9
 

Table 2-6. EBF Configurations .............................................................................................................. 2-22
 

Table 3-1. Seismic Performance Targets (from ASCE 41-06)................................................................. 3-2
 

Table 3-2. Seismic Performance Targets (from ASCE 41-13)................................................................. 3-2
 

Table 3-3. Spectral Response Parameters................................................................................................. 3-3
 

Table 3-4. Displacement multiplier—E-W (SMF) ................................................................................... 3-6
 

Table 3-5. Displacement Multiplier—N-S (EBF) .................................................................................... 3-6
 

Table 3-6. Analytical fundamental periods (seconds) .............................................................................. 3-8
 

Table 3-7. Empirical fundamental periods (seconds) ............................................................................... 3-8
 

Table 3-8. Story shear ratio – ELF ......................................................................................................... 3-12
 

Table 3-9. Story shear ratio – RSA ........................................................................................................ 3-12
 

Table 3-10. Basic m-factors for Linear Procedures, EBF ....................................................................... 3-28
 

Table 3-11. NSP General Information, 4-Story EBF (kip, inch)............................................................ 3-52
 

Table 3-12. CP NSP Analysis Parameters, 4-Story EBF BSE-2 CP (kip, inch) .................................... 3-52
 

Table 3-13. LS NSP Analysis Parameters, 4-Story EBF BSE-1 LS (kip, inch) ..................................... 3-52
 

Table 3-14. NSP General Information, 8-Story EBF (kip, inch)............................................................ 3-71
 

Table 3-15. CP NSP Analysis Parameters, 8-Story EBF BSE-2 CP (kip, inch) .................................... 3-72
 

Table 3-16. LS NSP Analysis Parameters, 8-Story EBF BSE-1 LS (kip, inch) ..................................... 3-72
 

Table 3-17. NSP General Information, 16-Story EBF (kip, inch) .......................................................... 3-96
 

Table 3-18. CP NSP Analysis Parameters, 16-Story EBF BSE-2 CP (kip, inch) .................................. 3-96
 

Table 3-19. LS NSP Analysis Parameters, 16-Story EBF BSE-1 LS (kip, inch) ................................... 3-96
 

Table 3-20. Performance Summary of Shear Links (SL) per Frame, Linear Procedures ..................... 3-109
 

Table 3-21. Effect of Design and Assessment Provisions on DCRN for LS at BSE-1 ......................... 3-109
 

Table 3-22. Performance Summary of Column Members (CM) per Frame, Linear Procedures ......... 3-110
 

Table 3-23. Performance Summary of Brace Members (BM) per Frame, Linear Procedures ............. 3-112
 

xiii 
Table 3-24. BSO Performance Summary of Archetype Buildings, Linear Procedures ....................... 3-114
 

Table 3-25. Summary of Base Shears, Linear Procedures (kips) ......................................................... 3-114
 

Table 3-26. Performance Summary of Shear Links (SL) per Frame, Nonlinear Procedures ............... 3-115
 

Table 3-27. Performance Summary of Column Hinges (CH) per Frame, Nonlinear Procedures ........ 3-116
 

Table 3-28. Performance Summary of Column Members (CM) per Frame, Nonlinear Procedures .... 3-117
 

Table 3-29. Performance Summary of Brace Hinges (BH) per Frame, Nonlinear Procedures ............ 3-117
 

Table 3-30. Performance Summary of Brace Members (BM) per frame, Nonlinear Procedures ........ 3-118
 

Table 3-31. BSO Performance Summary of Archetype Buildings, Nonlinear Procedures .................. 3-118
 

Table 3-32. BSO Performance Summary of Archetype Buildings....................................................... 3-119
 

Table A-1. Ground Motion Records for N-S Direction of ME4 ............................................................. A-3
 

Table A-2. Ground Motion Records for N-S Direction of ME8 ............................................................. A-6
 

Table A-3. Ground Motion Records for N-S Direction of ME16 ........................................................... A-9
 

Table B-1. Wind Forces on ME4 (kips) .................................................................................................. B-2
 

Table B-2. Wind Forces on ME8 (kips) .................................................................................................. B-2
 

Table B-3. Wind Forces on ME16 (kips) ................................................................................................ B-2
 

Table B-4. Effect Seismic Weights and Story Gravity Forces, ME4 (kips) ............................................ B-3
 

Table B-5. Effect Seismic Weights and Story Gravity Forces, ME8 (kips) ............................................ B-3
 

Table B-6. Effect Seismic Weights and Story Gravity Forces, ME16 (kips) .......................................... B-4
 

Table B-7. Seismic Strength Design Forces, E-W ME4 ......................................................................... B-4
 

Table B-8. Seismic Drift Forces, E-W ME4 ........................................................................................... B-5
 

Table B-9. ASCE 7 Allowable Drift and Stability Verification, E-W ME4 RSA ................................... B-6
 

Table B-10. ASCE 7 Allowable Drift and Stability Verification, E-W ME4 ELF ................................. B-7
 

Table B-11. Seismic Strength Design Forces, E-W ME8 ....................................................................... B-7
 

Table B-12. Seismic Drift Forces, E-W ME8 ......................................................................................... B-8
 

Table B-13. ASCE 7 Allowable Drift and Stability Verification, E-W ME8 RSA ................................. B-9
 

Table B-14. ASCE 7 Allowable Drift and Stability Verification, E-W ME8 ELF ................................. B-9
 

Table B-15. Summary of Seismic Strength Design Forces, E-W ME16 ............................................... B-10
 

Table B-16. Summary of Seismic Drift Forces, E-W ME16 ................................................................. B-11
 

Table B-17. ASCE 7 Allowable Drift and Stability Verification, E-W ME16 RSA ............................. B-12
 

Table B-18. ASCE 7 Allowable Drift and Stability Verification, E-W ME16 RSA ............................. B-13
 

Table B-19. Seismic Strength Design Forces, N-S ME4....................................................................... B-13
 

Table B-20. Seismic Drift Forces, N-S ME4 ......................................................................................... B-14
 

Table B-21. ASCE 7 Allowable Drift and Stability Verification, N-S ME4 RSA ................................ B-15
 

Table B-22. ASCE 7 Allowable Drift and Stability Verification, N-S ME4 ELF ................................ B-15
 

Table B-23. Seismic Strength Design Forces, N-S ME8....................................................................... B-16
 

xiv 
 

Table B-24. Seismic Drift Forces, N-S ME8.......................................................................................... B-16
 

Table B-25. ASCE 7 Allowable Drift and Stability Verification, N-S ME8 RSA .................................B-18
 

Table B-26. ASCE 7 Allowable Drift and Stability Verification, N-S ME8 ELF .................................B-18
 

Table B-27. Seismic Strength Design Forces, N-S ME16 .....................................................................B-18
 

Table B-28. Summary of Seismic Drift Forces, N-S ME16 ...................................................................B-19
 

Table B-29. ASCE 7 Allowable Drift and Stability Verification, N-S ME16 RSA ...............................B-21
 

Table B-30. ASCE 7 Allowable Drift and Stability Verification, N-S ME16 ELF ...............................B-21
 

Table B-31. Horizontal Irregularity Type 1 (a and b) Verification ........................................................B-22
 

Table B-32. Vertical Irregularity Type 1 (a and b) Verification (Exception 1)......................................B-22
 

Table B-33. Vertical Irregularity Type 5 (a and b) Verification, ELF (kip, feet) ...................................B-23
 

Table B-34. Vertical Irregularity Type 5 (a and b) Verification, RSA ...................................................B-23
 

Table B-35. Horizontal Irregularity Type 1 (a and b) Verification ........................................................B-24
 

Table B-36. Vertical Irregularity Type 1 (a and b) Verification (Exception 1)......................................B-24
 

Table B-37. Vertical Irregularity Type 5 (a and b) Verification, ELF (kip, feet) ...................................B-25
 

Table B-38. Vertical Irregularity Type 5 (a and b) Verification, RSA (kip, feet) ..................................B-25
 

Table B-39. AISC 360 Frame Stability (Effective Length Method), 4-Story SMF ELF (kip, inch) ......B-26
 

Table B-40. AISC 360 Frame Stability (Effective Length Method), 4-Story SMF RSA (kip, inch) .....B-26
 

Table B-41. AISC 360 Frame Stability (Effective Length Method), 8-Story SMF ELF (kip, inch) ......B-26
 

Table B-42. AISC 360 Frame Stability (Effective Length Method), 8-Story SMF RSA (kip, inch) .....B-26
 

Table B-43. AISC 360 Frame Stability (Effective Length Method), 16-Story SMF ELF (kip, inch)....B-27
 

Table B-44. AISC 360 Frame Stability (Effective Length Method), 16-Story SMF RSA (kip, inch) ...B-27
 

Table B-45. Adjusted Effective Length Factors – 4-Story SMF ............................................................B-27
 

Table B-46. Adjusted Effective Length Factors – 8-Story SMF ............................................................B-28
 

Table B-47. Adjusted Effective Length Factors – 16-Story SMF ..........................................................B-28
 

Table B-48. 4-Story EBF ELF, Shear Link Parameters .........................................................................B-29
 

Table B-49. 4-Story EBF RSA, Shear Link Parameters .........................................................................B-29
 

Table B-50. 8-Story EBF ELF, Shear Link Parameters .........................................................................B-30
 

Table B-51. 8-Story EBF RSA, Shear Link Parameters .........................................................................B-30
 

Table B-52. 16-Story EBF ELF, Shear Link Parameters .......................................................................B-31
 

Table B-53. 16-Story EBF RSA, Shear Link Parameters .......................................................................B-31
 

Table B-54. Controlling Load Combinations (kips, feet) .......................................................................B-35
 

Table B-55. Controlling Load Combinations (kips, feet) .......................................................................B-36
 

xv 
 

xvi
 
List of Figures 

Figure 2-1. Isometric View of ME4 Archetype Building ......................................................................... 2-2
 

Figure 2-2. Isometric View of ME8 Archetype Building ......................................................................... 2-2
 

Figure 2-3. Isometric View of ME16 Archetype Building ....................................................................... 2-3
 

Figure 2-4. Typical Floor Framing Plan, ME4 and ME8 ......................................................................... 2-4
 

Figure 2-5. Typical Floor Framing Plan, ME16 ....................................................................................... 2-4
 

Figure 2-6. Typical Type FR RBS Beam-to-Column Connection Assembly ........................................ 2-10
 

Figure 2-7. Type FR RBS Beam-To-Column Connection Subassembly Model for Linear Analysis .... 2-11
 

Figure 2-8. Brace-to-Beam Connection Subassembly Model for Linear Analysis ................................ 2-11
 

Figure 2-9. Flow Chart of SMF Design Process .................................................................................... 2-13
 

Figure 2-10. 4-Story SMF Schematic ..................................................................................................... 2-16
 

Figure 2-11. 8-Story SMF Schematic ..................................................................................................... 2-17
 

Figure 2-12. 16-Story SMF Schematic ................................................................................................... 2-19
 

Figure 2-13. Flow Chart of EBF Design Process ................................................................................... 2-21
 

Figure 2-14. Story Shear Demands and Nominal Strengths, 16-story EBF (N-S ME16) ...................... 2-23
 

Figure 2-15. 4-Story EBF Schematic ..................................................................................................... 2-25
 

Figure 2-16. 8-Story EBF Schematic ..................................................................................................... 2-26
 

Figure 2-17. 16-Story EBF Schematic ................................................................................................... 2-28
 

Figure 3-1. Acceleration Response Spectra .............................................................................................. 3-3
 

Figure 3-2. Generalized Component Backbone Curve (adopted from ASCE 41 Figure C2-1) ............... 3-9
 

Figure 3-3. NSP Process ......................................................................................................................... 3-11
 

 ................................................................................................................................................................. 3-25
 

Figure 3-4. P-M Interaction on Section m-factor (in-plane) and Member Instability (Primary Component)

Figure 3-5. Compactness Requirements as a Function of Axial Load Ratio, LS Acceptance Criteria .. 3-26
 

Figure 3-6. Acceptance Criteria as a Function of Axial Load Ratio and Section Compactness, LS 

Acceptance Criteria ................................................................................................................................. 3-27
 

Figure 3-7. Frame Capacity Schematic (m-factor), LS and CP, 4-Story EBF ELF and RSA ................ 3-29
 

Figure 3-8. Frame Capacity Schematic (m-factor), LS and CP, 8-Story EBF ELF and RSA ................ 3-29
 

Figure 3-9. Frame Capacity Schematic (m-factor), LS and CP, 16-Story EBF ELF and RSA .............. 3-30
 

Figure 3-10. EBF Analytical Modeling Schematic ................................................................................ 3-32
 

Figure 3-11. PERFORM-3D Link Beam Shear Hinge Calibration ........................................................ 3-33
 

Figure 3-12. In-plane Flexural Hinge Yield Surface Model (Including Force-Controlled Response) ... 3-36
 

Figure 3-13. Variation in Acceptance Criteria and Hinge Model for Axial Force ................................. 3-37
 

xvii 
Figure 3-14. P-M Interaction on Plastic Rotation, LS Acceptance Criteria (Primary Component) ....... 3-38
 

Figure 3-15. P-M Interaction Curve (Section Yield Surface)................................................................. 3-39
 

Figure 3-16. P-M Interaction Curve (Member Instability) ..................................................................... 3-39
 

Figure 3-17. Frame Capacity Schematic (Inelastic), LS and CP, 4-Story EBF – ELF ........................... 3-40
 

Figure 3-18. Frame Capacity Schematic (Inelastic), LS and CP, 4-Story EBF – RSA .......................... 3-40
 

Figure 3-19. Frame Capacity Schematic (Inelastic), LS and CP, 8-Story EBF – ELF ........................... 3-41
 

Figure 3-20. Frame Capacity Schematic (Inelastic), LS and CP, 8-Story EBF – ELF ........................... 3-42
 

Figure 3-21. Frame Capacity Schematic (Inelastic), LS and CP, 16-Story EBF – ELF ......................... 3-43
 

Figure 3-22. Frame Capacity Schematic (Inelastic), LS and CP, 16-Story EBF – RSA ........................ 3-44
 

Figure 3-23. LSP Assessment Results, 4-Story EBF ELF, BSE-1 LS ................................................... 3-46
 

Figure 3-24. LSP Assessment Results, 4-Story EBF RSA, BSE-1 LS ................................................... 3-46
 

Figure 3-25. LSP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-1 ........ 3-47
 

Figure 3-26. LSP Assessment Results, 4-Story EBF ELF, BSE-2 CP ................................................... 3-48
 

Figure 3-27. LSP Assessment Results, 4-Story EBF RSA, BSE-2 CP .................................................. 3-48
 

Figure 3-28. LSP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-2 ........ 3-48
 

Figure 3-29. LDP Assessment Results, 4-Story EBF ELF, BSE-1 LS ................................................... 3-49
 

Figure 3-30. LDP Assessment Results, 4-Story EBF RSA, BSE-1 LS .................................................. 3-49
 

Figure 3-31. LDP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-1 ........ 3-50
 

Figure 3-32. LDP Assessment Results, 4-Story EBF ELF, BSE-2 CP .................................................. 3-51
 

Figure 3-33. LDP Assessment Results, 4-Story EBF RSA, BSE-2 CP .................................................. 3-51
 

Figure 3-34. LDP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-2 ........ 3-51
 

Figure 3-35. 4-Story EBF ELF Pushover, BSE-2 .................................................................................. 3-53
 

Figure 3-36. 4-Story EBF RSA Pushover, BSE-2 .................................................................................. 3-53
 

Figure 3-37. 4-Story EBF ELF Pushover – Story Drift Ratios – BSE-2 ................................................ 3-54
 

Figure 3-38. 4-Story EBF RSA Pushover – Story Drift Ratios – BSE-2 ............................................... 3-54
 

Figure 3-39. Schematic of Flexural Actions in Components, 4-Story EBF (NSP and NDP) ................ 3-55
 

Figure 3-40. NSP Assessment Results, 4-Story EBF, BSE-1 LS (+push to left) ................................... 3-56
 

Figure 3-41. NSP Assessment Results, 4-Story EBF, BSE-2 CP (+push to left) ................................... 3-56
 

Figure 3-42. NDP Assessment Results, Shear Hinges, 4-Story EBF BSE-1 LS .................................... 3-57
 

Figure 3-43. NDP Assessment Results, Shear Hinges, 4-Story EBF BSE-2 CP .................................... 3-57
 

Figure 3-44. NDP Assessment Results, Column Hinges, 4-Story EBF ELF, BSE-2 Yield ................... 3-58
 

Figure 3-45. NDP Assessment Results, Column Hinges, 4-Story EBF RSA, BSE-2 Yield .................. 3-59
 

Figure 3-46. NDP Assessment Results, Column Members, 4-Story EBF ELF, BSE-2 ......................... 3-59
 

Figure 3-47. NDP Assessment Results, Column Members, 4-Story EBF RSA, BSE-2 ........................ 3-60
 

Figure 3-48. NDP Assessment Results, Brace Hinges, 4-Story EBF ELF, BSE-2 Yield ...................... 3-60
 

xviii 
Figure 3-49. NDP Assessment Results, Brace Hinges, 4-Story EBF RSA, BSE-2 Yield ...................... 3-61
 

Figure 3-50. NDP Assessment Results, Brace Members, 4-Story EBF ELF, BSE-2 ............................ 3-61
 

Figure 3-51. NDP Assessment Results, Brace Members, 4-Story EBF RSA, BSE-2 ............................ 3-62
 

Figure 3-52. LSP Assessment Results, 8-Story EBF ELF, BSE-1 LS ................................................... 3-63
 

Figure 3-53. LSP Assessment Results, 8-Story EBF RSA, BSE-1 LS ................................................... 3-63
 

Figure 3-54. LSP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-1 ........ 3-64
 

Figure 3-55. LSP Assessment Results, 8-Story EBF ELF, BSE-2 CP ................................................... 3-66
 

Figure 3-56. LSP Assessment Results, 8-Story EBF RSA, BSE-2 CP .................................................. 3-66
 

Figure 3-57. LSP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-2 ........ 3-67
 

Figure 3-58. LDP Assessment Results, 8-Story EBF ELF, BSE-1 LS ................................................... 3-68
 

Figure 3-59. LDP Assessment Results, 8-Story EBF RSA, BSE-1 LS .................................................. 3-68
 

Figure 3-60. LDP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-1 ........ 3-69
 

Figure 3-61. LDP Assessment Results, 8-Story EBF ELF, BSE-2 CP .................................................. 3-70
 

Figure 3-62. LDP Assessment Results, 8-Story EBF RSA, BSE-2 CP .................................................. 3-70
 

Figure 3-63. LDP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-2 ........ 3-71
 

Figure 3-64. 8-Story EBF ELF Pushover, BSE-2 .................................................................................. 3-72
 

Figure 3-65. 8-Story RSA ELF Pushover, BSE-2 .................................................................................. 3-73
 

Figure 3-66. 8-Story EBF ELF Pushover – Story Drift Ratios – BSE-2 ................................................ 3-73
 

Figure 3-67. 8-Story EBF RSA Pushover – Story Drift Ratios – BSE-2 ............................................... 3-74
 

Figure 3-68. Schematic of Flexural Actions in Components, 8-Story EBF (NSP and NDP) ................ 3-75
 

Figure 3-69. NSP Assessment Results, 8-Story EBF, BSE-1 LS (+push to left) ................................... 3-75
 

Figure 3-70. NSP Assessment Results, 8-Story EBF, BSE-2 CP (+push to left) ................................... 3-76
 

Figure 3-71. NDP Assessment Results, Shear Hinges, 8-Story EBF, BSE-1 LS ................................... 3-77
 

Figure 3-72. NDP Assessment Results, Shear Hinges, 8-Story EBF, BSE-2 CP ................................... 3-77
 

Figure 3-73. NDP Assessment Results, Column Hinges, 8-Story EBF ELF, BSE-2 Yield ................... 3-78
 

Figure 3-74. NDP Assessment Results, Column Hinges, 8-Story EBF RSA, BSE-2 Yield .................. 3-79
 

Figure 3-75. NDP Assessment Results, Column Members, 8-Story EBF ELF, BSE-2 ......................... 3-79
 

Figure 3-76. NDP Assessment Results, Column Members, 8-Story EBF RSA, BSE-2 ........................ 3-80
 

Figure 3-77. NDP Assessment Results, Brace Hinges, 8-Story EBF ELF, BSE-2 Yield ...................... 3-80
 

Figure 3-78. NDP Assessment Results, Brace Hinges, 8-Story EBF RSA, BSE-2 Yield ...................... 3-81
 

Figure 3-79. NDP Assessment Results, Brace Members, 8-Story EBF ELF, BSE-2 ............................ 3-81
 

Figure 3-80. NDP Assessment Results, Brace Members, 8-Story EBF RSA, BSE-2 ............................ 3-82
 

Figure 3-81. LSP Assessment Results, 16-Story EBF ELF, BSE-1 LS ................................................. 3-84
 

Figure 3-82. LSP Assessment Results, 16-Story EBF RSA, BSE-1 LS ................................................. 3-85
 

Figure 3-83. LSP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-1 ...... 3-86
 

xix 
 

Figure 3-84. LSP Assessment Results, 16-Story EBF ELF, BSE-2 CP ................................................. 3-87
 

Figure A-1. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S 

Figure A-2. Acceleration Response Spectra: Original and Scaled for Each Selected Record for N-S 

Figure A-3. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S 

Figure A-4. Acceleration Response Spectra: Original and Scaled for Each Selected Record for N-S 

Figure 3-85. LSP Assessment Results, 16-Story EBF RSA, BSE-2 CP ................................................ 3-88
 

Figure 3-86. LSP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-2 ...... 3-89
 

Figure 3-87. LDP Assessment Results, 16-Story EBF ELF, BSE-1 LS................................................. 3-90
 

Figure 3-88. LDP Assessment Results, 16-Story EBF RSA, BSE-1 LS ................................................ 3-91
 

Figure 3-89. LDP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-1 ...... 3-92
 

Figure 3-90. LDP Assessment Results, 16-Story EBF ELF, BSE-2 CP ................................................ 3-93
 

Figure 3-91. LDP Assessment Results, 16-Story EBF RSA, BSE-2 CP ................................................ 3-94
 

Figure 3-92. LDP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-2 ...... 3-95
 

Figure 3-93. 16-Story EBF ELF Pushover, BSE-2 ................................................................................ 3-96
 

Figure 3-94. 16-Story EBF RSA Pushover, BSE-2 ................................................................................ 3-97
 

Figure 3-95. 16-Story EBF ELF Pushover – Story Drift Ratios – BSE-2 .............................................. 3-98
 

Figure 3-96. 16-Story EBF RSA Pushover – Story Drift Ratios – BSE-2 ............................................. 3-98
 

Figure 3-97. Schematic of Flexural Actions in Components, 16-Story EBF (NSP and NDP) .............. 3-99
 

Figure 3-98. NSP Assessment Results, 16-Story EBF ELF, BSE-1 LS (+push to left) ....................... 3-100
 

Figure 3-99. NSP Assessment Results, 16-Story EBF RSA, BSE-2 CP (+push to left) ...................... 3-101
 

Figure 3-100. NDP Assessment Results, Shear Hinges, 16-Story EBF, BSE-1 LS ............................. 3-102
 

Figure 3-101. NDP Assessment Results, Shear Hinges, 16-Story EBF, BSE-2 CP ............................. 3-103
 

Figure 3-102. NDP Assessment Results, Column Hinges, 16-Story EBF ELF, BSE-2 Yield ............. 3-104
 

Figure 3-103. NDP Assessment Results, Column Hinges, 16-Story EBF RSA, BSE-2 Yield ............ 3-104
 

Figure 3-104. NDP Assessment Results, Column Members, 16-Story EBF ELF, BSE-2 ................... 3-105
 

Figure 3-105. NDP Assessment Results, Column Members, 16-Story EBF RSA, BSE-2 .................. 3-105
 

Figure 3-106. NDP Assessment Results, Brace Hinges, 16-Story EBF ELF, BSE-2 Yield ................ 3-106
 

Figure 3-107. NDP Assessment Results, Brace Hinges, 16-Story EBF RSA, BSE-2 Yield ................ 3-106
 

Figure 3-108. NDP Assessment Results, Brace Members, 16-Story EBF ELF, BSE-2 ...................... 3-107
 

Figure 3-109. NDP Assessment Results, Brace Members, 16-Story EBF RSA, BSE-2 ...................... 3-107
 

Figure 3-110. DCRN values for EBF columns and braces using LSP, BSE-1, LS BPL ....................... 3-113
 

Direction of ME4...................................................................................................................................... A-4
 

Direction of ME4...................................................................................................................................... A-5
 

Direction of ME8...................................................................................................................................... A-7
 

Direction of ME8...................................................................................................................................... A-8
 

xx 
Figure A-5. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S 

Direction of ME16.................................................................................................................................. A-10
 

Figure A-6. Acceleration Response Spectra: Original and Scaled for Each Selected Record for N-S 

Direction of ME16.................................................................................................................................. A-11
 

Figure A-7. 1994 Northridge Earthquake at Beverly Hills, Mulholland Drive Station, Comp. 009 ..... A-12
 

Figure A-8. 1994 Northridge Earthquake at Beverly Hills, Mulholland Drive Station, Comp. 279 ..... A-12
 

Figure A-9. 1994 Northridge Earthquake at Canyon Country WLC Station, Comp. 000 ..................... A-13
 

Figure A-10. 1994 Northridge Earthquake at Canyon Country WLC Station, Comp. 270 ................... A-13
 

Figure A-11. 1999 Duzce, Turkey Earthquake at Bolu Station, Comp. 000 ......................................... A-14
 

Figure A-12. 1999 Duzce, Turkey Earthquake at Bolu Station, Comp. 090 ......................................... A-14
 

Figure A-13. 1999 Hector Mine Earthquake at Hector Station, Comp. 000 ......................................... A-15
 

Figure A-14. 1999 Hector Mine Earthquake at Hector Station, Comp. 090 ......................................... A-15
 

Figure A-15. 1979 Imperial Valley Earthquake at Delta Station, Comp. 262 ....................................... A-16
 

Figure A-16. 1979 Imperial Valley Earthquake at Delta Station, Comp. 352 ....................................... A-16
 

Figure A-17. 1979 Imperial Valley Earthquake at El Centro Array Station #11, Comp. 140 ............... A-17
 

Figure A-18. 1979 Imperial Valley Earthquake at El Centro Array Station #11, Comp. 230 ............... A-17
 

Figure A-19. 1995 Kobe, Japan Earthquake at Nishi-Akashi Station, Comp. 000 ............................... A-18
 

Figure A-20. 1995 Kobe, Japan Earthquake at Nishi-Akashi Station, Comp. 090 ............................... A-18
 

Figure A-21. 1995 Kobe, Japan Earthquake at Shin-Osaka Station, Comp. 000 .................................. A-19
 

Figure A-22. 1995 Kobe, Japan Earthquake at Shin-Osaka Station, Comp. 090 .................................. A-19
 

Figure A-23. 1999 Kocaeli, Turkey Earthquake at Duzce Station, Comp. 180 .................................... A-20
 

Figure A-24. 1999 Kocaeli, Turkey Earthquake at Duzce Station, Comp. 270 .................................... A-20
 

Figure A-25. 1999 Kocaeli, Turkey Earthquake at Arcelik Station, Comp. 000................................... A-21
 

Figure A-26. 1999 Kocaeli, Turkey Earthquake at Arcelik Station, Comp. 090................................... A-21
 

Figure A-27. 1992 Landers Earthquake at Yermo Fire Station, Comp. 270 ......................................... A-22
 

Figure A-28. 1992 Landers Earthquake at Yermo Fire Station, Comp. 360 ......................................... A-22
 

Figure A-29. 1992 Landers Earthquake at Coolwater Station, Longitudinal Direction ........................ A-23
 

Figure A-30. 1992 Landers Earthquake at Coolwater Station, Transverse Direction ........................... A-23
 

Figure A-31. 1989 Loma Prieta Earthquake at Capitola Station, Comp. 000 ....................................... A-24
 

Figure A-32. 1989 Loma Prieta Earthquake at Capitola Station, Comp. 090 ....................................... A-24
 

Figure A-33. 1989 Loma Prieta Earthquake at Gilroy Array Station #3, Comp. 000 ........................... A-25
 

Figure A-34. 1989 Loma Prieta Earthquake at Gilroy Array Station #3, Comp. 090 ........................... A-25
 

Figure A-35. 1990 Manjil, Iran Earthquake at Abbar Station, Longitudinal Direction ........................ A-26
 

Figure A-36. 1990 Manjil, Iran Earthquake at Abbar Station, Transverse Direction ............................ A-26
 

Figure A-37. 1987 Superstition Hills Earthquake at El Centro, Imperial County, Comp. 000 ............. A-27
 

xxi 
Figure A-38. 1987 Superstition Hills Earthquake at El Centro, Imperial County, Comp. 090 ............. A-27
 

Figure A-39. 1987 Superstition Hills Earthquake at Poe Road, Comp. 270 ......................................... A-28
 

Figure A-40. 1987 Superstition Hills Earthquake at Poe Road, Comp. 360 ......................................... A-28
 

Figure A-41. 1992 Cape Mendocino Earthquake at Rio Dell Overpass, Comp. 270 ............................ A-29
 

Figure A-42. 1992 Cape Mendocino Earthquake at Rio Dell Overpass, Comp. 360 ............................ A-29
 

Figure A-43. 1999 Chi-Chi, Taiwan Earthquake at CHY101 Station, E-W Component ...................... A-30
 

Figure A-44. 1999 Chi-Chi, Taiwan Earthquake at CHY101 Station, N-S Component ....................... A-30
 

Figure A-45. 1999 Chi-Chi, Taiwan Earthquake at TCU045 Station, E-W Component ...................... A-31
 

Figure A-46. 1999 Chi-Chi, Taiwan Earthquake at TCU045 Station, N-S Component ....................... A-31
 

Figure A-47. 1971 San Fernando Earthquake at Los Angeles Hollywood Store Station, Comp. 090 .. A-32
 

Figure A-48. 1971 San Fernando Earthquake at Los Angeles Hollywood Store Station, Comp. 180 .. A-32
 

Figure A-49. 1976 Fruili, Italy Earthquake at Tolmezzo Station, Comp. 000 ...................................... A-33
 

Figure A-50. 1976 Fruili, Italy Earthquake at Tolmezzo Station, Comp. 270 ...................................... A-33
 

Figure B-1. Strength Design Lateral Forces and Story Shears................................................................ B-5
 

Figure B-2. Drift Design Lateral Forces and Story Shears ...................................................................... B-5
 

Figure B-3. Story Drift Ratios and Deflected Shape ............................................................................... B-6
 

Figure B-4. Strength Design Lateral Forces and Story Shears................................................................ B-7
 

Figure B-5. Drift Design Lateral Forces and Story Shears ...................................................................... B-8
 

Figure B-6. Story Drift Ratios and Deflected Shape ............................................................................... B-9
 

Figure B-7. Strength Design Lateral Forces and Story Shears .............................................................. B-10
 

Figure B-8. Drift Design Lateral Forces and Story Shears .................................................................... B-11
 

Figure B-9. Story Drift Ratios and Deflected Shape ............................................................................. B-12
 

Figure B-10. Strength Design Lateral Forces and Story Shears ............................................................ B-14
 

Figure B-11. Drift Design Lateral Forces and Story Shears .................................................................. B-14
 

Figure B-12. Story Drift Ratios and Deflected Shape ........................................................................... B-15
 

Figure B-13. Strength Design Lateral Forces and Story Shears ............................................................ B-16
 

Figure B-14. Drift Design Lateral Forces and Story Shears .................................................................. B-17
 

Figure B-15. Story Drift Ratios and Deflected Shape ........................................................................... B-17
 

Figure B-16. Strength Design Lateral Forces and Story Shears ............................................................ B-19
 

Figure B-17. Drift Design Lateral Forces and Story Shears .................................................................. B-20
 

Figure B-18. Story Drift Ratios and Deflected Shape ........................................................................... B-20
 

Figure B-19. Link Rotation Angle, 4-Story EBF ELF and RSA ........................................................... B-29
 

Figure B-20. Link Rotation Angle, 8-Story EBF ELF and RSA ........................................................... B-30
 

Figure B-21. Link Rotation Angle, 16-Story EBF ELF and RSA ......................................................... B-32
 

Figure B-22. EBF member sizes, 8-story RSA ..................................................................................... B-33
 

xxii 
 

xxiii
 
 

 

 

 

 

 

 

List of Abbreviations 

AISC American Institute of Steel Construction 

ASCE American Society of Civil Engineers 

ASTM American Society for Testing and Materials 

ATC Applied Technology Council 

BPL Building Performance Level 

BSE Basic Safety Earthquake 

BSO Basic Safety Objective 

BSSC Building Seismic Safety Council 

CBF Concentrically Braced Frame 

CP Collapse Prevention 

DC Deformation-Controlled 

DCR Demand to capacity ratio 

EBF Eccentrically Braced Frame 

EHL Earthquake Hazard Level 

ELF Equivalent Lateral Force 

E-W East-West 

FC Force-Controlled 

FEMA Federal Emergency Management Agency 

FR Fully Restrained 

GSA General Services Administration 

GCR Grant/Contract Report 

HD Highly Ductile 

HSS Hollow Structural Section 

IBC International Building Code 

ICC International Code Council 

IEBC International Existing Building Code 

IO Immediate Occupancy 

LC Load Combination 

LDP Linear Dynamic Procedure 

LFRS Lateral Force Resisting System 

LRFD Load and Resistance Factor Design 

xxiv 
 

 

 

 

 

 

 

 

LS Life Safety 

LSP Linear Static Procedure 

LTB Lateral Torsional Buckling 

MC Moment Curvature 

MCE (MCER) Maximum Considered Earthquake 

MD Moderately Ductile 

MR Moment Rotation 

MRSA Modal Response Spectrum Analysis 

MWFRS Main Wind Force Resisting System 

NDP Nonlinear Dynamic Procedure 

NEHRP National Earthquake Hazards Reduction Program 

NIBS National Institute of Building Sciences 

NIST National Institute of Standards and Technology 

NPL Nonstructural Performance Level 

N-S North-South 

NSP Nonlinear Static Procedure 

PBS Public Buildings Service 

PBSD Performance-Based Seismic Design 

RBS Reduced Beam Section 

RHA Response History Analysis 

RSA Response Spectrum Analysis 

SCBF Special Concentrically Braced Frame 

SCWB Strong Column Weak Beam 

SDC Seismic Design Category 

SDOF Single Degree of Freedom 

SEAONC Structural Engineers Association of Northern California 

SEI Structural Engineering Institute 

SFRS Seismic Force Resisting System 

SMF Special Moment Frame 

SPL Structural Performance Level 

SRSS Square Root Sum of the Squares 

W.P. Work Point 

xxv 
Executive Summary 

This report presents the results of a study investigating the correlation between the seismic performance of 

an ASCE 7 code-compliant building and its performance as quantified using ASCE 41 analysis procedures 

and structural performance metrics. This investigation is performed by evaluating a suite of structural steel 

buildings in a high seismicity region that are designed using ASCE 7 and evaluated using ASCE 41. The 

basic question is whether the standards for designing new steel buildings and assessing existing steel 

buildings provide consistent levels of performance. An additional outcome of this research is to advance 

the state-of-knowledge in PBSD and assessment of buildings using ASCE 41. Further, results provide the 

technical background for provisions that target equivalent seismic performance between a new building and 

an existing building that is required to meet the seismic performance objective of a new building. 

This report presents the results of a structural seismic performance assessment using ASCE 41 procedures 

and performance measures of buildings utilizing steel eccentrically braced frames (EBF) as the lateral forceresisting system (LFRS). 

A suite of archetype buildings that incorporate EBFs along one principal direction of the buildings is 

designed in accordance with ASCE 7. The suite consists of 4-, 8-, and 16-story buildings designed using 

both the Equivalent Lateral Force (ELF) Procedure and Modal Response Spectrum Analysis (RSA). Both 

analysis procedures are used to provide a generally applicable range of LFRS strength within the selected 

seismic intensity region. As such, an LFRS may include significant overstrength to resist nonseismic loads 

or to satisfy other design criteria. A design space is created to investigate the effects of design methodology, 

building height and other LFRS-specific geometric modifications on seismic performance. In reality, the 

design space is infinitely large and many design choices made in this study can also have different 

configurations to evaluate the variation in performance specific to a design choice. 

The seismic performance assessment of the building suite is conducted using both linear and nonlinear 

analysis procedures prescribed in ASCE 41: 

 Linear Static Procedure (LSP) 

 Linear Dynamic Procedure (Response Spectrum) (LDP) 

 Nonlinear Static Procedure (NSP) 

 Nonlinear Dynamic Procedure (NDP) 

For this study, the performance assessment targets the Basic Safety Objective (BSO) prescribed in ASCE 

41. This objective includes the interrelated goals of Life Safety (LS) Building Performance Level (BPL) at 

the Basic Safety Earthquake-1 (BSE-1) earthquake hazard level (EHL) and Collapse Prevention (CP) BPL 

at the BSE-2 EHL. This performance objective is chosen to align with the intended structural performance 

objective of an ordinary building in ASCE 7, which is qualitatively defined here as “life safety” provided 

by collapse prevention of the building, given a maximum considered earthquake (MCE) event. 

xxvi 
 

To evaluate seismic assessment criteria, each component of the EBFs is designated as a primary or 

component in accordance with ASCE 41 §2.2.5 (and ASCE 41 §2.4.4.2). Similarly, quantitative 

performance measures (i.e., acceptance criteria) for primary components are used for all assessment 

procedures, although performance measures for secondary components are permitted by ASCE 41 for some 

primary components. The consistent use of primary acceptance criteria keeps all components and associated 

assessment results correlated among the assessment procedures for this study. 

The goals of this research are as follows: 

 Assess new structural steel buildings utilizing EBFs designed per ASCE 7 requirements and, in 

turn, evaluated using ASCE 41, 

 Develop a qualitative link between the performance implied in ASCE 7 in light of the performance 

identified by ASCE 41 procedures and performance measures, 

 Provide guidance or technical support for improved or new provisions in ASCE 41 (and to a lesser 

extent, ASCE 7), 

 Reduce uncertainty in first-generation PBSD procedures for performance-based seismic 

assessment, and 

 Identify any inconsistencies, ambiguities, and confusing provisions in ASCE 41. 

The primary conclusions of this research can be divided into two parts: General Observations and Specific 

Observations about ASCE 41 analytical procedures. 

A. General Observations for Eccentrically Braced Frames: 

	 The LSP generally results in more conservative normalized demand to capacity ratios, DCRN, 

values than that of the LDP, because of the differences in the distribution of seismic demands and 

the lack of modal representation other than the fundamental mode in the LSP. 

	 The NSP generally results in less conservative DCRN values than that of the NDP, contrary to what 

would be expected with increasing the analytical complexity, because of the differences in the 

distribution of seismic demands and the lack of modal representation other than the fundamental 

mode in the NSP. 

	 The nonlinear procedures provide a more rigorous assessment approach as compared to the linear 

procedures. The results from the LSP, and to a lesser extent the LDP, indicate more performance 

failures in force-controlled components than identified using the nonlinear procedures. The results 

presented emphasize the inherent conservatism in the linear procedures. However, this 

conservatism is accompanied by a reduction in required analytical resources and proficiency of the 

analyst. 

 The linear procedures can illustrate the trend in demands but may fail to highlight critical 

performance zones within a given frame. 

 No clear consistency exists between linear assessment results and nonlinear assessment results for 

link beams. Contrary performance results indicate acceptance criteria that need further calibration. 

xxvii 
 

B. Specific Observations for Eccentrically Braced Frames: 

The following significant observations and conclusions are based on the collective results obtained from 

the assessment of the EBFs. More details about the specific items are in the relevant sections of the 

assessment discussion in Chapter 3. 

	 Analytical results based on component-level performances indicate that new long-period EBFs 

designed in accordance with ASCE 7, and its referenced standards, have difficulty achieving the 

ASCE 41 BSO for an existing building intended to be equivalent to a new building. This 

observation is driven by the performance of the link beams and, to a lesser extent, the columns and 

braces. Assessment results for the link beams from the nonlinear procedures provide a conclusion 

opposite to that provided for the linear procedures in that nonlinear assessment reveals higher DCRN 

values than the linear assessment. 

	 Assuming the archetype buildings meet the collapse performance objective of ASCE 7, the results 

of the assessment procedures indicate that ASCE 41 is generally conservative for EBFs. ASCE 41 

analysis would require retrofit or replacement of specific components of a code-compliant SFRS 

to satisfy the CP BPL, given an MCE event. The results highlight that columns (i.e., beam-columns) 

with high axial and flexural demands and link beams have difficulty in satisfying the performance 

criteria in ASCE 41. Future research is needed to couple the collapse performance objectives of the 

two standards, as well as other performance objectives associated with a seismic hazard with a 

lower return period. 

	 Analysis results indicate that the linear procedures generally give smaller DCRN values than that 

obtained from nonlinear procedures, contrary to what would be expected with increasing the 

analytical complexity. Given a properly designed new link beam, the linear procedures will result 

in a maximum DCRN value for a primary component of 0.72 for the BSE-1 EHL (0.76 for the BSE2 EHL). 

	 A significant number of link beams did not satisfy the acceptance criteria for the nonlinear 

procedures. This result was particularly problematic for EBFs as they quickly progressed towards 

a collapse state after the ultimate link capacity in the second story was reached. Though link beam 

performance is based on high fidelity analytical modeling parameters, enhanced modeling practices 

should be investigated. Research should investigate the influence of the loading protocol adopted 

to establish the deterministic acceptance criteria for short link beams. 

	 A significant number of columns, primarily at the base of the frame, did not satisfy the ASCE 41 

acceptance criteria (force-controlled). The results for columns can be enhanced by more 

mechanistically consistent assessment provisions and analytical modeling parameters for columns 

(e.g., column/brace-to-base connection modeling). 

	 Components of the EBFs that do not satisfy the CP acceptance criteria would need to be 

strengthened to achieve the performance required by ASCE 41. However, the results from the 

various assessment procedures were seen to be inconsistent in some cases for a given design routine 

(i.e., LSP vs. NDP) or the same assessment procedure was inconsistent between design routines 

(i.e., ELF and RSA). This makes it difficult to definitively suggest that using ASCE 41 to design a 

new EBF would produce a system capable of achieving the seismic performance objective of ASCE 

7. Future research is needed to evaluate the collapse probability of a new system strengthened by 

ASCE 41 relative to the seismic performance objective of ASCE 7. The same is required for a new 

xxviii 
system that has component strengths reduced from that required by ASCE 7 to meet an ASCE 41 

performance objective. Further, the adequacy of the components of the enhanced frame (those 

required to satisfy ASCE 41) would be dependent upon which analysis procedure is used to iterate 

between design and assessment, and therefore the fidelity of the analytical model and analysis 

parameters. 

	 Results of this study indicate that for ASCE 41 to be used as a seismic design procedure for new 

steel buildings, as a performance-based alternative to ASCE 7 (see ASCE 7 §1.3.1.3), acceptance 

criteria for the various analysis methods must be calibrated to each other to consistently result in a 

uniform collapse risk. Additionally, ASCE 41 would need to reference material-specific design 

standards (e.g., AISC 341) for their seismic design requirements, as well as consistent requirements 

for defining acceptance criteria for a component (e.g., plastic rotation). 

xxix 
 

Chapter 1 Introduction 

In 1997, the Federal Emergency Management Agency (FEMA) published FEMA 273: NEHRP Guidelines 

for the Seismic Rehabilitation of Buildings (FEMA 1997) as a first step towards standardizing seismic 

performance assessment procedures for existing buildings. This effort, produced under the Applied 

Technology Council’s project 33 (ATC-33), was the first significant step in implementing performancebased seismic design (PBSD) into practice. Subsequently in 2000, FEMA and the American Society of 

Civil Engineers (ASCE) published FEMA 356: Prestandard and Commentary for the Seismic 

Rehabilitation of Buildings (FEMA 2000e). This publication introduced many changes to FEMA 273 to 

refine the accuracy and applicability of the provisions. The changes are chronicled in FEMA 357: Global 

Topics Report on the Prestandard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 

2000f). In 2006 ASCE published ASCE/SEI 41-06: Seismic Rehabilitation of Existing Buildings (ASCE 

2006) as an ASCE Standard—hereafter referred to as ASCE 41. This document is referenced by the 

International Existing Building Code (IEBC) published by the International Code Council (ICC) (ICC 

2012a). 

ASCE 41 represents the current state-of-practice in seismic evaluation and rehabilitation of existing 

buildings. This standard is referenced by the California Building Standards Code (CBSC 2010), Federal 

government building standards (e.g., NIST 2011a), and a number of other local jurisdictions. ASCE 41 

provides analytical procedures and criteria for evaluating buildings and designing seismic retrofits based 

on a defined performance goal (i.e., Life Safety and Collapse Prevention). This ability to explicitly define 

a performance goal and then assess a building design against that goal has led practitioners to adapt ASCE 

41 methodology for use in new building design. The performance-based methodologies in ASCE 41 provide 

an alternative to the traditional prescriptive approaches used in the current standard for new buildings, 

ASCE/SEI 7-10: Minimum Design Loads for Buildings and Other Structures (ASCE 2010)—hereafter 

referred to as ASCE 7. Referenced by the International Building Code (IBC) (ICC 2012b), ASCE 7 is 

widely used throughout the country for seismic design of new buildings. However, with the trend toward 

performance-based design, the correlation between the performance of a building designed with the 

prescriptive provisions of ASCE 7 and assessed with the performance-based provisions of ASCE 41 is 

largely unknown. 

The next version of ASCE 41 (ASCE 41-131

) will offer a new track for application of the provisions to 

existing buildings whose performance goal is equivalent to that of a building designed with the new building 

standard. Consequently, this new track will allow direct seismic performance assessment of new buildings 

or, alternatively, a substitute seismic design approach via Chapter 1 of ASCE 7. For example, the PBSP100: Facility Standards for the Public Buildings Service (GSA 2012) prescribes that ASCE 41-06 shall 

1

 ASCE 41-13: Seismic Evaluation and Retrofit of Existing Buildings (ASCE 2014) was being developed during this project period. 

As such, new or updated provisions in ASCE 41-13 were not incorporated, except where changes were required to align with the 

seismic hazard prescribed in ASCE 7-10. 

1-1
 
 

 

be used for the seismic design of new GSA facilities2

 and that the guidelines from ASCE 41 are intended 

to be applied to new buildings. This document does not permit a building to be designed for seismic 

performance below the minimum level specified by IBC. The National Institute of Building Sciences 

(NIBS) is using PBS-P100 as the basis for developing their National Performance Based Design Guide 

(NIBS 2013). Further, the Provisions Update Committee for the Building Seismic Safety Council is 

currently deliberating expanded provisions for performing nonlinear response history analysis (Chapter 16 

in ASCE 7) for the 2015 edition of the NEHRP Recommend Provisions for Seismic Regulations for New 

Buildings and Other Structures (FEMA 2015). These expanded provisions reference ASCE 41-13 in the 

commentary for modeling and acceptance criteria for the design of new buildings. 

This report presents the results of a study investigating the correlation between the seismic performance of 

an ASCE 7 code-compliant building and its performance as quantified using ASCE 41 analysis procedures 

and structural performance metrics. This investigation is performed by evaluating a suite of structural steel 

buildings in a high seismicity region that are designed using ASCE 7 and evaluated using ASCE 41. The 

basic question is whether the standards for designing new steel buildings and assessing existing steel 

buildings provide consistent levels of performance. The intended outcome of this research is to advance the 

state-of-knowledge in performance-based seismic design and assessment of buildings using ASCE 41. 

Further, results provide the technical background for provisions that target equivalent seismic performance 

between a new building and an existing building that is required to meet the seismic performance objective 

of a new building. 

Applicability of ASCE 41-13 to this Study 

During this project, ASCE/SEI 41-13, Seismic Evaluation and Retrofit of Existing Buildings (ASCE 2014), 

completed committee balloting and was sent out for public comment as well as for approval for inclusion 

in the IEBC. Any significant differences between ASCE 41-06 and ASCE 41-13 regarding assessment of 

steel structural systems will be highlighted in the discussions where applicable—unless otherwise noted, 

reference to ASCE 41 refers only to ASCE 41-06. 

One significant addition to ASCE 41-13 is a process for applying the provisions for the seismic assessment 

of existing buildings where the intended performance is equivalent to that which is intended for new 

buildings designed in accordance with ASCE 7, including a correlation matrix between the two standards. 

While ASCE 41-06 is being used currently in practice to justify seismic performance of new buildings in 

compliance with ASCE 7 (as well as to identify noncompliance), this addition is the first step in 

conceptually aligning future editions of ASCE 41 and ASCE 7 so that ASCE 41 can be used for the seismic 

design of new buildings. Still, there are variations between material-specific provisions in ASCE 41 and 

provisions in material design standards referenced in ASCE 7 (e.g., AISC 360 and ACI 318) that need to 

be resolved. 

2

 The seismic hazard used to characterize the design basis earthquake is that with a 10% probability of exceedence in 50 years. This 

differs from that used in ASCE/SEI 7-05 (ASCE 2005)—two-thirds of that with a 2% probability of exceedence in 50 years—and 

ASCE 7-10—two-thirds of that producing a 1% probability of collapse in 50 years. 

1-2
 
 

In terms of assessment of steel systems, the technical content in ASCE 41-13 did not change in any 

significant manner that invalidates the results presented in this report. The few changes that would affect 

the results of individual components are highlighted where applicable. In fact, data from this study 

instigated some of these changes. 

1.1 Project Motivation and Background 

Traditional prescriptive seismic provisions for new buildings principally concentrate on the Life Safety 

objective applied to all-encompassing arrangements of similar lateral force-resisting systems. Little 

consideration is given to either the actual performance of individual buildings or the economic loss and 

occupancy interruption that may occur after an earthquake. Thus, a need arises for seismic provisions that 

allow engineers to design buildings and assess them against varying levels of performance associated with 

varying levels of earthquake hazard. So doing provides a method where desired building damage levels can 

be coupled to both quantitative and qualitative definitions of performance so that building and operational 

stakeholders are integrated into a project. Conceptually, PBSD was conceived to satisfy this need. The 

objective of PBSD is to provide a means of integrating additional performance objectives into the seismic 

design of new buildings that explicitly measure and account for risk of casualties, occupancy interruption, 

and economic loss including repair costs. 

Prescriptive building code procedures, such as those found in ASCE 7, tend to restrict design innovation 

and can lead to inefficient structural designs and higher construction costs. In lieu of its prescriptive 

provisions, ASCE 7 allows alternative “rational” design methods, such as PBSD, to be used in new building 

design. PBSD affords the designer the freedom to bypass prescriptive building code provisions by 

demonstrating that a building performs to an explicitly defined performance target that equals or exceeds 

the life safety objective in prescriptive provisions. The use of such methods must be approved by the local 

authority having jurisdiction and typically requires rigorous structural analysis coupled with a high level of 

expertise. 

Although ASCE 7 allows PBSD (see ASCE 7 §1.3.1.3) to be used in new building design, it provides no 

substantial guidance on implementing PBSD for this purpose. Therefore, many practitioners and local 

authorities have turned to the provisions in ASCE 41 as a way of implementing PBSD into new building 

design. These provisions, widely considered to be “first generation” PBSD principles, were originally 

intended to be used in the evaluation of existing buildings by assessing performance compliance with a 

selected rehabilitation objective. Since ASCE 41 is applicable to existing buildings, it does not provide a 

direct correlation between the rehabilitation objective and the intended performance of an ASCE 7 codecompliant new building (see Table 1-1). However, the IEBC does provide a correlation between ASCE 41 

performance levels and IBC (and thus ASCE 7) Risk Categories, thus providing the link between the 

prescriptive requirements for new building design and the nonprescriptive requirements of existing building 

assessment and PBSD. A matrix showing this correlation is shown in Table 1-2. Still, this matrix has not 

been comprehensively validated nor have the seismic performance expectations for new buildings been 

quantitatively assessed to standardize acceptable performance within the framework of ASCE 41, or vice 

versa. ASCE 7 has not expressly adopted Table 1-2 for seismic design. 

1-3
 
 

 

 

 

 

 

Table 1-1. Comparison of Seismic Hazard and Associated Performance for ASCE 7 and ASCE 41 

Target Building Performance Level 1 

Operational Immediate 

Occupancy 

(IO) 

Life Safety 

(LS) 

Collapse 

Prevention 

(CP) 

Earthquake Hazard Level 

ASCE 41 

50% / 50 year2 

ASCE 41 

(nonstructural) ASCE 41 Limited ASCE 41 Limited ASCE 41 Limited 

ASCE 41 

20% / 50 year2 

ASCE 41 

Enhanced ASCE 41 ASCE 41 Limited 

ASCE 41 

Limited 

ASCE 7 

“Frequent” 1 

ASCE 7 

Risk Category III 

& IV 

ASCE 7 Risk 

Category I & II 

(anticipated) 3 

N.A. N.A. 

ASCE 41 

BSE-1 

~ 10% / 50 year 2 

ASCE 41 

Enhanced 

ASCE 41 

Enhanced ASCE 41 BSO ASCE 41 

Limited 

ASCE 7 

2⁄3 × MCER 1 N.A. 

ASCE 7 

Risk Category III 

& IV 

ASCE 7 Risk 

Category I & II 

(design) 

N.A. 

ASCE 41 

BSE-2 

~ 2% / 50 year 2 

ASCE 41 

Enhanced 

ASCE 41 

Enhanced 

ASCE 41 

Enhanced ASCE 41 BSO 

ASCE 7 

MCER 1 N.A. N.A. 

ASCE 7 

Risk Category III 

& IV 

ASCE 7 Risk 

Category I & II 

(objective) 3 

1. Seismic hazard defined in ASCE 7-10. 

2. Seismic hazard defined in ASCE 41-06. 

3. See ASCE 7, Expanded Seismic Commentary (ASCE 7-10 3rd printing). 

Table 1-2. Performance Comparison between IBC and ASCE 41 – (From IEBC Table 301.1.4.1) 

Risk Category Performance Level for use with ASCE Performance Level for use with ASCE 

(Based on IBC Table 1604.5) 41 BSE-1 Earthquake Hazard Level 41 BSE-2 Earthquake Hazard Level 

I Life Safety (LS) Collapse Prevention (CP) 

II Life Safety (LS) Collapse Prevention (CP) 

III Note a Note a 

IV Immediate Occupancy (IO) Immediate Occupancy (IO) 

a.	 Acceptance criteria for Risk Category III shall be taken as 80 percent of the acceptance criteria specified for Risk Category II performance levels, but 

need not be less than the acceptance criteria specified for Risk Category IV performance levels 

In June 2008 the National Earthquake Hazards Reduction Program (NEHRP) sponsored a PBSD workshop 

for leading practitioners and researchers from around the United States to develop a comprehensive list of 

research needs to foster full development and implementation of PBSD. From this workshop, the Building 

Seismic Safety Council (BSSC) reported a prioritized list of key PBSD research and implementation needs 

in NIST GCR 09-917-2: Research Required to Support Full Implementation of Performance-Based Seismic 

Design (NIST 2009a). The highest priority need identified in this report was to “benchmark” current PBSD 

methodologies (e.g., ASCE 41) with code procedures for design of new buildings. Two observations from 

the report were that among workshop participants (1) ASCE 41 procedures are perceived to be overly 

1-4
 
 

conservative and (2) existing PBSD methods are not accepted by practitioners as providing a uniform level 

of confidence. A supporting reason for these two observations was that no systematic effort had been 

undertaken to benchmark structural performance as determined using ASCE 41 procedures, together with 

widely accepted procedures for designing new buildings using ASCE 7. 

Additionally, needs for the advancement of PBSD have been highlighted by other researchers and 

practitioners (Toranzo-Dianderas 2009, SEAONC 2010, Paret, Searer, and Freeman 2011, and Pekelnicky 

and Poland 2012). The needs identified include, but are not limited to the following: 

 Calibration / comparison of ASCE 41 to ASCE 7 

 Reduced conservatism in linear procedures and acceptance criteria 

 Better clarification of provisions and intent 

Therefore, the research study presented in this report was undertaken in an effort to address some of these 

needs. 

1.2 Scope of Project 

This report presents the results of a structural seismic performance assessment using ASCE 41 procedures 

and performance measures of buildings utilizing steel eccentrically braced frames (EBF) as the lateral forceresisting system (LFRS)3 

. 

A suite of archetype buildings that incorporate EBFs along one principal direction of the buildings is 

designed in accordance with ASCE 7. The suite consists of 4-, 8-, and 16-story buildings designed using 

both the Equivalent Lateral Force (ELF) Procedure and Modal Response Spectrum Analysis (RSA). Both 

analysis procedures are used to provide a generally applicable range of LFRS strength within the selected 

seismic intensity region. As such, components of an LFRS may include significant overstrength4

 to resist 

nonseismic loads or to satisfy other design criteria. A design space is created to investigate the effects of 

design methodology, building height, and other LFRS-specific geometric modifications on seismic 

performance. In reality, the design space is infinitely large and many design choices made in this study can 

also have different configurations to evaluate the variation in performance specific to a design choice (e.g., 

study of a range of doubler plate thicknesses in an SMF and the influence on frame column performance). 

The seismic performance assessment of the building suite is conducted using both linear and nonlinear 

analysis procedures prescribed in ASCE 41: 

 Linear Static Procedure (LSP) 

3 Although the LFRS is a component of a cohesive three-dimensional building system that includes structural framing intended to 

primarily resist gravity loads and nonstructural components, only the performance of the LFRS as identified by ASCE 41 

procedures and measures is presented. The performance of an LFRS can be influenced by the inclusion of gravity framing in a 

analysis. Based on the analytical modeling used in this study, this interaction is deemed to be negligible because the LFRS resists 

nearly all forces and deformations resulting from lateral loads and movement. 

4 Overstrength is defined here as the additional elastic strength in a component that is in excess of the required minimum seismic 

strength. 

1-5
 
 

 Linear Dynamic Procedure (Response Spectrum) (LDP) 

 Nonlinear Static Procedure (NSP) 

 Nonlinear Dynamic Procedure (NDP)
 

For this study, the performance assessment targets the Basic Safety Objective (BSO) prescribed in ASCE 

41. This objective includes the interrelated goals of Life Safety (LS) Building Performance Level (BPL) at 

the Basic Safety Earthquake-1 (BSE-1) earthquake hazard level (EHL) and Collapse Prevention (CP) BPL 

at the BSE-2 EHL (see Table 1-2 above). This performance objective is chosen to align with the intended 

structural performance objective of an ordinary building5

 in ASCE 7, which is qualitatively defined here as 

“life safety” provided by collapse prevention of the building, given a maximum considered earthquake 

(MCE) event. 

To evaluate seismic assessment criteria, each component of the EBFs is designated as a primary member 

(or component) in accordance with ASCE 41 §2.2.5 (and ASCE 41 §2.4.4.2). Similarly, quantitative 

performance measures (i.e., acceptance criteria) for primary components are used for all assessment 

procedures, although performance measures for secondary components are permitted by ASCE 41 for some 

primary components. The consistent use of primary acceptance criteria keeps all components and associated 

assessment results correlated among the assessment procedures for this study. 

The goals of this research are as follows: 

 Assess new structural steel buildings utilizing EBFs designed per ASCE 7 requirements and, in 

turn, evaluated using ASCE 41, 

 Develop a qualitative link between the performance implied in ASCE 7 in light of the performance 

identified by ASCE 41 procedures and performance measures, 

 Provide guidance or technical support for improved or new provisions in ASCE 41 (and to a lesser 

extent, ASCE 7), 

 Reduce uncertainty in first-generation PBSD procedures for performance-based seismic 

assessment, and 

 Identify any inconsistencies, ambiguities, and confusing provisions in ASCE 41. 

This report does not discuss the correlation between deterministic performance metrics for components 

(e.g., m-factor in ASCE 41) and the system (e.g., R-factor in ASCE 7)—a topic for future research and one 

that is required to establish the link between the performance of an ASCE 7 code-compliant design and the 

associated performance identified by ASCE 41 procedures and performance measures. Here, it is assumed 

that the acceptance criteria for each BPL in ASCE 41 Chapter 5 are quantitatively rational and accurate 

interpretations of what deformations / actions are appropriate for the intended structural performance (see 

ASCE 41 Tables C1-2, C1-3, and C1-4). Clearly, this is a subjective and, at times, controversial topic, as 

some component actions are physically qualified only by experimental test results (i.e., SAC project, see 

FEMA 351 (FEMA 2000b)), but not necessarily for all performance levels. 

5 Buildings assigned Risk Category I or II. 

1-6
 
 

In this report, the archetype building designs are presented in Chapter 2. Next, the results from the seismic 

assessment in accordance with ASCE 41 and supplementary discussions are presented in Chapter 3. In the 

discussion of the assessment results, special focus is given to highlighting any notable differences or 

similarities between ASCE 41 and ASCE 7 (including the referenced design standards in ASCE 7 for the 

design of structural steel buildings) and to making suggestions for improvements in ASCE 41. Conclusions 

are provided in Chapter 4. Selection and scaling of ground motions, including pertinent ground motion data, 

for the NDP are provided in Appendix A. Additional information applicable to the design of the archetype 

buildings and detailed design calculations for a few example members and connections are provided in 

Appendix B. Detailed assessment calculations for a few example members and connections are provided in 

Appendix C. 

The hope is that other follow-on projects will be undertaken by NIST and / or other organizations to provide 

additional data sets that advance the state-of-practice and state-of-knowledge and facilitate the 

implementation of performance-based seismic engineering in design of buildings. Further studies of 

structural steel systems (e.g., buckling-restrained braced frames), as well as studies of reinforced concrete 

moment frame and shear wall buildings, are planned as next steps at NIST. 

1-7
 
 

1-8
 
Chapter 2 Overview and Design of Archetype Buildings 

This chapter presents the design of the archetype buildings. General discussions are provided in Section 2.1 

on the geometry of the buildings and the design criteria, including sizes of structural members not 

considered to principally resist lateral loads. Section 2.2 discusses the structural design loads and associated 

design criteria specific to them. Section 2.3 presents information regarding the structural analysis and 

mathematical model used in the structural member selection process. Section 2.4 provides the design of the 

structural systems principally required to resist lateral loads and stabilize the buildings. 

2.1 General Information 

A suite of three steel-framed office buildings is investigated in this study. It is presumed that the archetype 

buildings will be constructed in a high seismicity area (e.g., somewhere along the west coast of the United 

States—see Earthquake Forces section below). Building stability and resistance to environmental loads and 

deformations is provided by special moment frames along the East-West (E-W) direction and eccentrically 

braced frames along the North-South (N-S) direction. All lateral force-resisting systems (LFRS) are 

symmetrically located at the perimeter of the building and orthogonal. For purposes of design, the identified 

LFRS acts as both the seismic force-resisting system (SFRS) and the main wind force-resisting system 

(MWFRS). For completeness of the full design of the archetype buildings, design of both LFRSs is 

presented below. However, only the assessment of the braced frames will be presented in this report. 

Assessment of the moment frames is presented in NIST TN 1863-1: Assessment of First Generation 

Performance-Based Design Methods for New Steel Buildings, Volume 1: Special Moment Frames (Harris 

and Speicher 2015a). 

Each building is rectangular in plan, with five 30-foot bays in the E-W direction and generally five 20-foot 

bays in the N-S direction. The plan dimensions for all floors and roofs are 152 feet in the E-W direction 

and 102 feet in the N-S direction. For all buildings, the height of the first story is 18 feet and the remaining 

story heights are 14 feet. A summary of the geometric structural characteristics of each building is provided 

in Table 2-1. Building schematics are shown in Figure 2-1 through Figure 2-3. The typical floor framing 

plan is shown in Figure 2-4 and Figure 2-5. For brevity, the building schematics do not show symmetrical 

elevator core or stairwell diaphragm openings. 

Table 2-1. Structural Characteristics of Archetype Buildings 

Bldg. ID Stories E-W 

Dimension 

N-S 

Dimension 

E-W 

LFRS 

N-S 

LFRS Notes 

ME4 4 150’ = 5 bays 

@ 30’ 

100’ = 5 bays 

@ 20’ SMF EBF 

SMF: 3–30-foot bays 

EBF: 1–20-foot bay short link with HSS 

braces 

ME8

ME16 

8 

16 

150’ = 5 bays 

@ 30’ 

150’ = 5 bays 

@ 30’ 

100’ = 5 bays 

@ 20’ 

100’ = Varies – 

see Figure 2-5 

SMF 

SMF 

EBF 

EBF 

SMF: 3–30-foot bays 

EBF: 1–20-foot bay short link with HSS 

braces 

SMF: 3–30-foot bays 

EBF: 1–30-foot bay short link with WSection braces 

2-1
 
Figure 2-1. Isometric View of ME4 Archetype Building 

Figure 2-2. Isometric View of ME8 Archetype Building 

2-2
 
Figure 2-3. Isometric View of ME16 Archetype Building 

2-3
 
 

 

5 @ 30'-0" = 150'-0" 

5 @ 20'-0" = 100'-0" 

W14×22 

See SMF Elev. 

Section 2.4.1 

W14×22 W14×22 

W16×26 

W16×26W16×26 

W27×84W27×84 

Sym. About 

Sym.

About 

W16×26 

See EBF Elev. 

Section 2.4.2 

A B C D E F 

1 

2 

3 

4 

5 

6 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

W16×26 

Note: All non-SFRS beams and girders are composite. 

Figure 2-4. Typical Floor Framing Plan, ME4 and ME8 

5 @ 30'-0" = 150'-0" 

30'-0" 

W14×22 

See SMF Elev. 

Section 2.4.1 

W14×22 W14×22 

W16×26 

W16×26W16×26 

W27×84W27×84 

Sym. About 

Sym.

About 

W16×26 

See EBF Elev. 

Section 2.4.2 

A B C D E F 

1 

2 

3 

4 

5 

6 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

W14×22 W14×22 

W14×22 

W14×22 W14×22 

W14×22 

W16×26 

40'-0" 

20'-0" 15'-0" 

Note: All non-SFRS beams and girders are composite. 

Figure 2-5. Typical Floor Framing Plan, ME16 

2-4 
The archetype buildings are analyzed and designed for all load effects in accordance with the following: 

 IBC 2012: International Building Code (ICC 2012b) 

 ASCE 7-10: Minimum Design Loads for Buildings and Other Structures (ASCE 2010) 

 AISC 360-10: Specification for Structural Steel Buildings (AISC 2010a) 

 AISC 341-10: Seismic Provisions for Structural Steel Building (AISC 2010b) 

 AISC 358-10: Prequalified Connections for Special and Intermediate Steel Moment Frames for 

Seismic Applications (AISC 2010c) 

The following material types and corresponding nominal properties were assumed in design: 

 Wide-Flange Sections: A992 Grade 50, Fy = 50 ksi, Ry = 1.1 

 HSS Sections: A500 Grade B, Fy = 46 ksi, Ry = 1.4 

 Connections: A572 Grade 50, Fy = 50 ksi, Ry = 1.1 

 E = 29000 ksi, G = 11200 ksi,  = 0.3 

The archetype buildings do not contain any geometry-based or configuration-based horizontal irregularities, 

Type 2, 3, 4, or 5 as defined in ASCE 7 Table 12.3-1. Horizontal irregularity Type 1 is dependent on postdesign analysis verification, and is presented in Appendix B. Similarly, the archetype buildings do not 

contain any geometry-based or configuration-based vertical irregularities, Type 2, 3, or 4 as defined in 

ASCE 7 Table 12.3-2. Vertical irregularity Types 1 and 5 are dependent on post-design analysis verification 

and are presented in Appendix B. The buildings are classified as Risk Category II structures in accordance 

with ASCE 7 §1.5. 

2.2 Structural Design Loads 

 Load Combinations 

Loads and load combinations used for analysis and strength design of members and connections are in 

accordance with ASCE 7 §2.3, including modifications to these combinations prescribed in ASCE 7 §12.4. 

This resulted in 189 load combinations for design of each component. Capacity design provisions for each 

SFRS type prescribed in AISC 341 as well as for beam-to-column connections in an SMF prescribed in 

AISC 358 provided several design load combinations in addition to those from ASCE 7. 

Loads and load combinations for serviceability analysis and verification (e.g., wind drift), and seismic drift 

analysis and allowable drift compliance verification are discussed subsequently under Environmental 

Loads, §2.2.3. 

 Gravity Loads 

The floor and roof dead load consists of the weight of the steel members, metal deck, and concrete slab 

weight (31⁄4 inch lightweight concrete at 110 pcf on 18-gage, 3 inch metal deck ≈ 46 psf). Superimposed 

dead loads are taken as 15 psf for floors and 10 psf for the roof, representing mechanical, electrical, 

plumbing, and miscellaneous dead loads. A 250 plf superimposed dead load is also applied to the perimeter 

2-5
 
6

 

 

horizontal framing to account for façade (curtain wall) weight. The edge of the slab is 1 foot from the 

perimeter framing. The design live load (unreduced) is 50 psf for floors and 30 psf for the roof (increased 

live load within egress areas is neglected in this study). A summary of the design gravity loads is presented 

in Table 2-2. 

Table 2-2. Design Gravity Loads 

Load Load Type Magnitude 

Dead, D Dead 46 psf 1 

Floor Superimposed Dead, SD Dead 15 psf 

Roof Superimposed Dead, SD Dead 10 psf 

Façade Dead (Curtain Wall), SD Dead 250 plf 

Unreduced Design Floor Live, Lo Floor Live 50 psf (Office) 

Unreduced Design Roof Live, Lo Roof Live 30 psf 2 

1 Weight of slab and metal deck only. Self-weight of steel components are included automatically in the structural analysis. 2 10 psf was added to the roof live load to represent non-inertial service equipment weight. 

Verification of serviceability criteria under gravity loads is performed per IBC §1604.3, ASCE 7 §1.3.2, 

and AISC 360 Chapter L.

 Environmental Loads 

Earthquake Forces 

The archetype buildings are located where it is assumed they would be assigned a Seismic Design Category 

(SDC) at the upper limit of D (i.e., Dmax—see footnote 6). Two designs are produced for each archetype 

building height and frame type as follows: 

 One design using the ELF procedure per ASCE 7 §12.8 to determine the equivalent seismic effects. 

 One design using the RSA procedure per ASCE 7 §12.9 to determine the equivalent seismic effects. 

Two designs are performed to provide a common range of potential system strengths for seismic assessment 

using ASCE 41, and to a lesser extent, provide comparison points between the two design methodologies. 

There are cases when the two designs do not result in different member sizes because of material-specific 

minimum requirements. Further, wind effects are determined from statically applied design forces and thus 

the analysis method for wind does not vary between the two seismic analyses. 

For the RSA procedure, enough modes are included in each principal direction to exceed 90 percent mass 

participation in both horizontal orthogonal directions. Masses were not modeled in the analysis to address 

vertical accelerations. Design forces determined from the RSA are scaled up so that the total modal base 

shear for design is equal to 85 percent of the corresponding base shear from applying the ELF procedure; 

story drifts are not scaled for verifying seismic drift compliance. Application of orthogonal seismic forces 

and accidental eccentricity prescribed in ASCE 7 §12.5 and ASCE 7 §12.8.4, respectively, are considered 

in the strength design analysis. The redundancy factor, , is taken as 1.0 for each SFRS, and therefore does 

not affect the allowable seismic drift limits along the E-W direction (moment frames). 

6 See FEMA P695: Quantification of Building Seismic Performance Factors (FEMA 2009a) for further information. 

2-6
 
 

Effective seismic weights for computing the horizontal earthquake forces are determined from dead loads 

plus 20 percent of the unreduced design floor live loads to represent partition weight (i.e., 0.2×50 psf = 10 

psf). The effective seismic weights (lumped at each level) are tabulated in Appendix B. It is assumed in this 

study that there is no snow load on the building. 

The story gravity loads for seismic drift analysis prescribed in ASCE 7 §12.8.6 (including period 

calculation) and stability verification prescribed in ASCE 7 §12.8.7 are determined from dead loads plus 

25 percent of the unreduced floor live loads (i.e., 0.25×Lo ≈ 0.5L where L is the reduced floor live loads). 

Roof live loads are considered not to be present for seismic drift analysis. The effective lumped gravity 

load acting on a story is tabulated in Appendix B. Vertical seismic loads are considered for strength design 

but not for drift or stability compliance. Similarly, application of orthogonal seismic forces and accidental 

eccentricity are not considered in the drift analysis because story drifts are computed at the center of mass 

(which aligns with the center of stiffness) of each story because of building symmetry and regularity. The 

centers of mass for all stories are vertically aligned. 

The seismic hazard in ASCE 7 is based on a risk-targeted design philosophy and is defined as ground 

motions having a one percent probability of causing total or partial structural collapse (i.e., “risk”) of an 

appropriately designed structure in 50 years (except in areas controlled by the deterministic cap7

 on ground 

motions). This ground motion intensity is denoted in ASCE 7 as MCER. The following parameters 

summarize the seismic hazard used for design: 

 Building Risk Category: II 

 Site Soil Conditions: Site Class D, Stiff Soil – ASCE 7 Table 20.3-1 

 Spectral Response Acceleration Parameters: shown in Table 2-3 

 SDC: D—taken as Dmax as used in FEMA P695 

Table 2-3. Spectral Response Acceleration Parameters 

SMS SM1 SDS SD1 Ss S1 3.5×TS SDC Fa Fv = FaSs = FvS1 = 2⁄3SMS = 2⁄3SM1 (g) (g) (sec) (g) (g) (g) (g) 

Dmax 1.50 0.60 1 1.00 1.50 1.50 0.90 1.00 0.60 2.1 

1. S1 is actually just under 0.60 (i.e., 0.599) 

Allowable seismic drift limit is set to hsx / 50 (for amplified story drifts, see ASCE 7 §12.12) where hsx is 

the story height below the level under consideration. Composite action between the beams of the SFRS and 

the concrete slab is not considered for checking seismic drifts or when computing the fundamental period, 

T1. This action is commonly neglected in seismic analysis and design because research has shown that the 

slab does not contribute significantly to the strength or stiffness of the assembly at significant inelastic 

deformations (see FEMA 355D (FEMA 2000c)). 

The seismic analysis and design parameters for each archetype building are provided in Table 2-4 for the 

E-W direction and Table 2-5 for the N-S direction. There are two archetype building systems that are not 

7 Regions where probabilistic-based ground motion parameters exceed those resulting from deterministic ground motions based 

on the characteristic magnitudes of earthquakes from well-defined active fault systems. 

2-7
 
 

 

 

 

 

 

permitted to be designed with the ELF procedure because its design period, CuTa, is greater than 3.5×Ts (see 

ASCE 7 §12.6): E-W component (SMF) and N-S component (EBF) of ME16—these systems are shaded 

in Table 2-4 and Table 2-5. These frames are included to make a seismic performance comparison. 

Furthermore, ASCE 7 is vague about which T is referenced in ASCE 7 §12.6. For example, although the 

capped fundamental period (T = CuTa) may satisfy 3.5×Ts, the actual fundamental period (T = T1) may not, 

indicating that the ELF procedure may be used for strength design but not used for drift verification per 

ASCE 7 §12.8.6.2. Consequently, the same analysis procedure was used for both strength design and 

computation of the design story drifts in this study. 

Table 2-4. Seismic Analysis and Design Parameters, E-W 

Building ME4 ME8 ME16 

SFRS SMF SMF SMF 

R, Cd, o 8, 5.5, 3 8, 5.5, 3 8, 5.5, 3 

CuTa (seconds) 1.04 1.76 3.02 

ELF Permitted? Yes Yes No 8 

Height Limit (feet) No Limit No Limit No Limit 

Analysis Procedure ELF RSA ELF RSA ELF RSA 

W 1

 (kips) 5132 5103 10566 10460 21900 21659 

Vb

 1 Design (kips) 374 316 467 2

 394 2 958 2 810 2 

Vb

 1 Drift (kips) 213 166 273 192 375 295 

Design = 93 Design = 101 Design = 134 RSA Scaling Factor 3 NA NA NA Drift = 266 Drift = 266 Drift =266 

T1

 4 (seconds) 1.82 2.22 2.91 3.81 4.36 5.01 

T2

 4 (seconds) 0.55 0.61 1.02 1.30 1.58 1.83 

T3

 4 (seconds) 0.26 0.29 0.56 0.68 0.91 1.05 

T1

 5 (seconds) 1.83 2.24 2.94 3.86 4.40 5.07 

T1

 6 (seconds) 1.77 2.12 2.79 3.55 4.15 4.70 

Steel Wgt.7

 (tons) 37 29 74 53 193 163 

Notes: 

1 Inertial mass computed from Dead + Superimposed Dead + 0.2×Floor Live. W for ELF and RSA differ because of member size differences. 2 0.044SDSIe min. controls strength design (not applied for drift). 3 Scaling for design = g×Ie / R×(0.85×Vb,ELF) / Vb,RSA. Scaling for drift = g×Ie / R×Cd / Ie. Scaling assumes the spectrum is defined as a function of g. 4 Computed from a second-order eigenvalue analysis with Dead + Superimposed Dead + 0.25×Floor Live gravity load. 5 Computed from a second-order eigenvalue analysis with 1.2×Dead + 1.2×Superimposed Dead + 0.25×Floor Live gravity load. 6 Computed from a first-order eigenvalue analysis. 7 Per single SFRS (see Table 1-1). Does not include connection or miscellaneous steel. 8 Analysis procedure not permitted per ASCE 7 §12.6. Shaded Area: design is included for seismic performance comparison purposes. 

The difference in the stiffness and strength of the EBFs provided by the ELF and RSA procedures is 

negligible when hn is less than say 60 ft. This effect is primarily due to design provisions prescribed in 

AISC 341 (e.g., minimum width-to-thickness ratios). A summary of the equivalent seismic forces for each 

archetype building is provided in Appendix B. 

Wind Forces 

Basic wind speeds are taken from the ASCE 7 wind maps based on locations along the west coast that 

would have a high probability of producing structures assigned to SDC D. The basic wind speed is taken 

to be 110 mph for the 700-year wind for strength design of components and 72 mph for the 10-year wind 

for verifying story drifts (serviceability). Each archetype building is assigned to Exposure B and is not 

considered rigid, with gust factors, Gf, for each principal direction computed assuming two percent 

damping. Torsional wind effects are considered, and the directionality factor, kd, is 0.85. A summary of the 

wind forces for each archetype building is provided in Appendix B. 

Allowable wind drift limit is set to hsx / 400 (elastic) for the 10-year wind. Composite action between the 

beams of the MWFRS and the concrete slab is considered for checking wind drift and when computing the 

2-8
 
 

 

 

 

 

 

 

fundamental period, T1, for wind vibrations using an average Ieff as recommended in AISC 360 commentary 

for Chapter I. The same gravity load combination used for the seismic drift analysis is used in the wind drift 

analysis (see previous discussion under Earthquake Forces—§2.2.3.1). 

Not all practitioners will use the 10-year wind to verify drift compliance (see ASCE 7 commentary for 

Appendix C); the 25-year or 50-year may be used, depending on project-specific requirements. The 10-year 

wind is considered appropriate for these structures, as the façade (curtain wall) is designed to accommodate 

large in-plane seismic movements, and period control (i.e., acceleration) is typically not a concern for 

building geometries in the range used for this investigation. 

Table 2-5. Seismic Analysis and Design Parameters, N-S 

Building ME4 ME8 ME16 

SFRS EBF EBF EBF 

R, Cd, o 8, 4, 2 8, 4, 2 8, 4, 2 

CuTa (seconds) 0.90 1.48 2.46 

ELF Permitted? Yes Yes No 8 

Height Limit (feet) 240 240 240 

Analysis Procedure ELF RSA ELF RSA ELF RSA 

W 1

 (kips) 5132 5103 10566 10460 21900 21659 

Vb

 1 Design (kips) 425 359 534 449 964 2 810 2 

Vb

 1 Drift (kips) 370 312 370 315 505 474 

Design = 56 Design = 69 Design = 83 RSA Scaling Factor 3 NA NA NA Drift = 193 Drift = 193 Drift = 193 

T1

 4 (seconds) 1.04 1.08 2.14 2.46 3.19 3.83 

T2

 4 (seconds) 0.41 0.42 0.72 0.79 0.99 1.11 

T3

 4 (seconds) 0.24 0.25 0.40 0.44 0.53 0.58 

T1

 5 (seconds) 1.04 1.09 2.15 2.47 3.21 3.85 

T1

 6 (seconds) 1.03 1.07 2.09 2.38 3.11 3.68 

Steel Wgt.7

 (tons) 11 11 28 21 123 88 

Notes: 

1 Inertial mass computed from Dead + Superimposed Dead + 0.2×Floor Live. W for ELF and RSA differ because of member size differences. 2 0.044SDSIe min. controls strength design (not applied for drift). 3 Scaling for design = g×Ie / R×(0.85×Vb,ELF) / Vb,RSA. Scaling for drift = g×Ie / R×Cd / Ie. Scaling assumes the spectrum is defined as a function of g. 4 Computed from a second-order eigenvalue analysis with Dead + Superimposed Dead + 0.25×Floor Live gravity load. 5 Computed from a second-order eigenvalue analysis with 1.2×Dead + 1.2×Superimposed Dead + 0.25×Floor Live gravity load. 6 Computed from a first-order eigenvalue analysis. 7 Per single SFRS (see Table 1-1). Does not include connection or miscellaneous steel. 8 Analysis procedure not permitted per ASCE 7 §12.6. Shaded Area: design is included for seismic performance comparison purposes. 

2.3 Structural Analysis and Mathematical Model 

The archetype buildings are analyzed in ETABS, ver. 9.7.4 (CSI 2011a). A conventional second-order 

elastic analysis is used to determine the required strength of components, and member and story 

deformation demands (elastic and virtual inelastic). This type of analysis uses a constant reduced stiffness 

matrix based on an initial gravity (i.e., P-) load combination applied in a pre-analysis as follows: 

 P- load combination for strength analysis: 1.2×Dead + 0.25×Floor Live 

 P- load combination for drift and stability verification analysis: 1.0×Dead + 0.25×Floor Live 

The analyses do not account for material nonlinearity or geometric imperfections (except for gravity-only 

load combinations—see AISC 360 Chapter C). Because the stiffness matrix remains constant for all loads, 

superposition of individual load effects in load combinations is applicable. 

2-9
 
 

Each building is considered globally restrained horizontally, vertically, and rotationally at the seismic base 

(taken at grade level). The base columns of the LFRSs are embedded into the foundation wall. As such, 

column bases are modeled as rotationally restrained in the plane of the frames and rotationally unrestrained 

out-of-plane. Non-SFRS gravity column bases are considered rotationally unrestrained in both orthogonal 

directions. 

The mathematical models are based on centerline dimensions with rigid end offsets at the beam-to-column, 

brace-to-beam / column, and brace-to-beam joints with panel zones explicitly modeled based on column 

web and doubler plate (if required) geometry. The slabs are modeled as semi-rigid membrane diaphragms 

(no out-of-plane bending stiffness) with a 0.5 in-plane stiffness modifier to account for cracking at the 

design loads—see NIST GCR 11-917-10: Seismic Design of Composite Steel Deck and Concrete-filled 

Diaphragms: A Guide for Practicing Engineers (NIST 2011b). 

In the moment frames, reduced beam sections (RBS) are explicitly modeled in all SMF beams by 

subdividing each member into seven segments; the RBS is modeled as two linearly-tapered sections. The 

typical fully restrained (FR) beam-to-column connection is illustrated in Figure 2-6, and the equivalent 

assembly model for linear analysis is shown in Figure 2-7. 

c 

c 

a b 

Section A-A 

Reduced Beam 

Section Continuity Plates 

typ., if required 

Doubler Plate, 

if required 

Panel Zone 

A A

Figure 2-6. Typical Type FR RBS Beam-to-Column Connection Assembly 

In the eccentrically braced frame, links beams are modeled with standard beam sections that span between 

the two work points. Rigid end zones are included to capture gusset plate rigidity outside the link—see 

Figure 2-8. The member ends of the EBF diagonal braces are rotationally unrestrained out-of-plane and 

restrained in-plane. Similarly, rigid end zones are included to capture gusset plate rigidity; the tangible 

length of EBF braces is approximately equal to 90 percent of the distance between work points, Lwp. Beams 

2-10
 
 

adjacent to links are fully restrained in the plane of the frame to the adjacent columns. All members were 

analyzed with gravity loads. 

a b 

c 

c 

Section A-A
 

Reduced Beam 

Section 

Column, EIc 

a b/2

node 

A 

Column, EIc 

Panel Zone Spring 

Line Element, 

typ. 

Panel Zone Boundary 

A
 

Rigid End
 

Zone, typ.
 

Beam, EIb 

Figure 2-7. Type FR RBS Beam-To-Column Connection Subassembly Model for Linear Analysis 

Figure 2-8. Brace-to-Beam Connection Subassembly Model for Linear Analysis 

Non-LFRS framing that primarily supports gravity loads is included in the mathematical models to capture 

the “leaning column” effect. The gravity beams are modeled as composite beams with rotationally 

2-11
 
unrestrained member ends (i.e., shear tab connections). The gravity columns are modeled as continuous 

along the height of the building and designed for deformation compatibility. The increase in lateral stiffness 

along the two principal axes due to these columns is negligible. Other than the columns, no other forms of 

lateral stiffness attributed to non-SFRS framing (e.g., stairs) and nonstructural components are considered 

in the mathematical model. 

2.4 SFRS Design 

 SMF Design 

SMF designs are included here to provide the required information of the building for EBF designs. For the 

SMF designs, seismic drift criteria prescribed in ASCE 7 §12.12 tended to control member sizes for both 

4-story archetype buildings and the 8-story ELF-designed archetype building. The seismic stability criteria 

prescribed in ASCE 7 §12.8.7 tended to control member sizes for the 8-story RSA-designed archetype 

building and both 16-story archetype buildings (ELF design was more drift controlled than the RSA design). 

The strong-column / weak-beam (SCWB) criteria using an amplified seismic load (axial) and section 

compactness requirements provided additional constraint on column sizes where required. 

The RBS beam-to-column connections were designed in accordance with AISC 358 with the flange cut out 

dimensions optimized to produce the lowest probable moment, Mpr. Because the bay length did not change, 

the same beam depth was used for a given floor for uniform connection constructability and plastic hinge 

sequencing optimization (i.e., yield rotation is theoretically equal). The panel zones are designed for 

demands based on the probable moment of the RBS projected to the column face using nominal material 

properties. AISC 360 §J10.6 (b) is applicable for panel zone design because the effect of panel zone 

deformations on frame stability is explicitly considered in the analysis. The flow chart in Figure 2-9 

illustrates the analysis and design process for an SMF. Additional details on design and construction of 

special moment frames can be found in NIST GCR 09-917-3: Seismic Design of Steel Special Moment 

Frames: A Guide for Practicing Engineers (NIST 2009b). 

To reflect industry practice and reduce fabrication costs, column sizes were increased from that required 

by analysis rather than adding doubler plates. AISC Design Guide 13 (AISC 1999) and Troup (1999) 

showed that increasing the column size by up to 100 plf to eliminate both continuity plates and doubler 

plates was often the more economical alternative. Some seismic specifications (e.g., AISC 341), however, 

either require or suggest the use of transverse stiffeners in all high seismic applications. For these cases, 

eliminating the need for doubler plates alone may still prove to be the economical choice (Lee et al. 2002). 

In this study, this increase typically occurred at interior frame columns and on average was 100 plf for the 

frame as a whole. 

The Effective Length Method (see AISC 360 §C1) is used for design of the SMF columns, with the Story 

Buckling Method (see commentary for AISC 360 Appendix 7) used to compute the effective length, KL = 

2-12
 
8

 

   

   

   

   

   

     

   

   

     

       

K2L (see footnote 8) for determining the nominal compression strength, Pn, of the column in the plane of 

the frame. In all but one SMF, at least one story had B2, as defined in AISC 360 Appendix 8, greater than 

1.1; all stories were less than 1.5 (see AISC 360 Appendix 7). Tabulated values for B2 are provided in 

Appendix B. KL = L was adopted for determining Pn of the column out-of-plane of the frame. 

Iterate analysis

and design

No Good?

Strength Analysis
 

per ASCE 7.
 

Design Frame
 

Beams and Beam‐

to‐Column
 

Connections
 

Capacity Design
 

Analysis per AISC
 

341.
 

Design Columns
 

and Panel Zones.
 

Drift and Stability

Analysis per

ASCE 7

Verify Design

Story Drift NOGOOD?

Update Member

Sizes

GOOD?

END

Good?

Figure 2-9. Flow Chart of SMF Design Process 

Computation of in-plane effective length factors is generally considered to be not required for columns in 

regular moment frames in high seismicity areas (i.e., adopting KL = L). Seismic story drift and stability 

requirements in ASCE 7 typically result in significant in-plane story strength and stiffness above that 

required by the analysis. However, the concept of story drift control without consideration of its effects on 

a moment frame is a nontechnical rationale for neglecting the effective length factors for in-plane seismic 

design of frame columns. Essentially, the effects of drift control reduce the error in calculating the beam8

 AISC 360-05 (AISC 2005) used the term K2 to define the in-plane effective length factor. AISC 360-10 Appendix 7 uses K in lieu 

of K2. However, K2 is still used in the commentary of Appendix 7. Therefore, K2 is also used here. Additional information can be 

found in Steel Design Guide 28: Stability Design of Steel Buildings (AISC 2013). 

2-13
 
 

column strength for load combinations including lateral forces because of the following (taken from White 

and Hajjar 1997): 

 The in-plane, strong-axis radius of gyration, rx, is increased thus lowering KL / rx in the design 

equation. Column strength varies little with large variations of KL / rx. 

 The columns are heavily restrained at each end by deep beams, and subjected to nearly doublecurvature bending under sideway of the frame. 

 The beam-column interaction check for the lateral force-resisting columns is dominated by the 

moment term. 

Designers must also consider the vertical strength of a story9

 loaded only with gravity-type loads, as well 

as the correlation of the actual demand relative to this vertical strength (e.g., Pstory / Pe,story as defined in 

AISC 360 Appendix 8). This story strength would represent the minimum value of Pn (in the absence of 

moment) for construction of the P-M interaction diagram for the in-plane strength of a frame column in the 

story. Fundamentally, the effective length factor for a column is a function of the frame deformation 

demands and the loading on the column. Consequently, a P-M interaction diagram would need to be 

constructed for each category of load combination (e.g., vertical load, vertical plus horizontal loads) 

considering the influence of the ratio of vertical to horizontal loading demands as well as which loading is 

being incremented until incipient buckling. Theoretically, KL = L should be adopted when the physical 

behavior of the column at its ultimate strength aligns with the theoretical definition of the compression 

strength. Future studies should investigate designing the selected frames using the Direct Analysis Method 

prescribed in AISC 360 Chapter C. 

In proportioning frame members for this study, section depths were selected to maintain a low in-plane 

relative beam-to-column stiffness ratio, G. AISC 360 commentary for Appendix 7 defines G for bending 

about the strong-axis as Equation (2-1)—see AISC 360 for definitions of the variables and subscripts. 

EI x,c

 b Lc G  (2-1) EI x,b

 Lb 

Other relationships can be used to show that G can be computed as function of the in-plane flexural section 

strength, Zx×Fy, independent of the in-plane flexural stiffness, E×Ix. Equation (2-2) shows that the strongaxis plastic section modulus, Zx, is a function of the strong-axis moment of inertia, Ix, and section depth, d. 

Equation (2-3) rewrites the SCWB equation in AISC 341 (see §E3.4a) for a wide-flange section. 

2I x Zx  (2-2) d 

9 The vertical story strength, Pe,story, is a function of the elastic lateral stiffness of the story. 

2-14
 
 

 

  P   u, min 1.18 1    ,1.0 ZF ,

M p c, 

 

 Py 

 

 xc y   Pu,   (2-3)  1 Z x,b  min 1.18 1    ,1.0  Zx,c M Z F P  

p b, x,b y   y  

 b d Lc b   G   P   d L u, b c (2-4) min 1.18 1    ,1.0  P    y    

In the previous equations, Pu, is the axial load demand in the column including the system overstrength 

factor, o, in ASCE 7 as required by AISC 341 §E3.4a. An additional rule of thumb is that dc ≥ db / 2 and 

dc ≤ db. For example, an 18-inch deep column and 24-inch deep beam were selected for the SMF in the 8­

story building. Conservatively assuming a 15 percent reduction in plastic flexural strength of the column 

leads to G = 1.9 (see Equation (2-5)). A 27-inch deep column and 36-inch deep beam could also have been 

selected, but this would have been at the expense of architectural constraints and construction budget. 

 b d L b 1.0 360 c dc 18 G    2.52 1.9  P dL 0.85 d 168 24 u,  o b c b (2-5) 1.18 1      Py 

This approach assists in selecting member depths while attempting to minimize relative elastic flexural 

stiffness variations between the beams and columns within a story, and between adjacent stories. As 

discussed previously, computing G is not required unless the size of the frame column is governed by 

strength requirements and one is using the Effective Length Method; tabulated values for K are provided in 

Appendix B. 

The lateral force distributions and story shears for each archetype building are provided in Appendix B. 

Allowable drift compliance verification is provided in Appendix B. Similarly, verification for drift 

amplification from global p-delta (P-) effects and ASCE 7 stability verification are also provided in 

Appendix B. Design calculations for select members and connections are provided to illustrate the design 

process in Appendix B. 

The 4-, 8-, and 16-story SMF frame designs are shown in Figure 2-10 through Figure 2-12. Each figure 

shows both the RSA design (a) and the ELF design (b)—underlined member sizes indicate changes from 

the RSA design. These figures also provide the RBS dimensions and fundamental periods of the archetype 

building for various gravity loads (e.g., drift and strength design). 

2-15
 
 

(a) RSA 

W14×132 W14×132

W14×193 W14×193 

(b) ELF 

W14×159 W14×145

W14×233 W14×257 

Figure 2-10. 4-Story SMF Schematic 

2-16
 
(a) RSA 

W18×175 W18×106

W18×192 W18×192 W18×143 W18×119 

W18×71 W18×55 

Figure 2-11. 8-Story SMF Schematic 

2-17
 
(b) ELF 

Figure 2-12. 8-Story SMF Schematic, Cont’d 

2-18
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 @ 30'-0" = 90'-0" 

Sym. A bou t 

= Panel Z on e 

= Colu mn Splice 

W33×13 0 RBS 

W27×33 6 W27×23 5

W27×36 8 W27×36 8 W27×28 1 W27×28 1 

W27×19 4 W27×16 1 

1 

1 2 3 

2 3 4 

5 

4 5 6 

6 7 8 

9 

7 8 9 

10 11 12 

13 

10 11 12 

14 15 16 

17 

13 14 15 

18 19 20 

21 

16 17 18 

22 23 24 

25 

19 20 21 

26 27 28 

29 

22 23 24 

30 31 32 

RBS Dim ension s: 

W24×55 a = 3.75", b = 16", c = 1.75" 

W27×94 a = 5.00", b = 18", c = 2.50" 

W30×10 8 a = 5.25", b = 20", c = 2.50" 

W33×13 0 a = 5.75", b = 22", c = 2.75" 

W27×94 RBS 

W27×94 RBS 

W24×55 RBS 

W24×55 RBS 

W27×14 6 W27×11 4

W27×23 5 W27×23 5 W27×12 9 W27×12 9 

W27×11 4 W27×94 

33 

25 26 27 

34 35 36 

37 

28 29 30 

38 39 40 

41 

31 32 33 

42 43 44 

45 

34 35 36 

46 47 48 

49 

37 38 39 

50 51 52 

53 

40 41 42 

54 55 56 

57 

43 44 45 

58 59 60 

61 

46 47 48 

62 63 64 

W30×10 8 RBS 

W30×10 8 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

W30×10 8 RBS 

W30×10 8 RBS 

W27×94 RBS 

W27×94 RBS 

W24×55 RBS 

W24×55 RBS 

B C D E 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same Roof
 

(ELEV = 228 ft.)
 

16th Fl o or
 

(ELEV = 214 ft.)
 

15th Fl o or
 

(ELEV = 200 ft.)
 

14th Fl o or
 

(ELEV = 186 ft.)
 

13th Fl o or
 

(ELEV = 172 ft.)
 

12th Fl o or
 

(ELEV = 158 ft.)
 

11th Fl o or
 

(ELEV = 144 ft.)
 

10th Fl o or
 

(ELEV = 130 ft.)
 

9th Floor
 

(ELEV = 116 ft.)
 

8th Floor
 

(ELEV = 102 ft.)
 

7th Floor
 

(ELEV = 88 ft.)
 

6th Floor
 

(ELEV = 74 ft.)
 

5th Floor
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Fundam ental Per iods 

T1 = 4.70 sec (First-Order) 

T1 = 5.01 sec (1.0D + 0.25Lo) 

T1 = 5.07 sec (1.2D + 0.25Lo) 

(a) RSA 

Figure 2-12. 16-Story SMF Schematic 

2-19
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 @ 30'-0" = 90'-0" 

Sym. A bou t 

= Panel Z on e 

= Colu mn Splice 

W33×13 0 RBS 

W27×53 9 W27 ×33 6

W27×36 8 W27 ×36 8 W27 ×30 7 W27×30 7 

W27×25 8 W27×21 7 

1 

1 2 3 

2 3 4 

5 

4 5 6 

6 7 8 

9 

7 8 9 

10 11 12 

13 

10 11 12 

14 15 16 

17 

13 14 15 

18 19 20 

21 

16 17 18 

22 23 24 

25 

19 20 21 

26 27 28 

29 

22 23 24 

30 31 32 

RBS Dim ension s: 

W24×55 a = 3.75", b = 16", c = 1.75" 

W27×94 a = 5.00", b = 18", c = 2.50" 

W30×10 8 a = 5.25", b = 20", c = 2.50" 

W33×13 0 a = 5.75", b = 22", c = 2.75" 

W27×16 1 W27×12 9

W27×28 1 W27×28 1 W27×23 5 W27×12 9 

W27×11 4 W27×94 

33 

25 26 27 

34 35 36 

37 

28 29 30 

38 39 40 

41 

31 32 33 

42 43 44 

45 

34 35 36 

46 47 48 

49 

37 38 39 

50 51 52 

53 

40 41 42 

54 55 56 

57 

43 44 45 

58 59 60 

61 

46 47 48 

62 63 64 

W30×10 8 RBS 

W30×10 8 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

W30×10 8 RBS 

W30×10 8 RBS 

W24×55 RBS 

W24×55 RBS 

B C D E 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

same 

W27×94 RBS 

W27×94 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

W33×13 0 RBS 

Roof
 

(ELEV = 228 ft.)
 

16th Fl o or
 

(ELEV = 214 ft.)
 

15th Fl o or
 

(ELEV = 200 ft.)
 

14th Fl o or
 

(ELEV = 186 ft.)
 

13th Fl o or
 

(ELEV = 172 ft.)
 

12th Fl o or
 

(ELEV = 158 ft.)
 

11th Fl o or
 

(ELEV = 144 ft.)
 

10th Fl o or
 

(ELEV = 130 ft.)
 

9th Floor
 

(ELEV = 116 ft.)
 

8th Floor
 

(ELEV = 102 ft.)
 

7th Floor
 

(ELEV = 88 ft.)
 

6th Floor
 

(ELEV = 74 ft.)
 

5th Floor
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Fundam ental Per iods 

T1 = 4.15 sec (First-Order) 

T1 = 4.36 sec (1.0D + 0.25Lo) 

T1 = 4.40 sec (1.2D + 0.25Lo) 

(b) ELF 

Figure 2-13. 16-Story SMF Schematic, Cont’d 

2-20
 
 

   

     

   

     

   

   

     

     

       

       

 EBF Design 

For the EBF designs, the seismic strength requirements prescribed in ASCE 7 controlled the link beam sizes 

for all archetype buildings. Section compactness and capacity design requirements prescribed in AISC 341 

governed brace sizes and initial column sizes. Limiting the plastic link rotation angle (i.e., story drift) to 

the allowable permitted by AISC 341 governed the size of columns in the 8- and 16-story ELF-designed 

frames. These columns are oversized from that required by ASCE 7 analysis to increase the flexural stiffness 

of these frames. The elastic lateral drift of a slender braced frame can be dominated by the global flexural 

mode of deformation more than the shear mode because of the prescribed lateral force distribution in ASCE 

7. This deformation patter can result in apparent high link rotation demands in the upper stories of tall 

frames, e.g., 8-stories or higher. Figure 2-13 illustrates the analysis and design process for an EBF. 

Strength Analysis

per ASCE 7.

Design Shear

Links.

Capacity Design

Analysis per AISC

341.

Design Braces,

Columns, and

Beams Outside of

Link.

Good?

Drift and Stability

Analysis per

ASCE 7

Verify Design

Story Drift

NOGOOD?

NOGOOD?

Update Member

Sizes

Update Member

Sizes

GOOD?

Verify Link

Rotation Angle

GOOD?

END

Iterate analysis

and design

No Good?

Figure 2-13. Flow Chart of EBF Design Process 

2-21
 

The Effective Length Method (see AISC 360 §C1) is used for design of the EBF braces, beams (adjacent 

to shear link beams), and columns. The effective length factor, K, was conservatively taken as unity for 

determining the nominal compression strength, Pn, of the EBF members, although a lower value could be 

justified by analysis. 

Table 2-6 summarizes the EBF layout for each building. Using a single bay for the SFRS results in  = 1.3 

per ASCE 7 §12.3.4. However, the increase of  to 1.3 was neglected in the design to minimize member 

overstrength contributions in the seismic performance assessment. 

Table 2-6. EBF Configurations 

No. of bays / No. of frame Bay width, Lb Link length, e Stories Design frame line lines (ft.) (in.) 

4 ELF

RSA 

1 

1 

2 (exterior) 

2 (exterior) 

20 

20 

30 

30 

8 ELF

RSA 

1 

1 

2 (exterior) 

2 (exterior) 

20 

20 

30 

30 

16 

ELF

RSA 

1 

1 

2 (exterior) 

2 (exterior) 

30 

30 

39 

39 

A 30-foot bay was adopted to minimize nonseismic contributions to member selections. This configuration 

change is similar to that done for the design of the 16-story SCBF in NIST TN 1863-2: Assessment of First 

Generation Performance-Based Design Methods for New Steel Buildings, Volume 2: Special 

Concentrically Braced Frames (Harris and Speicher 2015b). However, wind strength requirements 

governed link beam design within the lower stories of the 16-story archetype buildings, as shown in Figure 

2-14. Required shear strengths of link beams governed by seismic or wind necessitated two different design 

equations for computing the nominal shear strength, vVn, depending on the controlling load. Switching 

equations also assisted in minimizing nonseismic contributions to link beam design. 

Design for Wind (per AISC 360) →  V  1.0 0.6 F dt vn   y w (2-6) 

Design for Seismic (per AISC 341) → v n

V  0.9 0.6 F d  2t   y f w t (2-7) 

where d = section depth, tf = flange thickness, and tw = web thickness. Using AISC 341 purposefully to 

design for wind-controlled required strengths would have resulted in approximately a 20 percent increase 

in member design overstrength of the link as compared to that required for seismic design alone. In Figure 

2-14, the nominal story shear strength, Vn,story, is computed using Equation (2-8). 

Lb Vn story ,  v

Vn (2-8) hsx 

where Lb = the bay width and hsx = story height. Short links (e ≤ 1.6 Mp / Vp, see AISC 341 Chapter F3) are 

selected to achieve maximum shear strain ductility for each design; link beam length is kept constant over 

the height of the building for constructability and architectural considerations. A minimum link depth of 14 

inches (W14) is selected for connection constructability and gravity-load carrying capacity. Consequently, 

2-22
 
 

this minimum depth contributes to design overstrength of the link beams in the upper stories where story 

shear demands are relatively low. 

0 200 400 600 800 1000 1200 1400 1600 

Base 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

Story 

Design Story Shear Demand

 EQ (RSA)

 Wind (700-year) 

Nominal Story Shear Strength

 EQ (AISC 341)

 Wind (AISC 360) 

0 200 400 600 800 1000 1200 1400 1600 

Base 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

Story 

Design Story Shear Demand

 EQ (ELF)

 Wind (700-year) 

Nominal Story Shear Strength 

EQ (AISC 341)

 Wind (AISC 360) 

Story Shear (kips) Story Shear (kips) 

(a) RSA (b) ELF 

Figure 2-14. Story Shear Demands and Nominal Strengths, 16-story EBF (N-S ME16) 

In reference to the allowable story drift, assuming a rigid-plastic story mechanism, the (plastic) link rotation 

angle, p, in a given story is 

L  xp s,  p  b (2-9) e hsx 

where Lb = the bay width, e = the link length, hsx = story height, xp,s = the global plastic story shear distortion 

contribution of the design story drift. 

In reference to ASCE 7, the design story drift of story x, x, can be computed from Equation (2-10), which 

is the summation of the elastic, xe, and plastic, xp, story drifts. Each story drift component can be divided 

into a global story shear and flexural deformation components, denoted in Equation (2-10) using the 

subscript s and f, respectively. 

 design ,x

 elastic ,  plastic ,xp

d 

xe 

  (2-10)         C  xe s xe , , f  xe s xe , , f xp s , , xp f Ie 

The plastic story drift component is therefore equal to the difference between the design story drift and the 

elastic story drift component. 

2-23
 
 Cd     xp xp s , xp f ,	      1 , 

I  xe s xe, f  (2-11)  e 

Global flexural deformations do not theoretically contribute to link rotations. Ideally plastic story flexural 

deformations can be removed to get the story shear deformations. 

 C    xp xp s ,	         xp f I 

d 1 xe s , xe , f , (2-12)  e 

Assuming that elastic displacement is equivalent to yield displacement, it can rationally be assumed that 

the contribution of the plastic story flexural deformations to plastic story drift is theoretically zero. 

 Cd        1 xp xp , s  xe 	 (2-13) I  e 

x 3  xp s,   x  

4 4 x	 (2-14) 

Design link rotation angles are provided in Appendix B. 

HSS are used as diagonal braces in the 4- and 8-story archetype buildings, while keeping face dimensions 

within the adjacent column flange widths. Wide-flange sections are used as diagonal braces in the 16-story 

archetype building. The tangible length of the braces is taken equal to 90 percent of the distance between 

work points, Lwp. The effective length factor, K, was conservatively taken as unity for all members, although 

a lower value can be justified for computing the brace design strength for buckling in the plane of the frame. 

Diagonal braces are designed to carry gravity loads—see §2.3. 

The lateral force distributions and story shears for each archetype building are provided in Appendix B. 

Allowable drift compliance verification is provided in Appendix B. Similarly, verification for drift 

amplification from global p-delta (P-) effects and ASCE 7 stability verification are also provided in 

Appendix B. Design calculations for select members and connections are provided to illustrate the design 

process in Appendix B. 

The 4-, 8-, and 16-story EBF frame designs are shown in Figure 2-15 through Figure 2-17, respectively. 

Each figure shows both the RSA design (a) and the ELF design (b)—underlined member sizes indicate 

changes from the RSA design. These figures also provide the fundamental periods of the archetype building 

for various gravity loads (e.g., drift and strength design). 

2-24
 
(a) RSA 

(b) ELF 

Figure 2-15. 4-Story EBF Schematic 

2-25
 
(a) RSA 

Figure 2-16. 8-Story EBF Schematic 

2-26
 
(b) ELF 

W14×159 W14×211 W14×132 W14×82 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 11 

12 13 

14 15 

16 

Figure 2-16. 8-Story EBF Schematic, Cont’d 

2-27
 
(a) RSA 

Figure 2-17. 16-Story EBF Schematic 

2-28
 
(b) ELF 

Figure 2-17. 16-Story EBF Schematic, Cont’d 

2-29
 
 

2-30
 
 

Chapter 3 Seismic Assessment 

This chapter presents the results of the seismic assessment of the eccentrically braced frames in accordance 

with ASCE 41. Section 3.1 provides general discussions on the global analysis requirements for assessment. 

Analysis requirements specific to eccentrically braced frames and assessment results of primary 

components of the frames are provided in Section 3.2. 

3.1 Assessment Overview 

A seismic performance assessment of the eccentrically braced frames is conducted using both linear and 

nonlinear analysis procedures prescribed in ASCE 41 §2.4: 

 Linear Static Procedure [ASCE 41 §3.3.1] 

 Linear Dynamic Procedure (Response Spectrum) [ASCE 41 §3.3.2] 10 

 Nonlinear Static Procedure [ASCE 41 §3.3.3] 11 

 Nonlinear Dynamic Procedure [ASCE 41 §3.3.4] 

Seismic assessment analyses follow the guidelines outlined in ASCE 41 Chapters 1 through 3, and, where 

applicable, ASCE 41 Chapter 5. Foundations, including soil-structure interaction, and geological site 

hazards (ASCE 41 Chapter 4) are not considered in this study. Modeling and assessment requirements for 

steel structural systems follow the provisions in ASCE 41 Chapter 5. Any deviations from these ASCE 41 

guidelines are explained where applicable. 

The seismic performance target (i.e., ‘rehabilitation objective’) for this study is selected as the Basic Safety 

Objective (BSO) in ASCE 41 §1.4.1. This selection allows the correlation between the seismic performance 

objective intended by ASCE 41 and the intended design objective of ASCE 7 for an ordinary building12 to 

be evaluated. The BSO associated goals for Structural Performance Levels (SPLs) found in ASCE 41 §1.5.1 

and Earthquake Hazard Levels (EHLs) found in ASCE 41 §1.6 are given in Table 3-1. Nonstructural 

Performance Levels (NPLs) found in ASCE 41 §1.5.2 are not considered in this study. The target Building 

Performance Levels (BPLs) found in ASCE 41 §1.5.3 are given in Table 3-1. 

The only explicit connection between the target structural performance objectives (i.e., SPL) of the BSO 

in ASCE 41 and the intended structural design performance objective of ASCE 7 is ‘Collapse Prevention’ 

given an MCE event, assuming that the BSE-2 EHL is equivalent to the MCE defined by ASCE 7—see 

Table 1-1 and Table 3-1. It is presumed by ASCE 7 that an appropriately designed structure using a seismic 

hazard of 2⁄3×MCE will achieve this structural design performance objective. ASCE 7 does not explicitly 

10 The user can alternatively perform a linear response history analysis. This was not done in this study, although it would bypass 

the limitations of using modal response spectrum analysis. 11 Simplified Nonlinear Static Procedure (NSP) is not considered.
 12 Structures assigned to Risk Category II or lower.
 

3-1
 
 

1 

identify a target structural design performance objective for ‘Life Safety’ at 2⁄3×MCE. Rather, ASCE 7 

contains implicit life safety measures to protect against loss of life from nonstructural damage at the designlevel event, 2⁄3×MCE. 

Table 3-1. Seismic Performance Targets (from ASCE 41-06) 

Structural Earthquake Hazard Nonstructural Building Earthquake Intensity Performance Level	 Performance Level Performance Level Level 

BSE-1 – §1.6.1.2 2/3×BSE-2 Life Safety (S-3) Not Considered (N-E) Life Safety (3-E) 

Maximum Considered Collapse Collapse Prevention BSE-2 – §1.6.1.1 Not Considered (N-E) Earthquake (MCE) Prevention (S-5)	 (5-E) 

Prior to ASCE 7-10, the MCE was defined as a uniform seismic hazard associated with a two percent 

probability of being exceeded in 50 years, except near known faults where deterministic-based hazards 

controlled. ASCE 7-10 adopted a risk-targeted design philosophy that shifts from a uniform hazard design 

basis to a uniform risk design basis, and defines the MCE ground motion intensity (denoted as MCER) as 

ground motions having a one percent probability of causing total or partial structural collapse in 50 years. 

This risk has a conditional probability (‘anticipated reliability’) of ten percent probability of total or partial 

structural collapse conditioned on the occurrence of an MCE event—see ASCE 7 Table C.1.3.1b. Several 

reference documents are available for more information about this implementation (FEMA 2009b, 

commentary of ASCE 7-10 (3rd printing), and NIST 2012). Therefore, the approved MCE in ASCE 41-06 

§1.6.1.1 (see BSE-2 in Table 3-1) should be taken as the MCER in ASCE 7-10 to maintain equivalency 

between the standards. ASCE 41-13 §2.2.4 prescribes using the MCER to define the BSE-2 EHL for the 

new building equivalency track. The seismic performance targets for this study are taken from ASCE 41­

13 and are given in Table 3-2. 

Table 3-2. Seismic Performance Targets (from ASCE 41-13) 

Earthquake Hazard Structural Performance Nonstructural Building Performance Earthquake Intensity Level	 Level Performance Level Level 

BSE-1N 1

 – §2.4.1.2 2/3×BSE-2N Life Safety (S-3) Not Considered (N-E) Life Safety (3-E) 

Maximum Considered Collapse Prevention Collapse Prevention BSE-2N 1

 – §2.4.1.1 Not Considered (N-E) Earthquake (MCER) (S-5) (5-E) 

ASCE 41-13 expanded the term ‘BSE’ to include ‘N’ or ‘E’ depending on the chosen assessment track. For this project, the ‘N’ is dropped to follow the terminology used 

in ASCE 41-06. 

This study does not evaluate assessment results for earthquake hazard levels with return periods shorter 

than identified above or building performance levels below Life Safety. Future research efforts may 

evaluate incorporating other performance levels for design in ASCE 7—see NIST GCR 12-917-20: 

Tentative Framework for Development of Advanced Seismic Design Criteria for New Buildings (NIST 

2012). 

3-2
 
 

 

 

 

 Seismic Hazard 

The seismic hazard is defined in ASCE 41 §1.6. The spectral response parameters for the BSE-2 (≡ BSE2N—see above) and BSE-1 (≡ BSE-1N—see above) EHLs are given in Table 3-3. The parameters 

summarize the seismic hazard13 for Site Class D, Stiff Soil, in ASCE 41 §1.6.1.4.1. 

Table 3-3. Spectral Response Parameters 

SS S1 3 3 SXS SX1 EHL Fa Fv Ts (sec) T0 (sec) (g) (g) (g) (g) 

BSE-2 1.5 0.60 1 1.0 1.50 1.50 0.90 0.60 0.12
 

BSE-1 2

 1.5 0.60 1 1.0 1.50 1.00 0.60 0.60 0.12
 1 S1 is actually just under 0.60 (i.e., 0.599) 2 SS and S1 do not include 2/3 reduction prior to site class modification 3 See ASCE 41 Table 1-4 and Table 1-5 

Figure 3-1 illustrates the generalized response spectrum for BSE-1 and BSE-2. 

1.6 

Spectral Response Acceleration, S a (g) 

1.4 

1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

 BSE-2 (BSE-2N in ASCE 41-13)

 BSE-1 (BSE-1N in ASCE 41-13) 

0 1 2 3 4 5 

Period, T (seconds)

Figure 3-1. Acceleration Response Spectra 

General Analysis Requirements 

This section discusses the implementation of the general analysis requirements prescribed in ASCE 41 §3.2 

in this study. 

ASCE 41 §3.2.2—Mathematical Modeling: The archetype buildings are modeled in three-dimensions. 

Increased forces and displacements because of torsional demands are inherently addressed in the three13 The seismic hazard in ASCE 41-13 is the MCER, ground motion based on a risk-targeted design philosophy in which an 

appropriately designed structure will have a one percent probability of collapse (i.e., risk) in 50-years (except in areas controlled 

by the deterministic cap on ground motions—see ASCE 7 commentary for Chapter 11). 

3-3
 

 

dimensional analysis. Because of building symmetry, the inherent torsional moment at each floor is 

theoretically zero. Accidental torsional moment (i.e., five percent mass offset) at each floor is not 

considered in the assessment analyses because the displacement modifier, , associated with the applied 

loads including accidental torsion is less than 1.1 at every floor for all buildings (see Table 3-4 and Table 

3-5). The values in these tables for determining torsional irregularity are based on floor displacements 

relative to the base and not story drifts as used in ASCE 714 . 

All members and connections of the seismic force-resisting system (SFRS) are classified as primary 

components in accordance with ASCE 41 §2.4.4.2 for both linear and nonlinear assessment procedures. 

Gravity framing (non-SFRS members and shear tab connections) is assumed in this study to provide 

negligible analytical lateral stiffness and strength—see ASCE 41 §3.2.2.3. Therefore, components of the 

non-SFRS framing are classified as secondary components for both linear and nonlinear assessment 

procedures. Similar to the assumptions adopted for design, specific component stiffnesses (e.g., partially 

restrained shear tab connections and stairs) are not modeled explicitly in the mathematical model. This is 

done to minimize the influence of secondary components on the demands imposed on primary components. 

This will allow assessment results between linear and nonlinear analysis to be compared. Performance 

assessment of these secondary members is outside the scope of this study—though would need to be 

checked in a real retrofit design. In addition, foundation or soil flexibility is not included in the analysis. 

Models for anticipated component inelastic actions in nonlinear assessment procedures include both 

strength and stiffness degradation—discussed subsequently in §3.2. 

ASCE 41 §3.2.3—Configuration: Building irregularities are discussed in ASCE 41 §3.1.3.1. Building 

irregularities defined in ASCE 41 are used only to determine whether the linear procedures are applicable. 

ASCE 41 §3.2.4—Diaphragms: Floor diaphragms are modeled for analysis as semi-rigid membranes (i.e., 

stiff per ASCE 41). The same assumptions adopted in design are maintained for assessment. 

ASCE 41 §3.2.5—P- Effects: Global P- effects are considered in the linear and nonlinear analyses, for 

both static and dynamic. Local P- effects are not addressed either explicitly or implicitly in the analyses. 

ASCE 41 §3.2.6—Soil-Structure Interaction: Soil-Structure Interaction is not considered in the seismic 

assessment of the archetype buildings. 

ASCE 41 §3.2.7—Multidirectional Seismic Effects: The principal axes of the archetype buildings align 

directly with the E-W and N-S directions (performance in the E-W direction is presented in this report). 

Seismic effects are determined by applying the seismic forces independently in each of the two orthogonal 

directions. Per ASCE 41 §3.2.7.1, concurrent seismic effects are addressed in the assessment by combining 

the effects along each principal axes. 

14 Amplification of the accidental torsion, if required, is consistent between ASCE 41 and ASCE 7. 

3-4
 
ASCE 41 §3.2.7—Vertical Seismic Effects: Vertical seismic effects are not considered for seismic 

assessment of the archetype buildings. Masses are input for horizontal accelerations only for dynamic 

analysis. 

ASCE 41 §3.2.8—Gravity Loads: Gravity loads for the linear assessment procedures are applied using the 

following two load combinations (LC). Roof live loads are considered not to be present for seismic analysis. 

There is no snow load acting on the buildings. 

 LC1 = 1.1×(Dead+0.25×Unreduced Floor Live) 

 LC2 = 0.9×Dead 

A P- load combination based on LC1 above is used for the linear assessment analyses; consequently, this 

is conservative for analysis using LC2. 

Both gravity load combinations above are used for the nonlinear static procedure. The average of the two 

combinations (LC1 and LC2) is applied in the nonlinear dynamic procedure. 

 LC3 = 1.0×Dead+0.25×Unreduced Floor Live 

A P- load combination based on LC3 above is used for the nonlinear assessment analyses. 

ASCE 41 §3.2.9—Verification of Design Assumptions: The following design objectives are verified with 

the nonlinear dynamic procedure. 

 EBF—in-plane and out-of-plane stability of columns (AISC 360) 

 EBF—in-plane and out-of-plane stability of braces (AISC 341) 

 EBF—plastic hinges in beams adjacent to the link beam, columns and braces (AISC 341) 

ASCE 41 §3.2.10—Overturning: Overturning is not considered for design or seismic assessment of the 

archetype buildings. 

 Analysis Procedures 

This section discusses the implementation of the specific analysis procedures prescribed in ASCE 41 §3.3 

in this study. 

Linear Analysis Procedures 

The archetype buildings are modeled and analyzed in ETABS 9.7.4 (CSI 2011a) for the linear analyses. 

The assumptions used in the mathematical model and analysis techniques are the same as those adopted for 

design (see Chapter 2). Modeling and analysis considerations for the linear procedures are outlined in ASCE 

41 §3.2.2 with supplemental information provided in ASCE 41 §3.3.2.2 for the Linear Dynamic Procedure 

(LDP). Gravity loads and load combinations assumed present during the earthquake are computed from 

ASCE 41 §3.2.8 as discussed previously. The effective horizontal seismic weights, w, for analysis are 

3-5
 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

computed in accordance with ASCE 41 §3.3.1, and are the same as those used for design (see Chapter 2). 

Global P- effects (e.g., B2 in AISC 360 Appendix 8) are addressed in the analysis by using a simplified 

algorithm—see ETABS User Manual. ETABS does not explicitly include local P- effects (e.g., B1 in AISC 

360 Appendix 8). System specific modeling assumptions and analysis techniques are described in their 

respective sections. 

Table 3-4. Displacement multiplier—E-W (SMF) 

 = max / avg 

ME4 ME8 ME16 

Floor ELF RSA ELF RSA ELF RSA 

Roof - ­ ­ ­ 1.010 1.008 

16 - ­ ­ ­ 1.009 1.007 

15 - ­ ­ ­ 1.009 1.007 

14 - ­ ­ ­ 1.009 1.007 

13 - ­ ­ ­ 1.009 1.007 

12 - ­ ­ ­ 1.009 1.007 

11 - ­ ­ ­ 1.008 1.007 

10 - ­ ­ ­ 1.008 1.007 

9 (Roof ME8) - - 1.010 1.007 1.008 1.007 

8 - - 1.010 1.007 1.008 1.007 

7 - - 1.009 1.006 1.008 1.007 

6 - - 1.009 1.006 1.008 1.007 

5 (Roof ME4) 1.006 1.006 1.008 1.005 1.008 1.007 

4 1.006 1.006 1.008 1.005 1.008 1.007 

3 1.005 1.005 1.007 1.005 1.008 1.007 

2 1.005 1.005 1.007 1.005 1.008 1.007 

Values shown to four significant figures are for comparison purposes only. 

Table 3-5. Displacement Multiplier—N-S (EBF) 

 = max / avg 

ME4 ME8 ME16 

Floor ELF RSA ELF RSA ELF RSA 

Roof ­ ­ ­ ­ 1.075 1.072 

16 ­ ­ ­ ­ 1.075 1.072 

15 ­ ­ ­ ­ 1.075 1.072 

14 ­ ­ ­ ­ 1.076 1.072 

13 ­ ­ ­ ­ 1.076 1.073 

12 ­ ­ ­ ­ 1.077 1.073 

11 ­ ­ ­ ­ 1.077 1.074 

10 ­ ­ ­ ­ 1.077 1.074 

9 (Roof ME8) ­ ­ 1.075 1.078 1.078 1.075 

8 ­ ­ 1.076 1.079 1.079 1.075 

7 ­ ­ 1.076 1.080 1.079 1.076 

6 ­ ­ 1.078 1.080 1.080 1.077 

5 (Roof ME4) 1.084 1.088 1.079 1.081 1.081 1.078 

4 1.085 1.089 1.081 1.083 1.082 1.080 

3 1.086 1.090 1.083 1.085 1.082 1.082 

2 1.085 1.089 1.084 1.089 1.083 1.085 

Values shown to four significant figures are for comparison purposes only. 

3-6
 
 

 

ASCE 41 §2.4.1.1 prescribes restrictions on the use of the linear procedures. First, a retrofitted 15 SFRS 

must not contain certain types of structural irregularities where the earthquake demands on the primary 

components of the SFRS fail to comply with the demand capacity ratio (DCR) limitations. 

Q DCR  UD  2.0 (3-1) QCE 

where QUD is the demand on a component due to gravity and earthquake loads and QCE is the expected 

strength of the component. The archetype buildings do not contain any configuration-based in-plane or outof-plane irregularities. Further, a linear analysis procedure must be performed to determine whether a 

building contains a weak story or torsional strength irregularity. Because of plan symmetry and regularity 

of the archetype buildings, there are no torsional irregularities. The required weak story irregularity 

verifications are discussed subsequently in the linear static procedure for each specific system type. 

3.1.3.1.1 Linear Static Procedure 

The Linear Static Procedure (LSP) is outlined in ASCE 41 §3.3.1. The provisions of the LSP closely 

resemble those of the ELF procedure in ASCE 7; as such, no additional analysis details are presented here. 

However, one place where ASCE 7 and ASCE 41 differ is in the determination of the fundamental period, 

T, in the direction being analyzed. ASCE 41 does not place an upper-bound limit on the period used for 

assessment as ASCE 7 does for strength design. In this study, the fundamental periods are determined by 

eigenvalue analysis per ASCE 41 §3.3.1.2.1. 

Further restrictions on the use of the LSP are prescribed in ASCE 41 §2.4.1.2. The LSP cannot be used if 

any of the following occur: 

	 The fundamental period of the building T is greater than 3.5×Ts (= 3.5×0.6 = 2.1 seconds in this 

study). This trigger is similar to that used in ASCE 7; however, like ASCE 7, which computation 

method for T to be used in this evaluation is not clear. If the analytical method (ASCE 41 §3.3.1.2.1) 

is used, only the E-W component of the ELF-designed ME4 and the N-S component of the ELFand RSA-designed ME4 satisfy this requirement—see Table 3-6 (directional components that fail 

this criteria are shaded). If the empirical method (ASCE 41 §3.2.1.2.2) is used, all building 

components satisfy this constraint except the E-W component of ME16. In this study, this analysis 

constraint is disregarded to allow an assessment comparison between methods—see Table 3-7 

(directional components that fail this criteria are shaded). 

	 The building has a ratio of the horizontal dimension at any story to the corresponding dimension in 

an adjacent story that exceeds 1.4. In this study, this constraint is satisfied because the building 

plan does not change at any story. 

	 The building has a torsional stiffness irregularity. This limitation is satisfied as discussed previously 

under accidental torsion as well as in Chapter 2. In this study, this check is based on the individual 

story drift rather than the floor displacement relative to the base. 

	 The building has a vertical stiffness irregularity. In this study, this limitation is automatically 

satisfied by using ASCE 7 §12.3.2.2 Exception 1 for the design of the archetype buildings. 

15 This term is now used in lieu of ‘rehabilitation’. 

3-7
 
 

 

 

 

 

	 The building has a non-orthogonal SFRS. In this study, this limitation is not applicable to the 

archetype buildings. 

Regardless of the restrictions on using the LSP, results from applying the LSP to the archetype buildings 

are included for the purpose of seismic performance comparison between the various assessment 

methods in this study. 

Table 3-6. Analytical fundamental periods (seconds) 

ME4 ME8 ME16 

Direction SFRS ELF RSA ELF RSA ELF RSA 

E-W SMF 1.83 2.23 2.93 3.84 4.39 5.05 

N-S EBF 1.10 1.09 2.15 2.46 3.19 3.88 

Table 3-7. Empirical fundamental periods (seconds) 

ME4 ME8 ME16 

Direction SFRS ELF RSA ELF RSA ELF RSA 

E-W SMF 0.93 0.93 1.57 1.57 2.69 2.69 

N-S EBF 0.65 0.65 1.06 1.06 1.76 1.76 

3.1.3.1.2 Linear Dynamic Procedure 

The Linear Dynamic Procedure (LDP) is outlined in ASCE 41 §3.3.2. The LDP requires the use of either 

response spectrum analysis (RSA) or response history analysis (RHA)—only the RSA is presented in this 

report. Though there are significant benefits of using the RHA (e.g., maintaining sign convention on 

response), the RSA was selected to align with the design methodology. The provisions of the LDP closely 

resemble those of the RSA procedure in ASCE 7; as such, no additional analysis details are presented here, 

except that no base shear scaling is required by ASCE 41. Damping for analysis is taken as five percent of 

critical for all modes for dynamic analysis to match the response spectrum (see ASCE 41 §1.6.1.5.3). A 

sufficient number of modes is used in the analysis to capture at least 90 percent of the mass participation in 

each of the two horizontal principal directions. Masses were not modeled in the analysis to address vertical 

accelerations. Furthermore, the square root of the sum of the squares (SRSS) rule is used to combine the 

modal responses so as to obtain the maximum forces and deformations. 

Nonlinear Analysis Procedures 

The archetype buildings are modeled and analyzed in PERFORM-3D 5.0.0 (CSI 2011b) for the nonlinear 

procedures. Modeling and analysis considerations for the nonlinear procedures are outlined in ASCE 41 

§3.2.2 with supplemental information provided in ASCE 41 §3.3.3.2 for the Nonlinear Static Procedure 

(NSP) and ASCE 41 §3.3.4.2 for the Nonlinear Dynamic Procedure (NDP). Primary components of the 

SFRS expected to experience inelastic deformations are modeled using a full “backbone” curve that 

includes strength and stiffness (applicable only for the NDP) degradation and residual strength. For this 

study, all nonlinear components are modeled with the anchor points (A to E) bounding the full backbone 

curve as shown in ASCE 41 Figure C2-1 and Figure 5-1—see Figure 3-2. This topic will be discussed 

further in the respective analysis and system-specific sections. 

3-8
 
Gravity loads and corresponding load combination assumed to be present during the earthquake are 

computed from ASCE 41 §3.2.8 as discussed previously. The effective horizontal seismic weights, w, for 

analysis are computed in accordance with ASCE 41 §3.3.1 and are the same as those used for design (see 

Chapter 2). Global P- effects (e.g., B2 in AISC 360 Appendix 8) are addressed in the analysis by using a 

simplified algorithm—see PERFORM-3D User Guide (CSI 2011d). PERFORM-3D does not explicitly 

include local P- effects (e.g., B1 in AISC 360 Appendix 8). Building specific modeling assumptions and 

analysis techniques are described in their respective sections. 

Figure 3-2. Generalized Component Backbone Curve (adopted from ASCE 41 Figure C2-1) 

3-9
 
3.1.3.2.1 Nonlinear Static Procedure 

The Nonlinear Static Procedure (NSP) is outlined in ASCE 41 §3.3.3. ASCE 41 places limitations on the 

use of the NSP in ASCE 41 §2.4.2. First, if higher modes are significant, the NSP is permitted with 

supplemental verifications required using the LDP. Higher mode effects are consider significant when the 

story shear computed by analysis with at least 90 percent horizontal mass participation is at least 1.3 times 

greater than that computed considering only response in the fundamental mode. This condition is generally 

triggered in multistory buildings with fundamental periods greater than 1.0 second in the direction being 

considered (see Table 3-8 and Table 3-9—story shear ratios that fail this criteria are shaded). 

Second, if R > Rmax (as defined in ASCE 41 §3.3.3), dynamic instability is a potential failure mode and the 

NSP is not permitted. Information regarding this ductility criterion as applied to an idealized single-degreeof-freedom (SDOF) system is provided in FEMA 440: Improvements of Nonlinear Static Seismic Analysis 

Procedures (FEMA 2005). However, this verification is computationally cumbersome because a nonlinear 

static analysis has to be conducted to determine both R and Rmax, prior to knowing if the NSP is permitted. 

This verification is illustrated subsequently in the NSP assessment results. The NSP procedure is 

graphically illustrated in the flowchart of Figure 3-3. 

3-10
 
     

   

     

   

   

   

       

     

     

   

   

Structural System

Dynamic

Properties

T1, M1, K1, 1

Conduct Pushover

Analysis

Response

Properties

Te, Ke, ‐

factors

Modification

Factors

R, C0, C1, C2,

Sa

Is Rd < Rmax? No

Check member and

component capacities

(forces and deformations)

Yes

End

End

NSP Not Permitted

Note: Effective

properties are used

here not Modal

Figure 3-3. NSP Process 

3-11 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3-8. Story shear ratio – ELF 

Vstor

2.96

2.03

1.61

1.41

y / Vstory,1st mode 

ME4 ME8 ME16 ME4 ME8 ME16 

Story E-W E-W E-W N-S N-S N-S 

Roof - - - - 2.60 

16 - - - - 2.15 

15 - - - - 1.79 

14 - - - - 1.52 

13 - - 1.29 - - 1.33 

12 - - 1.20 - - 1.20 

11 - - 1.14 - - 1.13 

10 - - 1.09 - - 1.10 

9 (Roof) - 1.98 1.07 - 1.87 1.10 

8 - 1.41 1.07 - 1.48 1.12 

7 - 1.19 1.06 - 1.19 1.16 

6 - 1.10 1.07 - 1.05 1.22 

5 (Roof) 1.45 1.05 1.08 1.18 1.04 1.30 

4 1.10 1.03 1.11 1.03 1.11 1.38 

3 1.01 1.05 1.15 1.01 1.24 1.46 

2 1.06 1.10 1.19 1.04 1.35 1.51 

Table 3-9. Story shear ratio – RSA 

Vstor

3.10

2.11

1.65

1.42

1.30

y / Vstory,1st mode 

ME4 ME8 ME16 ME4 ME8 ME16 

Story E-W E-W E-W N-S N-S N-S 

Roof - - - - 3.04 

16 - - - - 2.44 

15 - - - - 1.96 

14 - - - - 1.60 

13 - - - - 1.37 

12 - - 1.22 - - 1.24 

11 - - 1.15 - - 1.18 

10 - - 1.11 - - 1.17 

9 (Roof) - 2.25 1.09 - 2.02 1.18 

8 - 1.50 1.09 - 1.52 1.21 

7 - 1.22 1.09 - 1.21 1.26 

6 - 1.12 1.09 - 1.07 1.34 

5 (Roof) 1.58 1.07 1.11 1.18 1.06 1.44 

4 1.14 1.05 1.15 1.03 1.14 1.56 

3 1.01 1.08 1.21 1.00 1.28 1.67 

2 1.08 1.16 1.26 1.03 1.40 1.74 

The mathematical model requirements for use with the NSP are outlined in ASCE 41 §3.2.2 and ASCE 41 

§3.3.3.2. Primary components of the SFRS expected to experience inelastic deformations are modeled 

using full backbone curves that include strength degradation and residual strength (see ASCE 41 §3.2.2.3 

and ASCE 41 §3.3.3.2). ASCE 41 §5.4.2.2.2 allows the generalized modeling parameters provided in 

ASCE 41 to model the full backbone curves of steel components for the NSP as an alternative to 

experimental calibration. In this study, all nonlinear components are modeled with the anchor points (A to 

E) bounding the full backbone curve as shown in Figure 3-2 and quantified in ASCE 41 Tables 5-6 and 5­

7. Component strength at the ultimate deformation, point E on the backbone curve, retains residual strength 

3-12
 
 

and does not experience complete strength loss. SFRS-specific modeling approaches are discussed in their 

respective sections. 

For the nonlinear static analysis algorithm in PERFORM-3D, the following apply: 

 The lateral force distribution is based on a non-adaptive first-mode shape (first-order elastic) and 

mass distribution. 

 Damping is set to zero percent for all modes with no supplemental Rayleigh damping. All elements 

are assigned a beta-K damping stiffness reduction factor of unity (no reduction). 

 Strength degradation is included in the analysis. 

 Global P- effects are directly included in the analysis. Local P- effects are not addressed in the 

analysis. Geometric nonlinearity is assigned to all elements. 

 Number of Steps is taken as 100 and Maximum Number of Events is taken as 1,000. 

 Roof displacement at the center of mass relative to the base is used as the target displacement. The 

reference drift is therefore taken as the roof drift; the maximum allowable drift is taken as 10 

percent. All story drifts are included in the list of Controlled Drifts. 

 See PERFORM-3D User Guide for additional information. 

3.1.3.2.2 Nonlinear Dynamic Procedure 

The Nonlinear Dynamic Procedure (NDP) is outlined in ASCE 41 §3.3.4. The NDP is intended to be the 

most rigorous of all the assessment procedures prescribed, with no limitations placed on types of buildings 

allowed for the assessment because of the intent of capturing the true behavior of the building subjected to 

strong ground motions. 

The mathematical model requirements for use with the NDP are outlined in ASCE 41 §3.2.2 and ASCE 41 

§3.3.4.2, except that the point-in-time gravity load present during strong ground motion is taken as (D + 

SD) + 0.25×Lo,floor, a slight but common alternative to ASCE 41 §3.2.8 (see ASCE 7 §16.2.3). Primary 

components of the SFRS expected to experience inelastic deformations are modeled using full backbone 

curves that include strength and stiffness degradation and residual strength (see ASCE 41 §3.2.2.3 and 

ASCE §3.3.4.2). 

For the NSP, ASCE 41 §5.4.2.2.2 allows using the generalized modeling parameters provided in Tables 5­

6 and 5-7 to model the full backbone curves of steel components as an alternative to experimental 

calibration. However, for the NDP, ASCE 41 §5.4.2.2.3 requires all component hysteretic behavior be based 

on experimental data unless permitted by the authority have jurisdiction. The benefit of calibrating 

component models with experimental results is that the force-deformation relationship will more accurately 

reflect strength and stiffness degradation, both cyclic and in-cycle—see NIST GCR 10-917-5: Nonlinear 

Structural Analysis for Seismic Design: A Guide for Practicing Engineers (NIST 2010a) and FEMA P440A: Effects of Strength and Stiffness Degradation on Seismic Response (FEMA 2009c). In this study, all 

nonlinear components are modeled with the anchor points (A to E) bounding the full backbone curve as 

shown in Figure 3-2 and quantified in ASCE 41 Tables 5-6 and 5-7. All nonlinear components are calibrated 

based on experimental results to determine cyclic and in-cycle stiffness degradation only; post-yield 

strength increases and strength degradation calibrations from experimental results were not included. 

Component strength at the ultimate deformation, point E on the backbone curve, retains the residual strength 

and does not experience complete strength loss. SFRS-specific modeling approaches are discussed in their 

3-13
 
 

 

 

respective sections. Therefore, the same PERFORM-3D model used in the NSP is also used in the NDP; 

analytical results from the two procedures are thus consistent and directly comparable. Future ASCE 41 

revisions should unify modeling practices for the NSP and NDP, as well as provide supporting data to the 

authority having jurisdiction. Future research should examine the response of these systems with hysteretic 

models calibrated completely to test results, including performing FEMA P695 analyses. 

The nonlinear dynamic analysis algorithm in PERFORM-3D used the following parameters: 

 Damping is taken as three percent of critical for all modes (elastic) and 0.3 percent of critical is 

added as Rayleigh damping (elastic stiffness component only, beta-K) for dynamic analysis. 

Damping computation in PERFORM-3D is not based on the tangent stiffness matrix. All elements 

are assigned a beta-K damping stiffness reduction factor of unity (no reduction). 

 Strength and stiffness degradation are included in the analysis. 

 Global P- effects are directly included in the analysis. Local P- effects are not addressed in the 

analysis. Geometric nonlinearity is assigned to all elements. 

 Maximum Number of Events for each time step is taken as 200. 

 Time steps for analysis are taken as the time step of the input motion, ranging from 0.005 to 0.02 

seconds—see FEMA P695 Appendix A. 

 See PERFORM-3D User Guide for additional information. 

A critical aspect of the NDP is the selection and scaling of input ground motions (free-field motions) which 

is described in ASCE 41 §1.6.2.2. The methodology adopted in this study is discussed in Appendix A. 

In addition to the analysis routine terminating when a solution fails to converge, the routine was also set to 

terminate when an arbitrarily selected roof drift ratio of twenty percent16 is achieved (story drift ratios can 

be higher). While both of these methods are used to indicate and rationalize total or partial collapse of a 

system, the indicator of collapse used in this study is the component demands measured against the 

nonlinear modeling parameters and acceptance criteria. These component limits will typically be reached 

prior to an analysis routine failing to converge or an excessive roof drift is reached. 

 Acceptance Criteria 

This section discusses the implementation of the acceptance criteria in ASCE 41 §3.4. Component actions 

are classified as force-controlled or deformation-controlled depending on the post-elastic behavior of the 

component (see ASCE 41 Table C2-1). Generally speaking, deformation-controlled actions are assigned to 

component actions capable of a ductile response (e.g., moment in a plastic hinge in a compact beam) and 

force-controlled actions are assigned to component actions with limited ductility (e.g., moment in a plastic 

hinge in a column with high axial load). Additionally, a knowledge factor, , is applied to account for 

uncertainties in the framing system and materials. Since the archetype buildings are new construction with 

quality control measures,  is taken as unity in this study to represent new component capacities or actions 

as discussed in ASCE 41 §2.2.2 and ASCE 41 Tables 2-1, 2-2, and 2-3. 

16 This value does not change the qualitative performance result of a component; however, it can influence the mean value of a 

performance response for a set of records. For example, mean values would be slightly larger than if ten percent was selected. 

3-14
 
Linear Procedures 

Acceptance criteria of components for linear assessment procedures are provided as m-factors. The m-factor 

is intended to account for the ductility associated with a specific action and depends on the SPL and 

component type. ASCE 41 Table 5-5 provides the m-factors for steel components for linear assessment 

procedures. Adjustments to the m-factors for member or connection characteristics are detailed in ASCE 

41 Chapter 5. In this study, actions in force-controlled components are assigned m = 1.0 for simplicity and 

computational consistency in developed assessment spreadsheets. It should be noted that ASCE 41 does 

not assign an m-factor to force-controlled components. 

3.1.4.1.1 Calculating Component Assessment Results 

Component forces and deformations obtained by the LSP or LDP are referred to as design actions, QU (e.g., 

flexure in a component). 

Component design actions classified as deformation-controlled, QUD, are computed by 

QUD  QG  QE (ASCE 41 §3.4.2.1.1) (3-2) 

Component design actions classified as force-controlled, QUF, are computed by 

QE QUF  QG  (ASCE 41 §3.4.2.1.2) (3-3) C C J 12 

where QG is the action due to gravity loads and QE is the action due to earthquake effects. Elastic forcecontrolled demands from earthquake effects are divided by C1C2 to remove the demand amplification for 

short period structures from non-ductile components (see ASCE 41 §3.3.1). Similarly, the demand is 

divided by J, which is the force-delivery reduction factor and is taken as the minimum demand capacity 

ration (DCR) of the components in the load path delivering force to the component. Alternatively, J can be 

taken as 2.0 when the system is located in a region of a high level of seismicity, independent of EHL. 

However, holding J constant for multiple performance levels (disregarding the change in intensity) is not 

consistent with a capacity design approach, resulting in potentially overly conservative estimates of 

component actions in force-controlled elements at the higher EHL, or vice versa. 

ASCE 41 §3.4.2.2 requires that deformation-controlled and force-controlled actions in primary and 

secondary components satisfy: 

Deformation-controlled: m Q CE  QUD (ASCE 41 §3.4.2.2.1) (3-4) 

Force-controlled:    QUF m QCL (ASCE 41 §3.4.2.2.2) (3-5)

3-15
 
where m is the component demand modification factor (taken as unity for force-controlled actions—see 

above),  is the knowledge factor (taken as unity in this study), QCE is the expected strength of the 

component, and QCL is the lower-bound strength of the component. 

The results of the linear assessment procedures are presented in this report as a normalized demand capacity 

ratio, DCRN, so that the acceptance criteria verification becomes a unity check similar to that done in modern 

component design standards (e.g., AISC 360). DCRN is computed by rearranging ASCE 41 Eq. 3-20 and 

ASCE 41 Eq. 3-21 as required. As such, a DCRN value greater than unity indicates that the component does 

not satisfy the performance criteria for a given SPL. DCRN is similar to, but different than, the DCR as used 

in ASCE 41. This approach is also a more consistent way to present results over the various types of 

assessment procedures used in this study. However, a slightly different interpretation is also taken in this 

study with regards to the DCRN: in lieu of m and  adjusting the apparent strength of a component, as 

illustrated in ASCE 41 §3.4.2.2, m and  act to reduce the elastic demand to the expected demand given an 

EHL. Where required, the DCRN is determined from an interaction equation from the appropriate equation. 

QUD DCR Deformation-controlled: DCR  	 N	 (3-6) m Q CE m 

Q Force-controlled: DCR N  UF [with m taken as 1.0] (3-7)   m Q CL 

Nonlinear Procedures 

Acceptance criteria of components for nonlinear assessment procedures are provided as plastic (inelastic) 

deformations dependent on the SPL and component type. ASCE 41 Tables 5-6 and 5-7 provide the plastic 

deformations limits for steel components for nonlinear assessment procedures. Adjustments to the 

acceptance criteria for member or connection characteristics are detailed in ASCE 41 Chapter 5. 

Inelastic deformation parameters in ASCE 41 are provided for steel components in terms of plastic 

deformations rather than total deformations. The choice of whether to use plastic deformations or total 

deformations will depend on what nonlinear component model is adopted for each component action in the 

structural analysis (e.g., moment-curvature hinge or moment-rotation hinge). Consequently, yield and postyield elastic deformations may need to be added to the values given in ASCE 41 to determine the total 

deformation for each SPL. 

In this study, demands on primary components of new buildings are measured against acceptance criteria 

for primary components. ASCE 41 §3.4.3.2 allows primary component demands to be within the 

acceptance criteria for secondary components for the NSP if degradation effects are explicitly modeled—a 

change introduced in FEMA 356. This also includes NDP, although not explicitly stated. This allowance is 

neglected in this study for the following reasons: 

	 Bypassing nonlinear acceptance criteria set for primary components suggests that acceptance 

criteria for primary components for linear and nonlinear assessment procedures are not calibrated. 

In this study, acceptance criteria for primary components are maintained for all assessment methods 

to provide a uniform comparison basis. 

3-16
 
	 There is no technical justification provided in ASCE 41 as to why comprehensive component 

models for primary components, which are required to stabilize the structure after a large 

earthquake, will allow them to deform to the extent given for a secondary component and maintain 

the structural integrity of the system. Analytically speaking, it is debatable if collapse prevention 

can be reliably achieved if a concentrated few SFRS components are deformed past the deformation 

associated with their peak strength and lose a considerable amount of strength and stiffness. 

Available literature has indicated the difficulty in solution convergence in analysis when 

component response is following a negative stiffness branch. Still, some liberties are provided, 

debatably, for existing buildings, but transferring this allowance to new buildings is also of 

debatable validity. Engineering judgment must be applied. Broadly speaking, the function that 

separating existing buildings and new buildings into bins plays in developing a resilient community 

must be clarified. 

	 Reliability issues arise when adopting secondary acceptance criteria for primary components. For 

example, the acceptance criterion of an RBS beam-to-column connection taken as a secondary 

component for the Life Safety SPL is beyond the peak deformation (“a” in Figure 3-2). In ASCE 

41, primary acceptance criteria for the Collapse Prevention SPL generally matches the deformation 

associated with the peak strength of a component. 

	 There is little empirical evidence supporting the acceptance criteria for secondary steel components 

permitted in ASCE 41 §3.4.3.2, other than for beam-to-column connections studied in the SAC 

project (see FEMA 350 series (FEMA 2000a through 2000d)). Experimental tests are rarely 

continued to achieve the peak deformations and the associated reserve strength of a component or 

subassembly after the required loading protocol is complete. 

As a side note, ASCE 41-13 has removed all acceptance criteria for primary components for nonlinear 

assessment. Future research should be conducted to evaluate the systems by measuring demands against 

acceptance criteria for secondary components—which can be done by inspection with the analysis results 

presented in this study. 

3.1.4.2.1 Calculating Component Assessment Results 

Component forces and deformations obtained by the NSP or NDP are referred to as design actions, QU (e.g., 

plastic rotation in a plastic hinge). Component design actions are computed as the action in the member or 

connection at the target displacement for the NSP and as the maximum value for a given earthquake for the 

NDP. Subsequently, a statistical average is computed from the maximum values from the suite of ground 

motions. In specific cases, the maximum value must be coupled with other actions in the component at the 

instant of computation of the maximum response. 

Component design actions classified as deformation-controlled, QUD, are computed by 

QUD  QG QE (ASCE 41 §3.4.3.2.1)	 (3-8) 

Component design actions classified as force-controlled, QUF, are computed by 

QUF  QG QE (ASCE 41 §3.4.3.2.3)	 (3-9) 

where QG is the action due to gravity loads (or associated deformation) and QE is the action due to 

earthquake effects (or associated deformations). Superposition of forces or deformations is not applicable 

3-17
 
 

in a nonlinear analysis; thus, gravity loads are directly applied in the analysis. The above equations are 

numerical interpretations of ASCE 41 §3.4.3.2. They are used in this study to maintain computational 

consistency over the various types of assessment procedures. 

ASCE 41 §3.4.3.2 requires that deformation-controlled and force-controlled actions in primary and 

secondary components satisfy: 

Deformation-controlled: QCE  QUD (ASCE 41 §3.4.2.2.1) (3-10) 

Force-controlled: QCL  QUF (ASCE 41 §3.4.2.2.2) (3-11) 

where QCE is the expected strength or deformation demand of a component, QCL is the lower-bound strength 

of a component, and  is the knowledge factor (taken as unity in this study). ASCE 41 Chapter 5 does not 

explicitly provide a relationship between QCE (or QCL) and Qy on the force-deformation curve. 

The results of the nonlinear assessment procedures are presented in this report as a normalized demand 

capacity ratio, DCRN, where the plastic or total deformation demands are normalized with respect to the 

plastic or total acceptance criteria, modified by  if required. The acceptance criteria verification then 

becomes a unity check similar to that done in modern component design standards (e.g., AISC 360). As 

such, a DCRN value greater than unity indicates that the component does not satisfy the performance criteria 

for a given SPL. This approach is a consistent way to present results over the various types of assessment 

procedures used in this study. 

  plastic elastic 

Total 

Q    pe  p AC  UD 

 y  ,

Deformation-controlled: DCR N    (3-12) Q CE   plastic Plastic    p AC ,

QUF Force-controlled: DCR N  (3-13) QCL 

where plastic is the plastic deformation of a component, elastic is the elastic deformation of a component, y 

is the yield deformation of a component, pe is the post-yield elastic deformation of a component, and p,AC 

is the acceptance criteria of a component based on plastic deformation. 

3-18
 
 

3.2 Eccentrically Braced Frame 

Seismic performance assessment of steel eccentrically braced frames is performed in accordance with 

ASCE 41 §5.5.3. The eccentrically braced frames in the archetype buildings are designed as an EBF as 

identified in ASCE 7 §12.2 (item B.1 in Table 12.2-1) and AISC 341 §F3.

 Assessment Methodology 

There are three primary characteristics of each component (i.e., member, connection, etc.) forming the 

structural model for each assessment method: 

1. Stiffness, ASCE 41 §5.5.3.2 

2. Strength, ASCE 41 §5.5.3.3 

3.	 Acceptance Criteria, ASCE 41 §5.5.3.4, and whether or not the component action is forcecontrolled or deformation-controlled. 

Each component characteristic is discussed in the appropriate linear and nonlinear assessment discussion. 

The following component design actions are assessed in this study: 

	 Link shear force or deformation 

 Beam, column, and brace flexural strength at potential plastic hinge zones (section strength)17 

	 Beam, column and brace axial-moment interaction strength (member strength) 

Linear Procedures 

This section discusses the three primary component characteristics listed in Section 3.2.1 and computation 

of the demand in the component for the linear assessment procedures. 

Stiffness 

The stiffnesses of all members and connections for linear assessment follow ASCE 41 §5.5.3.2. To account 

for the increased stiffness provided by brace-to-beam and brace-to-column (gusset plate) connections, an 

18-inch prismatic section with twice the flexural stiffness, EI, is used to connect the beam-to-column joint 

(outside the panel zone) to the beams and columns. Braces are modeled with a rigid end equal to 0.05Lwp, 

and are ‘pinned’ out-of-plane and ‘fixed’ in-plane (see Chapter 2). 

Strength 

The strength of all members and connections for linear assessment follow ASCE 41 §5.5.3.3. 

17 All components other than link beams are force-controlled per ASCE 41 §5.5.3.4. Brace connections are not assessed in this 

study because they are designed to resist forces computed using the maximum strengths of the brace. 

3-19
 
 

 

The expected shear strength of a link beam, QCE = VCE (= Qy), is computed as Equation (3-14)—ASCE 41 

Equation 5-31). 

VCE  0.6Fye d  2t f tw (3-14) 

For A992 steel, Fye = 1.1×Fy (see ASCE 41 Table 5-3) which corresponds to RyFy in AISC 341. This strength 

is slightly different that Vn in AISC 360 Chapter G and AISC 341 §F3. This strength is also slightly different 

than VCE of a standard beam (ASCE 41 Equation 5-7—also see below). These differences are not discussed 

in the commentary of ASCE 41. Having different shear strengths in AISC 360 and AISC 341, and then 

again in ASCE 41, results in inconsistent strength measures that can affect performance predictions of short 

beams. Additionally, there are no compactness requirements placed on a link beam in ASCE 41 to ensure 

full section yielding. 

The expected flexural strength of a member, QCE = MCE (= Qy), is computed as Mn from AISC 360 Chapter 

F18 with b = 1.0 and Fye in lieu of Fy. For ASTM A992 steel, Fye = 1.1×Fy (see ASCE 41 Table 5-3), which 

corresponds to RyFy in AISC 341. Composite action with the concrete slab is generally neglected in 

computing Mn for frame beams. In so doing, it is assumed that the plastic moment strength is achievable 

via adequate lateral bracing, thus Mn = Mp. If the flexural strength is less than Mp, then the available ductility 

of the member is significantly reduced because of member or cross-section instability (which also affects 

the acceptance criteria). ASCE 41 enforces section compactness requirements through the acceptance 

criteria—discussed subsequently. 

The lower-bound flexural strength of a member, QCL = MCL, is computed as Mn from AISC 360 Chapter F18 

with b = 1.0 and FyLB in lieu of Fy. For ASTM A992 steel, FyLB = 1.0×Fy (see ASCE 41 Table 5-2). 

Although not explicitly identified in ASCE 41 §5.4.2.3.2, the expected shear strength of a member, QCE = 

VCE (= Qy), is identical to that computed as Vn from AISC 360 Chapter G with v = 1.0 and Fye in lieu of Fy. 

Web slenderness, h / tw, is critical in developing a fully yielded cross-section. As such, there are cases when 

418 E h 640 E  2.45    3.76 (3-15) Fy Fy tw Fy Fy 

and the web is still capable of achieving full yield strength in shear. However, if the web slenderness 

approaches the upper limit (taken as the ‘compact’ limit in AISC 360 Table B4.1) then the beam may have 

difficulty achieving its plastic moment strength, Mp. There is no lower-bound shear strength, VCL, in ASCE 

41 or shear-moment interaction. 

The lower-bound compression strength of a member, QCL = PCL, is computed as Pn from AISC 360 Chapter 

E18 with c = 1.0 and FyLB in lieu of Fy. For ASTM A992 steel, FyLB = 1.0×Fy (see ASCE 41 Table 5-2). 

ASCE 41 allows the effective length factor, K, of a brace member to be taken as 0.8 for in-plane buckling 

18 ASCE 41 inadvertently states AISC 341. 

3-20
 
 

and 1.0 for out-of-plane buckling, and L is the clear length of the brace plus the gusset plate. For the 

archetype buildings in this study, KL is taken as 1.0×0.9Lwp for both axes, where Lwp is the length between 

work points, which is a conservative estimate for in-plane buckling. 

Though identified in ASCE 41 §5.4.2.3.2-2, no guidance is provided for computing the expected flexural 

strength, MCE, of a compression member if the axial load, P, exceeds 10 percent of the axial strength. This 

guidance would be useful for computing the flexural DCR at a given location, such as at the column base. 

The term axial strength of a compression member is also not well defined (i.e., is it Pye or PCL?). Similarly, 

the axial load, P, is not defined except in an unrelated provision for the NSP. ASCE 41 §5.4.2.2.2 states 

that P for a linear analysis is PUF. The flexural strength will also depend on the chosen P-M interaction 

curve, which will use MCE (or MCL) at P = 0 as the anchor point. There is little need to have triggering 

language based on 10 percent axial load ratio because it delineates no physical phenomenon and does not 

also influence computing the yield chord rotation, y. In fact, it adds complexities, which will be discussed 

subsequently in the Acceptance Criteria section. ASCE 41 does not delineate between orthogonal buckling 

axes and non-flexural buckling limit states (e.g., torsional, local buckling) for its interaction verification. 

This can significantly affect the assessment of beam-column members where high in-plane moment is 

associated with a buckling limit state other than in-plane flexural buckling. Beam-columns can be further 

penalized in linear assessment methods where PUF is highly affected by selecting a value for J. 

The expected tension strength of a member, QCE = TCE (= Qy), is computed as Ac×Fye, where Ac is the crosssectional area of the member. ASCE 41 does not provide other tensile strengths, potentially brittle, similar 

to AISC 360 Chapter D, e.g., net section fracture. 

The expected shear strength of a panel zone, QCE = VCE (= Qy), is computed as 0.55 Fye×db×tp. (ASCE 41 

Equation 5-519). This strength equates to 0.92×Vy from AISC 360 Chapter J10.6 with v = 1.0 and Fye in 

lieu of Fy. ASCE 41 does not provide additional panel zone strength to account for column flange bending. 

ASCE 41 does not provide explicit guidance on computing the strength of a beam-to-column connection in 

an EBF other than it shall be treated as force-controlled for all actions. Consequently, the controlling 

mechanism for a beam-to-column connection is taken as the lower-bound flexural strength, QCL, measured 

at the face of the column. This flexural strength is determined using AISC 360 with  = 1.0 and FyLB in lieu 

of Fy. Similarly, the lower-bound strength of a brace-to-beam and brace-to-beam/column connection is 

determined from AISC 360 and is force-controlled for all design actions. 

Acceptance Criteria 

The acceptance criteria of members and connections for linear assessment follow ASCE 41 §5.5.3.4. 

However, SCE 41 §5.5.3.4.1 requires that all columns, beams adjacent to link beams, braces, and all 

connections in an EBF to be force-controlled for axial force and flexure. 

19 The reason the shear yield stress for a column web (assuming it can be designated as a beam) being defined as 0.6×Fye is not 

clear, but if the same column web is a panel zone, the shear yield stress is 0.55×Fye. 

3-21
 
Shear Force in Link Beams 

The acceptance criteria for shear actions in link beams are provided in ASCE 41 Table 5-5 and dependent 

on the link length, e. Acceptance criteria for flexural actions (including P-M interaction) in link beams are 

provided in ASCE 41 Table 5-5 when applicable. However, ASCE 41 does not provide significant guidance 

on treatment of axial-moment or shear-moment interaction within link beams except that axial compression 

and tension actions are designated as force-controlled. Nonetheless, the acceptance criteria for flexural 

actions are dependent on this axial force. Furthermore, the shear-moment interaction for intermediate links 

is not well explained and inconsistent for the IO SPL. ASCE 41 does not provide compactness requirements 

of the cross section elements to ensure full shear yielding of the section and assumes that the link beam is 

a wide-flange section. 

Axial Force in Braces and Brace Connections 

ASCE 41 §5.5.3.4.1 requires that all axial actions in a brace and brace connection in an EBF be forcecontrolled for axial actions. 

Flexure in Beams, Beam-to-Column Connections, and Brace Connections 

ASCE 41 §5.5.3.4.1 requires that all flexural actions in beams (other than link beams) and all connections 

in an EBF be force-controlled. Though flexural action in these components is treated as force-controlled, 

the following discussion is presented assuming that these components are deformation-controlled for 

modelling and analysis purposes to align with other reports developed for this study (see NIST 2014a and 

2014b). Also, this allows comparison to other braced frame systems in ASCE 41—including bucklingrestrained braced frames found in ASCE 41-13. 

The acceptance criteria for flexural action at expected locations of plastic hinging in beams (members with 

axial load ratio less than or equal to 10 percent) are provided in ASCE 41 Table 5-5 and are dependent on 

web and flange slenderness. The range of flange limits match AISC 341 limits for highly and moderately 

ductile unstiffened compression elements. The range of web limits match AISC 341 limits for highly and 

moderately ductile stiffened compression elements taking at P = 0. The flange and web slenderness limits 

for moderately ductile sections are taken as a ‘compact’ compression element in AISC 360 (i.e., p). The 

lower-bound web slenderness limit is taken as that capable of fully section yielding in shear. These web 

slenderness limits were introduced in FEMA 356 whereas flange limits were introduced in FEMA 273 and 

subsequently modified in FEMA 356 (upper-bound limit was changed from a pure axial compression limit 

to a compression from flexure limit). 

In cases where the expected flexural strength of an unbraced segment is governed by instability (e.g., lateral 

torsional buckling (LTB)) rather than full section yielding, the m-factors in ASCE 41 Table 5-5 shall be 

reduced accordingly. Again, ASCE 41 inadvertently references AISC 341 for these calculations as well as 

uses the notation, Mr, which is no longer used in AISC 360. 

The acceptance criteria for beam-to-column connections (flexural hinge is located within the connection) 

are taken from Fully Restrained Moment Connections in ASCE 41 Table 5-5 and are dependent on 

3-22
 
 

connection detailing, panel zone strength in a balanced yield condition, and member and cross-section 

slenderness (see ASCE 41 §5.4.2.4.2, 4.1 to 4.4). It is assumed that the acceptance criteria for FR beam-tocolumn connections (m-factor) translated from results from the SAC project are applicable at the face of 

the column—see §3.2.1.2. Furthermore, the m-factors for beams are not applicable for flexural plastic 

hinges within the region20 demarcating the beam-to-column connection when connection components 

prevent the unobstructed spread of plasticity. ASCE 41 does not provide acceptance criteria for flexural 

actions for a beam-to-column connection that includes a brace connection (i.e., brace-to-beam/column) or 

a brace-to-beam connection. ASCE 41 requires that all beams, beam-to-column connections, and brace 

connections in an EBF be force-controlled for flexural actions. ASCE 41 §5.5.3.3.2 introduces the expected 

flexural strength of beams and columns, although they are required to be force-controlled. There is limited 

technical justification as to the reason beams adjacent to shear links as well as the beam-to-column and 

brace-to-beam connections are mandatorily force-controlled for the CP BPL at the BSE-2 EHL. In so doing, 

an EBF is potentially overly penalized by ASCE 41 as compared to a concentrically braced frame (CBF), 

which does not apply force-controlled designations on all components. 

Flexure in Columns, Braces, and Columns-to-Base Connections 

ASCE 41 §5.5.3.4.1 requires that all flexural actions in columns, braces, and all connections in an EBF be 

force-controlled. Though flexural action in these components is treated as force-controlled, the following 

discussion is presented assuming that these components are deformation-controlled for modelling and 

analysis purposes to align with other reports developed for this study (see NIST 2014a and 2014b). Also, 

this allows comparison to other braced frame systems in ASCE 41—including buckling-restrained braced 

frames found in ASCE 41-13. 

The acceptance criteria for flexural action at expected locations of plastic hinging in columns (members 

with axial load ratio greater than 10 percent) are provided in ASCE 41 Table 5-5 and are dependent on the 

axial load ratio, PUF / PCL, and web and flange slenderness. As discussed above, ASCE 41 does not delineate 

between orthogonal buckling axes and non-flexural buckling limit states (e.g., torsional, local buckling) for 

computing PCL. Consequently, this can significantly affect the assessment of beam-column members where 

a high in-plane moment is associated with a buckling limit state other than in-plane flexural buckling. If the 

axial load ratio is greater than 0.5, then flexural action is considered force-controlled and the flexural 

demand and strength are taken as MUF and MCL, respectively. Otherwise, the m-factor is adjusted for P-M 

interaction as shown in Figure 3-4 and the flexural demand and strength are taken as MUD and MCE, 

respectively. 

The flange slenderness limits for columns are the same as those for beams and are independent of axial 

load. The lower-bound web slenderness range is essentially21 75 percent of the slenderness limits in AISC 

341-02 (AISC 2002)—taken from FEMA (2000c)—at distinct axial force ratios (0.2 and 0.5). These ratios 

are at the upper range of axial force ratios in ASCE 41, albeit PUF / Pye and PUF / PCL represent two physically 

different phenomena in regards to plate buckling. The upper-bound web slenderness range is essentially the 

slenderness limits in AISC 341-02 at distinct axial force ratios (0.1 and 0.2). These ratios are at the lower 

20 This region is also used in AISC 341 to define the protected zone. 21 Work to develop FEMA 356 was conducted at the same time as the SAC project—see FEMA 350 series. 

3-23
 
range of axial force ratio in ASCE 41. Using fixed axial limits on slenderness can lead to excessive 

conservatisms because of step function triggers, as illustrated in Figure 3-5 for the LS SPL—AISC 341 web 

compactness limits for highly (HD) and moderately (MD) ductile compression elements are included for 

comparison. The spherical icons shown in the figure represent the web slenderness ratios for all wide-flange 

sections currently available. Essentially, 35 percent of these sections do not satisfy the lower-bound criteria 

in ASCE 41 whereas this value reduces to 12 percent when using the AISC 341 criteria for highly ductile 

elements. Ultimately, the step functions created by both the axial load ratios and the section compactness 

requirements result in a highly complex formulation that is difficult to implement, as illustrated in Figure 

3-6 for the LS SPL (plastic rotation is shown in lieu of m-factor). ASCE 41 could be simplified by 

combining the acceptance criteria for beams and columns into one set of criteria with no 10 percent axial 

load ratio trigger. 

In addition to the effect of P-M interaction on the m-factors (which is a section strength issue) for checking 

flexural actions in a column in accordance with ASCE 41 §3.4.2.2, member stability is also checked via 

global interaction equations in accordance with ASCE 41 §5.4.2.4, as shown in Figure 3-4 —see projection 

of axial and moment ratios. The discontinuous curve is a result of variable P-M interaction equations, with 

the discontinuity at PUF / PCL = 0.5 being smallest when MCL at PUF = 0 equals Mp, and gets larger as MUD / 

MUF increases. Future efforts should simplify the ASCE 41 interaction curves for consistency and 

applicability, including eliminating Fy,LB for a column that also uses Fye. 

Axial compression action in a column is always force-controlled due to significant reduction in ductility 

because of member and cross-sectional instability. Again, ASCE 41 is rather ambiguous when it comes to 

steel columns. First, there is no guidance on computing MCE for a column. Although ASCE 41 §5.4.2.4.2­

2 provides some information, it is not consistent with that required to define the expected flexural strength, 

MCE. Second, the m-factor is reduced for beams to account for LTB. Since this failure mode is also 

applicable to columns, the m-factor should similarly be reduced. However, a column that fails in LTB 

should be avoided, and m = 1 adopted since LTB is not a ductile phenomenon. Also,  is not in the 

interaction equations similar to other verification procedures, and it is unclear if these equations have any 

physical meaning because member stability and section yielding effects are combined. Moreover, these 

equations can be conservative when weak-axis buckling is coupled with in-plane (strong-axis) bending. 

ASCE 41 §5.5.3.3.2 introduces the expected flexural strength of columns and beams, although they are 

required to be force-controlled. However, ASCE 41 does not provide guidance on how to assess a forcecontrolled column for flexural when P ≤ 0.5PCL similar to that given for a moment frame or concentrically 

braced frame. For this study, assessment of columns and braces with P-M interaction is done using ASCE 

41 §5.4.2.4.2-2 (Equations 5-10, 5-11, and 5-12), with MCL used in lieu of MCE where applicable and the mfactor taken as unity. 

Columns are designed in accordance with capacity design provisions in AISC 341. ASCE 41 does similarly 

adopt a capacity design approach for the assessment of EBF columns and beams (see ASCE 41 §5.5.3.4.1). 

3-24
 
 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

0.0 

0.1 

0.2 

0.3 

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0.5 

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0.7 

0.8 

0.9 

1.0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 0.1  UF  0.2 

PCL 

P M UF UDx  1.0 

2P m M CL x CEx 

P 0.2  UF  0.5 

PCL PUF 

PCL PUF 8  M  UDx    1.0

PCL m M x CEx 9  

PUF 0.5  (m = 1.0)

x PCL 

P M UF UFx  1.0 

P M CL CLx 

P = P ( = 1.0) CL n,AISC

with F = F y yLB mx

MUx 

mM 

_ 

x C x _ Immediate Occupancy

Notes: Life Safety

 Collapse Prevention 1. Knowledge Factor, , taken as unity. 

2. m factors shown are not reduced to reflect compactness requirements or inelastic LTB. 

3. Beam-Column with P / P < 0.1 can be treated as a beam. UF CL

Figure 3-4. P-M Interaction on Section m-factor (in-plane) and Member Instability (Primary Component) 

3-25
 
E  Fye
 

h 640 4.0  tw Fye 

Wide-Flange Sections 

35% > Group A

 1% > Group B 

12% > AISC HD

3.5 

Life Safety 

 ASCE 41 Group A Compactness Limit

 ASCE 41 Group B Compactness Limit

 AISC 341-10 HD Compactness Limit

 AISC 341-10 MD Compactness Limit 

P   P P ( 1.0)  0.6 CL n AISC c ,	 ye 

3.0 3% > AISC MD F F   50 ksi h 460	 ye y  tw Fye
 

h 400
  2.5 t w Fye 

interpolate h 418 2.0 between limits t F 



w ye 

h 300  t 1.5 w Fye h 260  	 P hE P   tw Fye    0.125 2.45   1 0.93    cy P tF w y   c y P   AISC HD   



1.0  P hE P E   0.125 0.77 2.93    1.49   P tF F P 

P hE P 

 cy w y   cy y 

	      0.125 3.76   1 2.75  0.5   cy P tF w y c y P   AISC MD 

 P hE P E     0.125 1.12 2.33    1.49 

Width-to-Thickness Ratio, 

h/t 

w 



0.060.12 

    cy P t F w   c y P F  y 

0.0	 0.2 0.4 0.6 0.8 1.0
 

Axial Load Ratio, P/P
 

ye

Figure 3-5. Compactness Requirements as a Function of Axial Load Ratio, LS Acceptance Criteria 

y 

0.0
 

3-26
0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

0 

1 

2 

3 

4 

5 

6 

7 



E 

Primary Component Fye 

Life Safety 

Width-to-Thickness Ratio, 

h/t 

w 

P P  0.6 CL ye 

F   F ksi 50 ye y 

Plastic Rotation,  =  p y Axial Load Ratio, P/PCL 

 ASCE 41 Group A Compactness Limit

Notes: ASCE 41 Group B Compactness Limit

1. Knowledge Factor, , taken as unity. AISC 341-10 HD Compactness Limit

2. Beam-Column with P / P < 0.1 can be treated as a beam. CL AISC 341-10 MD Compactness Limit 

Figure 3-6. Acceptance Criteria as a Function of Axial Load Ratio and Section Compactness, LS Acceptance Criteria 

 

Shear in Panel Zones 

ASCE 41 requires that all panel zones in an EBF be force-controlled. 

Additional Commentary on the Forces in all EBF Components other than Link Beams 

As discussed previously, ASCE 41 §5.5.3.4.1 requires all component actions other than link beams to be 

force-controlled. However, ASCE 41 does not provide explicit guidance with regards to computing forces 

in force-controlled components in an EBF for linear assessment procedures. First, force-controlled actions 

are computed in accordance with ASCE 41 §3.4.2.1.2—either Method 1 or 2. Second, ASCE 41 §5.5.3.4.2 

requires components to be assessed for a maximum developed link force of 1.25 times the lesser of the 

expected flexural or shear strengths of the link beams. It is assumed in this study that this guidance is 

intended to outline ASCE 41 §3.4.2.1.2-1 (Method 1) for computing force-controlled component actions 

3-27
 

and that this guidance is not also applicable for ASCE 41 §3.4.2.1.2-2 (Method 2). Therefore, assessment 

of this framing system is done twice, using force-controlled actions computed (1) according to ASCE 41 

§3.4.2.1.2-2 and (2) according to ASCE 41 §3.4.2.1.2-1 assuming a maximum developed link force of 1.25 

times the lesser of the expected flexural or shear expected strengths of the link beams. The maximum value 

of the two will govern assessment procedures. 

The capacity design procedure described above matches that prescribed in AISC 341 §F2.3 for design of 

an EBF, except for negligible variation in the gravity load contribution and that qualified columns can be 

designed for 88 percent of the seismic demand. In regards to ASCE 41 assessment, setting c equal to unity 

to compute PCL effectively compensates for the 12 percent reduction provided for new EBF columns. 

Because the EBF in each archetype building is designed in accordance with AISC 341, the force-controlled 

components of each EBF satisfy ASCE 41 §3.4.2.1.2-1 by default and no further assessment is required. 

Consequently, assessment of the force-controlled components in this study is performed in accordance with 

ASCE 41 §3.4.2.1.2-2 for comparison purposes between the two methods. 

Demand 

The flexural demand, MUD or MUF, and axial force, PUF, for the columns and braces are taken as the moment 

and axial force at the face of the each beam (top and bottom) or brace connection, respectively. The flexural 

demand, MUD or MUF, for the beams is taken as the moment at the face of the brace connection. The flexural 

demand, MUD or MUF, for the beam-to-column connections is taken as the moment at the face of the column 

or edge of the brace connection. 

Table 3-10 summarizes the basic m-factors for the components of the EBF for the linear procedures. Figure 

3-7 through Figure 3-9 provide the load-independent m-factors—taking in to account force-controlled and 

deformation-controlled classifications (force-controlled component actions are assigned an m-factor of 

unity, see §3.1.4.1). These figures are referred to herein as “Frame Capacity Schematics.” 

Table 3-10. Basic m-factors for Linear Procedures, EBF 

Component - Action 

EBF Link Beam 

LS CP 

Performance Level 

a) 1.6 CE e M  V CE 9 13 

b) 2.6 CE e M  V CE Same as for beams 

b) 1.6 M CE 2.6 V e M CE   CE V CE linear in terp olatio n 

3-28
 
 

 

 

 

9.00 13.00 

1.00 1.00 

9.00 

1.00 

1.00 

9.00 

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1.00 1.00 1.00 

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1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-7. Frame Capacity Schematic (m-factor), LS and CP, 4-Story EBF ELF and RSA 

9.00 13.00 

1.00 1.00 

9.00 

1.00 

1.00 

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1.00 

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1

0 .0

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1

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1

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1

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1

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1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

1.00 1.00 1.00 1.00 

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-8. Frame Capacity Schematic (m-factor), LS and CP, 8-Story EBF ELF and RSA 

3-29
 
 

9.00 13.00 

1.00 

0 

0

.

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0

.

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1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-9. Frame Capacity Schematic (m-factor), LS and CP, 16-Story EBF ELF and RSA 

3-30
 
Nonlinear Procedures 

This section discusses the three primary component characteristics listed in Section 3.2.1 and computation 

of the demand in the component for the nonlinear assessment procedures. 

Stiffness, Strength, Acceptance Criteria, and Demand 

Component characteristics follow that outlined previously for the linear procedures. Although component 

stiffness is the primary characteristic in linear procedures, component strength is of equal importance in 

nonlinear procedures. 

As noted previously, ASCE 41 §5.5.3.4.1 requires that all components in an EBF other than the link beams 

be force-controlled. Though component actions are classified as force-controlled, the complete nonlinear 

response of these components is modeled for the NSP and NDP in this study. That is, the following 

discussion is presented assuming that these components are deformation-controlled for modelling and 

analysis purposes to align with other reports developed for this study (see NIST 2014a and 2014b). Also, 

this allows comparison to other braced frame systems in ASCE 41—including buckling-restrained braced 

frames found in ASCE 41-13. 

The stiffnesses of all members and connections for nonlinear assessment follow ASCE 41 §5.5.3.2.2 for 

the NSP and ASCE 41 §5.5.3.2.3 for the NDP. The strength of all members and connections for nonlinear 

assessment follow ASCE 41 §5.5.3.3.3 for the NSP and ASCE 41 §5.5.3.3.4 for the NDP. The same 

analytical model is used for both the NSP and NDP—see §3.1.3.2. 

Compound elements with elastic and inelastic components are used for constructing all members in 

PERFORM-3D. Elastic stiffness and strength characteristics for each component follow that outlined for 

the linear procedures. Nonlinear components include the column and brace flexural hinge modeled with 

axial-moment (P-M) interaction and the panel zone modeled using the Krawinkler model (Krawinkler 

1978). Gusset plate connections for braces are not explicitly modeled. The flexural rigidity, EI, of the 

portion of a member adjacent to a gusset plate is increased to approximate the effect of gusset plate rigidity 

in the plane of the frame. Figure 3-10 illustrates the analytical model of a brace-to-beam / column 

subassembly for nonlinear assessment procedures. In the figure, Default End Zones are modeled with a 

flexural rigidity factor of two; a higher end zone factor is potentially too rigid to capture flexural 

deformations within the joint region. Detailed information concerning all aspects of the analytical model 

for nonlinear analysis can be found in PERFORM-3D Components and Elements (CSI 2011c). 

Shear plasticity in a link beam is represented by a plastic shear strain hinge with a plastic hinge length equal 

to the link length, e. Inelastic strain parameters are taken from ASCE 41 Table 5-7. Shear strength and 

stiffness degradation are modeled based on calibrating the PERFORM-3D MODEL with experimental test 

data (see Figure 3-11—PERFORM-3D response is presented as “Analysis”). The shear hinge model in 

PERFROM-3D gives the response in terms of plastic strain. In this study, the shear yield force, Vy, is taken 

as 1.15×VCE as defined in ASCE 41 to account for the influence of the flanges at yield and the ultimate 

shear force is taken as 1.25×Vy (=1.4375×VCE)—see Figure 3-11. As will be graphically illustrated 

subsequently in the analysis results, this adopted link beam strength will increase the (axial) forces in the 

adjacent members beyond that determined from the capacity analysis prescribed in ASCE 41 §5.5.3.4.2. 

3-31
 
Inelastic 

Beam, EIb

W.P. 18" 

Pan e l Zo ne 

Inelastic Beam, EIb 

Shear hinge , 

plastic strain type 

lp = e 

C Sym. Ab out 

Inelastic Beam, EIb Guss et Elem ent, 2EIb

Brace, 2EIbr 

L = 0.05Lwp, t yp . 

db/2 

Guss et Inel ast ic Beam, EIb

Element, 2EIb 

Plastic Hinge, 

lp = db 

nod e 

db/2 L 

Guss et Plate (not m odeled) 

Increased joint stiff ness provid ed 

by gusset elemen ts 

Defau lt 

En d Zo ne 

Guss et 

Element, 

2EIc 

Inelastic Colum n Inelastic Colum n 

Defau lt 

En d Zo ne 

In elastic 

Column, 

EIc 

In elastic 

Column, 

EIc 

d c/2 18" d c/2 d b/2 d b/2 

Brace, EIbr 

L = 0.9Lwp 

Moment-Cu rvature 

PMM H in g e, t yp . 

Default

En d Zo ne 

In elastic Beam Inelastic Beam, EIb 

node 

18" 

In elastic 

Column, 

EIc 

In elastic 

Column, 

EIc 

Plastic Hinge

l p = d c 

Plastic Hinge

l p = d c 

W.P. 

Figure 3-10. EBF Analytical Modeling Schematic 

Flexural plasticity in beams and beam-columns is represented by nonlinear moment-curvature (MC) 

relationships which in turn are based on moment-chord rotation (MR) relationships provided by ASCE 41 

Table 5-6. This shift in basis highlights a discrepancy between ASCE 41 §5.4.2.2.2-2 and the prescribed 

acceptance criteria. Conversion between plastic rotation and plastic curvature is done using a defined plastic 

hinge length, lp. An MC hinge is preferred in lieu of an MR hinge, as yield rotation, y, specified in ASCE 

41 can lead to inconsistencies when beam models include rigid end offsets and when hinges are modeled 

away from the column faces. Further, ASCE 41 does not provide guidance on an appropriate beam length, 

3-32
 
lb (ASCE 41 Equation 5-1). Theoretically, there is no difference between an MC hinge and an MR hinge 

model as long as the conversion procedure for all nonlinear model parameters between the two is 

maintained. P-M interaction effects on a moment-curvature hinge are included in the analytical model 

(discussed subsequently). 

UTA Specimen 4A-RLP (Richards et al. 2007) 

150 

Shear Force, V 

100 

50 

0 

-50 

-100 

-150 

 Test Data

 Analysis

 Backbone 

W10×33 

e = 23" 

-0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 0.12 0.15 0.18 

Plastic Shear Strain,  p

Figure 3-11. PERFORM-3D Link Beam Shear Hinge Calibration 

Where needed to model a flexural hinge within a beam span or a flexural hinge within (or adjacent to) a 

connection (e.g., next to the brace-to-beam connection in the chevron frame), an MC hinge is placed at the 

center of the hinge with a plastic hinge length equal to the depth of the beam, d. Plastic rotation parameters 

modeling the backbone curve of the beam or connection hinge are taken from ASCE 41 Table 5-6. These 

values are converted to plastic curvature and, if needed, adjusted from application at the column face to the 

center of the hinge (no adjustment is needed for a conventional beam hinge) and other connection 

adjustments discussed next. The residual strength ratio (c in ASCE 41 Table 5-6) is normalized to the yield 

strength, MCE, not the ultimate strength as required in PERFORM-3D. 

Where applicable, the acceptance criteria for beam-to-column connections (flexural hinge is located within 

the connection) are taken from Fully Restrained Moment Connections in ASCE 41 Table 5-6 and are 

dependent on connection detailing, panel zone strength in a balanced yield condition, and member and 

cross-section slenderness (see ASCE 41 §5.4.2.4.3, 4.1 to 4.4). These reduction factors are also applied to 

the plastic rotation values defining the backbone curve. This is done because the CP acceptance criteria for 

a primary FR connection was taken to match a—see Figure 3-2, and therefore any connection configuration 

that affects the value for a also affects the acceptance criteria. Similarly, the acceptance criteria are 

converted to plastic curvature and the application point is adjusted to the center of the hinge. Expanded 

commentary on beam-to-column connection versus beam hinge acceptance criteria is needed in ASCE 41, 

as well as a discussion clarifying the reductions to the plastic rotation values defining the backbone curve 

3-33
 
 

and acceptance criteria. ASCE 41 does not provide acceptance criteria for flexural actions for a beam-tocolumn connection that includes a brace connection (i.e., brace-to-beam/column) or a brace-to-beam 

connection. ASCE 41 requires that connections in an EBF be force-controlled for all actions. 

Frame columns (i.e., beam-columns) are modeled similar to beams discussed previously, except that 

flexural PMM MC hinges that capture the combined effects of axial force and biaxial moments are placed 

near the joint region boundaries (see Figure 3-10). The plastic hinge length is assumed to be equal to the 

depth of the column, dc. Out-of-plane moments are small relative to the in-plane moments in the SFRS 

members because each SFRS is an isolated planar frame in the direction of loading. Plastic rotation 

parameters of the flexural PMM hinges are taken from “columns” in ASCE 41 Table 5-6 and converted to 

plastic curvature (no adjustment for hinge location is needed). Criteria for flexural hinges based on member 

buckling strengths can be complex and problematic in capturing the in-plane nonlinear flexure behavior. 

For example, yield rotation, y, for a column is based on section strength, Pye, while modeling parameters 

and acceptance criteria (function of y) are based on member strength, PCL, without regard to the plane of 

buckling. ASCE 41-13 took the first step in resolving some issues concerning steel columns by permitting 

the modeling parameters to be determined using P / PCL in the plane of buckling. Still, P-M interaction 

curves still require some clarification and guidance. In terms of assessment, ASCE 41 does not explicitly 

address column hinges near the column-to-base connections of a frame (similar to a beam-to-column 

connection). 

In this study, modeling and acceptance criteria for the beam-column flexural hinges are taken as those 

provided for columns in ASCE 41 Table 5-6. The P-M interaction effect on the in-plane flexural strength 

of a column hinge, MCEx, where x denotes the in-plane bending axis, is modeled by the section strength of 

the member (i.e., yield surface) using P / Pye in ASCE 41 Equation 5-4 (repeated below as Equation (3-16); 

see Figure 3-12, Figure 3-14, and Figure 3-15). P-M interaction relationships provided in PERFORM-3D 

for the yield surfaces of MC hinges in beam-columns are calibrated to approximate this curve as illustrated 

in Figure 3-15. 

 P 

MCEx 1.18M pe x , 1   M pe x , (ASCE 41, Equation 5-4) (3-16)  Pye   

ASCE 41 Equation 5-4 is based on plastic design theory and applicable for the in-plane section strength 

(strong-axis bending) of a wide flange section. AISC 360 Equation H1-1 can also be applied for computing 

the in-plane section strength by using P / Pye in lieu of Pr / Pc as defined in AISC 360. Plastic design theory 

also gives the out-of-plane section strength (weak-axis bending, with y denoting the out-of-plane bending 

axis) of a wide flange section as Equation (3-17). 

 2   P 

M 1.19 M 1 

    M (3-17) CEy pe y , pe y ,  P    ye  

3-34
 
P-M interaction effect on the plastic rotation parameters and acceptance criteria of a column hinge is 

modeled by member strength using PCL, computed for buckling about any axis or failure mode independent 

of the effect it may have on the in-plane flexure response of the column hinge (see Figure 3-12). 

First, ASCE 41 requires a column (i.e., flexural hinge in the column) to be force-controlled for flexure when 

P / PCL > 0.5 for the nonlinear procedures and references the same equation used for linear assessment. This 

can be extremely problematic as separate strengths and interaction equations create discontinuities that 

cannot be effectively addressed in analysis software (see Figure 3-12). This elastic interaction equation is 

neglected in this study for nonlinear assessment and the hinge model obeys ASCE 41 Equation 5-4 

independent of PCL. ASCE 41 Equation 5-12 is more applicable for checking member stability than defining 

the section yield surface; Equation (3-18) rearranges ASCE 41 Equation 5-12 in terms of the moment 

strength. 

 P  MCE  MCL 1  (from ASCE 41, Equation 5-12) (3-18)  PCL 

Second, flexural hinge model parameters and associated acceptance criteria are a function of the axial load 

ratio P / PCL. Provisions for this interaction in ASCE 41, however, create a discontinuity in the curve, as 

shown in Figure 3-13. , which cannot be effectively addressed in analysis software. PERFORM-3D 

provides a simplified curve to model the variation in acceptance criteria with axial force, also shown in 

Figure 3-13. The adopted curves in this study are conservative for P / PCL ≤ 0.2. Further, because of 

constraints on P-M hinge models in PERFORM-3D, the model parameters (a in ASCE 41 Table 5-6 plus 

the elastic component as shown in Figure 3-12, a plus elastic = DL in PERFORM-3D—see Figure 3-2 for 

a and DL) do not coincide for P / PCL > 0.2. A column hinge with high axial load can reach its peak strength 

(a plus elastic = CP in this case) in regards to the provisions of ASCE 41 yet still be able to maintain its 

flexural strength. In general, column hinges are not expected to be significantly strained; however, demands 

may affect the performance of base hinges, which can have detrimental effects on the system upon loss of 

strength. More detailed information can be found in the PERFORM-3D User Guide (CSI 2011d) and 

PERFORM-3D Components and Elements (CSI 2011c). Lastly, it is of questionable validity to allow a 

primary column component in a SFRS to have acceptance criteria based on a secondary component when 

based on a function of P / PCL as was mentioned earlier. 

The ultimate flexural strength of the MC hinge is taken as 1.1 times MCE at P = 0. This flexural strength 

increase is held constant for all values of axial force in PERFORM-3D. The residual strength ratio (c in 

ASCE 41 Table 5-6) is normalized to the yield strength, MCE, at distinct P / PCL values (not P / Pye, which 

is used to compute MCE) and not the ultimate strength as required in PERFORM-3D. 

Stability of a beam-column needs to be addressed in addition to capturing flexural plasticity. However, 

ASCE 41 does not provide explicit provisions to check member stability when P / PCL ≤ 0.5 for nonlinear 

procedures. When P / PCL > 0.5, ASCE 41 Equation 5-12 (primarily used for the linear procedures) can be 

used, but is not recommended as discussed previously. 

In this study, section strength flags are applied to the frame columns as an indicator of member instability. 

For in-plane buckling and strong axis bending, a PM strength flag is placed at the ends of the column using 

3-35
 
AISC 360 §H1.3(a) for the interaction curve using Pn,x as Pc. This approach closely aligns with ASCE 41 

Equations 5-10, 5-11, and 5-12. The in-plane effective length of the column is taken as that computed for 

design (i.e., adjusted K factor—see Chapter 2). This is considered a conservative practice as the analysis 

adjusts the stiffness matrix (only for material nonlinearity) at every time step and the leaning column effect 

is explicitly included. However, geometric imperfections (system and member), residual stresses, and 

epistemic uncertainties (i.e.,  factor) are not included in the mathematical model. Consequently, member 

strengths based on the actual unbraced length (i.e., KLx = Lx) is of questionable validity, but so is using the 

design value based on a vertical load-only load combination. Research is needed concerning in-plane 

dynamic instability of inelastic members. 

1.0 

P / P 

ye 

0.8 

0.6 

0.4 

0.2 

0.0 

0.0 0.2 0.4 0.6 0.8 1.0 

 ASCE 41 Eq. 5-4

 ASCE 41 Eq. 5-12

 Single Curve Hinge Model 

PCL = P 

n,y

 = 0.6 P 

ye 

MCL = (1.0/1.1) MCE 

M / MCE

Figure 3-12. In-plane Flexural Hinge Yield Surface Model (Including Force-Controlled Response) 

For out-of-plane buckling and strong axis bending, a PM strength flag is placed at the ends of the column 

using AISC 360 §H1.3(b) for the interaction curve and the effective length is taken as the actual unbraced 

length (i.e., KLy = Ly). Adopting ASCE 41 Equations 5-10, 5-11, and 5-12 as an indicator of weak-axis 

instability coupled with in-plane bending can be highly conservative. PERFORM-3D uses a single 

continuous interaction curve as shown in Figure 3-16 which illustrates several interactions curves together 

with the approximations from PERFORM-3D. Similar to beams, section strengths are modified as needed 

based on cross-section geometry, member strengths (commonly controls columns in compression), and 

design-assessment criteria prescribed in ASCE 41. 

ASCE 41 requires that columns and braces in an EBF be force-controlled for flexure. However, ASCE 41 

does not provide guidance on how to assess the component when P ≤ 0.5PCL, other than referencing 

provisions given for a concentrically braced frame, which in turn references provisions applicable for the 

expected strength of components in a moment frame. Further, the use of FyLB needs clarification in terms 

of determination of section compactness and member slenderness requirements for force-controlled 

components. 

3-36
 
a + elastic - ASCE 41 Table 5-6 

Total Curvature ( x106 ) 

4000 

3500 

3000 

2500 

2000 

1500 

1000 

500 

0 

LS 

CP 

W18×175 

L = 18'-0" 

PCL = P n,y = 0.6 P ye 

a + elastic - PERFORM-3D (= DL)

 Life Safety AC - ASCE 41 Table 5-6 

 Life Safety AC - PERFORM-3D 

Collapse Prevention AC - ASCE 41 Table 5-6

 Collapse Prevention AC - PERFORM-3D 

0.0 0.1 0.2 0.3 0.4 0.5 

P / PCL 

Figure 3-13. Variation in Acceptance Criteria and Hinge Model for Axial Force 

For this study, force-controlled flexural hinges in columns and braces are modeled as discussed above, 

which is the same as a deformation-controlled flexural hinge in a moment frame and concentrically braced 

frame. The acceptance criterion for these force-controlled hinges and compression members is therefore 

based on (1) the expected yield strength of the section and whether or not the section develops a plastic 

hinge and (2) member instability using the expected PM interaction strength, respectively. Modeling and 

assessment of force-controlled components in an EBF for nonlinear assessment methods is a topic that 

needs further clarification in ASCE 41. 

Figure 3-17 through Figure 3-22provide the load-independent acceptance criteria—with consideration of 

force-controlled and deformation-controlled classifications. These figures are referred to herein as “Frame 

Capacity Schematics.” The two values given for a column represent the cases when PUF / PCL = 0.2 and 0.5, 

adjusted for section compactness requirements. As a side note, the LS acceptance criterion for the link 

rotation angle in ASCE 41 is 1.375 times the allowable rotation angle prescribed in AISC 341 (= 0.08 

radians) at the BSE-1 EHL (when taken as 2⁄3×MCER)—the CP acceptance criterion is 1.625 times this 

rotation angle at the BSE-1 EHL. 

3-37
 
0.2 

0.4 

0.6 

0.8 

1.0 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

0 

1 

2 

3 

4 

5 

6 

7 

Primary Component

Life Safety
 

Axial Load Ratio, 

P/P 

ye 

discontinuity in 

interaction curve 

Rotation Ductility
 

Limits, (

y

 + 

p

) / 

y

Moment Ratio, M/M 

pe Yield Surface (ASCE 41 Eq. 5-4)

1. Knowledge Factor, , taken as unity. 

 Rotation Ductility PCL Notes: = Pye

 Rotation Ductility PCL = 0.85P ye

2.  =  values shown are not reduced to reflect compactness requirements. p y Rotation Ductility PCL = 0.75P ye

 = 0.60P ye 

3. Beam-Column with PUF / PCL < 0.1 can be treated as a beam. Rotation Ductility PCL

Figure 3-14. P-M Interaction on Plastic Rotation, LS Acceptance Criteria (Primary Component) 

3-38
1.0 

0.8 

Axial Force Ratio (P / P ye ) Axial Force Ratio (P / P ye ) 

0.2 

0.4 

0.6 

 ASCE 41 In-Plane Yield Surface

 (Eq. 5-4)

 AISC In-Plane Yield Surface

 (H1-1, P n = P ye )

 PERFORM-3D In-Plane Yield Surface

 ( = 1.5,  = 1.1)

 Out-of-Plane Yield Surface

 (H1-1, P n = P ye )

 PERFORM-3D Out-of-Plane Yield Surface

 ( = 2.5,  = 1.1) 

0.0 0.2 

0.0 

0.4 0.6 0.8 1.0 

Moment Ratio (M / M pe )

Figure 3-15. P-M Interaction Curve (Section Yield Surface) 

 

1.0 

0.2 

0.4 

0.6 

0.8 

 

 

 

 

 

 

 

 

 ASCE 41 In-Plane Yield Surface

 (Eq. 5-4)

 AISC In-Plane Stability (Cb

 > 1)

 (H1-1, P c = P ne,x )

 PERFORM-3D In-Plane Stability (Truncated)

 ( = 1.75,  = 1.0)

 AISC Out-of-Plane Stability (Cb

 > 1)

 (H1-1, P c = P ne,y )

 PERFORM-3D Out-of-Plane Stability

 ( = 1.3,  = 1.0)

 AISC Out-of-Plane Stability (Cb

 > 1)

 (H1-2, P cy = P ne,y )

 PERFORM-3D Out-of-Plane Stability

 ( = 1.0,  = 1.5)

 PERFORM-3D Out-of-Plane Stability (Truncated)

 ( = 2.5,  = 1.25) 

0.00 

0.0 

0.25 0.50 0.75 1.00 1.25 1.50 

Moment Ratio (M / M pe )

Figure 3-16. P-M Interaction Curve (Member Instability) 

3-39
 

Figure 3-17. Frame Capacity Schematic (Inelastic), LS and CP, 4-Story EBF – ELF 

Figure 3-18. Frame Capacity Schematic (Inelastic), LS and CP, 4-Story EBF – RSA 

3-40
 
Figure 3-19. Frame Capacity Schematic (Inelastic), LS and CP, 8-Story EBF – ELF 

3-41
 
 

Figure 3-20. Frame Capacity Schematic (Inelastic), LS and CP, 8-Story EBF – ELF 

3-42
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sym. Abou t 

Shear Hinges 

3 

CP → 130 

LS → 110 

2 

Roof 

Brace Hi nges Col umn Hinges (ELEV = 228 ft.) CP → T=B=4691, 1269 CP → T=B=4299, 968 

LS → T =B=3470, 970 LS → T=B=3210, 769 

YD → T=B=317, 232 YD → T=B=276, 202 16th Fl o or 

Brace Hi nges Col umn H inges (ELEV = 214 ft.) CP → T=B=4691, 1269 CP → T=B=4299, 968
 

LS → T=B=3470, 970 LS → T=B=3210, 769
 

YD → T=B=317, 232 YD → T=B=276, 202
 15th Fl o or 

Brace Hi nges Col umn H inges (ELEV = 200 ft.) CP → T=B=1143, 850 CP → T=B=3808, 868
 

LS → T=B=846, 633 LS → T=B=2849, 692
 

YD → T=B=315, 231 YD → T=B=260, 191
 14th Fl o or 

Brace Hi nges Col umn H inges (ELEV = 186 ft.) CP → T=B=1143, 850 CP → T=B=3808, 868
 

LS → T=B=846, 633 LS → T=B=2849, 692
 

YD → T=B=315, 231 YD → T=B=260, 191
 13th Fl o or 

Brace Hi nges Col umn Hinges (ELEV = 172 ft.) CP → T=B=3111, 1070 CP → T=B=3700, 846 

LS → T =B=2302, 811 LS → T=B=2769, 676 

YD → T=B=313, 229 YD → T=B=258, 189 12th Fl o or 

Brace Hi nges Col umn H inges (ELEV = 158 ft.) CP → T=B=3111, 1070 CP → T=B=3700, 846
 

LS → T=B=2302, 811 LS → T=B=2769, 676
 

YD → T=B=313, 229 YD → T=B=258, 189
 11th Fl o or 

Brace Hi nges Col umn H inges (ELEV = 144 ft.) CP → T=B=5716, 1363 CP → T=B=3296, 765 

LS → T=B=4230, 1048 LS → T=B=2472, 614 

YD → T=B=311, 228 YD → T=B=246, 180 10th Fl o or 

Brace Hi nges Col umn H inges (ELEV = 130 ft.) CP → T=B=5716, 1363 CP → T=B=3296, 765 

LS → T=B=4230, 1048 LS → T=B=2472, 614 

YD → T=B=311, 228 YD → T=B=246, 180 9th Flo or 

Brace Hi nges Col umn H inges (ELEV = 116 ft.) CP → T=B=5716, 1363 CP → T=B=2965, 697 

LS → T=B=4230, 1048 LS → T=B=2228, 562 

YD → T=B=311, 228 YD → T=B=236, 173 8th Flo or 

Brace Hi nges Col umn H inges (ELEV = 102 ft.) CP → T=B=7205, 1520 CP → T=B=2965, 697
 

LS → T=B=5333, 1178 LS → T=B=2228, 562
 

YD → T=B=307, 225 YD → T=B=236, 173
 7th Flo or 

Brace Hi nges Col umn H inges (ELEV = 88 ft.) CP → T=B=7205, 1520 CP → T=B=2703, 643 

LS → T=B=5333, 1178 LS → T=B=2034, 521 

YD → T=B=307, 225 YD → T=B=227, 166 6th Flo or 

Brace Hi nges Col umn H inges (ELEV = 74 ft.) CP → T=B=7205, 1520 CP → T=B=2703, 643
 

LS → T=B=5333, 1178 LS → T=B=2034, 521
 

YD → T=B=307, 225 YD → T=B=227, 166
 5th Flo or 

Brace Hi nges Col umn H inges (ELEV = 60 ft.) CP → T=B=7205, 1520 CP → T=B=2458, 593 

LS → T=B=5333, 1178 LS → T=B=1854, 482 

YD → T=B=307, 225 YD → T=B=218, 160 4th Flo or 

Brace Hi nges Col umn H inges (ELEV = 46 ft.) CP → T=B=7205, 1520 CP → T=B=2458, 593 

LS → T=B=5333, 1178 LS → T=B=1854, 482 

YD → T=B=307, 225 YD → T=B=218, 160 3rd Flo or 

Brace Hi nges Col umn H inges (ELEV = 32 ft.) CP → T=B=7205, 1520 CP → T=B=2208, 540
 

LS → T=B=5333, 1178 LS → T=B=1669, 442
 

YD → T=B=307, 225 YD → T=B=208, 152
 2nd Flo or 

Brace Hi nges Col umn H inges (ELEV = 18 ft.) CP → T=B=7936, 1651 CP → T=B=2772, 644
 

LS → T=B=5863, 1272 LS → T=B=2079, 517
 

YD → T=B=303, 222 YD → T=B=208, 152
 

YD → 2.7 

Links = Plastic Shear Strain ×103
 

Braces = Curvature×106 (for P/PCL = 0.2, 0.5)
 

Columns = Total Curvature×106

 (for P/PCL = 0.2, 0.5)
 

CP = Collaps e Prev en tion, LS = Life Safety, YD = Yield
 

T = Top Hinge, B = Botto m Hin ge
 

All values are for Primary Components
 

Figure 3-21. Frame Capacity Schematic (Inelastic), LS and CP, 16-Story EBF – ELF 

3-43
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sym. A bou t 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges
 

CP → T=B=7205, 1520 CP → T=B=3069, 718
 

LS → T=B=5333, 1178 LS → T=B=2304, 578
 

YD → T=B=307, 225 YD → T=B=239, 175
 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

Brace Hi nges Col umn H inges 

3 2 

Shea r Hinge s 

CP → 130 

LS → 110 

YD → 2.7 

Roof 

(ELEV = 228 ft.)
 CP → T=B=4691, 1269 CP → T=B=4512, 1011
 

LS → T=B=3470, 970 LS → T=B=3367, 801
 

YD → T=B=317, 232 YD → T=B=282, 207
 16th Flo or 

(ELEV = 214 ft.)
 CP → T=B=4691, 1269 CP → T=B=4512, 1011
 

LS → T=B=3470, 970 LS → T=B=3367, 801
 

YD → T=B=317, 232 YD → T=B=282, 207
 15th Flo or 

(ELEV = 200 ft.)
 CP → T=B=4691, 1269 CP → T=B=4252, 958
 

LS → T=B=3470, 970 LS → T=B=3176, 761
 

YD → T=B=317, 232 YD → T=B=275, 201
 14th Flo or 

(ELEV = 186 ft.)
 CP → T=B=4691, 1269 CP → T=B=4252, 958
 

LS → T=B=3470, 970 LS → T=B=3176, 761
 

YD → T=B=317, 232 YD → T=B=275, 201
 13th Flo or 

(ELEV = 172 ft.) CP → T=B=1143, 850 CP → T=B=3756, 880
 

LS → T=B=846, 633 LS → T=B=2809, 700
 

YD → T=B=315, 231 YD → T=B=266, 195
 12th Flo or 

(ELEV = 158 ft.) CP → T=B=1143, 850 CP → T=B=3756, 880
 

LS → T=B=846, 633 LS → T=B=2809, 700
 

YD → T=B=315, 231 YD → T=B=266, 195
 11th Flo or 

(ELEV = 144 ft.) CP → T=B=5716, 1363 CP → T=B=3894, 885
 

LS → T=B=4230, 1048 LS → T=B=2912, 706
 

YD → T=B=311, 228 YD → T=B=263, 193
 10th Flo or 

(ELEV = 130 ft.) CP → T=B=5716, 1363 CP → T=B=3894, 885
 

LS → T=B=4230, 1048 LS → T=B=2912, 706
 

YD → T=B=311, 228 YD → T=B=263, 193
 9th Fl o or 

(ELEV = 116 ft.) CP → T=B=5716, 1363 CP → T=B=3518, 809
 

LS → T=B=4230, 1048 LS → T=B=2635, 648
 

YD → T=B=311, 228 YD → T=B=252, 185
 8th Fl o or 

(ELEV = 102 ft.) CP → T=B=5716, 1363 CP → T=B=3518, 809
 

LS → T=B=4230, 1048 LS → T=B=2635, 648
 

YD → T=B=311, 228 YD → T=B=252, 185
 7th Fl o or 

(ELEV = 88 ft.) CP → T=B=5716, 1363 CP → T=B=3296, 765
 

LS → T=B=4230, 1048 LS → T=B=2472, 614
 

YD → T=B=311, 228 YD → T=B=246, 180
 6th Fl o or 

(ELEV = 74 ft.) CP → T=B=5716, 1363 CP → T=B=3296, 765
 

LS → T=B=4230, 1048 LS → T=B=2472, 614
 

YD → T=B=311, 228 YD → T=B=246, 180
 5th Fl o or 

(ELEV = 60 ft.) 

4th Fl o or 

(ELEV = 46 ft.) CP → T=B=7205, 1520 CP → T=B=3069, 718
 

LS → T=B=5333, 1178 LS → T=B=2304, 578
 

YD → T=B=307, 225 YD → T=B=239, 175
 3rd Floor 

(ELEV = 32 ft.) CP → T=B=7205, 1520 CP → T=B=2773, 658
 

LS → T=B=5333, 1178 LS → T=B=2087, 532
 

YD → T=B=307, 225 YD → T=B=229, 168
 2nd Flo or 

(ELEV = 18 ft.) CP → T=B=7936, 1651 CP → T=B=3493, 790
 

LS → T=B=5863, 1272 LS → T=B=2610, 628
 

YD → T=B=303, 222 YD → T=B=229, 168
 

Links = Plastic Shear Strain×103
 

Braces = Curvature×106 (for P/PCL = 0.2, 0.5)
 

Columns = Total Curv ature×106

 (for P/PCL = 0.2, 0.5)
 

CP = Collaps e Prev en tion, LS = Life Safety, YD = Yield
 

T = Top Hinge, B = Bottom Hinge
 

All values are for Primary Components
 

Figure 3-22. Frame Capacity Schematic (Inelastic), LS and CP, 16-Story EBF – RSA 

3-44
 
 

Seismic Assessment Results 

The results for the EBFs assessed using each of the four analysis procedures are presented in this section. 

The following section highlights any failure to satisfy the acceptance criteria. 

For the LSP and LDP, force-controlled column compression demands, PUF, are computed by taking J in 

ASCE 41 §3.4.2.1.2-2 as the minimum DCR—as defined in ASCE 41—of the component(s) (i.e., link 

beams) delivering force to the member, but not less than 2.0. In this case, this method generally provides 

the least conservative axial force demand estimates than that determined from a fully yielded capacity design 

analysis per ASCE 41 §3.4.2.1.2-1 following ASCE 41 §5.5.3.4.2. The capacity design analysis22 used in 

this study to determine the maximum axial load demands to satisfy ASCE 41 §3.4.2.1.2-1 assumes that all 

yielding components have achieved their maximum strength simultaneously (i.e., link beams achieving 

their maximum shear strength as defined by ASCE 41 §5.5.3.4.2). This axial load will be roughly ten 

percent larger than that computed using AISC 341 provisions for design of columns in new EBFs. Further, 

axial force demand estimates from the capacity design procedure using the system overstrength factor, , 

in ASCE 7 are included with those determined from ASCE 41 in the respective analysis sections below. 

Force-controlled component actions are assigned an m-factor of unity, see §3.1.4.1. 

Analysis results (e.g., DCRN) for the NDP using the ground motion record set are statistically summarized 

by the median, mean, 84th percentile, and mean plus one standard deviation response for both the LS BPL 

(given the BSE-1 EHL) and the CP BPL (given the BSE-2 EHL). Mean and median response are presented 

because (1) ASCE 41 does not discuss how to process the results in the event of a structural collapse under 

a given record in the set, (2) new provisions under investigation for inclusion in the 2015 NEHRP Provisions 

are being debated as to how to process results from eleven records (an increase from seven in ASCE 7-10), 

and (3) the difference is small for well-performing systems that remain stable for all motions in a set. It is 

the goal here that showing the mean and median will assist in developing future code provisions. 

For comparison purposes only, the DCRN values obtained from the LSP, LDP, and NSP are superimposed 

on the figures showing the results obtained from the NDP. Results from the NSP and NDP can be directly 

compared because the basis of measurement is identical. However, caution should be used when comparing 

linear and nonlinear results by inspection because the nature of the analysis is fundamentally different; 

presenting them together here is not intended to imply they are equivalent. Results from the two are not 

always directly comparable as linear results would first need to be converted to total demand where 

applicable, and in certain cases not based on an interaction equation. Results from the linear assessment 

procedures are presented alongside results from the nonlinear assessment procedures primarily to highlight 

the distribution of performance predictions between the analytical methods. 

For comparison purposes only, the base shears computed using the LSP and LDP are provided in §3.2.3.1.3. 

22 ASCE 41 §3.4.2.1.2-1 refers to this type of analysis as a “limit state” analysis. 

3-45
 
 

Four-Story Eccentrically Braced Frame 

3.2.2.1.1 Linear Static Procedure 

3.2.2.1.1.1 BSE-1 Earthquake Hazard Level (LS BPL) 

In this section, the following apply: 

	 Figure 3-23 and Figure 3-24 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-25 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All component actions satisfy the LS BPL acceptance criteria. 

0.40	 9.00 

0.13 0.13 1.00 1.00 

0.35 0.35 1.00 1.00 

0.23 0.23 1.00 1.00 

0.58 0.58 1.00 1.00 

0.82 

0.55 

0.82 

0.93 

0.54 

0.93 

0.79 

0.52 

0.79 

0.88 

0.88 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-23. LSP Assessment Results, 4-Story EBF ELF, BSE-1 LS 

0.40 9.00 

0.13 0.13 1.00 1.00

0.36 0.36 1.00 1.00 

0.24 0.24 1.00 1.00 

0.59 0.59 1.00 1.00 

0.76 

0.56 

0.76 

0.85 

0.60 

0.85 

0.81 

0.60 

0.81 

0.86 

0.86 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-24. LSP Assessment Results, 4-Story EBF RSA, BSE-1 LS 

3-46
 
 

2 

3 

4 

Roof 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

4 

3 

2 

Base Base 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-25. LSP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-1 

3.2.2.1.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-26 and Figure 3-27 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, at the LSP at the BSE-2 EHL. In these figures, DCRN values greater 

than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can be 

obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-28 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All component actions satisfy the CP BPL acceptance criteria. The DCRN results for the force-controlled 

components (columns and braces) are the same for both LSP LS and LSP CP because all link beams have 

yielded, capping the force delivered to the components based on the minimum DCR. In the case of the 

columns, the minimum DCR is computed at the top story link beam, and is greater than 2.0. If J were set 

to the default of 2.0, then the DCRN values would differ, which would not be consistent with the actual 

plastic mechanism (see 16-story LSP results). The DCRN results for the link beams differ for LSP LS and 

LSP CP by approximately (13/9)/1.5 = 0.963 times the DCRN, approximate because of second-order effects. Floor 

3-47
 
 

 

0.13 

0.35 

0.23 

0.58 

0.13 

0.36 

0.24 

0.59 

3 

4 

Floor 

0.42 13.00 

0.13 1.00 

0.35 1.00 

0.23 1.00 

0.58 1.00 

0

1.00 .82 

0.57 

0.82 

0.93 

0.56 

0.93 

0.79 

0.54 

0.79 

0.88 

0.88 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-26. LSP Assessment Results, 4-Story EBF ELF, BSE-2 CP 

0.41 13.00 

0.76 

0.59 

0.76 

0.85 

0.62 

0.85 

0.81 

0.63 

0.81 

0.86 

0.86 

0.13 1.00 

0.36 1.00 

0.24 1.00 

0.59 1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-27. LSP Assessment Results, 4-Story EBF RSA, BSE-2 CP 

Roof Roof

0 500 1000 1500 2000 2500 3000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

P (ASCE 7) u,Omega

P (ASCE 41) u,Capacity Design

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Floor 

2 2

Base Base

Axial Load Demand, P (kips) 

0 500 1000 1500 2000 2500 3000 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

P (ASCE 41) u,Capacity Design

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

(a) ELF (b) RSA 

Figure 3-28. LSP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-2 

4 

3 

3-48
 
 

3.2.2.1.2 Linear Dynamic Procedure 

3.2.2.1.2.1 BSE-1 Earthquake Hazard Level (LS BPL) 

In this section, the following apply: 

	 Figure 3-29 and Figure 3-30 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LDP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-31 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All component actions satisfy the LS BPL acceptance criteria. 

0.34	 9.00 

0.13 0.13 1.00 1.00 

0.38 0.38 1.00 1.00 

0.24 0.24 1.00 1.00 

0.57 0.57 1.00 1.00 

0.82 

0.45 

0.82 

0.93 

0.45 

0.93 

0.79 

0.45 

0.79 

0.90 

0.90 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-29. LDP Assessment Results, 4-Story EBF ELF, BSE-1 LS 

0.36	 9.00 

0.13 0.13 1.00 1.00 

0.38 0.38 1.00 1.00 

0.25 0.25 1.00 1.00 

0.57 0.57 1.00 1.00 

0.76 

0.47 

0.76 

0.85 

0.50 

0.85 

0.81 

0.53 

0.81 

0.87 

0.87 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-30. LDP Assessment Results, 4-Story EBF RSA, BSE-1 LS 

3-49
 
 

2 

3 

4 

Roof Roof 

4 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Floor 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Floor 

3 

2 

Base Base

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-31. LDP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-1 

3.2.2.1.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-32 and Figure 3-33 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LDP at the BSE-2 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-34 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All component actions satisfy the CP BPL acceptance criteria. The DCRN results for the force-controlled 

components (columns and braces) are the same for both LDP LS and LDP CP because all link beams have 

yielded—see §3.2.2.1.1.1 for additional information. 

3-50
 
 

 

0.12 

0.39 

0.24 

0.55 

0.13 

0.38 

0.25 

0.57 

3 

4 

Floor 

0.38 13.00 

0.12 1.00 

0.39 1.00 

0.24 1.00 

0.55 1.00 

0

1.00 .82 

0.48 

0.82 

0.93 

0.47 

0.93 

0.79 

0.47 

0.79 

0.90 

0.90 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-32. LDP Assessment Results, 4-Story EBF ELF, BSE-2 CP 

0.37 13.00 

0.76 

0.49 

0.76 

0.85 

0.52 

0.85 

0.81 

0.55 

0.81 

0.87 

0.87 

0.13 1.00 

0.38 1.00 

0.25 1.00 

0.57 1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-33. LDP Assessment Results, 4-Story EBF RSA, BSE-2 CP 

Roof Roof

0 250 500 750 1000 1250 1500 1750 2000 2250 2500 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

0 250 500 750 1000 1250 1500 1750 2000 2250 2500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

P (ASCE 7) u,Omega

P (ASCE 41) u,Capacity Design

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Floor 

2 2

Base Base

Axial Load Demand, P (kips) 

4 

3 

(a) ELF (b) RSA 

Figure 3-34. LDP Assessment Results, Compression in Exterior Columns, 4-Story EBF, BSE-2 

3-51
 
 

 

 

 

 

 

 

 

 

 

3.2.2.1.3 Nonlinear Static Procedure 

In this section, the following apply: 

	 Table 3-11 through Table 3-13 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-35 and Figure 3-36 illustrate the monotonic pushover curves for the ELF- and RSAdesigned frames, respectively, and the associated pushover parameters from ASCE 41 at the BSE2 EHL. Roof displacement is measured at the Center of Mass (CoM). A significant change in base 

shear is due to component strength loss of components (e.g., link beams), notated in the figures. 

First-order and second-order responses, shown in these figures, aids in computing a physically 

meaningful value for P- used in ASCE 41 Equation 3-17. 

	 Figure 3-37 and Figure 3-38 illustrate the story drift ratios in terms of the roof drift ratio. 

As discussed in §3.1.3.2.1, the NSP is permitted, but requires supplemental verification using the LDP— 

see §3.2.2.1.2. In this case, the target displacement governs d for the ELF-designed frame at both the BSE1 and BSE-2 EHLs and the RSA-designed frame at the BSE-1 EHL, whereas the displacement at the 

maximum base shear governs the RSA-designed frame at the BSE-2 EHL. The change in d between BSE1 and BSE-2 adds complexity to NSP process by changing the pushover variables. Further, when d is 

governed by the target displacement, the system can have an increased Rmax. Axial compression force in the 

exterior columns at the target displacement are shown previously in the linear assessment sections. 

Table 3-11. NSP General Information, 4-Story EBF (kip, inch) 

Design T1 K1 y Vy Ke Te h peak Vpeak W Cm C0 

ELF 1.03 303.0 2.7 813 303.0 1.03 1.00 12.1 919.6 5132 1.00 1.30 

RSA 1.08 286.1 2.6 743 286.1 1.08 1.01 11.1 851.6 5103 1.00 1.30 

Table 3-12. CP NSP Analysis Parameters, 4-Story EBF BSE-2 CP (kip, inch) 

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.90 5.68 1.00 1.00 12.0 919.6 12.0 0.04 -0.08 -0.01 -0.03 14.60 OK 

RSA 0.90 6.19 1.00 1.00 13.3 745.0 11.1 0.05 -0.07 -0.01 -0.02 14.89 OK 

Table 3-13. LS NSP Analysis Parameters, 4-Story EBF BSE-1 LS (kip, inch) 

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.60 3.79 1.00 1.00 8.0 897.3 8.0 0.05 -0.06 -0.01 -0.02 14.75 OK 

RSA 0.60 4.12 1.00 1.00 8.9 840.8 8.9 0.05 -0.06 -0.01 -0.02 14.91 OK 

3-52
 
 

Roof Drift Ratio at CoM (%) 

0.0 0.3 0.6 0.8 1.1 1.4 1.7 1.9 2.2 2.5 2.8 

1000 0.19 

Total Base Shear (Kips) Total Base Shear (Kips) 

Total Base Shear / W Total Base Shear / W 

900 

0 2 4 6 8 10 12 14 16 18 20 

(2.7,813.4) 

(12.0,919.6) 

Pt. A: Shear Hinge reaches CP on 2nd Floor 

Pt. B: Shear Hinge reaches CP on 3rd Floor 

Pt. C: Shear Hinge reaches CP on 4th Floor 

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

A 

B C 

0.18 

800 0.16 

700 0.14 

600 0.12 

500 0.10 

400 0.08 

300 0.06 

200 0.04 

100 0.02 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-35. 4-Story EBF ELF Pushover, BSE-2 

Roof Drift Ratio at CoM (%) 

0.0 0.3 0.6 0.8 1.1 1.4 1.7 1.9 2.2 2.5 2.8 

1000 0.20 

700 

0 2 4 6 8 10 12 14 16 18 20 

(2.6,742.5) 

(11.1,851.6) 

Pt. A: Shear Hinge reaches CP on 3rd Floor 

Pt. B: Shear Hinge reaches CP on 2nd Floor 

Pt. C: Shear Hinge reaches CP on 4th Floor C 

 RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

A 

B 

0.14 

900 0.18 

800 0.16 

600 0.12 

500 0.10 

400 0.08 

300 0.06 

200 0.04 

100 0.02 C

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-36. 4-Story EBF RSA Pushover, BSE-2 

3-53
 
 

0.0% 0.5% 1.0% 1.5% 2.0% 

0.0% 

0.5% 

1.0% 

1.5% 

2.0% 

2.5% 

3.0% 

Story Drift Ratio (%) 

1st Story

 2nd Story

 3rd Story

 4th Story

 Roof 

Roof Drift Ratio (%)

Figure 3-37. 4-Story EBF ELF Pushover – Story Drift Ratios – BSE-2 

0.0% 0.5% 1.0% 1.5% 2.0% 

0.0% 

0.5% 

1.0% 

1.5% 

2.0% 

2.5% 

3.0% 

Story Drift Ratio (%) 

1st Story

 2nd Story

 3rd Story

 4th Story

 Roof 

Roof Drift Ratio (%)

Figure 3-38. 4-Story EBF RSA Pushover – Story Drift Ratios – BSE-2 

3-54
 
 

 

 

 

 

 

 

 

Figure 3-39 illustrates which frame components are force-controlled for flexure for both the NSP and NDP; 

red circles indicate anticipated plastic hinge locations that are force-controlled for flexure at the target 

displacement. Figure 3-40 and Figure 3-41 illustrate the DCRN values if greater than unity for the ELF- and 

RSA-designed frames at the target displacement for the LS BPL at the BSE-1 EHL and CP BPL at the BSE2 EHL. The figures illustrate demands when the system is loaded to the left. Nearly all shear actions in the 

link beams satisfy the LS and CP BPL acceptance criteria except for the third floor link beam in the RSAdesigned frame for the CP BPL. 

All other force-controlled component actions satisfy the LS BPL acceptance criteria. However, base column 

hinges do not satisfy the criteria for the CP BPL for both the ELF- and RSA-designed frames. This effect 

is two-fold: a consequence of modeling rotationally restrained base connections, which more closely 

characterizes how the base connection is detailed in these buildings than assuming rotationally unrestrained 

connections as is commonly done in practice, and, to a lesser extent, the minor increase in PE because the 

shear strength, VCE, of the link beams was increased by 15 percent for nonlinear analysis—see §3.2.1.2. As 

discussed in §3.2.1.2, the flexural hinge model for force-controlled components obeys ASCE 41 Equation 

5-4 (yield surface for the section). As such, unsatisfactory performance is demarcated by section yielding. 

Sym. About 

4 3 

All colum ns, braces, and beams 

adjacent to link beams are 

for ce-controlled (FC ) for flex ur e 

Roof
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Flo or
 

(ELEV = 32 ft.)
 

2nd Flo or
 

(ELEV = 18 ft.)
 

Figure 3-39. Schematic of Flexural Actions in Components, 4-Story EBF (NSP and NDP) 

3-55
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 3 

Roof
 

(ELEV = 6 0 ft.)
 

4th Fl o or
 

(ELEV = 4 6 ft.)
 

3rd Flo or
 

(ELEV = 3 2 ft.)
 

2nd Floor
 

(ELEV = 1 8 ft.)
 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

4 3 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

Roof
 

(ELEV = 60 ft .)
 

4th Floor
 

(ELEV = 46 ft .)
 

3rd Fl o or
 

(ELEV = 32 ft .)
 

2nd Floor
 

(ELEV = 18 ft .)
 

(a) ELF (b) RSA 

Figure 3-40. NSP Assessment Results, 4-Story EBF, BSE-1 LS (+push to left) 

1.13 

4 3 4 3 

Roof
 

(ELEV = 60 ft .)
 

4th Floor
 

(ELEV = 46 ft .)
 

3rd Fl o or
 

(ELEV = 32 ft .)
 

2nd Floor
 

(ELEV = 18 ft .)
 

2.53 1.81 

1.33 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

Roof
 

(ELEV = 60 ft .)
 

4th Floor
 

(ELEV = 46 ft .)
 

3rd Fl o or
 

(ELEV = 32 ft .)
 

2nd Floor
 

(ELEV = 18 ft .)
 

(a) ELF (b) RSA 

Figure 3-41. NSP Assessment Results, 4-Story EBF, BSE-2 CP (+push to left) 

3.2.2.1.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the N-S direction of MC4 is shown in Appendix A. For the ELF 

and RSA design, the analysis successfully completed for all 14 records at the BSE-1 and BSE-2 EHL. 

Maximum axial compression force in the exterior column lines from the record set are shown previously in 

the linear assessment sections. 

Figure 3-42 and Figure 3-43 show the performance of the link beams at the BSE-1 (LS BPL) and BSE-2 

(CP BPL) for the ELF- and RSA-designed frames, respectively. The results from the LSP, LDP, and NSP 

(loaded to the left) are included in the figures. Comparison discussions between the various procedures are 

addressed subsequently. As is evident in the figures, the ELF-designed frame performs slightly better than 

the RSA-designed frame—a corollary of the two frame designs being nearly the same. The results indicate 

that several link beams in both designs do not satisfy the CP BPL acceptance criteria using the mean 

3-56
 
 

response. In contrast to the mean response, the median response indicates better performance because it is 

less influenced by large deformations resulting from component strength loss potentially resulting in 

collapse of the system. Consequently, the median is potentially a more stable performance metric when 

analyzing a large number of ground motion records, but should be restrained relative to a mean value. The 

average ratio of secondary to primary component acceptance criteria for a wide-flange section with the 

configuration in this frame is 1.14 for the CP SPL (1.27 for the LS SPL). A DCRN value of 0.73 equates to 

a plastic rotation angle of 0.08 radians at the BSE-1 EHL (0.62 at the BSE-2 EHL). 

Roof 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = Plastic Deformation / LS Acceptance Criteria 

Median 

Mean 

84th 

Mean+1std

 NSP 

LSP 

LDP 

Roof 

4 

Median 

Mean 

84th 

Mean+1std

 NSP 

LSP 

LDP 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

4 

Floor ID Floor ID 

Floor ID 

3 3 

2 2 

Base Base 

DCRN = Plastic Deformation / LS Acceptance Criteria 

(a) ELF (b) RSA 

Figure 3-42. NDP Assessment Results, Shear Hinges, 4-Story EBF BSE-1 LS 

0.0 0.5 1.0 1.5 2.0 2.5 

DCRN = Plastic Deformation / CP Acceptance Criteria 

Roof Roof 

Median Median 

Mean Mean 

84th 84th 

Mean+1std Mean+1std

 NSP 4 NSP 4

LSP LSP

LDP LDP 

0.0 0.5 1.0 1.5 2.0 2.5 

Floor ID 

3 3

2 2

Base 

DCRN = Plastic Deformation / CP Acceptance Criteria 

Base 

(a) ELF (b) RSA 

Figure 3-43. NDP Assessment Results, Shear Hinges, 4-Story EBF BSE-2 CP 

3-57
 
 

 

Figure 3-44 and Figure 3-45 show the curvature ductility demand of the column hinges (i.e., section 

strength) at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. Figure 3-46 and Figure 

3-47 show the elastic member strength interaction results at the BSE-2 EHL—see discussion on column 

strength modeling in §3.2.1.2. Column hinges at the base above the brace connection experience inelastic 

strain demands (yield corresponds to a DCRN = 1 in the figures). The deformation demands are considerably 

lower than the primary CP acceptance criteria for a Column. Still, the base column hinges do not satisfy the 

criteria for the CP BPL for both the ELF- and RSA-designed frames. This effect is two-fold: a consequence 

of modeling rotationally restrained base connections, which more closely characterizes how the base 

connection is detailed in these buildings than assuming rotationally unrestrained connections as is 

commonly done in practice, and, to a lesser extent, the minor increase in PE because the shear strength, VCE, 

of the link beams was increased by 15 percent for nonlinear analysis—see §3.2.1.2 and §3.2.2.1.3. 

The DCRN results for the LSP and LDP are based on an interaction equation and not from MUD / m×MCE, or 

MUF / MCL, which would be a more physically consistent metric for comparison against the results from the 

nonlinear assessment procedures. Nonetheless, the linear results are generally applicable here because the 

columns are force-controlled for flexure in the linear assessment procedures. Though there is a fundamental 

difference in how the DCRN is computed for the linear and nonlinear procedures, the linear assessment 

results show similar distributions of demands and location of potential performance concerns. 

0 1 2 3 4 5 6 

Base 

2 

3 

4 

Roof 

Col. Line B 

Floor ID 

0 1 2 3 4 5 6 

Col. Line C Median 

Mean 

84th 

Mean+1std

 NSP

 LSP

 LDP 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-44. NDP Assessment Results, Column Hinges, 4-Story EBF ELF, BSE-2 Yield 

3-58
 
4 

Roof 

Col. Line B Col. Line C Median

Mean

84th

Mean+1std

 NSP

 LSP

 LDP 

Floor ID Floor ID

3 

2 

Base 

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 
 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2
 

Figure 3-45. NDP Assessment Results, Column Hinges, 4-Story EBF RSA, BSE-2 Yield 

 

Roof 

Median

Mean

84th

Mean+1std

4 

Col. Line B Col. Line C

 LSP

 LDP 

3 

2 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
 

DCRN = P-M Interaction Value
 

Figure 3-46. NDP Assessment Results, Column Members, 4-Story EBF ELF, BSE-2 

 

3-59
Roof Col. Line B Col. Line C Median

Mean

84th

Mean+1std

4 LSP

 LDP 

Floor ID

3 

2 

0.0 

Base 

Figure 3-47. NDP Assessment Results, Column Members, 4-Story EBF RSA, BSE-2 

0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Value 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Figure 3-48 and Figure 3-49 show the curvature ductility demand of the brace hinges (i.e., section strength) 

at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. Figure 3-50 and Figure 3-51 

show the elastic member strength interaction results at the BSE-2 EHL—see discussion on column strength 

modeling in—see discussion on column strength modeling in §3.2.1.2. Brace hinges at the base above the 

brace connection experience inelastic strain demands (yield corresponds to a DCRN = 1 in the figures). The 

deformation demands are considerably lower than the primary CP acceptance criteria for a Column. Still, 

the brace hinges do not satisfy the criteria for the CP BPL for both the ELF- and RSA-designed frames— 

see previous discussion on column results for additional information. 

Roof 

Left Brace Right Brace Median

Mean

84th

Mean+1std

4 NSP

 LSP

 LDP 

Floor ID

3 

2 

Base 

0.0 0.5 	 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 
 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2
 

Figure 3-48. NDP Assessment Results, Brace Hinges, 4-Story EBF ELF, BSE-2 Yield 

3-60
Floor ID Floor ID 

Roof 

Left Brace Right Brace Median

Mean

84th

Mean+1std

4 NSP

 LSP

 LDP 

3 

2 

0.0 

Base 

0.5 

Figure 3-49. NDP Assessment Results, Brace Hinges, 4-Story EBF RSA, BSE-2 Yield 

 

1.0 1.5 2.0 2.5 3.0 3.5 4.0 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

4 

Roof 

Left Brace Right Brace Median

Mean

84th

Mean+1std

 LSP

 LDP 

3 

2 

0.0 

Base 

0.2 0.4 0.6 0.8 1.0 1.2 

DCR 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Figure 3-50. NDP Assessment Results, Brace Members, 4-Story EBF ELF, BSE-2 

 

3-61
 

 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Base 

2 

3 

4 

Roof 

Left Brace 

DCR 

Floor ID 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Right Brace Median 

Mean 

84th 

Mean+1std

 LSP

 LDP 

Figure 3-51. NDP Assessment Results, Brace Members, 4-Story EBF RSA, BSE-2 

Eight-Story Eccentric Braced Frame 

3.2.2.2.1 Linear Static Procedure 

3.2.2.2.1.1 BSE-1 Earthquake Hazard Level (LS BPL) 

In this section, the following apply: 

	 Figure 3-52 and Figure 3-53 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-54 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the LS BPL acceptance criteria. 

Base columns do not satisfy the LS BPL acceptance criteria (force-controlled) using the interaction equation 

because of the combination of high axial force and moment. High flexural demand at the base of the frame 

is a consequence of modeling rotationally restrained base connections, which more closely characterizes 

how the base connection is detailed in these buildings than assuming rotationally unrestrained connections 

as is commonly done in practice. As discussed previously in §3.2.2, PUF is determined by taking J (ASCE 

41 §3.4.2.1.2-2) as the minimum DCR of the component(s) delivering force to the column, but not less than 

2.0. This approach produces an upper-bound estimate for PUF for the LS SPL as compared to ASCE 41 

§3.4.2.1.2-1 (based on ASCE 41 §5.5.3.4.2), as shown in Figure 3-54. 

3-62
 
 

0.28 9.00 

0.11 0.75 

0.43 

0.75 

0.85 

0.47 

0.85 

0.82 

0.46 

0.82 

0.82 

0.47 

0.82 

0.86 

0.44 

0.86 

0.80 

0.45 

0.80 

0.70 

0.43 

0.70 

0.84 

0.84 

0.11 1.00 1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

1.00 

0.10 0.10 1.00 1.00 

0.24 0.24 1.00 1.00 

0.44 0.44 1.00 1.00 

0.55 0.55 1.00 1.00 

0.78 0.78 1.00 1.00 

0.77 0.77 1.00 1.00 

1.13 1.13 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-52. LSP Assessment Results, 8-Story EBF ELF, BSE-1 LS 

0.26 9.00 

0.19 0.74 

0.47 

0.74 

0.77 

0.54 

0.77 

0.76 

0.58 

0.76 

0.79 

0.55 

0.79 

0.83 

0.52 

0.83 

0.79 

0.47 

0.79 

0.81 

0.40 

0.81 

0.82 

0.82 

0.19 1.00 1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1

0 .0

9.00 

1

0 .0

1

0 .0

9.00 

1

0 .0

1

0 .0

9.00 

1

0 .0

1

0 .0

9.00 

1

0 .0

1

0 .0

1

0 .0

1.00 

0.39 0.39 1.00 1.00 

0.58 0.58 1.00 1.00 

1.04 1.04 1.00 1.00

0.67 0.67 1.00 1.00 

0.96 0.96 1.00 1.00 

1.08 1.08 1.00 1.00

1.46 1.46 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-53. LSP Assessment Results, 8-Story EBF RSA, BSE-1 LS 

3-63
 
 

 

5 

6 

7 

8 

0 1000 2000 3000 4000 5000 6000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Roof Roof Floor 

8 

7 

0 1000 2000 3000 4000 5000 6000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

6 

Floor 

5 

4 4 

3 3 

2 2 

Base Base 

Axial Load Demand, P (kips) Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-54. LSP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-1 

One could initially argue that columns in an EBF frame (greater than three stories) designed per AISC 341 

would satisfy ASCE 41 criteria by default. Following ASCE 41 §5.5.3.4.2 results in the following for the 

base column (RSA-designed frame is used here): 

o PCL = 1721 kips 

o PGravity = 259 kips 

o PUF = 2265 kips (determined using J equal to the minimum DCR = 2.36) 

 PUF / PCL = 1.32 (MUF / MCL = 0.16) → interaction result = 1.46 (fails) 

o PUF = 1626 kips (determined from a fully yielded frame per ASCE 41§5.5.3.4.2) 

 PUF / PCL = 0.95 (MUF / MCL = 0.16) → interaction result = 1.09 (fails) 

o PUF = 1469 kips (determined from a fully yielded frame per AISC 341 §F3.3) 

 PUF / PCL = 0.85 (MUF / MCL = 0) → interaction result = 0.85 (passes) 

PUF computed per ASCE 41 §5.5.3.4.2 is slightly larger than that computed from AISC 341 §F3.3 because 

of the 12 percent reduction in PEQ allowed by AISC 341. Furthermore, ASCE 41 does not provide guidance 

on how to compute MUF in a column—AISC 341 states the flexural forces due to seismic drift can be 

neglected. Consequently, the P-M interaction equation used for assessment can be a combination of ASCE 

41 §3.4.2.1.2-1 (PUF) and ASCE 41 §3.4.2.1.2-2 (MUF). This combination can be inconsistent and, as shown 

above, ASCE 41 §3.4.2.1.2-2 can overestimate the force demands in the column (almost 40 percent in this 

example). Still, the question remains whether ASCE 41 should adopt AISC 341 §F3.3 in its entirety in 

ASCE 41 §5.5.3.4.2. 

3-64
 
3.2.2.2.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-55 and Figure 3-56 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-57 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the CP BPL acceptance criteria. 

Similar to the LSP LS results, base columns do not satisfy the CP BPL assessment criteria (force-controlled) 

using the interaction equation because of the combination of high axial force and moment. High flexural 

demand at the base of the frame is a consequence of modeling rotationally restrained base connections, 

which more closely characterizes how the base connection is detailed in these buildings than assuming 

rotationally unrestrained connections as is commonly done in practice. 

The DCRN interaction results for force-controlled components are the same between LSP LS and LSP CP 

because all links have yielded, capping the force delivered to the columns based on the minimum DCR of 

all links. In this case, the minimum DCR of the top story link is greater than 2.0. If J were set to the default 

of 2.0 then the interaction values would differ, which would not be consistent with the actual plastic 

mechanism (see 16-story LSP results). The results for the links differ by approximately (13/9)/1.5 = 0.963 

times the DCRN, approximate because of second-order effects. 

3-65
 
0.29 13.00 

0.11 0.75
 

0.44
 

0.75
 

0.85
 

0.49
 

0.85
 

0.82
 

0.47
 

0.82
 

0.82
 

0.48
 

0.82
 

0.86
 

0.46
 

0.86
 

0.80
 

0.47
 

0.80
 

0.70
 

0.45
 

0.70
 

0.84
 

0.84
 

0.11 1.00
 1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

0.10 0.10 1.00 1.00 

0.24 0.24 1.00 1.00 

0.44 0.44 1.00 1.00 

0.55 0.55 1.00 1.00 

0.78 0.78 1.00 1.00 

0.77 0.77 1.00 1.00 

1.13 1.13 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-55. LSP Assessment Results, 8-Story EBF ELF, BSE-2 CP 

0.27 13.00 

0.19 0.74
 

0.49
 

0.74
 

0.77
 

0.56
 

0.77
 

0.76
 

0.61
 

0.76
 

0.79
 

0.57
 

0.79
 

0.83
 

0.54
 

0.83
 

0.79
 

0.48
 

0.79
 

0.81
 

0.41
 

0.81
 

0.82
 

0.82
 

0.19 1.00
 1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1

0 .0

13.00 

1

0 .0

1

0 .0

13.00 

1

0 .0

1

0 .0

13.00 

1

0 .0

1

0 .0

13.00 

1

0 .0

1

0 .0

1

0 .0

1.00 

0.39 0.39 1.00 1.00 

0.58 0.58 1.00 1.00 

1.04 1.04 1.00 1.00

0.67 0.67 1.00 1.00 

0.96 0.96 1.00 1.00 

1.08 1.08 1.00 1.00

1.47 1.47 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-56. LSP Assessment Results, 8-Story EBF RSA, BSE-2 CP 

3-66
 
5 

6 

7 

8 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof Roof Floor 

8 

7 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

6 

Floor 

5 

4 4

3 3

2 2

Base Base

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-57. LSP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-2 

3.2.2.2.2 Linear Dynamic Procedure 

3.2.2.2.2.1 BSE-1 Earthquake Hazard Level (LS BPL) 

In this section, the following apply: 

	 Figure 3-58 and Figure 3-59 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-2 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-60 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the LS BPL acceptance criteria. 

Base columns do not satisfy the LS BPL acceptance criteria (force-controlled) using the interaction equation 

because of the combination of high axial force and moment—see §3.2.2.2.1 for more information. As 

discussed previously in §3.2.2, PUF is determined by taking J (ASCE 41 §3.4.2.1.2-2) as the minimum DCR 

of the component(s) delivering force to the column, but not less than 2.0. This approach produces a lowerbound estimate for PUF for the LS SPL as compared to ASCE 41 §3.4.2.1.2-1 (based on ASCE 41 

§5.5.3.4.2), as shown in Figure 3-60. 

3-67
 
0.31 9.00 

0.09 0.76 

0.40 

0.76 

0.85 

0.37 

0.85 

0.82 

0.33 

0.82 

0.82 

0.34 

0.82 

0.86 

0.34 

0.86 

0.81 

0.40 

0.81 

0.71 

0.41 

0.71 

0.88 

0.88 

0.09 1.00 1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

1.00 

0.12 0.12 1.00 1.00 

0.23 0.23 1.00 1.00 

0.38 0.38 1.00 1.00 

0.42 0.42 1.00 1.00 

0.56 0.56 1.00 1.00 

0.51 0.51 1.00 1.00 

0.82 0.82 1.00 1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-58. LDP Assessment Results, 8-Story EBF ELF, BSE-1 LS 

0.29 9.00 

0.16 0.75 

0.43 

0.75 

0.77 

0.41 

0.77 

0.76 

0.41 

0.76 

0.79 

0.39 

0.79 

0.83 

0.40 

0.83 

0.80 

0.41 

0.80 

0.83 

0.38 

0.83 

0.88 

0.88 

0.16 1.00 1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1

0 .0

9.00 

1

0 .0

1

0 .0

9.00 

1

0 .0

1

0 .0

9.00 

1

0 .0

1

0 .0

9.00 

1

0 .0

1

0 .0

1

0 .0

1.00 

0.40 0.40 1.00 1.00 

0.53 0.53 1.00 1.00 

0.84 0.84 1.00 1.00 

0.49 0.49 1.00 1.00 

0.64 0.64 1.00 1.00 

0.70 0.70 1.00 1.00 

1.02 1.02 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-59. LDP Assessment Results, 8-Story EBF RSA, BSE-1 LS 

3-68
 
5 

6 

7 

8 

Roof 

0 500 1000 1500 2000 2500 3000 3500 4000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

8 

7 

0 500 1000 1500 2000 2500 3000 3500 4000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

6 

5 

4 4 

3 3 

2 2 

Base Base 

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-60. LDP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-1 

3.2.2.2.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-61 and Figure 3-62 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-63 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the CP BPL acceptance criteria. For all intents and purpose, all 

column actions also satisfy the CP BPL. 

As discussed previously in §3.2.2, PUF is determined by taking J (ASCE 41 §3.4.2.1.2-2) as the minimum 

DCR of the component(s) delivering force to the column, but not less than 2.0. This approach produces a 

lower-bound estimate for PUF for the LS SPL as compared to ASCE 41 §3.4.2.1.2-1 (based on ASCE 41 

§5.5.3.4.2), as shown in Figure 3-63. Further, the DCRN interaction results for force-controlled components 

are the same between LDP LS and LSP CP because all links have yielded capping the force delivered to 

the columns based on the minimum DCR of all links—see §3.2.2.2.1.2 for additional information. Floor 

3-69
 
0.33 13.00 

0.09 0.76 

0.41 

0.76 

0.85 

0.38 

0.85 

0.82 

0.34 

0.82 

0.82 

0.35 

0.82 

0.86 

0.36 

0.86 

0.81 

0.42 

0.81 

0.71 

0.43 

0.71 

0.88 

0.88 

0.09 1.00 1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

1.00 

0.12 0.12 1.00 1.00 

0.23 0.23 1.00 1.00 

0.38 0.38 1.00 1.00 

0.42 0.42 1.00 1.00 

0.56 0.56 1.00 1.00 

0.51 0.51 1.00 1.00 

0.82 0.82 1.00 1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-61. LDP Assessment Results, 8-Story EBF ELF, BSE-2 CP 

0.30 13.00 

0.16 0.75 

0.45 

0.75 

0.77 

0.43 

0.77 

0.76 

0.42 

0.76 

0.79 

0.41 

0.79 

0.83 

0.42 

0.83 

0.80 

0.43 

0.80 

0.83 

0.39 

0.83 

0.88 

0.88 

0.16 1.00 1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1

0 .0

13.00 

1

0 .0

1

0 .0

13.00 

1

0 .0

1

0 .0

13.00 

1

0 .0

1

0 .0

13.00 

1

0 .0

1

0 .0

1

0 .0

1.00 

0.40 0.40 1.00 1.00 

0.53 0.53 1.00 1.00 

0.84 0.84 1.00 1.00 

0.49 0.49 1.00 1.00 

0.64 0.64 1.00 1.00 

0.70 0.70 1.00 1.00 

1.02 1.02 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-62. LDP Assessment Results, 8-Story EBF RSA, BSE-2 CP 

3-70
 
 

 

 

 

5 

6 

7 

8 

Roof 

0 1000 2000 3000 4000 5000 6000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

8 

7 

0 1000 2000 3000 4000 5000 6000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

6 

Floor 

5 

4 4 

3 3 

2 2 

Base Base 

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-63. LDP Assessment Results, Compression in Exterior Columns, 8-Story EBF, BSE-2 

3.2.2.2.3 Nonlinear Static Procedure 

In this section, the following apply: 

	 Table 3-14 through Table 3-16 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-64 and Figure 3-65 illustrate the monotonic pushover curves for the ELF- and RSAdesigned frames, respectively, and the associated pushover parameters from ASCE 41 at the BSE2 EHL. Roof displacement is measured at the Center of Mass (CoM). A significant change in base 

shear is due to component strength loss of components (e.g., link beams), notated in the figures. 

First-order and second-order responses, shown in these figures, aids in computing a physically 

meaningful value for P- used in ASCE 41 Equation 3-17. 

	 Figure 3-66 and Figure 3-67 illustrate the story drift ratios in terms of the roof drift ratio. 

As discussed in §3.1.3.2.1, the NSP is permitted, but requires supplemental verification using the LDP— 

see §3.2.2.2.2. In this case, the displacement at the maximum base shear governs d for both the ELF- and 

RSA-designed frame for both the BSE-1 and BSE-2 EHLs. Axial compression force in the exterior columns 

at the target displacement are shown previously in the linear assessment sections. Results indicate that the 

NSP generally results in a lower estimate of the axial force demands compared to the other methods used 

in this study. This is partly because the fundamental mode-based lateral force distribution does not 

adequately capture higher mode effects. Also, the target displacement at the roof computed based on 

fundamental mode properties may underestimate the story demands in the upper stories. 

Table 3-14. NSP General Information, 8-Story EBF (kip, inch) 

Design T1 K1 y Vy Ke Te h peak Vpeak W Cm C0 

ELF 2.05 123.6 7.7 946 123.1 2.06 1.11 16.4 1068.2 10566 1.00 1.36 

RSA 2.34 92.1 7.7 706 91.9 2.34 1.13 15.0 787.7 10460 1.00 1.35 

3-71
 
 

 

 

 

 

 

 

 

 

 

Table 3-15. CP NSP Analysis Parameters, 8-Story EBF BSE-2 CP (kip, inch) 

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.45 5.03 1.00 1.00 25.2 809.6 16.4 0.11 -0.13 -0.02 -0.05 9.66 OK 

RSA 0.39 5.80 1.00 1.00 28.2 501.5 15.0 0.12 -0.11 -0.02 -0.04 12.66 OK 

Table 3-16. LS NSP Analysis Parameters, 8-Story EBF BSE-1 LS (kip, inch) 

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.30 3.35 1.00 1.00 16.8 1068.2 16.4 0.11 -0.13 -0.02 -0.05 9.66 OK 

RSA 0.26 3.87 1.00 1.00 18.8 781.5 15.0 0.12 -0.11 -0.02 -0.04 12.66 OK 

Roof Drift Ratio at CoM (%) 

0.0 0.4 0.7 1.1 1.4 1.8 2.2 2.5 2.9 

1200 0.11 

0 5 10 15 20 25 30 35 40 

(7.7,945.6) 

(16.4,1068.2) 

Pt. A: Shear Hinge reached CP on 4th and 5th Floor 

Pt. B: Shear Hinge reached CP on 3rd and 6th Floor 

Pt. C: Ext. Beam Hinges reached CP on 2nd Floor 

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

A 

B 

C 

1000 0.09 

Total Base Shear (Kips) 800 0.08 

Total Base Shear / W 

600 

400 

0.06 

0.04 

200 0.02 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-64. 8-Story EBF ELF Pushover, BSE-2 

3-72
 
 

 

Roof Drift Ratio at CoM (%) 

0.0 0.4 0.7 1.1 1.4 1.8 2.2 2.5 2.9 

1200 

0 5 10 15 20 25 30 35 40 

(7.7,706.0) 

(15.0,787.7) 

Pt. A: Shear Hinge reached CP on 5th and 6th Floor 

Pt. B: Shear Hinge reached CP on 4th and 7th Floor 

Pt. C: Ext. Beam Hinges reached CP on 4th Flo or 

 RSA (First-Order)

 RSA (Second-Order) 

RSA Idealized Backbone 

A 

B 

C 

0.11 

1000 0.10 

800 0.08 

600 0.06 

400 0.04 

200 0.02 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-65. 8-Story RSA ELF Pushover, BSE-2 

3.0% 

0.0% 0.5% 1.0% 1.5% 2.0% 

1st Story

 2nd Story

 3rd Story

 4th Story

 5th Story

 6th Story

 7th Story

 8th Story

 Roof 

2.5% 

2.0% 

1.5% 

1.0% 

0.5% 

0.0% 

Story Drift Ratio (%) 

Roof Drift Ratio (%)

Figure 3-66. 8-Story EBF ELF Pushover – Story Drift Ratios – BSE-2 

Total Base Shear (Kips) 

Total Base Shear / W 

3-73
 
0.0% 0.5% 1.0% 1.5% 2.0% 

0.0% 

0.5% 

1.0% 

1.5% 

2.0% 

2.5% 

3.0% 

Story Drift Ratio (%) 

1st Story

 2nd Story

 3rd Story

 4th Story

 5th Story

 6th Story

 7th Story

 8th Story

 Roof 

Roof Drift Ratio (%)

Figure 3-67. 8-Story EBF RSA Pushover – Story Drift Ratios – BSE-2 

Figure 3-68 illustrates which frame components are force-controlled for flexure for both the NSP and NDP; 

red circles indicate anticipated plastic hinge locations that are force-controlled for flexure at the target 

displacement. Figure 3-69 and Figure 3-70 illustrate the DCRN values if greater than unity for the ELF- and 

RSA-designed frames at the target displacement for the LS BPL at the BSE-1 EHL and CP BPL at the BSE2 EHL. The figures illustrate demands when the system is loaded to the left. All shear actions satisfy the 

LS BPL acceptance criteria for both designs. However, several link beams near the mid-height of the frame 

do not satisfy the CP BPL acceptance criteria for both designs—RSA-designed frame performs markedly 

poorer than the ELF-designed frame. 

All other force-controlled component actions satisfy the LS BPL acceptance criteria. However, base column 

hinges do not satisfy the criteria for the CP BPL for the ELF-designed frames. This effect is two-fold: a 

consequence of modeling rotationally restrained base connections, which more closely characterizes how 

the base connection is detailed in these buildings than assuming rotationally unrestrained connections and, 

to a lesser extent, the minor increase in PE because the shear strength, VCE, of the link beams was increased 

by 15 percent for nonlinear analysis—see §3.2.1.2. As discussed in §3.2.1.2, the flexural hinge model for 

force-controlled components obeys ASCE 41 Equation 5-4 (yield surface for the section). As such, 

unsatisfactory performance is characterized by section yielding. 

3-74
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 3

Sym. About 

Roof
 

(ELEV = 116 ft.)
 

8th Floor
 

(ELEV = 102 ft.)
 

7th Floor
 

(ELEV = 88 ft.)
 

6th Floor
 

(ELEV = 74 ft.)
 

5th Floor
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Fl o or
 

(ELEV = 32 ft.)
 

2nd Fl o or
 

(ELEV = 18 ft.)
 

All colum ns, braces, and beams 

adjacent to link beams are 

force-controlled (FC) for flexure 

Figure 3-68. Schematic of Flexural Actions in Components, 8-Story EBF (NSP and NDP) 

4 3 

Roof 

4 3 

Roof 

(ELEV = 116 ft.) (ELEV = 116 ft.) 

8th Flo or 8th Flo or 

(ELEV = 102 ft.) (ELEV = 102 ft.) 

7th Flo or 7th Flo or 

(ELEV = 88 ft.) (ELEV = 88 ft.) 

6th Flo or 6th Flo or DCRN ≥ 1.0 DCRN ≥ 1.0 (ELEV = 74 ft.) (ELEV = 74 ft.) 

0.9 ≤ DCRN < 1.0 0.9 ≤ DCRN < 1.0 

5th Flo or 5th Flo or 

0.8 ≤ DCRN < 0.9 0.8 ≤ DCRN < 0.9 (ELEV = 60 ft.) (ELEV = 60 ft.) 

0.7 ≤ DCRN < 0.8 0.7 ≤ DCRN < 0.8 

4th Flo or 4th Flo or 

DCRN < 0.7 DCRN < 0.7 (ELEV = 46 ft.) (ELEV = 46 ft.) 

3rd Floor 3rd Floor 

(ELEV = 32 ft.) (ELEV = 32 ft.) 

2nd Flo or 2nd Flo or 

(ELEV = 18 ft.) (ELEV = 18 ft.) 

(a) ELF (b) RSA 

Figure 3-69. NSP Assessment Results, 8-Story EBF, BSE-1 LS (+push to left) 

3-75
 
 

 

 

 

 

 

 

 

 

 

 

 

 

4 3 4 3 

Roof Roof 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

1.45 

1.51 

1.26 

(ELEV = 116 ft.) 

8th Flo or 

(ELEV = 102 ft.) 

7th Flo or 

(ELEV = 88 ft.) 

6th Flo or 

(ELEV = 74 ft.) 

5th Flo or 

(ELEV = 60 ft.) 

4th Flo or 

(ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Flo or 

(ELEV = 18 ft.) 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

1.45 

2.18 

2.04 

1.02 

1.15 

(ELEV = 116 ft.) 

8th Flo or 

(ELEV = 102 ft.) 

7th Flo or 

(ELEV = 88 ft.) 

6th Flo or 

(ELEV = 74 ft.) 

5th Flo or 

(ELEV = 60 ft.) 

4th Flo or 

(ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Flo or 

(ELEV = 18 ft.) 

(a) ELF (b) RSA 

Figure 3-70. NSP Assessment Results, 8-Story EBF, BSE-2 CP (+push to left) 

3.2.2.2.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the N-S direction of ME8 is shown in Appendix A. For the ELF 

design, the analysis successfully completed for all 14 records at the BSE-1 EHL whereas four did not 

complete successfully at the BSE-2 EHL because of excessive lateral drifts. For the RSA design, the 

analysis successfully completed for all 14 records at the BSE-1 EHL whereas five did not complete 

successfully at the BSE-2 EHL because of excessive lateral drifts. Maximum axial compression force in 

the exterior column lines from the record set are shown previously in the linear assessment sections. 

Figure 3-71 and Figure 3-72 show the performance of the link beams at the BSE-1 (LS BPL) and BSE-2 

(CP BPL) for the ELF and RSA design, respectively, in terms of a DCRN. The DCRN results from the LSP, 

LDP, and NSP (loaded to the left) are included in the figures. Comparison discussions of the various 

procedures are addressed subsequently. As is evident in the figures, the ELF-designed frame performs 

noticeably better than the RSA-designed frame. The results indicate that several links in the RSA-designed 

frame do not satisfy the LS BPL acceptance criteria. Both the ELF- and RSA-designed frames perform 

markedly poorer at the BSE-2 EHL, with nearly all links not satisfying the CP BPL acceptance criteria 

using both median and mean metric. A DCRN value of 0.73 equates to a plastic rotation angle of 0.08 radians 

at the BSE-1 EHL (0.62 at the BSE-2 EHL). 

The average ratio of secondary to primary component acceptance criteria for a wide-flange section with the 

configuration in this frame is 1.14 for the CP SPL (1.27 for the LS SPL). The figures for the ELF- and 

RSA-designed frame illustrate that this value is exceeded in a number of stories at the BSE-1 EHL and 

3-76
 
5 

BSE-2 EHL. This highlights the rapid analytical progression towards a collapsed state when several 

components are strained past the deformation associated with their peak strength—see §3.1.4.2. 

Roof Roof 

Median

8 Mean 8 

84th

7 Mean+1std 7 

 NSP

6 

LSP

LDP 6 

Floor ID

5 

Floor ID

5 

Median 4 4 

Mean

84th

3 3 Mean+1std

 NSP

2 2 LSP

LDP 

Base Base 

01234 01234 

DCRN = Plastic Deformation / LS Acceptance Criteria DCRN = Plastic Deformation / LS Acceptance Criteria 

(a) ELF (b) RSA 

Figure 3-71. NDP Assessment Results, Shear Hinges, 8-Story EBF, BSE-1 LS 

 

Roof Median Roof Median

Mean Mean

8 84th 8 84th

Mean+1std Mean+1std

7 NSP 7 NSP

LSP LSP

6 LDP 6 LDP 

Floor ID

Floor ID

5 

4 4 

3 3 

2 2 

Base Base 

012345678 012345678 

DCRN = Plastic Deformation / CP Acceptance Criteria DCRN = Plastic Deformation / CP Acceptance Criteria 

(a) ELF (b) RSA 

Figure 3-72. NDP Assessment Results, Shear Hinges, 8-Story EBF, BSE-2 CP 

Figure 3-73 and Figure 3-74 show the curvature ductility demand of the column hinges (i.e., section 

strength) at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. Figure 3-75 and Figure 

3-77
 

 

3-76 show the elastic member strength interaction results at the BSE-2 EHL—see discussion on column 

strength modeling in §3.2.1.2. Column hinges at the base above the brace connection experience inelastic 

strain demands (yield corresponds to a DCRN = 1 in the figures). The deformation demands are considerably 

lower than the primary CP acceptance criteria for a Column. Still, the base column hinges do not satisfy the 

criteria for the CP BPL for both the ELF- and RSA-designed frames. This effect is two-fold: a consequence 

of modeling rotationally restrained base connections, which more closely characterizes how the base 

connection is detailed in these buildings than assuming rotationally unrestrained connections and, to a lesser 

extent, the minor increase in PE because the shear strength, VCE, of the link beams was increased by 15 

percent for nonlinear analysis—see §3.2.1.2 and §3.2.2.1.3. 

The DCRN results for the LSP and LDP are based on an interaction equation and not from MUD / m×MCE, or 

MUF / MCL, which would be a more physically consistent metric for comparison against the results from the 

nonlinear assessment procedures. Nonetheless, the linear results are generally applicable here because the 

exterior frame columns are force-controlled for flexure in the linear assessment procedures. Though there 

is a fundamental difference in how the DCRN is computed for the linear and nonlinear procedures, the linear 

assessment results show similar distributions of demands and location of potential performance concerns. 

0 2 4 6 8 10 12 14 16 18 20 22 

Base 

2 

3 

4 

5 

6 

7 

8 

Roof Col. Line B 

Floor ID 

0 2 4 6 8 10 12 14 16 18 20 22 

Col. Line C Median 

Mean 

84th 

Mean+1std

 NSP

 LSP

 LDP 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-73. NDP Assessment Results, Column Hinges, 8-Story EBF ELF, BSE-2 Yield 

3-78
 
Roof 

Median

Mean

Col. Line B Col. Line C

8 84th

Mean+1std

7 NSP

 LSP

 LDP 6 

Floor ID

5
 

4
 

3
 

2
 

Base 

0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18
 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2
 

Figure 3-74. NDP Assessment Results, Column Hinges, 8-Story EBF RSA, BSE-2 Yield 

 

Roof Median

Mean

Col. Line B Col. Line C

8 84th

Mean+1std

7 LSP

 LDP 

6 

Floor ID

5 

4 

3 

2 

0.0 

Base 

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 

DCRN = P-M Interaction Value 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 

Figure 3-75. NDP Assessment Results, Column Members, 8-Story EBF ELF, BSE-2 

3-79
6 

7 

8 

Roof Col. Line B Col. Line C Median

Mean

84th

Mean+1std

 LSP

 LDP 

5 

4 

3 

2 

0.0 

Base 

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 

DCRN = P-M Interaction Value 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 

Figure 3-76. NDP Assessment Results, Column Members, 8-Story EBF RSA, BSE-2 

Floor ID 

Figure 3-77 and Figure 3-78 show the curvature ductility demand of the brace hinges (i.e., section strength) 

at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. Figure 3-79 and Figure 3-80 

show the elastic member strength interaction results at the BSE-2 EHL—see discussion on column strength 

modeling in—see discussion on column strength modeling in §3.2.1.2. Brace hinges at the base above the 

brace connection experience inelastic strain demands (yield corresponds to a DCRN = 1 in the figures). The 

deformation demands are considerably lower than the primary CP acceptance criteria for a Column. Still, 

the brace hinges do not satisfy the criteria for the CP BPL for both the ELF- and RSA-designed frames— 

see previous discussion on column results for additional information. 

Roof 

8 

Left Brace Right Brace Median

Mean

84th

Mean+1std

7 NSP

 LSP

6 LDP 

Floor ID

5
 

4
 

3
 

2
 

Base 

0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12
 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2
 

Figure 3-77. NDP Assessment Results, Brace Hinges, 8-Story EBF ELF, BSE-2 Yield 

3-80 
6 

7 

8 

Roof 

Left Brace Right Brace Median

Mean

84th

Mean+1std

 NSP

 LSP

 LDP 

Floor ID Floor ID

5 

4 

3 

2 

0 

Base 

1 

Figure 3-78. NDP Assessment Results, Brace Hinges, 8-Story EBF RSA, BSE-2 Yield 

2 3 4 5 6 7 8 9 10 11 12 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

0 1 2 3 4 5 6 7 8 9 10 11 12 

Roof Left Brace Right Brace Median

Mean

8 84th

Mean+1std

7 LSP

 LDP 

6 

5 

4 

3 

2 

0.0 

Base 

0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Value 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Figure 3-79. NDP Assessment Results, Brace Members, 8-Story EBF ELF, BSE-2 

3-81
 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Base 

2 

3 

4 

5 

6 

7 

8 

Roof Left Brace 

Floor ID 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Right Brace Median 

Mean 

84th 

Mean+1std

 LSP

 LDP 

DCRN = P-M Interaction Value 

Figure 3-80. NDP Assessment Results, Brace Members, 8-Story EBF RSA, BSE-2 

Sixteen-Story Eccentrically Braced Frame 

3.2.2.3.1 Linear Static Procedure 

3.2.2.3.1.1 BSE-1 Earthquake Hazard Level (LS BPL) 

In this section, the following apply: 

	 Figure 3-81 and Figure 3-82 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-83 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the LS BPL acceptance criteria. 

Base columns in the RSA-designed frame do not satisfy the LS BPL acceptance criteria (force-controlled) 

using the interaction equation because of the combination of high axial force and moment. High flexural 

demand at the base of the frame is a consequence of modeling rotationally restrained base connections, 

which more closely characterizes how the base connection is detailed in these buildings than assuming 

rotationally unrestrained connections. As discussed previously in §3.2.2, PUF is determined by taking J 

(ASCE 41 §3.4.2.1.2-2) as the minimum DCR of the component(s) delivering force to the column, but not 

less than 2.0. This approach produces an upper-bound estimate for PUF for the LS SPL as compared to 

ASCE 41 §3.4.2.1.2-1 (based on ASCE 41 §5.5.3.4.2), as shown in Figure 3-83. 

3-82
 
 

Similar to the discussion in §3.2.2.2.1.1, one could initially argue that columns in an EBF frame (greater 

than three stories) designed per AISC 341 would satisfy ASCE 41 criteria by default. Following ASCE 41 

§5.5.3.4.2 results in the following for the base column (RSA-designed frame is used here): 

o PCL = 5215 kips 

o PGravity = 655 kips 

o PUF = 5399 kips (determined using J equal to 2.0) 

 PUF / PCL = 1.03 (MUF / MCL = 0.11) → interaction result = 1.13 (fails) 

o PUF = 4742 kips (determined from a fully yielded frame per ASCE 41§5.5.3.4.2) 

 PUF / PCL = 0.91 (MUF / MCL = 0.11) → interaction result = 1.01 (fails—?) 

o PUF = 4269 kips (determined from a fully yielded frame per AISC 341 §F3.3) 

 PUF / PCL = 0.82 (MUF / MCL = 0) → interaction result = 0.82 (passes) 

Adopting a full frame plastic mechanism to represent the peak dynamic demands in the columns can 

penalize force-controlled columns in an EBF. As an alternative, ASCE 41 could allow EBF columns to be 

deformation-controlled similar to a CBF, ASCE 41 §5.5.2, and follow AISC 341 provisions to reduce the 

axial load demands by 12 percent. The maximum axial load demand from the NDP is 4528 kips, a 5 percent 

reduction, including the effect of increasing VCE for nonlinear analysis—see §3.2.1.2 and §3.2.2.1.3. 

3-83
 
 

0.11 9.00 

0.09 

.

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

0.21 

0.22 

0

1 .2

0 4 .5

0.28 

0 4 .5

0 2 .5

0.34 

0 2 .5

0 2 .5

0.34 

0 2 .5

0 5 .5

0.35 

0 5 .5

0 7 .5

0.34 

0 7 .5

0 8 .5

0.35 

0 8 .5

0 8 .5

0.34 

0 8 .5

0 0 .6

0.32 

0 0 .6

0

1 .6

0.32 

0

1 .6

0 0 .6

0.33 

0 0 .6

0 0 .6

0.33 

0 0 .6

0 0 .6

0.33 

0 0 .6

0 0 .6

0.33 

0 0 .6

0 0 .6

0.31 

0 0 .6

0 3 .5

0 3 .5

0.09 

0.13 0.13 

0.12 0.12 

0.27 0.27 

0.40 0.40 

0.54 0.54 

0.49 0.49 

0.62 0.62 

0.57 0.57 

0.69 0.69 

0.64 0.64 

0.73 0.73 

0.68 0.68 

0.76 0.76 

0.69 0.69 

0.90 0.90 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-81. LSP Assessment Results, 16-Story EBF ELF, BSE-1 LS 

3-84
 
 

0.10 9.00 

0.11 

.

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

0.19 

0.21 

0 9 .1

0 9 .4

0.31 

0 9 .4

0 4 .5

0.39 

0 4 .5

0 4 .5

0.46 

0 4 .5

0 5 .4

0.41 

0 5 .4

0 2 .5

0.39 

0 2 .5

0 7 .4

0.38 

0 7 .4

0 0 .5

0.35 

0 0 .5

0 5 .5

0.35 

0

5 .5

0 5 .5

0.33 

0

5 .5

0 7 .5

0.33 

0 7 .5

0 7 .5

0.32 

0 7 .5

0 4 .5

0.32 

0 4 .5

0 4 .5

0.31 

0 4 .5

0 4 .5

0.28 

0 4 .5

0

1 .5

0

1 .5

0.11 

0.35 0.35 

0.39 0.39 

0.66 0.66 

0.53 0.53 

0.75 0.75 

0.80 0.80 

0.98 0.98 

0.81 0.81 

0.96 0.96 

0.91 0.91 

1.04 1.04 

0.97 0.97 

1.07 1.07 

0.95 0.95 

1.13 1.13 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-82. LSP Assessment Results, 16-Story EBF RSA, BSE-1 LS 

3-85
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0 2000 4000 6000 8000 10000 12000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

16 

15 

14 

13 

0 2000 4000 6000 8000 10000 12000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

12 

11 

Floor 

10 

9 

8 

7 7
 

6
 6
 

5
 5
 

4
 4
 

3
 3
 

2
 2
 

Base
 Base 

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-83. LSP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-1 

3.2.2.3.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-84 and Figure 3-85 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LSP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-86 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the CP BPL acceptance criteria. 

Similar to the LSP LS results, several frame columns in the ELF- and RSA-designed frames do not satisfy 

the CP BPL assessment criteria using the force-controlled interaction equation because of the combination 

of high axial force and moment. As discussed previously in §3.2.2, PUF is determined by taking J (ASCE 

41 §3.4.2.1.2-2) as the minimum DCR of the component(s) delivering force to the column, but not less than 

2.0. This approach produces a high estimate for PUF for the LS SPL as compared to ASCE 41 §3.4.2.1.2-1 

(based on ASCE 41 §5.5.3.4.2), as shown in Figure 3-86. 

The DCRN interaction results for force-controlled columns (and a few braces) are not the same between 

LSP LS and LSP CP because J was set to the default of 2.0 in this frame. This default value is not consistent 

with the actual plastic mechanism, J for the CP SPL should be 2 / 2⁄3 = 3 assuming all links yield (or J = 2 

× 2⁄3 for the LS SPL). The effect on axial load demand by maintaining J can be seen in Figure 3-86. The 

results for the links differ by approximately (13/9)/1.5 = 0.963 times the DCRN, approximate because of 

second-order effects. 

3-86
 
 

0.12 13.00 

0.12 

5

5

6

6

6

6

6

6

6

6

6

6

6

6

6

6

5

5

5

5

5

5

5

5

5

5

5

5

5

5

4

0.41 

0.23 

0

1 .4

0 4 .5

0.29 

0 4 .5

0 2 .5

0.35 

0 2 .5

0 2 .5

0.35 

0 2 .5

0 5 .5

0.37 

0 5 .5

0 7 .5

0.35 

0 7 .5

0 8 .5

0.36 

0 8 .5

0 8 .5

0.35 

0 8 .5

0 0 .6

0.33 

0 0 .6

0

1 .6

0.33 

0

1 .6

0 0 .6

0.34 

0 0 .6

0 0 .6

0.34 

0 0 .6

0 0 .6

0.35 

0 0 .6

0 0 .6

0.34 

0 0 .6

0 0 .6

0.32 

0 0 .6

0 3 .5

0 3 .5

0.12 

0.17 0.17 

0.17 0.17 

0.38 0.38 

0.56 0.56 

0.78 0.78 

0.71 0.71 

0.88 0.88 

0.82 0.82 

0.99 0.99 

0.92 0.92 

1.06 1.06 

0.98 0.98 

1.10 1.10 

1.00 1.00 

1.31 1.31 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-84. LSP Assessment Results, 16-Story EBF ELF, BSE-2 CP 

3-87
 
 

0.10 13.00 

0.15 

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

4

4

5

5

4

4

5

5

5

5

5

5

3

0.36 

0.21 

0 6 .3

0 3 .5

0.32 

0 3 .5

0 4 .5

0.40 

0 4 .5

0 4 .5

0.48 

0 4 .5

0 5 .4

0.43 

0 5 .4

0 2 .5

0.41 

0 2 .5

0 7 .4

0.40 

0 7 .4

0 0 .5

0.36 

0 0 .5

0 5 .5

0.36 

0

5 .5

0 5 .5

0.34 

0

5 .5

0 7 .5

0.35 

0 7 .5

0 7 .5

0.33 

0 7 .5

0 4 .5

0.33 

0 4 .5

0 4 .5

0.32 

0 4 .5

0 4 .5

0.29 

0 4 .5

0

1 .5

0

1 .5

0.15 

0.44 0.44 

0.53 0.53 

0.91 0.91 

0.77 0.77 

1.05 1.05 

1.14 1.14 

1.40 1.40 

1.16 1.16 

1.38 1.38 

1.30 1.30 

1.49 1.49 

1.39 1.39 

1.54 1.54 

1.36 1.36 

1.64 1.64 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-85. LSP Assessment Results, 16-Story EBF RSA, BSE-2 CP 

3-88
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

16 

15 

14 

13 

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

12 

11 

10 

9 

8 

7 7
 

6
 6
 

5
 5
 

4
 4
 

3
 3
 

2
 2
 

Base
 Base 

Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-86. LSP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-2 

3.2.2.3.2 Linear Dynamic Procedure 

3.2.2.3.2.1 BSE-1 Earthquake Hazard Level (LS BPL) 

In this section, the following apply: 

	 Figure 3-87 and Figure 3-88 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LDP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-89 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All component actions satisfy the LS BPL acceptance criteria. As discussed previously in §3.2.2, PUF is 

determined by taking J (ASCE 41 §3.4.2.1.2-2) as the minimum DCR of the component(s) delivering force 

to the column, but not less than 2.0. This approach produces a lower-bound estimate for PUF for the LS SPL 

as compared to ASCE 41 §3.4.2.1.2-1 (based on ASCE 41 §5.5.3.4.2), as shown in Figure 3-89. Floor 

3-89
 
 

0.16 9.00 

0.10 

.

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

0.38 

0.27 

0 8 .3

0 5 .5

0.28 

0 5 .5

0 2 .5

0.30 

0 2 .5

0 2 .5

0.27 

0 2 .5

0 5 .5

0.26 

0 5 .5

0 7 .5

0.24 

0 7 .5

0 8 .5

0.24 

0 8 .5

0 8 .5

0.24 

0 8 .5

0

1 .6

0.23 

0

1 .6

0

1 .6

0.24 

0

1 .6

0

1 .6

0.26 

0

1 .6

0

1 .6

0.28 

0

1 .6

0

1 .6

0.31 

0

1 .6

0

1 .6

0.32 

0

1 .6

0

1 .6

0.31 

0

1 .6

0 5 .5

0

5 .5

0.10 

0.14 0.14 

0.13 0.13 

0.30 0.30 

0.40 0.40 

0.50 0.50 

0.42 0.42 

0.49 0.49 

0.43 0.43 

0.49 0.49 

0.45 0.45 

0.50 0.50 

0.46 0.46 

0.51 0.51 

0.46 0.46 

0.68 0.68 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-87. LDP Assessment Results, 16-Story EBF ELF, BSE-1 LS 

3-90
 
 

0.16 9.00 

0.14 

.

. .

. .

. .

. .

.

.

.

.

. .

. .

. .

. .

. .

. .

. .

. .

. .

0.39 

0.27 

0 9 .3

0 4 .5

0.33 

0 4 .5

0 4 .5

0.35 

0 4 .5

0 4 .5

0.37 

0 4 .5

0 5 .4

0.30 

0 5 .4

0 2 .5

0.28 

0 2 .5

0 7 .4

0.27 

0 7 .4

0 0 .5

0.25 

0 0 .5

0 6 .5

0.26 

0 6 .5

0 6 .5

0.26 

0 6 .5

0 8 .5

0.27 

0 8 .5

0 8 .5

0.29 

0 8 .5

0 6 .5

0.31 

0 6 .5

0 6 .5

0.33 

0 6 .5

0 6 .5

0.30 

0 6 .5

0 5 .5

0

5 .5

0.14 

0.44 0.44 

0.47 0.47 

0.77 0.77 

0.55 0.55 

0.71 0.71 

0.69 0.69 

0.79 0.79 

0.61 0.61 

0.69 0.69 

0.63 0.63 

0.70 0.70 

0.64 0.64 

0.71 0.71 

0.63 0.63 

0.84 0.84 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

9.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-88. LDP Assessment Results, 16-Story EBF RSA, BSE-1 LS 

3-91
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof Roof Floor 

16 

15 

14 

13 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

12 

11 

10

Floor 

9 

8 

7
 

6
 

7 

6
 

5
 5
 

4
 4
 

3
 3
 

2
 2
 

Base
 Base 

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-89. LDP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-1 

3.2.2.3.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-90 and Figure 3-91 provide the DCRN and load-dependent m-factor values for the ELF 

and RSA designs, respectively, for the LDP at the BSE-1 EHL. In these figures, DCRN values 

greater than unity are highlighted in red and underlined. DCR values, as defined by ASCE 41, can 

be obtained by multiplying DCRN by m and , see Eq. 3-6. 

	 Figure 3-92 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All link beam and brace actions satisfy the CP BPL acceptance criteria. 

Base columns in the RSA-designed frame do not satisfy the LS BPL acceptance criteria using the forcecontrolled interaction equation because of the combination of high axial force and moment. High flexural 

demand at the base of the frame is a consequence of modeling rotationally restrained base connections, 

which more closely characterizes how the base connection is detailed in these buildings than assuming 

rotationally unrestrained connections. As discussed previously in §3.2.2, PUF is determined by taking 

(ASCE 41 §3.4.2.1.2-2) as the minimum DCR of the component(s) delivering force to the column, but not 

less than 2.0. This approach produces a lower-bound estimate for PUF for the LS SPL as compared to ASCE 

41 §3.4.2.1.2-1 (based on ASCE 41 §5.5.3.4.2), as shown in Figure 3-92. 

The DCRN interaction results for force-controlled columns (and a few braces) are not the same between 

LSP LS and LSP CP because J was set to the default of 2.0 in this frame. This default value is not consistent 

with the actual plastic mechanism—see §3.2.2.3.1.2 for more information. The results for the links differ 

by approximately (13/9)/1.5 = 0.963 times the DCRN, approximate because of second-order effects. 

3-92
 
 

0.16 13.00 

0.14 

5

5

6

6

6

6

6

6

6

6

6

6

6

6

6

6

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

0.53 

0.28 

0 3 .5

0 5 .5

0.29 

0 5 .5

0 2 .5

0.31 

0 2 .5

0 2 .5

0.28 

0 2 .5

0 5 .5

0.27 

0 5 .5

0 7 .5

0.25 

0 7 .5

0 8 .5

0.25 

0 8 .5

0 8 .5

0.25 

0 8 .5

0

1 .6

0.24 

0

1 .6

0

1 .6

0.25 

0

1 .6

0

1 .6

0.27 

0

1 .6

0

1 .6

0.30 

0

1 .6

0

1 .6

0.32 

0

1 .6

0

1 .6

0.33 

0

1 .6

0

1 .6

0.32 

0

1 .6

0 5 .5

0

5 .5

0.14 

0.29 0.29 

0.17 0.17 

0.40 0.40 

0.54 0.54 

0.69 0.69 

0.58 0.58 

0.68 0.68 

0.59 0.59 

0.68 0.68 

0.61 0.61 

0.68 0.68 

0.62 0.62 

0.69 0.69 

0.63 0.63 

0.93 0.93 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-90. LDP Assessment Results, 16-Story EBF ELF, BSE-2 CP 

3-93
 
 

0.17 13.00 

0.18 

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

4

4

5

5

4

4

5

5

5

5

5

5

5

0.53 

0.28 

0 3 .5

0 4 .5

0.34 

0 4 .5

0 4 .5

0.36 

0 4 .5

0 4 .5

0.38 

0 4 .5

0 5 .4

0.31 

0 5 .4

0 2 .5

0.29 

0 2 .5

0 7 .4

0.28 

0 7 .4

0 0 .5

0.26 

0 0 .5

0 6 .5

0.27 

0 6 .5

0 6 .5

0.27 

0 6 .5

0 8 .5

0.28 

0 8 .5

0 8 .5

0.30 

0 8 .5

0 6 .5

0.32 

0 6 .5

0 6 .5

0.34 

0 6 .5

0 6 .5

0.31 

0 6 .5

0 5 .5

0

5 .5

0.18 

0.55 0.55 

0.61 0.61 

1.01 1.01 

0.75 0.75 

0.94 0.94 

0.91 0.91 

1.05 1.05 

0.81 0.81 

0.91 0.91 

0.83 0.83 

0.93 0.93 

0.85 0.85 

0.94 0.94 

0.84 0.84 

1.13 1.13 

(a) DCRN

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

13.00 

1.00 

1.00 

1.00 

(b) m-factors 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

(c) Key 

Figure 3-91. LDP Assessment Results, 16-Story EBF RSA, BSE-2 CP 

3-94
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

0 2000 4000 6000 8000 10000 12000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof Roof Floor 

16 

15 

14 

13 

0 2000 4000 6000 8000 10000 12000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design(ASCE 41) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

12 

11 

10 

Floor 

9 

8 

7 7

6 6

5 5

4 4

3 3

2 2

Base Base

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-92. LDP Assessment Results, Compression in Exterior Columns, 16-Story EBF, BSE-2 

3.2.2.3.3 Nonlinear Static Procedure 

	 Table 3-17 to Table 3-19 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-93 and Figure 3-94 illustrate the monotonic pushover curves for the ELF- and RSAdesigned frames, respectively, and the associated pushover parameters from ASCE 41 at the BSE2 EHL. Roof displacement is measured at the Center of Mass (CoM). A significant change in base 

shear is due to component strength loss of components (e.g., link beams), notated in the figures. 

First-order and second-order responses, shown in these figures, aids in computing a physically 

meaningful value for P- used in ASCE 41 Equation 3-17. 

	 Figure 3-95and Figure 3-96 illustrate the story drift ratios in terms of the roof drift ratio. 

As discussed in §3.1.3.2.1, the NSP is permitted, but requires supplemental verification using the LDP— 

see §3.2.2.3.2. In this case, the displacement at the maximum base shear governs d for the RSA-designed 

frame for both BSE-1 and BSE-2 EHLs and ELF frame for BSE-2 EHL whereas the target displacement 

governs the ELF-designed frame for BSE-1 EHL. The change in d between BSE-1 and BSE-2 adds 

complexity to NSP process by changing the pushover variables. Further, when d is governed by the target 

displacement, the system can have an increased Rmax. Axial compression force in the exterior columns at 

the target displacement are shown previously in the linear assessment sections. Results indicate that the 

NSP generally results in a lower estimate of the axial force demands compared to the other methods used 

in this study. This is partly because the fundamental mode-based lateral force distribution does not 

adequately capture higher mode effects. Also, the target displacement at the roof computed based on 

fundamental mode properties may underestimate the story demands in the upper stories. 

3-95
 
 

 

 

 

 

 

 

 

 

 

 

Table 3-17. NSP General Information, 16-Story EBF (kip, inch) 

Design T1 K1 y Vy Ke Te h peak Vpeak W Cm C0 

ELF 3.02 106.2 16.5 1748 105.8 3.03 1.17 28.8 2008.8 21900 1.00 1.43 

RSA 3.55 70.9 18.5 1300 70.4 3.57 1.19 28.1 1429.7 21659 1.00 1.46 

Table 3-18. CP NSP Analysis Parameters, 16-Story EBF BSE-2 CP (kip, inch) 

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.30 3.76 1.00 1.00 38.4 1457.0 28.8 0.20 -0.23 -0.05 -0.08 6.32 OK 

RSA 0.26 4.28 1.00 1.00 46.8 844.5 28.1 0.19 -0.34 -0.05 -0.11 5.01 OK 

Table 3-19. LS NSP Analysis Parameters, 16-Story EBF BSE-1 LS (kip, inch) 

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.20 2.51 1.00 1.00 25.6 1967.8 25.6 0.23 -0.20 -0.05 -0.08 6.50 OK 

RSA 0.17 2.86 1.00 1.00 31.2 1421.0 28.1 0.19 -0.34 -0.05 -0.11 5.01 OK 

Roof Drift Ratio at CoM (%) 

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.6 

2400 0.110 

2200 0.100 

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 

(16.5,1748.0) 

(28.8,2008.8) 

(68.0,1048.8) 

D 

Pt. A: Shear Hinge reached CP on 5th and 6th Floor 

Pt. B: Shear Hinge reached CP on 4th Floor 

Pt. C: Shear Hinge reached CP on 7th Floor 

Pt. D: Shear Hinge reached CP on 3rd and 8th Floor 

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

A 

B 

C 

2000 

Total Base Shear (Kips) 1800 

1600 

1400 

1200 

1000 

800 

0.091 

0.082 

0.073 

0.064 

0.055 

0.046 

0.037 

Total Base Shear / W 

600 

400 

200 

0 

0.027 

0.018 

0.009 

0.000 

Roof Displacement at CoM (Inches)

Figure 3-93. 16-Story EBF ELF Pushover, BSE-2 

3-96
 
 

Roof Drift Ratio at CoM (%) 

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.6 

2400 0.111 

1800 

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 

(18.5,1300.0) 

(28.1,1429.7) 

(55.0,780.0) 

Pt. A: Shear Hinge reached CP on 12th and 13th Floor 

Pt. B: Shear Hinge reached CP on 11th Floor 

Pt. C: Shear Hinge reached CP on 14th Floor 

 RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

A 

B 

C 

0.083 

1600 0.074 

2200 0.102 

2000 0.092 

Total Base Shear (Kips) 

Total Base Shear / W 

1400 0.065 

1200 0.055 

1000 0.046 

800 0.037 

600 0.028 

400 0.018 

200 0.009 

0 0.000 

Roof Displacement at CoM (Inches)

Figure 3-94. 16-Story EBF RSA Pushover, BSE-2 

Figure 3-97 illustrates which frame components are force-controlled for flexure for both the NSP and NDP; 

red circles indicate anticipated plastic hinge locations that are force-controlled for flexure at the target 

displacement. 

Figure 3-98 and Figure 3-99 illustrate the DCRN values if greater than unity for the ELF- and RSA-designed 

frames at the target displacement for the LS BPL at the BSE-1 EHL and CP BPL at the BSE-2 EHL. The 

figures illustrate demands when the system is loaded to the left. All shear actions for the ELF-designed 

frame satisfy the LS BPL acceptance criteria; however, one link beam in the RSA-designed frame does not 

satisfy the same criteria. Several link beams in both designs do not satisfy the CP BPL acceptance criteria. 

These failures occur at different locations within the frame, illustrating the variation in the distribution of 

link beam strengths from the ELF and RSA design procedures. 

All other force-controlled component actions adjacent to the link beams do satisfy the LS BPL acceptance 

criteria. Although the same observation is evident for the ELF-designed frame for the CP BPL acceptance 

criteria, several hinges in columns and beams in the RSA-designed frame do not satisfy the criteria for the 

CP BPL. This result is a consequence of the target displacement being much greater than the displacement 

at the peak base shear. There are several frame column hinges (not at the base) in the RSA-designed frame 

that do not satisfy the criteria for the CP BPL. This effect is primarily because of the minor increase in PE 

because the shear strength, VCE, of the link beams was increased by 15 percent for nonlinear analysis—see 

§3.2.1.2. As discussed in §3.2.1.2, the flexural hinge model for force-controlled components obeys ASCE 

3-97
 
41 Equation 5-4 (yield surface for the section). As such, unsatisfactory performance is characterized by 

section yielding. 

0.0% 0.5% 1.0% 1.5% 2.0% 

0.0% 

0.5% 

1.0% 

1.5% 

2.0% 

2.5% 

3.0% 

Story Drift Ratio (%) 

1st Story

 2nd Story

 3rd Story

 4th Story

 5th Story

 6th Story

 7th Story

 8th Story

 9th Story

 10th Story

 11th Story

 12th Story

 13th Story

 14th Story

 15th Story

 16th Story

 Roof 

Roof Drift Ratio (%)

Figure 3-95. 16-Story EBF ELF Pushover – Story Drift Ratios – BSE-2
 

0.0% 0.5% 1.0% 1.5% 2.0% 

0.0% 

0.5% 

1.0% 

1.5% 

2.0% 

2.5% 

3.0% 

Story Drift Ratio (%) 

1st Story

 2nd Story

 3rd Story

 4th Story

 5th Story

 6th Story

 7th Story

 8th Story

 9th Story

 10th Story

 11th Story

 12th Story

 13th Story

 14th Story

 15th Story

 16th Story

 Roof 

Roof Drift Ratio (%)

Figure 3-96. 16-Story EBF RSA Pushover – Story Drift Ratios – BSE-2 

3-98
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sym. About 

4 3 

Roof
 

(ELEV = 228 ft.)
 

16th Fl o or
 

(ELEV = 214 ft.)
 

15th Fl o or
 

(ELEV = 200 ft.)
 

14th Fl o or
 

(ELEV = 186 ft.)
 

13th Fl o or
 

(ELEV = 172 ft.)
 

12th Fl o or
 

(ELEV = 158 ft.)
 

11th Fl o or
 

(ELEV = 144 ft.)
 

10th Fl o or
 

(ELEV = 130 ft.)
 

9th Flo or
 

(ELEV = 116 ft.)
 

8th Flo or
 

(ELEV = 102 ft.)
 

7th Flo or
 

(ELEV = 88 ft.)
 

6th Flo or
 

(ELEV = 74 ft.)
 

5th Flo or
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Fl o or
 

(ELEV = 32 ft.)
 

2nd Fl o or
 

(ELEV = 18 ft.)
 

All colum ns, braces, and beams 

adjacent to link beams are 

force-controlled (FC) for flexur e 

Figure 3-97. Schematic of Flexural Actions in Components, 16-Story EBF (NSP and NDP) 

3-99
 
 

 

 

 

 

 

 

 

 

 

 

 

 

Roof
 

(ELEV = 228 ft.)
 

16th Floor
 

(ELEV = 214 ft.)
 

15th Floor
 

(ELEV = 200 ft.)
 

14th Floor
 

(ELEV = 186 ft.)
 

13th Floor
 

(ELEV = 172 ft.)
 DCRN ≥ 1.0 

12th Floor 

(ELEV = 158 ft.) 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

11th Floor 

(ELEV = 144 ft.) 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

10th Floor 

(ELEV = 130 ft.) 

9th Flo or 

(ELEV = 116 ft.) 

8th Flo or 

(ELEV = 102 ft.) 

7th Flo or 

(ELEV = 88 ft.) 

6th Flo or 

(ELEV = 74 ft.) 

5th Flo or 

(ELEV = 60 ft.) 

4th Flo or 

(ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Flo or 

(ELEV = 18 ft.) 

4 3 4 3 

1.07 

Roof
 

(ELEV = 228 ft.)
 

16th Floor 

(ELEV = 214 ft.) 

15th Floor 

(ELEV = 200 ft.) 

14th Floor 

(ELEV = 186 ft.) 

13th Floor 

(ELEV = 172 ft.) DCRN ≥ 1.0 

12th Floor 

(ELEV = 158 ft.) 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

11th Floor 

(ELEV = 144 ft.) 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

10th Floor 

(ELEV = 130 ft.) 

9th Flo or 

(ELEV = 116 ft.) 

8th Flo or 

(ELEV = 102 ft.) 

7th Flo or 

(ELEV = 88 ft.) 

6th Flo or 

(ELEV = 74 ft.) 

5th Flo or 

(ELEV = 60 ft.) 

4th Flo or 

(ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Flo or 

(ELEV = 18 ft.) 

(a) ELF (b) RSA 

Figure 3-98. NSP Assessment Results, 16-Story EBF ELF, BSE-1 LS (+push to left) 

3-100
 
 

 

 

 

 

 

 

 

 

 

 

 

 

1.54 

1.91 

1.70 

4 3 

Roof
 

(ELEV = 228 ft.)
 

16th Floor 

(ELEV = 214 ft.) 

15th Floor 

(ELEV = 200 ft.) 

14th Floor 

(ELEV = 186 ft.) 

13th Floor 

(ELEV = 172 ft.) DCRN ≥ 1.0 

12th Floor 

(ELEV = 158 ft.) 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

11th Floor 

(ELEV = 144 ft.) 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

10th Floor 

(ELEV = 130 ft.) 

9th Flo or 

(ELEV = 116 ft.) 

8th Flo or 

(ELEV = 102 ft.) 

7th Flo or 

(ELEV = 88 ft.) 

6th Flo or 

(ELEV = 74 ft.) 

5th Flo or 

(ELEV = 60 ft.) 

4th Flo or 

(ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Flo or 

(ELEV = 18 ft.) 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

4 3 

2.32 

3.66 

3.38 

2.10 

1.09 

1.12 

1.04 

1.15 1.11 

Roof
 

(ELEV = 228 ft.)
 

16th Floor
 

(ELEV = 214 ft.)
 

15th Floor
 

(ELEV = 200 ft.)
 

14th Floor
 

(ELEV = 186 ft.)
 

13th Floor
 

(ELEV = 172 ft.)
 

12th Floor
 

(ELEV = 158 ft.)
 

11th Floor
 

(ELEV = 144 ft.)
 

10th Floor
 

(ELEV = 130 ft.)
 

9th Flo or
 

(ELEV = 116 ft.)
 

8th Flo or
 

(ELEV = 102 ft.)
 

7th Flo or
 

(ELEV = 88 ft.)
 

6th Flo or
 

(ELEV = 74 ft.)
 

5th Flo or
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

(a) ELF (b) RSA 

Figure 3-99. NSP Assessment Results, 16-Story EBF RSA, BSE-2 CP (+push to left) 

3.2.2.3.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the N-S direction of ME16 is shown in Appendix A. For the ELF 

design, the analysis successfully completed for all 14 records at the BSE-1 EHL whereas three did not 

complete successfully at the BSE-2 EHL because of excessive lateral drifts. For the RSA design, the 

3-101
 
 

analysis successfully completed for all 14 records at the BSE-1 EHL whereas four did not complete 

successfully at the BSE-2 EHL because of excessive lateral drifts. Maximum axial compression force in 

the exterior column lines from the record set are shown previously in the linear assessment sections. 

Figure 3-100 and Figure 3-101 show the performance of the link beams at the BSE-1 (LS BPL) and BSE2 (CP BPL) for the ELF and RSA design, respectively, in terms of a DCRN. The DCRN results from the 

LSP, LDP, and NSP (loaded to the left) are included in the figures. Comparison discussions of the various 

procedures are addressed subsequently. As is evident in the figures, the ELF-designed frame performs 

noticeably better than the RSA-designed frame. The results indicate that several links in the RSA-designed 

frame do not satisfy the LS BPL acceptance criteria. Both the ELF- and RSA-designed frames perform 

markedly poorer at the BSE-2 EHL, with several links not satisfying the CP BPL acceptance criteria using 

both median and mean metric. The distribution of demands is somewhat similar between the two designs 

illustrating the effect of higher modes on the response. A DCRN value of 0.73 equates to a plastic rotation 

angle of 0.08 radians at the BSE-1 EHL (0.62 at the BSE-2 EHL). 

The average ratio of secondary to primary component acceptance criteria for a wide-flange section with the 

configuration in this frame is 1.14 for the CP SPL (1.27 for the LS SPL). The figures for the ELF- and 

RSA-designed frame illustrate that this value is exceeded in a number of stories at the BSE-1 EHL and 

BSE-2 EHL. This highlights the rapid analytical progression towards a collapsed state when several 

components are strained past the deformation associated with their peak strength—see §3.1.4.2. 

Roof Roof 

Median 16 16 Mean 

15 15 84th 

14 

13 

14 Mean+1std

 NSP 13 

12 LSP 12 

LDP 11 11

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 

10 

9 

8 

7 

10 

9

Floor ID 

Floor ID

8 Median 

Mean 7 

84th 6 6

Mean+1std

5 5 NSP 

4 4 LSP 

3 3 LDP 

2 2

Base Base 

DCRN = Plastic Deformation / LS Acceptance Criteria DCRN = Plastic Deformation / LS Acceptance Criteria 

(a) ELF (b) RSA 

Figure 3-100. NDP Assessment Results, Shear Hinges, 16-Story EBF, BSE-1 LS 

3-102
 
Roof Roof Median Median 

16 Mean 16 Mean 

15 84th 15 84th 

14 Mean+1std 14 Mean+1std

13 NSP 13 NSP 

12 LSP 12 LSP

LDP LDP 11 11 

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 

Floor ID 

10 

9 

8 

7 

Floor ID 

10 

9 

8 

7 

6 6 

5 5 

4 4 

3 3 

2 2 

Base Base 

DCRN = Plastic Deformation / CP Acceptance Criteria DCRN = Plastic Deformation / CP Acceptance Criteria 

(a) ELF (b) RSA 

Figure 3-101. NDP Assessment Results, Shear Hinges, 16-Story EBF, BSE-2 CP 

Figure 3-102 and Figure 3-103 show the curvature ductility demand of the column hinges (i.e., section 

strength) at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. Figure 3-104 and 

Figure 3-105 show the elastic member strength interaction results at the BSE-2 EHL—see discussion on 

column strength modeling in §3.2.1.2. Column hinges at the base above the brace connection experience 

inelastic strain demands (yield corresponds to a DCRN = 1 in the figures). The deformation demands are 

considerably lower than the primary CP acceptance criteria for a ‘column’. Still, the base column hinges 

do not satisfy the criteria for the CP BPL for both the ELF- and RSA-designed frames. This effect is twofold: a consequence of modeling rotationally restrained base connections, which more closely characterizes 

how the base connection is detailed in these buildings than assuming rotationally unrestrained connections 

and, to a lesser extent, the minor increase in PE because the shear strength, VCE, of the link beams was 

increased by 15 percent for nonlinear analysis—see §3.2.1.2 and §3.2.2.1.3. There is also evidence of 

column hinging in stories other than at the base at the BSE-2 EHL, which is additionally a consequence of 

the strength loss experienced by the links in those stories. 

The DCRN results for the LSP and LDP are based on an interaction equation and not from MUD / m×MCE, or 

MUF / MCL, which would be a more physically consistent metric for comparison against the results from the 

nonlinear assessment procedures. Nonetheless, the linear results are generally applicable here because the 

exterior frame columns are force-controlled for flexure in the linear assessment procedures. Though there 

is a fundamental difference in how the DCRN is computed for the linear and nonlinear procedures, the linear 

assessment results show similar distributions of demands and location of potential performance concerns. 

3-103
 
11 

12 

13 

14 

15 

16 

Roof 

Col. Line B Col. Line C Median

Mean

84th

Mean+1std

 NSP

 LSP

 LDP 

Floor ID Floor ID

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0 1 2 3 4 5 6 0 1 2 3 4 5 6 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-102. NDP Assessment Results, Column Hinges, 16-Story EBF ELF, BSE-2 Yield 

 

15 

16 

Roof 

Col. Line B Col. Line C Median

Mean

84th

14 Mean+1std

13 NSP

12 LSP

11 LDP 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

01 2 345 67 89 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-103. NDP Assessment Results, Column Hinges, 16-Story EBF RSA, BSE-2 Yield 

3-104 
11 

12 

13 

14 

15 

16 

Roof Col. Line B Col. Line C Median

Mean

84th

Mean+1std

 LSP

 LDP 

Floor ID

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 

DCRN = P-M Interaction Value 

Figure 3-104. NDP Assessment Results, Column Members, 16-Story EBF ELF, BSE-2 

 

Roof Col. Line B Col. Line C Median

16 Mean

15 84th

14 Mean+1std

13 LSP

 LDP 12 

11 

Floor ID

10
 

9
 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
 

DCRN = P-M Interaction Value
 

Figure 3-105. NDP Assessment Results, Column Members, 16-Story EBF RSA, BSE-2 

Figure 3-106 and Figure 3-107 show the curvature ductility demand of the brace hinges (i.e., section 

strength) at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. Figure 3-108 and 

Figure 3-109 show the elastic member strength interaction results at the BSE-2 EHL—see discussion on 

column strength modeling in—see discussion on column strength modeling in §3.2.1.2. Brace hinges at the 

base above the brace connection experience inelastic strain demands (yield corresponds to a DCRN = 1 in 

the figures). The deformation demands are considerably lower than the primary CP acceptance criteria for 

a Column. Still, the brace hinges do not satisfy the criteria for the CP BPL for both the ELF- and RSAdesigned frames—see previous discussion on column results for additional information. 

3-105
11 

12 

13 

14 

15 

16 

Roof Left Brace Right Brace Median

Mean

84th

Mean+1std

 NSP

 LSP

 LDP 

Floor ID

10
 

9
 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base 

0 1 2 3 4 5 0 1 2 3 4 5 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-106. NDP Assessment Results, Brace Hinges, 16-Story EBF ELF, BSE-2 Yield 

 

16 

Roof Left Brace Right Brace Median

Mean

15 84th

14 Mean+1std

13 NSP

12 LSP

11 LDP 

Floor ID

10
 

9
 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base 

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 
 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2
 

Figure 3-107. NDP Assessment Results, Brace Hinges, 16-Story EBF RSA, BSE-2 Yield 

3-106
11 

12 

13 

14 

15 

16 

Roof Left Brace Right Brace Median

Mean

84th

Mean+1std

 LSP

 LDP 

Floor ID

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Value 

Figure 3-108. NDP Assessment Results, Brace Members, 16-Story EBF ELF, BSE-2 

 

16 

Roof Left Brace Right Brace Median

Mean

15 84th

14 Mean+1std

13 LSP

12 LDP 

11 

Floor ID

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 

DCRN = P-M Interaction Value 

Figure 3-109. NDP Assessment Results, Brace Members, 16-Story EBF RSA, BSE-2 

 

3-107
 

Seismic Assessment Discussion 

The discussion in this section focuses on the following component design actions: 

 Link shear force 

 Beam, column, and brace flexure within anticipated plastic hinge zones (section strength)23 

 Column and brace axial-moment interaction strength (member strength) 

ASCE 41 requires all frame components that do not satisfy the acceptance criteria to be retrofitted or 

replaced, even if only a small percentage of the total components fail the criteria (see ASCE 41 §5.5.3.5). 

Therefore, a building can only satisfy a selected BPL when all structural components satisfy the 

corresponding SPL. Building behavior is rarely governed by the response of a single component, with the 

one notable exception being collapse resulting from failure of a column. It can be argued that a shortcoming 

of ASCE 41 is the focus on component performance to ensure that all elements pass the evaluation, when 

failures of individual elements may not lead to catastrophic failure. Further, ASCE 41 requires that all brace 

connections are force-controlled and does not provide generalized modeling parameters of a brace 

connection for nonlinear analysis as done for a “ductile” beam-to-column connection in a moment frame. 

As such, the performance of a brace-to-beam connection adjacent to a link beam, as well as a brace-tocolumn connection, is not considered in the assessment. 

Design choices, constructability considerations, code requirements, nonseismic loads, analytical modeling 

assumptions, and other project specific requirements may add strength to critical components in a frame. 

Further, allocation of component strengths within the frame because of the lateral force distribution adopted 

in design can cause deviations of the component strengths from one story to another. Thus, capturing all 

possible permutations, in essence, would create an infinitely large design space. Nonetheless, the change in 

component strengths can significantly influence the DCRN values obtained from the ASCE 41 assessments. 

Linear Procedures 

The following discusses the analytical results for the noted components from the linear procedures for each 

archetype building. 

3.2.3.1.1 Link Beams 

Table 3-20 provides a summary of the performance of the shear links for each linear assessment procedure 

and each BPL. The link beams consistently satisfy the performance criteria for the LS and CP BPL for both 

linear procedures. The DCRN values all remained relatively low, 0.2–0.6, indicating potentially that either 

(1) the design criteria for new EBFs introduces significant member overstrength in reference to the 

acceptance criteria, (2) the acceptance criteria in ASCE 41 is overly generous for short link beams, or (3) a 

combination thereof. 

23 All components other than link beams are force-controlled per ASCE 41 §5.5.3.4. Brace connections are not assessed in this 

study because they are designed to resist forces computed using the maximum strengths of the brace. 

3-108
 
 

Table 3-20. Performance Summary of Shear Links (SL) per Frame, Linear Procedures 

Archetype Design LS

LSP

 CP LS 

LDP 

CP 

4-Story 

ELF 

RSA 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

8-Story ELF 

RSA 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

16-Story 

ELF 

RSA 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

All SL Pass 

As a side note, Table 3-21 summarizes the effects of design (AISC 341) and assessment (ASCE 41) 

provisions on the DCRN for a link beam at 2⁄3×MCER for the LS BPL. On the component capacity side, the 

shear yield strength prescribed in ASCE 41, VCE, and AISC 341, Vn, have the same underlying equation; 

differences arise when using nominal versus expected material properties and a strength reduction factor, 

v = 0.9, resulting in a capacity ratio (ASCE 41 / AISC 341) of 1.22. On the component demand side, 

assuming an eigenvalue analysis is conducted, ASCE 41 allows the use of the period determined from 

analysis, Tanalysis, whereas ASCE 7 will limit this period to CuTa when greater than. If this limit is triggered, 

the demand in the link beams will generally increase for design resulting in a demand ratio (ASCE 41 / 

ASCE 7) less than unity. Additionally, ASCE 41 effectively divides the demand by m (= 9 for a link beam) 

while ASCE 7 divides the demand by R (= 8 for an EBF). Thus, for a link beam designed per ASCE 7 and 

its referenced standards whose design strength exactly equals the demand, the corresponding DCRN for the 

linear assessment will be less than or equal to 0.72. This value increases to 0.76 for the CP SPL at the BSE2. Conversely, a link beam that exactly satisfies the ASCE 41 assessment criteria will have a demand equal 

to 1.4 times the design strength—larger than what would be comfortably accepted in practice. This indicates 

an area where ASCE 41 linear assessment procedures are potentially unconservative. 

Table 3-21. Effect of Design and Assessment Provisions on DCRN for LS at BSE-1 

Demand Capacity Effect on DCRN 

a) ASCE 41 Sa at T = Tanalysis 

1 1 9 m  V F A CE  0.6 1.1  y w  # 1.0 0.88  

1.22 

DCRN

 

0.72  DCRN 

b) ASCE7 and AISC 341 Sa at T = 

min[Tanalysis, CuTa] 

1 1 8 R  vn 

V F  0.9 0.6  y w A 

Ratio (a/b) ab  1.0 ab  0.8 8 ab  1.1 0.9 1.2 2 

In addition to the above performance observations, the effects of additional strengthening of link beams in 

design should be recognized. For instance, specific link beams may require additional strength above that 

required for seismic demands when wind effects govern the elastic design. AISC 360 prescribes a slightly 

different shear strength, vVn, than AISC 341. This situation occurs in the lower stories of the 16-story 

frames (see Appendix B). Also, link rotation limits as well as section compactness limits played a role in 

member selection. The cumulative effects of these requirements resulted in additional strength in specific 

link beams, which can further reduce the DCRN values obtained from an ASCE 41 assessment. ASCE 41 

requires modification of the modelling parameters and acceptance criteria when link beams do not satisfy 

the AISC 341 criteria—see footnotes for ASCE 41 Table 5-6. More comprehensive guidance for assessment 

of these link beams would allow for a greater range of retrofit options. The linear assessment procedures 

also address neither the shear-moment interaction as the link length varies from long to short nor the axialmoment interaction, both of which could further impact the DCRN. 

3-109
 
 

3.2.3.1.2 Member Cross-section Strength (flexural hinge) and Global Strength (member stability) 

Table 3-22 provides a summary of the performance of the column members for each linear assessment 

procedure and each BPL. The number listed in parentheses denotes the number of failed components in the 

frame—shown as bolded text. Also shown in the table is the percentage of failed components compared to 

the total number of similar components. Recall that section strength and member strength of a column is 

combined into a single P-M interaction equation for linear assessment procedures in ASCE 41 (see ASCE 

41 Equations 5-10, 5-11, and 5-12.) Consequently, identifying an efficient retrofit option for a column can 

be challenging because understanding and isolating the failure mechanism of the column can be difficult. 

Recall from previous discussions that all members other than the link beam in an EBF are force-controlled 

per ASCE 41. In applying ASCE 41 §3.4.2 to compute PUF and MUF, J was taken as the minimum DCR (as 

defined by ASCE 41) from all link beams at or above the column under investigation. 

Table 3-22. Performance Summary of Column Members (CM) per Frame, Linear Procedures 

Archetype Design LS

LSP

 CP LS 

LDP 

CP 

4-Story 

ELF 

RSA 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

8-Story 

ELF 

RSA 

Ext CM Fail (2) 

13% 

Ext CM Fail (6) 

38% 

Ext CM Fail (2) 

13% 

Ext CM Fail (6) 

38% 

All CM Pass 

Ext CM Fail (2) 

13% 

All CM Pass 

Ext CM Fail (2) 

13% 

16-Story 

ELF 

RSA 

All CM Pass 

Ext CM Fail (6) 

19% 

Ext CM Fail (6) 

Ext CM Fail (22) 

69% 

All CM Pass 

All CM Pass 

All CM Pass 

Ext CM Fail (6) 

19% 

Several columns do not satisfy the assessment criteria using the interaction equation because of high axial 

force and moment in the 8-story and 16-story archetype buildings. The first floor columns consistently have 

the most difficulty satisfying the assessment criteria because of high axial load combined with significant 

flexural demand because of the fixity assigned to the column-to-base connection. ASCE 41 does not provide 

guidance on how to assess column-to-base connections similar to beam-to-column connections in a moment 

frame—albeit they are force-controlled. In reality, it is likely that the flexural demand will not be as great 

(as that computed in the analysis) at large deformations because some of the fixity would be relieved 

because of bolt elongation, weld fracture, and/or gusset plate damage. This relief would effectively reduce 

some of the moment demand, reducing the likelihood of a flexural hinge being formed. However, the 

alternative is to model the base connection as pinned, which would not capture the rigidity of the columnto-base connection assumed in design. In this study the base connections are maintained as fixed throughout 

the analysis, thus being conservative on the treatment of the flexural demand. 

As noted previously, the force distribution prescribed in the LSP is one of the main factors in producing 

high column forces. However, the estimated axial load demands in the columns in many cases are the least 

conservative approximations, as compared to more rigorous analysis procedures (see axial load figures 

(e.g., Figure 3-60)). Regardless, there are many columns that pass the assessment criteria. It is unclear 

whether certain upper story columns fail by instability or section hinging due to the adopted interaction 

3-110
 
 

equation. Additionally, it is difficult to assess column failures indicated by interaction results barely over 

1.0 due to the uncertainties in the analysis procedures and conservatisms in the assessment provisions. 

ASCE 41 would benefit from decoupling the single interaction curve for member stability and section 

strength into two separate interaction equations as done in AISC ASD Chapter N, Plastic Design (AISC 

1989). Decoupling the stability and strength would provide a clearer picture of potential retrofit schemes 

for frame columns. Nonetheless, some member stability equations were derived from beam-columns test 

results where column ends did not translate relative to each other. Future research is required to justify 

updated interaction equations for assessment of beam-columns with ASCE 41, as well as a critical 

examination of the acceptance criteria in regard to experimental test results. 

In addition to the above performance observations, the effects of additional strengthening of columns in 

design should be recognized. Several link beams in the 8- and 16-story ELF-designed frames were 

controlled by link rotation requirements prescribed in AISC 341. Because the link rotations are tied to the 

design story drift in ASCE 7 that was in turn driven by a global flexural deformation mode, the lower-level 

frame columns were upsized to limit these rotations and satisfy the requirements. The RSA-designed frames 

were not affected by this as significantly as the ELF-designed frames were, because of differences in the 

lateral load distributions resulting in less global flexural deformations. Regardless, this effort still did not 

result in all base columns passing the acceptance criteria. 

Recall that section strength and member strength of a column is combined into a single P-M interaction 

equation for linear assessment procedures in ASCE 41 (see ASCE 41 Equations 5-10, 5-11, and 5-12.) 

Consequently, identifying an efficient retrofit option for a column can be challenging because 

understanding and isolating the failure mechanism of the column can be difficult. Recall from previous 

discussions that all members other than the link beam in an EBF are force-controlled per ASCE 41. In 

applying ASCE 41 §3.4.2 to compute PUF and MUF, J was taken as the minimum DCR (as defined by ASCE 

41) from all link beams at or above the column under investigation. 

Table 3-23 provides a summary of the performance of the brace members for each linear assessment 

procedure and each BPL. The number listed in parentheses denotes the number of failed components in the 

frame—shown as bolded text. Recall that section strength and member strength of a column is combined 

into a single P-M interaction equation for linear assessment procedures in ASCE 41 (see ASCE 41 

Equations 5-10, 5-11, and 5-12.) Consequently, identifying an efficient retrofit option for a column can be 

challenging because understanding and isolating the failure mechanism of the column can be difficult. 

Recall from previous discussions that all members other than the link beam in an EBF are force-controlled 

per ASCE 41. In applying ASCE 41 §3.4.2 to compute PUF and MUF, J was taken as the minimum DCR (as 

defined by ASCE 41) from the adjacent link in the story under investigation. Brace members consistently 

satisfy the performance criteria for the LS and CP BPL for both linear procedures. 

ASCE 41 §5.5.3.4.2 requires design actions in EBF columns and braces to be computed in accordance with 

ASCE 41 §3.4.2.1.2. This assessment criterion is further expounded in ASCE 41 §5.5.3.4.2, which states 

that the columns and braces should be assessed assuming that every link has fully yielded and strain– 

hardened, resulting in a force of 1.25×VCE. This requirement originated from an earlier edition of the AISC 

seismic provisions (now AISC 341) for design of new buildings. Consequently, the columns and braces in 

the archetype buildings have been capacity-designed. Therefore, these members (by default) should pass 

3-111
 
 

 

the force-controlled assessment criteria in ASCE 41 and thus should yield essentially equivalent results as 

design (and not require an ancillary assessment). However, this does not occur because of variations 

between ASCE 41 and AISC 341 provisions—see §3.2.2.2.1.1. 

Table 3-23. Performance Summary of Brace Members (BM) per Frame, Linear Procedures 

Archetype Design LS

LSP

 CP LS 

LDP 

CP 

4-Story ELF 

RSA 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

8-Story ELF 

RSA 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

16-Story ELF 

RSA 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

All BM Pass 

ASCE 41 does not provide specific guidance on how to perform the analysis prescribed in ASCE 41 

§5.5.3.4.2. It is assumed that this provision is intended to provide guidance on implementing ASCE 41 

§3.4.2.1.2-1. As such, the method outlined in AISC 341 §F3.3 is adopted in this study. Accordingly, it is 

assumed that the flexural forces from seismic drift resulting in fully yielded links can be ignored, per AISC 

341 §F3.3 exception (2). This exception is interpreted to mean that the flexural forces in the columns and 

braces caused by the application of 1.25×VCE at each link can be neglected. As such, the acceptance check 

on the braces and columns is based primarily on the axial load demand. Presumably, a capacity analysis as 

outlined in AISC 341 gives results that match closely with the maximum expected demands, although the 

conservatism of assuming simultaneous yielding of all links may be too stringent. Regardless of the 

approach, it is recommended that additional guidance be provided to ensure proper application of the 

provisions. 

In contrast to using the capacity design approach discussed above, ASCE 41 §3.4.2.1.2-2 permits an 

alternative method to compute force-controlled design actions (i.e., PUF and MUF) by dividing the 

earthquake demand by the force-delivery reduction factor, J. In so doing, J can be taken as the minimum 

DCR of the components (i.e., link beams) delivering force to the columns and braces. It is assumed that this 

method does not remove the capacity design requirement described above. However, ASCE 41 is not clear 

in this regard and needs improvement in the analysis guidance for force-controlled demands. Consequently, 

assessment of the force-controlled components in this study is performed in accordance with this method 

(ASCE 41 §3.4.2.1.2-2) for comparison purposes between the two methods. 

The 8-story ELF-designed EBF presents a good example. Figure 3-110 illustrates the variation in DCRN 

values for the columns and braces using three different approaches. The easiest and most conservative 

approach is to adopt J = 2.0 (assuming high seismicity), with the corresponding DCRN values shown in (a). 

Alternatively, J can be set to the minimum DCR, as discussed previously, in an attempt to compute a more 

realistic demand and embody a capacity-design philosophy. The corresponding DCRN values are shown in 

(b). Finally, in lieu of (a) and (b), a capacity-design approach is used and the corresponding DCRN values 

are shown in (c)—flexural forces form seismic drift is neglected. Furthermore, it is interesting to note that 

(b) and (c) in this case give reasonably similar results for the braces and lower-level columns—PUF is 

slightly greater in (b) than in (c), see Figure 3-54. 

3-112
 
 

 

 

0.28 0.28 1.25 

0.13 

.

6

8 

1

.

5 

5

1 .

7

5 

1

.

0 

7

77 1

7 . 1

5

.6

6 1

0 . 1

5 . 1

.5

8

.3

3 1

16 1

1 . 1

0.95 

0.43 

0.95 

1.59 

0.47 

1.59 

1.70

0.46 

1.70

1.65

0.47 

1.65

1.77

0.44 

1.77

1.55

0.45 

1.55

1.38

0.43 

1.38

1.61

1.61

0.13 

0.12 0.12 

0.29 0.29 

0.54 0.54 

0.68 0.68 

0.97 0.97 

0.95 0.95 

1.41 1.41 

0.11 

0.10 

0.24 

0.44 

0.55 

0.78 

0.77 

1.13 

0.75 

0.43 

0.75 

0.85 

0.47 

0.85 

0.82 

0.46 

0.82 

0.82 

0.47 

0.82 

0.86 

0.44 

0.86 

0.80 

0.45 

0.80 

0.70 

0.43 

0.70 

0.84 

0.84 

0.11 0.05 

0.10 0.42 

0.24 0.47 

0.44 0.77 

0.55 0.54 

0.78 0.73 

0.77 0.70 

1.13 0.93 

0.66 

1.25 

0.66 

0.81 

1.25 

0.81 

0.76 

1.25 

0.76 

0.80 

1.25 

0.80 

0.85 

1.25 

0.85 

0.77 

1.25 

0.77 

0.65 

1.25 

0.65 

0.84 

0.84 

0.05 

0.42 

0.47 

0.77 

0.54 

0.73 

0.70 

0.93 

2.55 

.

. .

. .

. .

. .

. .

. .

. .

. 2 55

2

5 .5

3

4 .8

3 4 .8

4 3 .2

4 3 .2

4

1 .1

4

1 .1

4 9 .1

4 9 .1

3

7 .9

3

7 .9

4 6 .0

4 6 .0

3

9 .8

3

9 .8

2.55 

2.55 2.55 

2.55 2.55 

2.55 2.55 

2.55 2.55 

2.55 2.55 

2.55 2.55 

2.55 2.55 

(a) J = 2 (b) J = min(DCR) (c) capacity analysis (d) J-factor for (b) 

Figure 3-110. DCRN values for EBF columns and braces using LSP, BSE-1, LS BPL 

3.2.3.1.3 Summary 

Table 3-24 summarizes the performance of the archetype buildings in reference to the BSO for both linear 

procedures. The LDP consistently results in lower DCRN values than the LSP for both the ELF- and RSAdesigned frames for all archetype buildings, an indication that a more accurate distribution of seismic 

demands (based on elastic modes) is better captured in taller frames. However, assessment of the RSAdesigned frame consistently illustrates inferior performance using the LSP compared to the LDP because 

of the variation between the distribution of seismic demands and the allocation of component strengths 

within the frame. This variation is not as substantial when assessing the ELF-designed frame with the LDP. 

Moreover, the lateral force distribution in the LSP does not capture higher modes well, leading to 

conservative estimates of column forces in the taller frames. This can be problematic for beam-columns 

due to the lower-bound estimate of compressive strength, PCL. 

Table 3-25 provides the base shears computed with the linear assessment procedures. Column performance 

(primarily at the base) from both assessment procedures controls the overall assessment of the frames. 

However, in this analytical context, base column failure is not detrimental to the overall structural 

performance unless total strength loss of the column or adjacent braces occurs. As noted above, additional 

research is needed on assessment criteria for columns. The qualitative ratings are assigned primarily based 

on the performance of the column members. In the end, the 8- and 16-story ELF-designed frames satisfy 

the seismic performance objective using only the LDP (recall from Chapter 2 that the ELF procedure is not 

3-113
 
 

 

 

 

 

 

 

 

permitted for design of the 16-story EBF), with the 4-story frames satisfying the criteria using both linear 

procedures—a corollary of the two frame designs being nearly the same. 

The assessment results from the LSP and LDP illustrate that, on average, the ELF-designed EBF performs 

better than the RSA-designed EBF for all archetype buildings. This result can be attributed to the increased 

strength and stiffness provided to the ELF-designed frames (see Table 2-5) by differences in the ELF and 

RSA procedures, including associated scaling provisions, in ASCE 7. 

Table 3-24. BSO Performance Summary of Archetype Buildings, Linear Procedures 

Archetype Design Link 

LSP 

CM BM Design Link 

LDP 

CM BM 

4-Story 

8-Story 

16-Story 

ELF

RSA 

ELF 

RSA 

ELF 

RSA 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Fail 

Fail 

Fail 

Fail 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA 

ELF 

RSA 

ELF 

RSA 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Fail 

Pass 

Fail 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

The LDP consistently results in lower DCRN values than the LSP for both the ELF- and RSA-designed 

frames for all archetype buildings, an indication that a more accurate distribution of seismic demands (based 

on elastic modes) is better captured in taller frames. However, assessment of the RSA-designed frame 

consistently illustrates inferior performance using the LSP compared to the LDP because of the variation 

between the distribution of seismic demands and the allocation of component strengths within the frame. 

This variation is not as substantial when assessing the ELF-designed frame with the LDP. Moreover, the 

lateral force distribution in the LSP does not capture higher modes well, leading to conservative estimates 

of column forces in the taller frames. This can be problematic for beam-columns due to the lower-bound 

estimate of compressive strength, PCL. 

Table 3-25. Summary of Base Shears, Linear Procedures (kips) 

ME4 ME8 ME16 

EHL Routine ELF RSA ELF RSA ELF RSA 

LSP 2809 2819 2953 2548 4117 3351 

BSE-1 LDP 2433 2498 2893 2512 4195 3765 

Ratio 0.87 0.89 0.98 0.99 1.02 1.12 

LSP 4213 4229 4430 3821 6176 5027 

BSE-2 LDP 3708 3748 4339 3769 6292 5647 

Ratio 0.88 0.89 0.98 0.99 1.02 1.12 

Analytical results based on component-level performances obtained from the LSP and LDP suggest that 

some long-period eccentrically braced frames designed in accordance with ASCE 7 and its referenced 

standards have difficulty achieving the selected seismic performance objective of an existing building 

intended to be equivalent to a new building. This notion is driven by the performance of the columns. 

Conversely, results from the linear procedures can be enhanced by more mechanistically consistent column 

provisions and analytical modeling parameters. 

3-114
 
Nonlinear Procedures 

The following discusses the analytical results for the noted components from the nonlinear procedures for 

each archetype building. 

As noted previously, the NSP is permitted for the 8- and 16-story frames but requires supplemental 

verification using the LDP. The following summaries for the NSP reflect results only from the NSP (see 

previous for the linear verification using the LDP). For the NDP, results are mainly discussed in reference 

to the mean response from the set of records except where noted otherwise. 

3.2.3.2.1 Link Beams 

Table 3-26 provides a summary of the performance of the shear links for each nonlinear assessment 

procedure and each BPL. The number listed in parentheses denotes the number of failed components in the 

frame—shown as bolded text. Also shown in the table is the percentage of failed components compared to 

the total number of similar components. Contrary to the results from the linear procedures, the link beams 

consistently do not satisfy the performance criteria for the LS and CP BPL for both nonlinear procedures. 

Although the median response is less biased by a collapsed state of a given frame than the mean response, 

the results are, in general, marginally improved for the NDP. Additionally, the NDP consistently indicates 

poorer performance of the link beams than that given by the NSP. 

Table 3-26. Performance Summary of Shear Links (SL) per Frame, Nonlinear Procedures 

Archetype Design NSP NDP 

(based on mean response of record set) 

LS CP LS CP 

4-Story 

ELF 

RSA 

All SL Pass 

All SL Pass 

All SL Pass 

Link Fail (1) 

25% 

All SL Pass 

All SL Pass 

Link Fail (2) 

50% 

Link Fail (3) 

75% 

8-Story 

ELF 

RSA 

All SL Pass 

Link Fail (2) 

25% 

Link Fail (3) 

38% 

Link Fail (4) 

50% 

All SL Pass 

Link Fail (5) 

63% 

Link Fail (5) 

63% 

Link Fail (6) 

75% 

16-Story 

ELF 

RSA 

All SL Pass 

Link Fail (2) 

13% 

Link Fail (3) 

19% 

Link Fail (4) 

25% 

All SL Pass 

Link Fail (3) 

19% 

Link Fail (5) 

31% 

Link Fail (10) 

63% 

The distribution of link beam failures in the NDP illustrates the effect of higher modes on the frames. Some 

of the higher mode periods for these archetype buildings fall directly in the constant acceleration region of 

the spectrum where input energy is the highest—see Appendix A. In fact, the second mode produced the 

highest modal base shear in design of the 8- and 16-story frames. In reference to design, the design force 

distribution in the ELF and RSA procedure is potentially inadequate when frames exhibit increased higher 

mode participation and a high level of nonlinearity. Additional discussion regarding the NSP and NDP is 

provided subsequently in the summary section. 

3-115
 
 

3.2.3.2.2 Member Cross-section Strength (flexural hinge) and Global Strength (member stability) 

Table 3-27 provides a summary of the performance of the column hinges for each nonlinear assessment 

procedure for the CP BPL. The number listed in parentheses denotes the number of failed components in 

the frame—shown as bolded text. Also shown in the table is the percentage of failed components compared 

to the total number of similar components. In general, column hinges satisfy the performance criteria for 

the LS and CP BPL for both procedures. However, base column hinges at the exterior of both 8-story frames 

consistently fail the performance criteria using the NDP. These failures are a corollary of the column-tobase connection assumptions adopted for analysis, the modeling parameters for P-M hinges in ASCE 41 

(see linear discussion), and the slight increase in VCE of the link beams for nonlinear analyses. As discussed 

above in the linear assessment discussion, changes in (i.e., up sizing) column sizes to limit design link 

rotations appear to have contributed to the satisfactory performance of the column hinges (except at the 

base). 

Table 3-27. Performance Summary of Column Hinges (CH) per Frame, Nonlinear Procedures 

Archetype Design NSP NDP 

(based on mean response of record set) 

LS CP LS CP 

4-Story 

ELF

RSA 

--­

---

Ext CH Fail (2) 

13% 

Ext CH Fail (2) 

13% 

--­

---

Ext CH Fail (2) 

13% 

Ext CH Fail (2) 

13% 

8-Story 

ELF

RSA 

--­

---

Ext CH Fail (2) 

6% 

All CH Pass 

--­

---

Ext CH Fail (2) 

6% 

Ext CH Fail (2) 

6% 

ELF --­ All CH Pass --- Ext CH Fail (2) 

3% 

16-Story 

RSA --­ All CH Pass --- Ext CH Fail (22) 

34% 

As detailed in previous discussions, all members other than the link beam in an EBF are force-controlled 

per ASCE 41. Further, the 16-story RSA-designed frame indicates significantly poorer column hinge 

performance partly because four of the ground motion records triggered “collapse”. Still, the axial force 

demand, Pmax, is from an individual record and is, therefore, biased by the behavior of the frame to that 

record. As such, it is difficult to capture record-to-record variability on force- and deformation-controlled 

response directly in the analysis for a set of ground motion records. Recall that the linear procedures also 

identified concerns with these columns. 

Establishing the in-plane column hinge model and performance metrics as a function of the out-of-plane 

flexural buckling strength, when governs PCL, can be problematic for wide-flange columns. More so, when 

the gravity load alone produces an axial force greater than 0.2×PCL. Consequently, modeling the section 

flexural strength of a column hinge using the section axial strength of that section would not result in a 

force-controlled condition. This was the approach taken in FEMA 273, the predecessor of ASCE 41. It is 

theoretically inconsistent to model the component strengths within the same column as a function of both 

Pye and PCL. 

3-116
 
 

 

Table 3-28 summarizes the performance of the column member strength for each nonlinear assessment 

procedure for the CP BPL. ASCE 41 does not provide guidance on checking column member stability when 

using the nonlinear procedures unless the column is designated as force-controlled (as is the case with an 

EBF). Except for the 8- and 16-story frames, which indicate column hinges developing in the base columns 

using the NDP, analytical results of the member strength interaction curves indicate that column members 

satisfy the performance criteria. Nonetheless, the in-plane stability of a column with plastic hinges from inplane flexure is highly complex and is a topic that is not well understood in the literature or implicitly or 

explicitly addressed in ASCE 41 for the nonlinear procedures. Experimental testing on shallow wideflanged steel beam-columns has illustrated that the weak-axis buckling strength of a wide-flange is not 

affected by plastic hinges from in-plane flexure. 

Table 3-28. Performance Summary of Column Members (CM) per Frame, Nonlinear Procedures 

Archetype Design NSP NDP 

(based on mean response of record set) 

LS CP LS CP 

4-Story 

ELF 

RSA 

--­

--­

All CM Pass 

All CM Pass 

--­

--­

All CM Pass 

All CM Pass 

8-Story ELF 

RSA 

--­

--­

All CM Pass 

All CM Pass 

--­

--­

All CM Pass 

All CM Pass 

16-Story 

ELF 

RSA 

--­

--­

All CM Pass 

All CM Pass 

--­

--­

All CM Pass 

All CM Pass 

The EBF force-controlled columns consistently satisfy the performance objective, indicating that the 

capacity design provisions in AISC 341 result in adequate column sizes. These results are somewhat 

contrary to that suggested by the analytical results using the linear procedures. Still, the linear procedures 

have limitations in capturing a realistic force demands in the base columns and braces, thus contributing to 

the cause of this unanticipated discrepancy. 

Table 3-29 provides a summary of the performance of the brace hinges for each nonlinear assessment 

procedure for the CP BPL. The number listed in parentheses denotes the number of failed components in 

the frame—shown as bolded text. Also shown in the table is the percentage of failed components compared 

to the total number of similar components. In general, brace hinges consistently satisfy the performance 

criteria using the NSP. However, braces at the base of the frame consistently fail the performance criteria 

using the NDP. These failures are a corollary of the column-to-base connection assumptions adopted for 

analysis, the modeling parameters for P-M hinges in ASCE 41 (see linear discussion), and the slight increase 

in VCE of the link beams for nonlinear analyses. Similarly, brace hinge performance is strongly biased by a 

collapsed state of a given frame (e.g., 16-story RSA). 

Table 3-30 summarizes the performance of the brace member strength for each nonlinear assessment 

procedure for the CP BPL. ASCE 41 does not provide guidance on checking brace member stability when 

using the nonlinear procedures unless the brace is designated as force-controlled (as is the case with an 

EBF). Analytical results of the member strength interaction curves indicate that brace members satisfy the 

performance criteria. This result is similar to that indicated by the linear procedures. 

The EBF force-controlled braces consistently satisfy the performance objective, indicating that the capacity 

design provisions in AISC 341 result in adequate brace sizes. 

3-117
 
 

 

 

 

 

Table 3-29. Performance Summary of Brace Hinges (BH) per Frame, Nonlinear Procedures 

Archetype Design NSP NDP 

(based on mean response of record set) 

LS CP LS CP 

4-Story 

ELF 

RSA 

--­

--­

All BH Pass 

All BH Pass 

--­

---

Ext CH Fail (2) 

13% 

Ext CH Fail (2) 

13% 

8-Story 

ELF 

RSA 

--­

--­

All BH Pass 

All BH Pass 

--­

---

Ext CH Fail (2) 

6% 

Ext CH Fail (2) 

6% 

ELF --­ All BH Pass --- Ext CH Fail (2) 

3% 

16-Story 

RSA --­ All BH Pass --- Ext BH Fail (24) 

38% 

Table 3-30. Performance Summary of Brace Members (BM) per frame, Nonlinear Procedures 

Archetype Design NSP NDP 

(based on mean response of record set) 

LS CP LS CP 

4-Story 

ELF 

RSA 

--­

--­

All BM Pass 

All BM Pass 

--­

--­

All BM Pass 

All BM Pass 

8-Story ELF 

RSA 

--­

--­

All BM Pass 

All BM Pass 

--­

--­

All BM Pass 

All BM Pass 

16-Story 

ELF 

RSA 

--­

--­

All BM Pass 

All BM Pass 

--­

--­

All BM Pass 

All BM Pass 

3.2.3.2.3 Summary 

Table 3-31 summarizes the performance of the archetype buildings in reference to the BSO for both 

nonlinear procedures. Link beam performance from both assessment procedures controls the overall 

assessment of the frames. Similar to the linear assessments, column-to-base connection assumptions led to 

performance issues for the force-controlled base columns. In the end, none of the designed frames satisfy 

the seismic performance objective using the NSP or NDP (recall from Chapter 2 that the ELF procedure is 

not permitted for design of the 16-story EBF). Diagonal brace members consistently satisfy the performance 

criteria using the NSP, but consistently fail the criteria using the NDP. 

Table 3-31. BSO Performance Summary of Archetype Buildings, Nonlinear Procedures 

Archetype Design 

Link CH 

NSP 

CM BH BM 

Design 

NDP 

(based on mean response of record set) 

Link CH CM BH BM 

4-Story ELF 

RSA

Pass 

Fail 

Fail 

Fail 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass Fail Pass 

Fail Fail Pass Fail Pass 

8-Story ELF 

RSA

Fail 

Fail 

Fail 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass Fail Pass 

Fail Fail Pass Fail Pass 

16-Story 

ELF 

RSA

Fail 

Fail 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass Fail Pass 

Fail Fail Pass Fail Pass 

3-118
 
The assessment results from the NSP and NDP illustrate that, on average, the ELF-designed EBF performs 

better than the RSA-designed EBF for all archetype buildings. This result can be attributed to the increased 

strength and stiffness provided to the ELF-designed frames (see Table 2-5) by differences in the ELF and 

RSA procedures, including associated scaling provisions, in ASCE 7. 

The NSP (without supplemental verification) consistently results in lower DCRN values than the NDP for 

both the ELF- and RSA-designed frames for all archetype buildings, an indication that a more accurate 

distribution of seismic demands is not well captured in taller frames using the NSP (LDP results are 

consistently greater than NSP, albeit a direct comparison is problematic as discussed previously). Nonlinear 

results indicate that the NSP has a tendency to underestimate the demands in the upper stories. This occurs 

primarily because of the differences in the distribution of seismic demands and the lack of modal 

representation other than the fundamental mode in the NSP. This effect was also noticed in NIST GCR 10­

917-9: Applicability of Nonlinear Multi-Degree-of-Freedom Modeling for Design (NIST 2010c). 

The results from the NDP are sensitive to excitation input, analysis parameters, and component modeling. 

In this study, generalized component models were incorporated with degradation effects calibrated to an 

experimental test. Future research should critically examine the applicability of the generalized modeling 

parameters for steel components in ASCE 41. Experimental research has shown that subassembly tests can 

have large scatter in acceptable performance given the stochastic variations in the type of loading, that being 

cyclical, near-fault, random, etc. Future research should investigate the influence of the loading protocol 

adopted to establish the deterministic acceptance criteria for short link beams. 

Analytical results based on component-level performances obtained from the NSP and NDP suggest that 

long-period eccentrically braced frames designed in accordance with ASCE 7 and its referenced standards 

have difficulty achieving the selected seismic performance objective of an existing building intended to be 

equivalent to a new building. This notion is driven by the performance of the link beams and, to a lesser 

extent, the columns and braces. The results for the columns can be enhanced by more mechanistically 

consistent column provisions and analytical modeling parameters. The results for the link beams provide a 

contrary inference to that provided for the linear procedures. Although link beam performance is based on 

high fidelity analytical modeling parameters, enhanced modeling practices could be investigated. 

Comparison between Linear and Nonlinear Assessment Results 

Table 3-32 summarizes the performance of the archetype buildings for each analysis procedure. The results 

indicate that the linear procedures do not consistently provide DCRN values greater than that given by the 

nonlinear procedures. As discussed previously, direct comparison of results between linear and nonlinear 

procedures can be problematic, except for direct comparison of the distribution of results. Some consistency 

is evident in the global performance rating of the 8-story EBF as well as frames designed per the MRSA 

procedure among the various assessment procedures. However, not all component performance failures 

align between the procedures, as discussed previously (e.g., link beams). The conservatism of the linear 

procedures is also apparent, as expected. 

The nonlinear procedures provide a more rigorous assessment approach as compared to the linear 

procedures. However, the results from the nonlinear procedures indicate more performance failures in the 

3-119
 
 

 

link beams than identified using the linear procedures, which is contrary to the assumption that the linear 

procedures are more conservative. Several factors contribute to this outcome, but it is difficult to narrow 

down any single primary contributor. Certainly for the NDP, the effects of ground motion selection and 

scaling can be significant, including the number of records adopted to achieve a reasonable level of 

statistical confidence and the method by which the records were chosen with a bias to achieve an unfairly 

beneficial binary outcome. Moreover, some of the higher mode periods fall directly in localized high energy 

regions of the response spectrum resulting in increased axial demands that cannot be captured efficiently in 

a linear analysis using a smooth generalized spectrum. Furthermore for the NSP, the force distribution is 

potentially inadequate for frames that exhibit increased higher mode participation, either elastically or 

triggered by nonlinearity. 

Table 3-32. BSO Performance Summary of Archetype Buildings 

NDP 

Archetype Design LSP LDP NSP (based on mean 

response of 

record set) 

4-Story 

ELF

RSA 

Pass 

Pass 

Pass 

Pass 

Fail 

Fail 

Fail 

Fail 

8-Story ELF 

RSA 

Fail 

Fail 

Pass 

Fail 

Fail 

Fail 

Fail 

Fail 

16-Story 

ELF 

RSA 

Fail 

Fail 

Pass 

Fail 

Fail 

Fail 

Fail 

Fail 

In contrast to the nonlinear procedures, the linear analysis model and assessment is implied to be less 

rigorous and more conservative. As already discussed, the linear procedures yielded less conservative 

results for the deformation-controlled link beams. In contrast, the force-controlled members (i.e., columns 

and braces) were seemingly overconservative when using the simplified “J-factor” approach. The linear 

procedures can also illustrate the trend in demands but may fail to highlight critical performance zones 

within a given frame. A case in point is the acceptable DCRN values of the link beams while the nonlinear 

procedures illustrate that the link beams fail the acceptance criteria. 

The failure of the EBF using the NDP exposes the need for more sophisticated assessment guidance. A 

building with seemingly reasonable strength distribution and ductility is seen to be prone to high 

concentration of demands in lower-to-middle stories, which went undetected during the (linear) design 

process and the ensuing linear assessment. High demands resulted in several link beams losing their load 

carrying ability and the analysis ultimately terminating prior to record completion because of set limits to 

represent a collapsed state of the frame. Problems with an EBF have been documented in a few other studies, 

although many questions still remain (Koboevic et al., 2012). At the component level, link beams in an 

EBF are well understood and have been thoroughly tested. However, at the system level, analysis and 

experience (e.g., Christchurch, NZ 2010 earthquake) have shown that an EBF may behave in a manner that 

is undesirable, or at least as not predicted. 

3-120
 
Chapter 4 Summary, Conclusions, and 

Recommendations 

This report presents the results of a study investigating the correlation between the seismic performance of 

an ASCE 7 code-compliant building and its performance as quantified using ASCE 41 analysis procedures 

and structural performance metrics. This investigation is performed by evaluating a suite of structural steel 

buildings in a high seismicity region that are designed using ASCE 7 and evaluated using ASCE 41. The 

basic question is whether the standards for designing new steel buildings and assessing existing steel 

buildings provide consistent levels of performance. An additional outcome of this research is to advance 

the state-of-knowledge in PBSD and assessment of buildings using ASCE 41. Further, results provide the 

technical background for provisions that target equivalent seismic performance between a new building and 

an existing building that is required to meet the seismic performance objective of a new building. 

This chapter highlights significant observations and conclusions from the seismic assessment of the 

archetype buildings using four assessment procedures in ASCE 41. General findings and recommendations 

are based on the collective results for the seismic force-resisting system. More in-depth findings specific to 

the system are in the relevant subsections in this chapter, as well as in relevant sections of the assessment 

discussion in Chapter 3. Although the primary emphasis of this study is on benchmarking ASCE 41 

assessment procedures, questions arise that may be more applicable to the design criteria used rather than 

to the assessment results—these items are identified in the section about future research. 

4.1 Summary of Project Work 

This report presents the results of a structural seismic performance assessment using ASCE 41 procedures 

and performance measures of buildings utilizing steel eccentrically braced frames (EBF) as the lateral forceresisting system (LFRS). 

A suite of archetype buildings that incorporate EBFs along one principal direction of the buildings is 

designed in accordance with ASCE 7. The suite consists of 4-, 8-, and 16-story buildings designed using 

both the Equivalent Lateral Force (ELF) Procedure and Modal Response Spectrum Analysis (RSA). Both 

analysis procedures are used to provide a generally applicable range of LFRS strength within the selected 

seismic intensity region. As such, an LFRS may include significant overstrength to resist nonseismic loads 

or to satisfy other design criteria. A design space is created to investigate the effects of design methodology, 

building height and other LFRS-specific geometric modifications on seismic performance. In reality, the 

design space is infinitely large and many design choices made in this study can also have different 

configurations to evaluate the variation in performance specific to a design choice. 

The seismic performance assessment of the building suite is conducted using both linear and nonlinear 

analysis procedures prescribed in ASCE 41: 

4-1
 
 Linear Static Procedure (LSP) 

 Linear Dynamic Procedure (Response Spectrum) (LDP) 

 Nonlinear Static Procedure (NSP) 

 Nonlinear Dynamic Procedure (NDP)
 

For this study, the performance assessment targets the Basic Safety Objective (BSO) prescribed in ASCE 

41. This objective includes the interrelated goals of Life Safety (LS) Building Performance Level (BPL) at 

the Basic Safety Earthquake-1 (BSE-1) earthquake hazard level (EHL) and Collapse Prevention (CP) BPL 

at the BSE-2 EHL. This performance objective is chosen to align with the intended structural performance 

objective of an ordinary building in ASCE 7, which is qualitatively defined here as “life safety” provided 

by collapse prevention of the building, given a maximum considered earthquake (MCE) event. 

To evaluate seismic assessment criteria, each component of the EBFs is designated as a primary member 

(or component) in accordance with ASCE 41 §2.2.5 (and ASCE 41 §2.4.4.2). Similarly, quantitative 

performance measures (i.e., acceptance criteria) for primary components are used for all assessment 

procedures, although performance measures for secondary components are permitted by ASCE 41 for some 

primary components. The consistent use of primary acceptance criteria keeps all components and associated 

assessment results correlated among the assessment procedures for this study. 

The goals of this research are as follows: 

 Assess new structural steel buildings utilizing EBFs designed per ASCE 7 requirements and, in 

turn, evaluated using ASCE 41, 

 Develop a qualitative link between the performance implied in ASCE 7 in light of the performance 

identified by ASCE 41 procedures and performance measures, 

 Provide guidance or technical support for improved or new provisions in ASCE 41 (and to a lesser 

extent, ASCE 7), 

 Reduce uncertainty in first-generation PBSD procedures for performance-based seismic 

assessment, and 

 Identify any inconsistencies, ambiguities, and confusing provisions in ASCE 41. 

In reference to developing a link between ASCE 7 and ASCE 41, the primary difficulty in equating the two 

standards is rooted in their disjointed performance objectives. That is, acceptance criteria for a component 

in ASCE 41 are not directly calibrated to the seismic performance objective of ASCE 7, which is a 10 

percent probability of partial or total collapse given an MCE event—that is MCER (or one percent 

probability of partial or total collapse in 50 years). Equating the two objectives of the standards would imply 

that only one structural performance level with an associated earthquake hazard level can be coupled: that 

being, CP at the MCER. However, this would be difficult based on a member-level binary performance 

solution. Consequently, the question becomes what percentage of components needs to fail the associated 

CP SPL to achieve a 10 percent probability of total or partial collapse given an MCER event? Future research 

should assess the archetype buildings in FEMA P695 analysis to ascertain the collapse probability in 

relation to the ASCE 7 performance objective. Results from that study can be used to probabilistically relate 

the R-factor in ASCE 7 to the m-factors and inelastic deformations using story drift. Clearly, the study 

presented in this report presumes that the R-factor used for design has been derived to provide the intended 

4-2
 
 

collapse performance objective. As such, the analysis results do not necessarily reflect satisfactory or 

unsatisfactory performance in relation to the seismic performance objective of ASCE 7. 

A consequence of a deterministic-type component evaluation (i.e., pass or fail) is that analytical results, 

depending on the accuracy of the model and analysis algorithms, can be independent of the behavior of the 

system. Individual member performance and the potential need to retrofit or replace it are therefore based 

on an analysis output rather than the influence of the component performance on the system performance. 

This is a challenging issue to overcome, and only recently has there been some progress made (e.g., FEMA 

P695 and FEMA P-58 (FEMA 2012)) toward having the ability to probabilistically correlate member 

performance to system performance. However, these efforts are not without their limitations and debatable 

performance metrics. It is still yet to be determined whether practitioners will accept these developing 

methods because of the time and resources needed to successfully apply their recommendations. However, 

ASCE 41 is available and being used for performance-based seismic engineering of building systems and 

components. In many cases, the acceptance criteria in ASCE 41 are being used to justify computed seismic 

performance to buildings officials as being satisfactory. The question is what seismic performance is being 

justified: the objective defined in ASCE 41 or that intended in ASCE 7? If satisfying ASCE 7, then this 

would infer that the CP SPL associated with the MCER (taken as the BSE-2) defined in ASCE 41 matches 

the intended collapse performance of ASCE 7. A significant effort is still needed to bring ASCE 41 to the 

state-of-the-art and equivalent to ASCE 7. In this regard, assessment provisions are meaningless without 

the technical support provided by experimental research and subsequent case studies that evaluate how the 

research findings affect component and system performance. 

4.2 Assumptions and Limitations of this Study 

The following discussion summarizes notable assumptions employed in this study and other limitations of 

the work that could impact the results, which form the basis for the conclusions and observations. 

Building System and Component Characteristics for Design and Assessment 

	 The archetype buildings are representative of a specific type of building, which uses a seismically 

designed system to resist lateral loads and deformations. The selected system in this study 

represents one design option out of the many available for steel framed buildings. In designing the 

SFRS, there are many specific design assumptions made that play an important role in resisting 

lateral loads and deformations. Different selections for frame configuration, plan layout, bay 

spacing, height, connection details, and magnitude of non-seismic loads all could affect the 

assessment results. 

	 The buildings are regular in layout and configuration as defined in both ASCE 7 and ASCE 41. 

Irregular building configurations can affect seismic performance and are not addressed in this 

study, as they could complicate the comparisons that are being made. 

	 The archetype buildings are simple in concept and do not contain stairwells, elevator cores, 

architectural setbacks, atriums or other features found in typical buildings. The goal here is to study 

the basic performance of the SFRS in resisting lateral loads and deformations without the 

complexity posed by other attributes found in buildings today. 

4-3
 
	 Strength and stiffness of specific secondary components, as defined in ASCE 41, were not fully 

represented in the mathematical model for linear and nonlinear analyses (e.g., shear tab connection 

for gravity framing, façade, stairs, etc.). This assumption, while reasonable from an analysis 

standpoint, highlights a difference in requirements between ASCE 7 provisions for design and 

ASCE 41 provisions for assessment (ASCE 7 §12.7 and ASCE 41 §3.2.2). 

	 Composite action developed between primary and secondary structural components and the portion 

of slab they support was not included in the mathematical model for seismic design or assessment. 

This approach is consistent with that used by many practitioners and provides presumably 

conservative results because floor slabs are not active in providing composite action and added 

moment capacity. Composite action was included for the moment frame beams for verifying elastic 

story drifts under service-level wind loading. 

	 The column-to-base connections of the SFRS and the seismic base of the buildings were assumed 

to be horizontally, vertically, and rotationally restrained, resulting in a “fixed” connection to the 

ground. The base of non-SFRS columns were rotationally unrestrained. Soil-structure interaction 

effects, modeling the flexibility of the soil and / or the foundation components, and modelling 

partially-restrained column-to-base connections were not included in this study. Inclusion of these 

effects would likely affect the assessment results. However, inclusion of the effects of the soilfoundation flexibility into the analysis is complex and not well established at the present time. 

Moreover, current design practice commonly does not include soil-foundation effects; column-tobase connections to the building foundations are often idealized models, as is done in this study. 

	 No formal investigation was included in this study to evaluate the accuracy of the quantitative 

modeling parameters for nonlinear analysis or acceptance criteria for linear and nonlinear analysis 

provided in ASCE 41 for primary or secondary component models. There is a project currently 

ongoing with ATC (ATC-114: Development of Accurate Models and Efficient Simulation 

Capabilities for Collapse Analysis to Support Implementation of Performance Based Seismic 

Engineering) that will examine the component modelling parameters and acceptance criteria for 

specific components. 

Structural Analysis 

	 No formal investigation was included in this study to evaluate the accuracy of the analysis 

algorithms in the software packages used for structural analysis. These software packages are the 

same as those used by practitioners. The stability of solution algorithms when the stiffness and 

strength of the component models have significantly degraded can vary between software packages. 

Therefore, any software accuracy limitations encountered in this study are consistent with those 

present in design offices. 

	 The methodology used in this study for ground motion selection and scaling resulted in a set of 

earthquake records that may not be applicable or suitable for a specific site. A different record set— 

selected by engineering judgment, selected by revising the parameters of the methodology, or 

developed from an alternative methodology—could affect the assessment results. However, the 

process employed here is consistent with that used in practice, representing a typical building site 

in an area with a high level of seismicity. 

4-4
 
 

 

No formal investigation was included in this study to evaluate all potential sources of uncertainty or error, 

or whether multiple sources of error are correlated. The question of uncertainties in the analytical models, 

solution algorithms, material properties and even potential as-built final dimensions and positions of 

members are all beyond the scope of this study. The load and resistance factor design (LRFD) philosophy 

in use for structural design today are based on pioneering work on uncertainties in material and load 

characterizations performed starting in the 1950’s. Whether a new similar large national effort to that 

conducted for LRFD is required today is not clear. Quantifying the effect of any source of uncertainty or 

error, as it relates to the design or assessment of buildings to resist earthquake motions, is a significant issue 

and would require its own research program to study all of the aspects. 

4.3 Conclusions and Observations 

This section highlights significant observations and conclusions from the seismic assessment of the 

archetype buildings. Topics are categorized as general or system specific. Additionally, more in-depth 

discussions of the observations and conclusions specific to the SFRS are in the relevant subsections in this 

chapter as well as in relevant summary sections of the assessment discussion. 

 ASCE 41 

The following observations and conclusions can be drawn from this study. Topics are grouped by either 

general applicability to ASCE 41 assessment procedures or specific to the structural system. 

General 

The following general topics focus on observations identified by the assessment provisions for the selected 

assessment methods: 

	 The LSP generally results in more conservative normalized demand to capacity ratios, DCRN, 

values than that of the LDP, because of the differences in the distribution of seismic demands and 

the lack of modal representation other than the fundamental mode in the LSP. 

	 The NSP generally results in less conservative DCRN values than that of the NDP, contrary to what 

would be expected with increasing the analytical complexity, because of the differences in the 

distribution of seismic demands and the lack of modal representation other than the fundamental 

mode in the NSP. 

	 The nonlinear procedures provide a more rigorous assessment approach as compared to the linear 

procedures. The results from the LSP, and to a lesser extent the LDP, indicate more performance 

failures in force-controlled components than identified using the nonlinear procedures. The results 

presented emphasize the inherent conservatism in the linear procedures. However, this 

conservatism is accompanied by a reduction in required analytical resources and proficiency of the 

analyst. 

 The linear procedures can illustrate the trend in demands but may fail to highlight critical 

performance zones within a given frame. 

 No clear consistency exists between linear assessment results and nonlinear assessment results for 

link beams. Contrary performance results indicate acceptance criteria that need further calibration. 

4-5
 
 

Eccentrically Braced Frame 

The following significant observations and conclusions are based on the collective results obtained from 

the assessment of the EBFs. More details about the specific items are in the relevant sections of the 

assessment discussion in Chapter 3. 

	 Analytical results based on component-level performances indicate that new long-period EBFs 

designed in accordance with ASCE 7, and its referenced standards, have difficulty achieving the 

ASCE 41 BSO for an existing building intended to be equivalent to a new building. This 

observation is driven by the performance of the link beams and, to a lesser extent, the columns and 

braces. Assessment results for the link beams from the nonlinear procedures provide a conclusion 

opposite to that provided for the linear procedures in that nonlinear assessment reveals higher DCRN 

values than the linear assessment. 

	 Assuming the archetype buildings meet the collapse performance objective of ASCE 7, the results 

of the assessment procedures indicate that ASCE 41 is generally conservative for EBFs. ASCE 41 

analysis would require retrofit or replacement of specific components of a code-compliant SFRS 

to satisfy the CP BPL, given an MCE event. The results highlight that columns (i.e., beam-columns) 

with high axial and flexural demands and link beams have difficulty in satisfying the performance 

criteria in ASCE 41. Future research is needed to couple the collapse performance objectives of the 

two standards, as well as other performance objectives associated with a seismic hazard with a 

lower return period. 

	 Analysis results indicate that the linear procedures generally give smaller DCRN values than that 

obtained from nonlinear procedures, contrary to what would be expected with increasing the 

analytical complexity. Given a properly designed new link beam, the linear procedures will result 

in a maximum DCRN value for a primary component of 0.72 for the BSE-1 EHL (0.76 for the BSE2 EHL). 

	 A significant number of link beams did not satisfy the acceptance criteria for the nonlinear 

procedures. This result was particularly problematic for EBFs as they quickly progressed towards 

a collapse state after the ultimate link capacity in the second story was reached. Though link beam 

performance is based on high fidelity analytical modeling parameters, enhanced modeling practices 

should be investigated. 

	 A significant number of columns, primarily at the base of the frame, did not satisfy the ASCE 41 

acceptance criteria (force-controlled). The results for columns can be enhanced by more 

mechanistically consistent assessment provisions and analytical modeling parameters for columns 

(e.g., column/brace-to-base connection modeling). 

	 Components of the EBFs that do not satisfy the CP acceptance criteria would need to be 

strengthened to achieve the performance required by ASCE 41. However, the results from the 

various assessment procedures were seen to be inconsistent in some cases for a given design routine 

(i.e., LSP vs. NDP) or the same assessment procedure was inconsistent between design routines 

(i.e., ELF and RSA). This makes it difficult to definitively suggest that using ASCE 41 to design a 

new EBF would produce a system capable of achieving the seismic performance objective of ASCE 

7. Future research is needed to evaluate the collapse probability of a new system strengthened by 

ASCE 41 relative to the seismic performance objective of ASCE 7. The same is required for a new 

system that has component strengths reduced from that required by ASCE 7 to meet an ASCE 41 

4-6
 
performance objective. Further, the adequacy of the components of the enhanced frame (those 

required to satisfy ASCE 41) would be dependent upon which analysis procedure is used to iterate 

between design and assessment, and therefore the fidelity of the analytical model and analysis 

parameters. 

	 Results from this study indicate that for ASCE 41 to be used as a seismic design procedure for new 

steel buildings, as a performance-based alternative to ASCE 7 (see ASCE 7 §1.3.1.3), acceptance 

criteria for the various analysis methods must be calibrated to each other to consistently result in a 

uniform collapse risk. Additionally, ASCE 41 would need to reference material-specific design 

standards (e.g., AISC 341) for their seismic design requirements, as well as consistent requirements 

for defining acceptance criteria for a component (e.g., plastic rotation). 

4.4 Recommendations for Future Research 

The following sections identify items for future research. The recommendations are grouped by the 

applicable standard: ASCE 41, ASCE 7, and AISC 341 / 360 / 358.

 ASCE 41 

General 

The following items are general considerations for future studies to enhance ASCE 41 assessment 

provisions: 

	 The archetype buildings should be analyzed using the methodology formulated in FEMA P695. 

This will provide the requisite data to identify the collapse probability of the systems (or frames) 

in relation to the intended collapse objective of ASCE 7. However, the same seismic performance 

factors as used in design should be used in the analysis. Results from this study can be used to 

probabilistically relate the R-factor in ASCE 7 to m-factors and inelastic deformations using story 

drift. 

	 Research should investigate the implementation of risk-targeted collapse assessment criteria into 

ASCE 41 similar to the design philosophy introduced in ASCE 7-10. As such, comparison of 

system fragility curves should be done to correlate the risk-target of ASCE 7 and the risk-target of 

an existing building intended to be equivalent to a new building. 

 Research should evaluate the influence of gravity framing (e.g., partially restrained shear tab 

connections) on assessment results of the primary components of the SFRS. 

 Research should investigate alternative lateral force distributions for taller systems for the NSP, 

including comparison between adaptive and non-adaptive loading. 

	 Research should be conducted to determine the number of components that do not need to satisfy 

the ASCE 41 component acceptance criteria while still permit the building to be classified as 

meeting a performance objective. 

	 Research should evaluate the systems used in this study by measuring demands against acceptance 

criteria for secondary components to quantify variations in performance results; for example, the 

link beams in the ME8 buildings. Even if secondary component criteria were implemented, the 

DCRN values still indicate unsatisfactory performance in the several floors. The primary acceptance 

4-7
 
 

criteria for the nonlinear procedures has been removed in ASCE 41-13. Based on some trends seen 

in this study, this should be done only if the acceptance criteria for linear and nonlinear procedures 

have been correlated and calibrated. 

	 Enhanced commentary is needed in ASCE 41, similar to the effort used to develop FEMA 274. 

Commentary can be used to explain differences in component strengths between ASCE 41 and 

ASCE 7 and its reference standards (e.g., AISC 341 and AISC 360). This effort would include 

cleaning up incorrect references (e.g., AISC 341 or AISC 360, FEMA 355F or FEMA 355D). 

Similarly, the commentary can detail the experimental tests used to derive the acceptance criteria. 

	 Consideration should be given to reorganize Chapter 5 (Chapter 9 in ASCE 41-13) to remove 

system-to-system references, most notably when they are not applicable. For example, a forcecontrolled column in an EBF cannot reference provisions for a column in a moment frame. This 

chapter would benefit with an outline similar to AISC 341, where the section on member strength 

is outlined similar to AISC 360. Therefore, the individual systems would reference a member 

strength in lieu of another system that may or may not be applicable. 

Eccentrically Braced Frames 

The following items are considerations for future studies to enhance ASCE 41 assessment provisions for 

eccentrically braced frames: 

	 Research should critically examine the applicability of the generalized modeling parameters for 

shear hinges used in link beams for use in the nonlinear procedures. 

	 Research should investigate the correlation between acceptance criteria for the linear and nonlinear 

procedures. This effort can include the influence of shear-moment interaction and axial-moment 

interaction on the acceptance criteria. 

 Research should investigate the influence of the loading protocol adopted to establish the 

deterministic acceptance criteria for shear hinges in link beams. 

 Research is needed to develop acceptance criteria and modeling parameters for column / brace-tobase connections, including embedded connections. 

	 Research should investigate the use of acceptance criteria and modeling parameters for brace 

connections. Similarly, guidance is needed concerning adjusting acceptance criteria and modeling 

parameters to simulate the change in response of a component due to damage of a brace connection. 

	 Removing the force-controlled requirement for all members except the link (or conversely apply 

this philosophy to a CBF) should be considered. If so, research is required to justify updated 

interaction equations for assessment of beam-columns using ASCE 41, as well as a critical 

examination of the acceptance criteria in regard to experimental test results. Decoupling interaction 

equations into specific failure mechanisms and referencing highly vetted design standards should 

be considered. Removing PCL as the basis for force-controlled response and acceptance criteria for 

a column hinges (i.e., revert back to FEMA 273) and using PCE when Fye is used to assess a flexure 

hinge in the same column should also be considered. 

 ASCE 7 

The following items are considerations for future studies to enhance ASCE 7 provisions: 

4-8
 
	 The assessment results illustrate that on average the ELF-designed frames perform better than the 

RSA-designed frames for all archetype buildings. However, the ELF procedure is not permitted in 

some cases. Research should investigate the applicability of the analysis limitations in terms of the 

intended collapse objective of ASCE 7. 

	 Research should investigate the lateral design force distributions in ASCE 7 and modal scaling 

provisions, and their influence on the allocation of component strengths within a frame. Research 

has indicated that higher modal base shear scaling may be warranted (NIST 2010b and NIST 2012). 

Potential modifications to the MRSA procedure could also include scaling provisions to 

additionally account for higher mode effects resulting from nonlinear response. Provisions can be 

directly transferred to the linear procedures in ASCE 41. 

	 Research efforts should evaluate incorporating other performance levels for design into ASCE 7 

(NIST 2012). 

AISC 341 / 360 / 358 

Eccentrically Braced Frames 

The following items are considerations for future studies to enhance AISC 341 provisions of eccentrically 

braced frames: 

	 Research should investigate the Response Modification Factor, R, assigned to an EBF. Results from 

the assessment suggest that an assigned value of 8 (equal to that for an SMF) may be high. A side 

study examined an EBF designed with R = 6. Preliminary results indicate similar performance to 

the results presented here. Adjustments to R would require extensive nonlinear analysis that could 

impact the assessment provisions of ASCE 41. This system has not been evaluated in a FEMA 

P695-type analysis. 

	 Research should investigate the Displacement Amplification Factor, Cd, assigned to an EBF, and 

its influence on separation of flexural and shear deformation modes of a story to determine a 

representative plastic link rotation. Adjustments to Cd would require extensive nonlinear analysis 

that could impact the assessment provisions of ASCE 41. 

	 Research should investigate the approximate period formulation, CuTa, assigned to an EBF. 

Adjustments to CuTa would require extensive nonlinear analysis that could impact the assessment 

provisions of ASCE 41. 

	 Research should investigate the applicability of the maximum shear strength of a link beam and 

correlation with the loading sequence on the plastic link rotation. 

	 The provisions should revisit the methodology on determining the plastic link rotation angle when 

using an elastic analysis. As other researchers have shown, basing the link rotation limits off of 

total story drift can be excessively conservative for taller frames. Similarly, the allowable link 

rotation angle in AISC 341 is not a function of the Risk Category, Ie, assigned to the building. As 

such, frame in buildings assigned to higher risk categories than Class II—Ordinary, see ASCE 7— 

will always satisfy AISC 341 due to stricter story drift requirements in ASCE 7. 

	 Analysis results are dependent on link beam calibration with experimental test results that dictated 

a higher overstrength than 1.25×Vp as used in design. As such, the axial force demand in the 

columns from the capacity analysis is consistently lower than the results from the NDP. This trend 

4-9
 
is also true for the braces. Still, the columns and braces consistently satisfied the stability criteria 

using the NDP; this may be partly due to the columns having been upsized to limit plastic link 

rotations in the ELF-design frames. Research should data mine existing research to explore the 

possibility of using a larger overstrength on short link beams. Further, ASCE 41 can provide more 

guidance on analytical modeling techniques for this capacity analysis. 

	 Research should unify the nominal shear strength equations in AISC 341 and AISC 360 for compact 

wide-flange sections. 

4-10
 
Appendix A Ground Motions for Response History 

Analysis 

A.1 Ground Motion Record Set 

The far-field record set (22 records, each with two horizontal components) from FEMA P695 (FEMA 

2009a) is selected as the input motion database for the NDP; 14 of the 44 horizontal component records are 

selected as the ground motion set for each archetype building, with no two records coming from the same 

station. The records are normalized for magnitude, distance, and source conditions as discussed in FEMA 

P695. 

The scaled record set (see Ground Motion Selection and Scaling section below) for each archetype building 

is taken directly as the Basic Safety Earthquake-2 (BSE-2) earthquake hazard level (EHL). Although this 

EHL is not strictly the same as having a two percent probability of exceedance in 50 years, it is comparable, 

and anticipated future changes in ASCE 41-13 will likely match the seismic hazard defined in ASCE 7-10 

(see Chapter 3). The scaled record set is factored by two-thirds to represent the BSE-1 EHL in lieu of 

explicitly determining the ground motion parameters with a ten percent probability of exceedance in 50 

years. No spectral shape modifier, , is used to adjust the seismic demands for either BSEs (FEMA 2009a; 

Haselton et al. 2009), this is a topic of needed research. 

As a side note, the goal initially was to analyze the archetype buildings using seven scaled pairs of ground 

motion records along each principal axis of the structure (14 records in each direction). However, because 

of complications in scaling orthogonal pairs for the maximum direction of response when a structure has 

significantly different periods along the principal axes, it was decided to analyze 14 unique records 

independently along each principal axis—see above. This is permitted by ASCE 41 since requirements for 

considering multidirectional seismic effects are not triggered in this study—see ASCE 41 §3.2.7. Further, 

there is no guidance regarding the application of scaled ground motion pairs for the maximum direction of 

response when a structure has significantly different periods along the principal axes. Future research is 

needed to provide provisions on scaling and application of ground motion pairs. 

A.2 Ground Motion Selection and Scaling 

The ground motion selection and scaling procedure for each archetype building is described below. This 

procedure was developed in consultation with select members of the peer review team. Each set of records 

(14 total) is used for both the equivalent lateral force (ELF) and response spectrum analysis (RSA) designs 

to gauge performance between the two. The process is as follows: 

1.	 Determine the fundamental lateral mode period, T1, of the building in the direction being 

considered not including gravity load effects (i.e., first-order period) for both the ELF and RSA 

A-1 
 

 

designs. Second-order periods may also be computed with expected point-in-time gravity loads 

rather than factored loads. Determine the average (arithmetic mean) of the periods for the ELF and 

RSA designs, T1,avg. This will keep the scaling of the two designs consistent. 

2.	 For each of the 44 far-field component records (not the records computed from the square root of 

the sum of the squares (SRSS) of the two horizontal components of an event), compute the error 

between Sa from the recorded spectrum and Sa from the maximum considered earthquake (MCER) 

design spectrum at each period between 0.2×T1,avg and 1.5×T1,avg. The period step used here is 0.01 

second. The error at each period ranges from 0 to 1, with 0 being an identical match. 

3.	 Sum the error values over the periods between 0.2×T1,avg and 1.5×T1,avg to get a single composite 

error value for each record. 

4.	 Scale each record to minimize the total error from step 3. 

5.	 Select the 14 records with least total error. If both horizontal components of a specific station are 

in the set, then remove the record with the larger error of the pair and select the next unique record 

from the remaining record set. This step is repeated as needed until all records selected are from 

different stations. 

6.	 Compute the average spectrum from the record set (14 total) from step 5. 

7.	 Scale the average spectrum from step 6 so that no value between 0.2×T1,avg and 1.5×T1,avg is less 

than the MCER spectrum. The 1.3 factor in ASCE 41 §1.6.2 is not included here, so as to address 

the change of spectrum parameters from geomean to maximum direction response in ASCE 7 (this 

factor will be removed in ASCE 41-13). 

8.	 Scale the record set from step 5 by the value computed in step 7. Therefore, there are two scaling 

factors: step 4 and step 7. 

9.	 Apply the total scaling factor (step 4 times step 7) to each component record in the set from step 5 

and perform analysis. 

For comparison purposes, the process in ASCE 41 §1.6.2.2 is summarized as follows: 

1.	 Select a minimum of three recorded events (each event is a data set), each with two horizontal 

components. 

2.	 Take the SRSS of the two horizontal components of each selected data set from step 1. 

3.	 Select a scaling factor for each SRSS from step 2. Note that application of a scaling factor to the 

unscaled SRSS is equivalent to taking the SRSS of the similarly scaled components. 

4.	 Compute the average of the scaled SRSS spectra from step 3 for all selected events. 

5.	 Scale the average spectrum from step 4 so that no value between 0.2×T1,avg and 1.5×T1,avg is less 

than 1.3 times the design spectrum. 

6.	 Apply the total scaling factor (step 3 times step 5) to each component record in an event and perform 

analysis. 

The selection and scaling procedure in this study differs slightly from that found in ASCE 41. Because this 

study investigates a generalized SDC Dmax analysis without a specific location, it is difficult to select a site 

and apply common selection and scaling processes typically performed by a geotechnical engineer. In lieu 

of taking the SRSS of the two horizontal components of an event and having 22 SRSS spectra and in turn 

computing the error of the SRSS records and associated scaling factor for the event, the error and scaling 

factor were computed for each component (44 spectra). 14 unique records were selected per principal 

A-2 
 

 

 

 

 

 

 

 

direction and the average of this set scaled to meet the target spectrum. In summary, steps 1 to 5 in the 

process identify the “best fit” to the ASCE 41 code spectrum (which matches ASCE 7). The average of this 

set is computed and scaled similarly to that in ASCE 41—without the 1.3 factor. 

Other ground motion selection and scaling methods are discussed in NIST GCR 11-917-15: Selecting and 

Scaling Earthquake Ground Motions for Performing Response-History Analyses (NIST 2011d). 

A.3 Four-Story Archetype Building 

4-Story Eccentrically Braced Frame 

Table A-1 summarizes the 14 strong motion records used for the nonlinear dynamic procedure (NDP) for 

the N-S direction of ME4 eccentrically braced frame (EBF). Figure A-1 illustrates the set of acceleration 

response spectra, original and scaled, and the scaled average spectrum. Figure A-2 illustrates the 

acceleration response spectra, original and scaled, for each select record. For comparison, the ASCE 41 

code spectrum is shown in the figures. All analyses completed for the BSE-1 and BSE-2 for the ELF and 

RSA design. 

Table A-1. Ground Motion Records for N-S Direction of ME4 

ID EQ No. Event Name Station Comp.1 Error2 BSE-2 

Scaling3 

BSE-1 

Scaling3 Step4

 Time5 

1 35 Cape Mendocino Rio Dell Overpass 1 15 1.879 1.253 0.020 36 

2 34 Superstition Hills Poe Road (temp) 2 17 3.083 2.055 0.010 23 

3 17 Kocaeli, Turkey Duzce 1 17 2.524 1.683 0.005 28 

4 31 Superstition Hills El Centro Imp. Co. 1 18 2.308 1.539 0.005 40 

5 19 Kocaeli, Turkey Arcelik 1 19 8.166 5.444 0.005 30 

6 2 Northridge Beverly Hills - Mulhol 2 20 1.093 0.729 0.010 30 

7 10 Imperial Valley Delta 2 21 2.293 1.529 0.010 100 

8 16 Kobe, Japan Shin-Osaka 2 22 2.668 1.778 0.010 41 

9 4 Northridge Canyon Country-WLC 2 26 1.622 1.082 0.010 20 

10 43 Friuli, Italy Tolmezzo 1 26 4.163 2.775 0.005 37 

11 28 Loma Prieta Gilroy Array #3 2 27 2.285 1.523 0.005 40 

12 24 Landers Coolwater 2 27 1.832 1.221 0.003 28 

13 30 Manjil, Iran Abbar 2 28 1.834 1.222 0.020 54 

14 6 Duzce, Turkey Bolu 2 28 1.192 0.795 0.010 56 

Notes: 

1. Component Number. See FEMA P-695 Appendix A for additional parameters associated to each component of an event. 

2. Single composite error value computed in Step 3. 

3. Scaling factor for the component for the BSE-2 or BSE-1 EHL (BSE-1 = 2⁄3×BSE-2). 

4. Time step in seconds. 

5. Total time of record in seconds. 

A-3 
3 7 

 Code Code

 121321 121321

 121222 6 121222

Original EQ 120811

 121211

Scaled EQ 120811

 121211

5

Spectral Acceleration (g) 

 120821

2 121411

 120112

 120612

 120722

 120122

 121711

 121022

1 120922

 121112

 Average 

Spectral Acceleration (g) 

 120821

 121411

 120112

4 120612

 120722

 120122

3 121711

 121022

 120922

2 121112

 Average 

1 

01 

0 

2 3 

Period (sec)

4 5 6 01 

0 

2 3 

Period (sec)

4 5 6 

3 

Scaled Average Spectrum 

Spectral Acceleration (g) 2 

Scaled to 100% of MCE r 

between 0.2 and 1.5T1,avg 

1 

 Code

 Average

 0.2T1,avg

 1.5T1,avg

T1,avg 

01 

0 

2 3 4 5 6 

Period (sec)

Figure A-1. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S Direction of ME4 

A-4 
2 4 3 

EQ 1 3 EQ 2 EQ 3 

2 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

 Code Code

 120811 Scaled

 120811 Unscaled 

 Code 1 2 121222 Scaled 121321 Scaled 121222 Unscaled 121321 Unscaled 

1 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 6 3 

5
 

EQ 4
 EQ 5 EQ 6 

2 

1 

 Code

 121211 Scaled

 121211 Unscaled 

4 

 Code

 120821 Scaled 3 120821 Unscaled 

2 

2 

1 

 Code

 121411 Scaled

 121411 Unscaled 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 2 

EQ 7 EQ 8 EQ 9 

2 

1 

 Code

 120112 Scaled

 120112 Unscaled 

2 

 Code

 120612 Scaled

 120612 Unscaled 

1 

 Code

1 120722 Scaled

 120722 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 4 4 

EQ 10 3 EQ 11 3 EQ 12 

2 Code

 120122 Scaled

 120122 Unscaled 

 Code

 121022 Scaled Code

2 121711 Scaled 2 121022 Unscaled 121711 Unscaled 

1 

1 1 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

3 4 

EQ 13 3 EQ 14 

Spectral Acceleration (g) 2 

 Code

 120922 Scaled

 120922 Unscaled 

1 

Spectral Acceleration (g) 

 Code

 121112 Scaled 2 121112 Unscaled 

1 

0 0 

012 3456 012 3456 

Period (sec) Period (sec)

Figure A-2. Acceleration Response Spectra: Original and Scaled for Each Selected Record for N-S Direction of ME4 

A-5 
 

 

 

 

 

 

 

 

 

 

 

 

A.4 Eight-Story Archetype Building 

8-Story Eccentrically Braced Frame 

Table A-2 summarizes the 14 strong motion records used for the NDP for the N-S direction of ME8 (EBF). 

Figure A-3 illustrates the set of acceleration response spectra, original and scaled, and the scaled average 

spectrum. Figure A-4 illustrates the acceleration response spectra, original and scaled, for each select 

record. For comparison, the ASCE 41 code spectrum is shown in the figures. All analyses completed for 

the BSE-1 for the ELF and RSA design. All analyses except those using records 1, 4, 5, and 6 completed 

for the BSE-2 for the ELF design. All analyses except those using records 1, 4, 5, 6, and 10 completed for 

the BSE-2 for the RSA design. 

Table A-2. Ground Motion Records for N-S Direction of ME8 

I 

D EQ No. Event Name Station Comp.1

 Error2 BSE-2 

Scaling3 

BSE-1 

Scaling3 Step4

 Time5 

1 12 Imperial Valley El Centro Array #11 2 28 4.120 2.747 0.005 40 

2 34 Superstition 

Hills Poe Road (temp) 2 28 3.000 2.000 0.010 23 

3 5 Duzce, Turkey Bolu 1 35 2.055 1.370 0.010 56 

4 10 Imperial Valley Delta 2 40 2.464 1.643 0.010 100 

5 20 Kocaeli, Turkey Arcelik 2 42 5.781 3.854 0.005 30 

6 21 Landers Yermo Fire Station 1 48 2.928 1.952 0.020 44 

7 31 Superstition 

Hills El Centro Imp. Co. 1 44 2.849 1.899 0.005 40 

8 38 Chi-Chi, Taiwan CHY101 2 52 1.182 0.788 0.005 90 

9 42 San Fernando LA - Hollywood Stor 2 55 8.024 5.350 0.010 28 

10 29 Manjil, Iran Abbar 1 57 3.127 2.085 0.020 54 

11 15 Kobe, Japan Shin-Osaka 1 46 3.067 2.045 0.010 41 

12 28 Loma Prieta Gilroy Array #3 2 48 2.098 1.399 0.005 40 

13 7 Hector Mine Hector 1 58 4.731 3.154 0.010 46 

14 3 Northridge Canyon Country-WLC 1 57 2.235 1.490 0.010 20 

Notes: 

1. Component Number. See FEMA P-695 Appendix A for additional parameters associated to each component of an event. 

2. Single composite error value computed in Step 3. 

3. Scaling factor for the component for the BSE-2 or BSE-1 EHL (BSE-1 = 2⁄3×BSE-2). 

4. Time step in seconds. 

5. Total time of record in seconds. 

A-6 
3 7 

 Code Code

 120622 120622

 121222 6 121222

 120411 Scaled EQ 120411 Original EQ 

Spectral Acceleration (g) 

 120612

Spectral Acceleration (g) 

 120612

 120822 5

2 120911

 121211

 121412

 121512

 121111

 120721

 121022

1 120521

 120121

 Average 

 120822

 120911

 121211

4 121412

 121512

 121111

3 120721

 121022

 120521

2 120121

 Average 

1 

01 

0 

2 3 

Period (sec)

4 5 6 01 

0 

2 3 

Period (sec)

4 5 6 

3 

Scaled Average Spectrum 

Spectral Acceleration (g) 2 

Scaled to 100% of MCER 

between 0.2 and 1.5T1,avg 

 Code

 Average

 0.2T1,avg

1 1.5T1,avg

T1,avg 

0 

01 2 3 4 5 6 

Period (sec)

Figure A-3. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S Direction of ME8 

A-7 
6 3 5 

5 

EQ 1 EQ 2 4 EQ 3 

4 2 

3 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

 Code

 121222 Scaled

 121222 Unscaled 

 Code

 120411 Scaled

 120411 Unscaled 

 Code 3 120622 Scaled

 120622 Unscaled 2 

1 

2 1 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 2

EQ 4 EQ 5 EQ 6 

 Code

1 120911 Scaled

 120911 Unscaled 

2 

1 

2 

 Code Code

 120612 Scaled

 120612 Unscaled 

 120822 Scaled

 120822 Unscaled 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 2 5 

EQ 7 EQ 8 4 EQ 9 

2 

1 

 Code

 121211 Scaled

 121211 Unscaled 

3 

 Code

 121512 Scaled

 121512 Unscaled 

2 

1 

 Code

 121412 Scaled

1 121412 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

6 3 3 

5 

EQ 10 EQ 11 EQ 12 

4 

3 

2 

1 

 Code

 120721 Scaled

 120721 Unscaled 

2 

1 

 Code

 121022 Scaled

 121022 Unscaled 

 Code

 121111 Scaled

 121111 Unscaled 

2 

1 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

4 4 

3 EQ 13 3 EQ 14 

Spectral Acceleration (g) 

 Code

 120521 Scaled 2 120521 Unscaled 

1 

Spectral Acceleration (g) 

 Code

 120121 Scaled 2 120121 Unscaled 

1 

0 0 

012 3456 012 3456 

Period (sec) Period (sec)

Figure A-4. Acceleration Response Spectra: Original and Scaled for Each Selected Record for N-S Direction of ME8 

 

A-8 
 

 

 

 

 

 

 

 

 

 

A.5 Sixteen-Story Archetype Building 

16-Story Eccentrically Braced Frame 

Table A-3 summarizes the 14 strong motion records used for the NDP for the N-S direction of ME16 (EBF). 

Figure A-5 illustrates the set of acceleration response spectra, original and scaled, and the scaled average 

spectrum. Figure A-6 illustrates the acceleration response spectra, original and scaled, for each select 

record. For comparison, the ASCE 41 code spectrum is shown in the figures. All analyses completed for 

the BSE-1 and BSE-2 for the ELF design. All analyses completed for the BSE-1 for the RSA design. All 

analyses except those using records 1, 2, 6, and 11 completed for the BSE-2 for the RSA design. 

Table A-3. Ground Motion Records for N-S Direction of ME16 

ID EQ No. Event Name Station Comp. 1 Error2 BSE-2 

Scaling3 

BSE-1 

Scaling3 Step4

 Time5 

1 12 Imperial Valley El Centro Array #11 2 31 3.845 2.563 0.005 40 

2 10 Imperial Valley Delta 2 59 2.330 1.554 0.01 100 

3 19 Kocaeli, Turkey Arcelik 1 67 8.791 5.861 0.005 30 

4 42 San Fernando LA - Hollywood Stor 2 67 6.744 4.496 0.01 28 

5 29 Manjil, Iran Abbar 1 64 3.072 2.048 0.02 54 

6 21 Landers Yermo Fire Station 1 59 2.799 1.866 0.02 44 

7 27 Loma Prieta Gilroy Array #3 1 61 5.487 3.658 0.005 40 

8 7 Hector Mine Hector 1 74 5.273 3.515 0.01 46 

9 5 Duzce, Turkey Bolu 1 65 2.043 1.362 0.01 56 

10 34 Superstition Hills Poe Road (temp) 2 68 3.154 2.103 0.01 23 

11 44 Friuli, Italy Tolmezzo 2 82 9.497 6.331 0.005 37 

12 14 Kobe, Japan Nishi-Akashi 2 103 4.017 2.678 0.01 41 

13 17 Kocaeli, Turkey Duzce 1 100 1.688 1.125 0.005 28 

14 31 Superstition Hills El Centro Imp. Co. 1 78 2.864 1.909 0.005 40 

Notes: 

1. Component Number. See FEMA P-695 Appendix A for additional parameters associated to each component of an event. 

2. Single composite error value computed in Step 3. 

3. Scaling factor for the component for the BSE-2 or BSE-1 EHL (BSE-1 = 2⁄3×BSE-2). 

4. Time step in seconds. 

5. Total time of record in seconds. 

A-9 
3 7 

 Code Code

 120622 120622

 120612 6 120612

Original EQ 120821

 121512

Scaled EQ 120821

 121512

5

Spectral Acceleration (g) 

 121111

2 120911

 121021

 120521

 120411

 121222

 121712

 120712

1 120811

 121211

 Average 

Spectral Acceleration (g) 

 121111

 120911

 121021

4 120521

 120411

 121222

3 121712

 120712

 120811

2 121211

 Average 

1 

0 0
 

0123456 0123456 
 

Period (sec) Period (sec)

4 

Scaled Average Spectrum 

3 Scaled to 100% of MCE r 

between 0.2 and 1.5T1,avg 

Spectral Acceleration (g) 2 Code

 Average

 0.2T1,avg

 1.5T1,avg

1 T1,avg 

0 

01 2 3 4 5 6 

Period (sec)

Figure A-5. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S Direction of ME16 

 

A-10 
6 3 6 

5 5 

EQ 1 EQ 2 EQ 3 

4 2 4 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

 Code

 120612 Scaled

 120612 Unscaled 

 Code

3 120821 Scaled

 120821 Unscaled 

2 

 Code 3 120622 Scaled

 120622 Unscaled 

2 1 

1 1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

5 6 2 

5 4 EQ 4 EQ 5 EQ 6 

4 

3 

2 

 Code

 121111 Scaled

 Code

 121512 Scaled

 121512 Unscaled 

 Code

3 1 120911 Scaled 121111 Unscaled 120911 Unscaled 

2 

1 1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

11 4 5 

10 

9 

EQ 7 3 EQ 8 4 EQ 9 8 

7 3 

 Code

 120411 Scaled

 120411 Unscaled 

2 

1 

 Code

6 Code 120521 Scaled

 121021 Scaled 120521 Unscaled 

5 121021 Unscaled 

4 

3 

2 

1 

2 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 10 6 

9
 

5
 

EQ 10 8
 EQ 11 EQ 12 

7 

6 

2 

1 

 Code

 121222 Scaled

 121222 Unscaled 

4 

 Code

 120712 Scaled Code

5 121712 Scaled 3 120712 Unscaled 121712 Unscaled 

4 

3 

2 

2 

1 

1 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

2 3 

EQ 13 EQ 14 

Spectral Acceleration (g) 

 Code

 120811 Scaled 1 120811 Unscaled 

Spectral Acceleration (g) 2 

 Code

 121211 Scaled

 121211 Unscaled 

1 

0 0 

012 3456 012 3456 

Period (sec) Period (sec)

Figure A-6. Acceleration Response Spectra: Original and Scaled for Each Selected Record for N-S Direction of ME16 

A-11 
 

 

A.6 FEMA P-695 Far-Field Record Set 

Figure A-7 through Figure A-50 illustrate the recorded ground motion, Fourier amplitude (frequency and 

period), and the five percent damped response spectra (displacement, velocity, acceleration) for each 

component. 

EQ1-NORTHR/ MUL009	 EQ1-NORTHR/MUL009 - Respons e Spectra - 5% Damping A c celeration (g) Velocity (inches/sec) Displacement (inches)15 

10 

5 

0 

0.4 

0.2 

0 

-0. 2 

-0. 4 

Acceleration (g) Acceleration (g) 

0 5 10 15 20 25 0 0.5 1 1.5	 2 2.5 3 3.5 4 4.5 

Time (sec.)	 Period (sec ) 

80 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

2 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5	 2 2.5 3 3.5 4 4.5 

1.5 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-7. 1994 Northridge Earthquake at Beverly Hills, Mulholland Drive Station, Comp. 009 

EQ2-NORTHR/ MUL279	 EQ2-NORTHR/MUL279 - Respons e Spectra - 5% Damping Velocity (inches/sec) Displacement (inches) A c celeration (g) 15 

10 

5 

0 

0.5 

0 

-0. 5 

0 5 10 15 20 25 0 0.5 1 1.5	 2 2.5 3 3.5 4 4.5 

Time (sec.)	 Period (sec ) 

80 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5	 2 2.5 3 3.5 4 4.5 

2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-8. 1994 Northridge Earthquake at Beverly Hills, Mulholland Drive Station, Comp. 279 

A-12 

5 

5 

5 

5 
 

 

0 

0 

0.5 

EQ3-NORTHR/ LOS000	 EQ3-NORTHR/LOS000 - Response Spectra - 5% Damping 

15 

10 

0.4 

0.2 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 

-0. 2 

-0. 4 

0 2 4 6 8 10 12 14 16 18 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-9. 1994 Northridge Earthquake at Canyon Country WLC Station, Comp. 000 

EQ4-NORTHR/ LOS270	 EQ4-NORTHR/LOS270 - Response Spectra - 5% Damping 

8 

6 

4 

2 

0 -0. 5 Velocity (inches/sec) Displacement (inches) 

0 2 4 6 8 10 12 14 16 18 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

2 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 1.5 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-10. 1994 Northridge Earthquake at Canyon Country WLC Station, Comp. 270 

A-13 
 

 

 

 

0 

0.5 

0 

0.5 

EQ5-DUZCE / B OL000	 EQ5-DUZCE/BOL000 - Response Spectra - 5% Damping 

20 

15 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 10 

5 

0 

-0. 5 

0 10 20 30 40 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-11. 1999 Duzce, Turkey Earthquake at Bolu Station, Comp. 000 

EQ6-DUZCE / B OL090	 EQ6-DUZCE/BOL090 - Response Spectra - 5% Damping Velocity (inches/sec) Displacement (inches) 15 

10 

5 

0 

-0. 5 

0 10 20 30 40 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

80 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-12. 1999 Duzce, Turkey Earthquake at Bolu Station, Comp. 090 

A-14 
 

 

 

 

0 

0.2 

0 

0.2 

EQ7-HECTOR/HEC000 - Response Spectra - 5% Damping EQ7-HECTOR/ HEC000 10 

5 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

-0. 2 

0 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.6 

0.4 

0.2 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-13. 1999 Hector Mine Earthquake at Hector Station, Comp. 000 

EQ8-HECTOR/ HEC090	 EQ8-HECTOR/HEC090 - Response Spectra - 5% Damping Velocity (inches/sec) Displacement (inches) 10 

5 

0 

-0. 2 

0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-14. 1999 Hector Mine Earthquake at Hector Station, Comp. 090 

A-15 
 

 

 

0 

0.2 

0 

0.2 

EQ9-IMPVALL/H-DLT262 - Response Spectra - 5% Damping EQ9-IMPVALL/H-DLT262 20 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 

-0. 2 

0 10 20 30 40 50 60 70 80 90 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.6 

0.4 

0.2 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-15. 1979 Imperial Valley Earthquake at Delta Station, Comp. 262 

EQ10-IMPVALL/H-DLT352 - Respons e Spectra - 5% Damping EQ10-IMPVALL/H-DLT352 30 

20 

10 

0 

Velocity (inches/sec) Displacement (inches) 

-0. 2 

0 10 20 30 40 50 60 70 80 90 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 

1 

0.5 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-16. 1979 Imperial Valley Earthquake at Delta Station, Comp. 352 

A-16 
 

 

 

 

0 

0.2 

0.4 

0 

EQ11-IMPVALL/H-E11140	 EQ11-IMPVALL/H-E11140 - Respons e Spectra - 5% Damping 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 

-0. 2 

-0. 4 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-17. 1979 Imperial Valley Earthquake at El Centro Array Station #11, Comp. 140 

EQ12-IMPVALL/H-E11230	 EQ12-IMPVALL/H-E11230 - Respons e Spectra - 5% Damping 

15 

10 

5 

0 

0.4 

0.2 

-0. 2 

-0. 4 

Velocity (inches/sec) Displacement (inches) 

0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

2 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 1.5 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-18. 1979 Imperial Valley Earthquake at El Centro Array Station #11, Comp. 230 

A-17 
 

 

0 

0.5 

0 

0.5 

EQ13-KOBE/NIS000	 EQ13-KOBE/NIS000 - Response Spectra - 5% Damping 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 -0. 5 

0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

80 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-19. 1995 Kobe, Japan Earthquake at Nishi-Akashi Station, Comp. 000 

EQ14-KOBE/NIS090	 EQ14-KOBE/NIS090 - Response Spectra - 5% Damping 

15 

10 

5 

0 -0. 5 Velocity (inches/sec) Displacement (inches) 

0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

2 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 1.5 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-20. 1995 Kobe, Japan Earthquake at Nishi-Akashi Station, Comp. 090 

A-18 
 

 

0 

0 

0.2 

EQ15-KOBE/SHI000	 EQ15-KOBE/SHI000 - Response Spectra - 5% Damping 

10 

0.2 

0.1 

5 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

-0. 1 

-0. 2 

0 0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-21. 1995 Kobe, Japan Earthquake at Shin-Osaka Station, Comp. 000 

EQ16-KOBE/SHI090 - Response Spectra - 5% Damping EQ16-KOBE/SHI090 Velocity (inches/sec) Displacement (inches) 8 

6 

4 

2 

0 -0. 2 

0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.6 

0.4 

0.2 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-22. 1995 Kobe, Japan Earthquake at Shin-Osaka Station, Comp. 090 

A-19 
 

 

0 

0.2 

0 

0.2 

EQ17-KOCAELI/DZC180	 EQ17-KOCAELI/DZC180 - Response Spectra - 5% Damping 

40 

30 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 20 

10 

0 

-0. 2 

0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-23. 1999 Kocaeli, Turkey Earthquake at Duzce Station, Comp. 180 

EQ18-KOCAELI/DZC270	 EQ18-KOCAELI/DZC270 - Response Spectra - 5% Damping 

20 

15 

10 

5 

0 

Velocity (inches/sec) Displacement (inches) 

-0. 2 

0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ac celeration (g) 

1 

0.5 

0 

Period (sec .)	 Period (sec) 

Figure A-24. 1999 Kocaeli, Turkey Earthquake at Duzce Station, Comp. 270 

A-20 
 

 

-0.2 

0 

0.2 

0 

0.1 

EQ19-KOCAELI/ARC000 - Res ponse Spectra - 5% Damping EQ19-KOCAELI/ARC000 6 

4 

Acceleration (g) Acceleration (g) 

Displacement (inches) 2 

0 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec.)	 Period (sec ) Velocity (inches/sec) 15 

10 

5 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.6 

0.4 

0.2 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-25. 1999 Kocaeli, Turkey Earthquake at Arcelik Station, Comp. 000 

EQ20-KOCAELI/ARC090 - Res ponse Spectra - 5% Damping EQ20-KOCAELI/ARC090 Velocity (inches/sec) Displacement (inches) 30 

20 

10 

0 

-0.1 

0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.6 

0.4 

0.2 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-26. 1999 Kocaeli, Turkey Earthquake at Arcelik Station, Comp. 090 

A-21 
 

 

0 

0 

0.1 

EQ21-LANDERS/YER270	 EQ21-LA NDERS/YER270 - Res pons e Spec t ra - 5% Damping 

30 

0.2 

0.1 20 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 10 

0 

-0. 1 

-0. 2 

0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 0.6 

0.4 

0.2 

0 

Period (sec.)	 Period (sec ) 

Figure A-27. 1992 Landers Earthquake at Yermo Fire Station, Comp. 270 

EQ22-LANDERS/YER360	 EQ22-LA NDERS/YER360 - Res pons e Spec t ra - 5% Damping 

20 

15 

10 

5 

0 

Velocity (inches/sec) Displacement (inches) 

-0. 1 

0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 0.6 

0.4 

0.2 

0 

Period (sec.)	 Period (sec ) 

Figure A-28. 1992 Landers Earthquake at Yermo Fire Station, Comp. 360 

A-22 
 

 

-0.2 

0 

0.2 

EQ23-LANDERS/ CLW -LN	 EQ23-LANDERS/CLW -LN - Response Spectra - 5% Damping 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-29. 1992 Landers Earthquake at Coolwater Station, Longitudinal Direction 

EQ24-LANDERS/ CLW -TR	 EQ24-LANDERS/CLW -TR - Response Spectra - 5% Damping 

10 

5 

0 

Velocity (inches/sec) Displacement (inches) 

0.4 

0.2 

0 

-0.2 

-0.4 

0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-30. 1992 Landers Earthquake at Coolwater Station, Transverse Direction 

A-23 
 

 

 

 

0 

0.5 

0 

0.2 

0.4 

EQ25-LOMAP/CAP000	 EQ25-LOMAP/CAP000 - Response Spectra - 5% Damping 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 -0. 5 

0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-31. 1989 Loma Prieta Earthquake at Capitola Station, Comp. 000 

EQ26-LOMAP/CAP090	 EQ26-LOMAP/CAP090 - Response Spectra - 5% Damping 

-0. 2 

-0. 4 

Displacement (inches) 8 

6 

4 

2 

0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec.)	 Period (sec ) Velocity (inches/sec) 60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-32. 1989 Loma Prieta Earthquake at Capitola Station, Comp. 090 

A-24 
 

 

-0.5 

0 

0.5 

0.2 

0.4 

Acceleration (g) Acceleration (g) 

EQ27-LOMAP/G03000	 EQ27-LOMAP/G03000 - Response Spectra - 5% Damping 

8 

6

Displacement (inches) 4 

2 

0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec.)	 Period (sec ) Velocity (inches/sec) 40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-33. 1989 Loma Prieta Earthquake at Gilroy Array Station #3, Comp. 000 

EQ28-LOMAP/G03090	 EQ28-LOMAP/G03090 - Response Spectra - 5% Damping 

0 

-0.2 

-0.4 

Velocity (inches/sec) Displacement (inches) 15 

10 

5 

0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

2 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 1.5 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-34. 1989 Loma Prieta Earthquake at Gilroy Array Station #3, Comp. 090 

A-25 
 

 

0 

0.5 

0 

0.5 

EQ29-MANJIL/ABBAR--L	 EQ29-MANJIL/ABBAR--L - Response Spectra - 5% Damping 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 -0. 5 

0 5 10 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-35. 1990 Manjil, Iran Earthquake at Abbar Station, Longitudinal Direction 

EQ30-MANJIL/ABBAR--T	 EQ30-MANJIL/ABBAR--T - Response Spectra - 5% Damping 

-0. 5 

Velocity (inches/sec) Displacement (inches) 30 

20 

10 

0 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-36. 1990 Manjil, Iran Earthquake at Abbar Station, Transverse Direction 

A-26 
 

 

-0.2 

0 

0.2 

0.1 

0.2 

EQ31-SUPERST/B-ICC000 - Response Spectra - 5% Damping EQ31-SUPERST/B-ICC000 15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.5 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-37. 1987 Superstition Hills Earthquake at El Centro, Imperial County, Comp. 000 

EQ32-SUPERST/B-ICC090	 EQ32-SUPERST/B-ICC090 - Response Spectra - 5% Damping 

20 

15 

10 

5 

0 

Velocity (inches/sec) Displacement (inches) 

0 

-0.1 

-0.2 

0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 0.6 

0.4 

0.2 

0 

Period (sec.)	 Period (sec ) 

Figure A-38. 1987 Superstition Hills Earthquake at El Centro, Imperial County, Comp. 090 

A-27 
 

 

0 

0 

0.2 

EQ33-SUPERST/B-POE270	 EQ33-SUPERST/B-POE270 - Response Spectra - 5% Damping 

10 0.4 

0.2 

5 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

-0. 2 

-0. 4 0 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-39. 1987 Superstition Hills Earthquake at Poe Road, Comp. 270 

EQ34-SUPERST/B-POE360	 EQ34-SUPERST/B-POE360 - Response Spectra - 5% Damping Velocity (inches/sec) Displacement (inches) 15 

10 

5 

0 

-0. 2 

0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-40. 1987 Superstition Hills Earthquake at Poe Road, Comp. 360 

A-28 
 

 

 

 

-0.4 

-0.2 

0 

0.2 

0.4 

0 

0.5 

EQ35-CAPEMEND/RIO270	 EQ35-CAPEMEND/RIO270 - Response Spectra - 5% Damping 

8 

6 

4 

Acceleration (g) Acceleration (g) 

Displacement (inches) 2 

0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Acceleration (g) Velocity (inches/sec) 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-41. 1992 Cape Mendocino Earthquake at Rio Dell Overpass, Comp. 270 

EQ36-CAPEMEND/RIO360	 EQ36-CAPEMEND/RIO360 - Response Spectra - 5% Damping Displacement (inches) 8 

6 

4 

2 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

-0.5 

0 5 10 15 20 25 30 35 

Time (sec.)	 Period (sec ) Velocity (inches/sec) 60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

3 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 2 

1 

0 

Period (sec.)	 Period (sec ) 

Figure A-42. 1992 Cape Mendocino Earthquake at Rio Dell Overpass, Comp. 360 

A-29 
 

 

0 

0.2 

0 

EQ37-CHICHI/CHY101-E - Res pons e Spec tra - 5% Damping EQ37-CHICHI/ CHY 101-E 40 

30 

20 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 10 

0 

-0. 2 

0 10 20 30 40 50 60 70 80 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

80 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.5 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-43. 1999 Chi-Chi, Taiwan Earthquake at CHY101 Station, E-W Component 

EQ38-CHICHI/ CHY 101-N	 EQ38-CHICHI/CHY101-N - Res pons e Spec tra - 5% Damping 

100 

50 

0 

Velocity (inches/sec) Displacement (inches) 

0.4 

0.2 

-0. 2 

-0. 4 

0 10 20 30 40 50 60 70 80 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

150 

100 

50 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-44. 1999 Chi-Chi, Taiwan Earthquake at CHY101 Station, N-S Component 

A-30 
 

 

 

 

-0.5 

0 

0.5 

0 

0.5 

EQ39-CHICHI/TCU045-E - Response Spectra - 5% Damping EQ39-CHICHI/ TCU045-E 20 

15 

10 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 0 10 20 30 40 50 60 70 80 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 

1 

0.5 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-45. 1999 Chi-Chi, Taiwan Earthquake at TCU045 Station, E-W Component 

EQ40-CHICHI/ TCU045-N - Res pons e S pec t ra - 5% Damping EQ40-CHICHI/ TCU045-N Velocity (inches/sec) Displacement (inches) 8 

6 

4 

2 

0 -0.5 

0 10 20 30 40 50 60 70 80 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

40 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 

1 

0.5 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-46. 1999 Chi-Chi, Taiwan Earthquake at TCU045 Station, N-S Component 

A-31 
 

 

0 

0 

0.1 

EQ41-SFERN/PEL090	 EQ41-SFERN/PEL090 - Response Spec tra - 5% Damping 

15 

10 

0.2 

0.1 

Acceleration (g) Acceleration (g) 

Velocity (inches/sec) Displacement (inches) 

5 

0 

-0. 1 

-0. 2 

0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 0.6 

0.4 

0.2 

0 

Period (sec.)	 Period (sec ) 

Figure A-47. 1971 San Fernando Earthquake at Los Angeles Hollywood Store Station, Comp. 090 

EQ42-SFERN/PEL180 - Response Spec tra - 5% Damping EQ42-SFERN/PEL180 8 

6 

4 

2 

0 

Velocity (inches/sec) Displacement (inches) 

-0. 1 

0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time (sec.)	 Period (sec ) 

15 

10 

5 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

0.8 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Acceleration (g) 0.6 

0.4 

0.2 

0 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Period (sec.) Period (sec ) 

Figure A-48. 1971 San Fernando Earthquake at Los Angeles Hollywood Store Station, Comp. 180 

A-32 
 

 

-0.2 

0 

0.2 

0 

0.2 

Acceleration (g) Acceleration (g) 

EQ43-FRIULI/ A-TM Z000	 EQ43-FRIULI/A-TMZ000 - Response Spectra - 5% Damping 

3 

2

Displacement (inches) 1 

0 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec.)	 Period (sec ) Velocity (inches/sec) 30 

20 

10 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-49. 1976 Fruili, Italy Earthquake at Tolmezzo Station, Comp. 000 

EQ44-FRIULI/ A-TM Z270	 EQ44-FRIULI/A-TMZ270 - Response Spectra - 5% Damping Displacement (inches) 6 

4 

2 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

-0.2 

0 5 10 15 20 25 30 35 

Time (sec.)	 Period (sec ) Velocity (inches/sec) 60 

40 

20 

0 

Amplitude Amplitude 0	 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Frequency (hz) Period (sec ) 

1.5 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Acceleration (g) 

1 

0.5 

0 

Period (sec.)	 Period (sec ) 

Figure A-50. 1976 Fruili, Italy Earthquake at Tolmezzo Station, Comp. 270 

A-33 
A-34 
Appendix B Supplemental Design Information and Design 

Examples 

This appendix presents supplemental information and details on the design of each archetype building. 

Section B.1 provides information about the following: 

 Wind forces both for strength and drift analyses 

 Effective seismic weights and story gravity forces 

 Seismic forces both for strength and drift analyses 

 Lateral story drifts and displacements (ASCE 7 §2.8.6) 

 ASCE 7 stability verification (ASCE 7 §12.8.7) 

Section B.2 provides information regarding horizontal and vertical irregularities of the SFRS. 

Section B.3 provides information regarding the AISC 360 frame stability calculation (B2 for the effective 

length method) for the moment frame designs. 

Section B.4 provides information regarding the AISC 341 plastic rotation requirement of the link beams in 

the eccentric braced frame designs. 

Section B.5 provides example calculations for the strength design of a few specific members and 

components: 

 EBF link 

 EBF brace 

 EBF column 

B.1 Horizontal Design Forces 

 Wind Forces 

Table B-1 through Table B-3 provide the horizontal wind forces for the 700-year wind for strength design 

of the members and components of the MWFRS and wind forces for the 10-year wind for verification of 

serviceability criteria for each archetype building. In these tables, Fx represents wind forces in the E-W 

direction and Fy represents wind in the N-S direction. Slight differences in applied wind forces are due to 

stiffness variations between the ELF and RSA designs. 

B-1 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-1. Wind Forces on ME4 (kips) 

Diaphragm Forces (kips), Applied at Geometric Center 

Level Elevation 

(ft) 

700-Year Wind (Design) 

RSA ELF 

10-Year Wind (Drift) 

RSA ELF 

Fx Fy Fx Fy Fx Fy Fx Fy 

Roof 60 36.09 52.43 35.30 52.43 14.82 22.46 14.67 22.46 

4 46 35.48 50.50 33.98 50.50 13.99 21.63 13.69 21.63 

3 32 33.21 47.53 31.81 47.53 13.09 20.36 12.82 20.36 

2 18 34.36 49.60 32.91 49.60 13.55 21.25 13.26 21.25 

Base 0 139.14 200.06 134.01 200.06 55.46 85.71 54.44 85.71 

Table B-2. Wind Forces on ME8 (kips) 

Diaphragm Forces (kips), Applied at Geometric Center 

Level Elevation 

(ft) 

700-Year Wind (Design) 

RSA ELF 

10-Year Wind (Drift) 

RSA ELF 

Fx Fy Fx Fy Fx Fy Fx Fy 

Roof 116 46.18 65.78 44.19 65.22 18.47 27.23 18.00 27.13 

8 102 49.32 67.67 45.43 66.58 18.55 27.14 17.64 26.94 

7 88 47.98 65.97 44.20 64.91 18.05 26.46 17.16 26.26 

6 74 46.48 64.07 42.81 63.04 17.49 25.70 16.62 25.51 

5 60 44.76 61.89 41.23 60.90 16.84 24.82 16.00 24.64 

4 46 42.72 59.31 39.35 58.36 16.07 23.79 15.28 23.61 

3 32 40.18 56.09 37.01 55.19 15.12 22.50 14.37 22.33 

2 18 41.88 59.00 38.58 58.05 15.76 23.66 14.98 23.49 

Base 0 359.49 499.77 332.81 492.24 136.35 201.31 130.04 199.90 

Table B-3. Wind Forces on ME16 (kips) 

Diaphragm Forces (kips), Applied at Geometric Center 

Level Elevation 

(ft) 

700-Year Wind (Design) 

RSA ELF 

10-Year Wind (Drift) 

RSA ELF 

Fx Fy Fx Fy Fx Fy Fx Fy 

Roof 228 56.78 82.70 55.35 82.17 22.58 33.58 22.22 33.46 

16 214 62.23 89.05 59.41 88.00 23.22 34.48 22.50 34.26 

15 200 61.44 88.01 58.66 86.97 22.93 34.08 22.22 33.86 

14 186 60.61 86.92 57.86 85.89 22.62 33.66 21.92 33.44 

13 172 59.74 85.76 57.03 84.75 22.29 33.21 21.60 32.99 

12 158 58.81 84.54 56.14 83.54 21.95 32.73 21.27 32.52 

11 144 57.82 83.23 55.20 82.25 21.58 32.23 20.91 32.02 

10 130 56.76 81.83 54.19 80.86 21.18 31.69 20.53 31.48 

9 116 55.62 80.32 53.10 79.37 20.76 31.10 20.11 30.90 

8 102 54.37 78.67 51.91 77.74 20.29 30.46 19.66 30.26 

7 88 53.00 76.85 50.60 75.94 19.78 29.76 19.16 29.56 

6 74 51.46 74.81 49.12 73.93 19.20 28.97 18.61 28.78 

5 60 49.69 72.48 47.44 71.62 18.54 28.06 17.97 27.88 

4 46 47.60 69.71 45.44 68.89 17.76 26.99 17.21 26.82 

3 32 44.98 66.25 42.94 65.47 16.79 25.66 16.26 25.49 

2 18 47.26 70.24 45.12 69.41 17.64 27.20 17.09 27.02 

Base 0 878.18 1271.37 839.50 1256.80 329.11 493.87 319.23 490.74 

B-2 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Seismic Forces 

Effective Seismic Weights and Story Gravity Forces 

Table B-4 through Table B-6 provide the effective seismic weights lumped at each story as well as the 

lumped gravity force acting on each story for each building design. The gravity force is computed using the 

two load combinations as discussed in Chapter 2. 

Table B-4. Effect Seismic Weights and Story Gravity Forces, ME4 (kips) 

RSA ELF 

Level, x wx 

1 Pstory 

2 Px 

3 wx 1 Pstory 

2 Px

 3 

Roof 1085 1302 1085 1086 1304 1086 

4 1333 2909 2457 1339 2919 2465 

3 1338 4523 3834 1348 4544 3851 

2 1351 6152 5223 1363 6187 5253 

Total 5107 ­ - 5137 ­ -

1. Inertial weight computed from Dead + Superimposed Dead + 0.2×Floor Live 

2. Computed from 1.2×Dead + 1.2×Superimposed Dead + 0.25×Floor Live gravity load 

3. Computed from Dead + Superimposed Dead + 0.25×Floor Live gravity load 

Table B-5. Effect Seismic Weights and Story Gravity Forces, ME8 (kips) 

RSA ELF 

Level, x wx 

1 Pstory 

2 Px 

3 wx 1 Pstory 

2 Px

 3 

Roof 1078 1294 1078 1082 1299 1082 

8 1321 2887 2439 1328 2900 2449 

7 1327 4488 3805 1343 4519 3830 

6 1332 6094 5175 1351 6148 5220 

5 1341 7711 6555 1358 7786 6617 

4 1347 9335 7941 1363 9429 8019 

3 1353 10967 9333 1367 11077 9425 

2 1368 12617 10740 1382 12743 10845 

Total 10469 - - 10574 - -

1. Inertial weight computed from Dead + Superimposed Dead + 0.2×Floor Live 

2. Computed from 1.2×Dead + 1.2×Superimposed Dead + 0.25×Floor Live gravity load 

3. Computed from Dead + Superimposed Dead + 0.25×Floor Live gravity load 

B-3 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-6. Effect Seismic Weights and Story Gravity Forces, ME16 (kips) 

RSA ELF 

Level, x wx

 1 Pstory 

2 Px 

3 wx 1 Pstory 

2 Px 

3 

Roof 1084 1301 1084 1086 1303 1086 

16 1329 2903 2452 1331 2907 2455 

15 1332 4510 3823 1346 4530 3840 

14 1336 6120 5197 1355 6164 5233 

13 1349 7747 6585 1362 7806 6634 

12 1356 9382 7980 1366 9453 8039 

11 1360 11022 9379 1371 11106 9449 

10 1364 12666 10781 1377 12767 10865 

9 1370 14318 12190 1387 14438 12290 

8 1376 15977 13605 1393 16118 13723 

7 1380 17641 15024 1399 17805 15160 

6 1385 19310 16447 1405 19498 16604 

5 1397 20995 17883 1414 21202 18056 

4 1405 22688 19327 1423 22917 19518 

3 1413 24392 20779 1435 24646 20991 

2 1440 26128 22258 1469 26416 22498 

Total 21677 - - 21917 - -

1. Inertial weight computed from Dead + Superimposed Dead + 0.2×Floor Live 

2. Computed from 1.2×Dead + 1.2×Superimposed Dead + 0.25×Floor Live gravity load 

3. Computed from Dead + Superimposed Dead + 0.25×Floor Live gravity load 

Horizontal Seismic Forces, E-W Direction 

B.1.2.2.1 ME4 (Special Moment Frame) 

Table B-7 and Table B-8 provide the horizontal seismic forces and story shears for each building design 

for the seismic strength analysis and the drift analysis. The data are also graphically illustrated in Figure 

B-1 through Figure B-3. In these tables, Fx represents the seismic forces acting in the E-W direction only. 

The equivalent story forces for the RSA design are backed out from the story shears computed via a modal 

combination procedure. Although not theoretically correct, the forces provide a comparison basis for 

evaluating variations in the vertical distribution. 

Table B-7. Seismic Strength Design Forces, E-W ME4 

RSA ELF Wind (700-Year) 

Level, x Fx 

(kips) 

Vi 

(kips) 

Fx 

(kips) 

Vi 

(kips) 

VELF / 

VRSA 

Fx 

(kips) 

Vi 

(kips) 

Roof 145 145 138 138 1.05 36 36 

4 68 213 121 259 0.82 35 72 

3 46 259 77 336 0.77 33 105 

2 56 316 38 374 0.84 34 139 

B-4 
 

 

 

 

 

2 

3 

4 

Roof 36 138145 

Floor 

Floor 

Roof 

4 

3 

2 

0 40 80 120 160 

145 

68 

46 

56 

138 

121 

77 

38 

36 

35 

33 

34 

RSA

 ELF

 Wind (700-Year) 

Floor 

0 100 200 300 400 

213 

259 

316 

316 

259 

336 

374 

374 

72 

105 

139 

139 

 RSA

 ELF

 Wind (700-Year) 

4 

3 

2 

Base Base

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral Forces (b) Story Shears 

Figure B-1. Strength Design Lateral Forces and Story Shears 

Table B-8. Seismic Drift Forces, E-W ME4

 RSA ELF Wind (10-Year) 

Level, x Fx 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fx 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fx 

(kips) 

Vi 

(kips) 

Roof 76 76 11.82 1.88 0.011 89 89 12.13 2.28 0.014 15 15 

4 36 112 9.94 2.73 0.016 70 159 9.85 3.00 0.018 14 29 

3 24 136 7.21 3.39 0.020 39 198 6.85 3.33 0.020 13 42 

2 30 166 3.82 3.82 0.018 15 213 3.51 3.51 0.016 14 55 

Roof 76 89 Roof 15 

0 20 40 60 80 100 

76 

36 

24 

30 

89 

70 

39 

15 

15 

14 

13 

14 

RSA

 ELF

 Wind (10-Year) 

0 50 100 150 200 250 

112 

136 

166 

166 

159 

198 

213 

213 

29 

42 

55 

55 

 RSA

 ELF

 Wind (10-Year) 

4 

Floor

3 

2 

Base Base 

Lateral Force, F x (kips) Story Shear, V (kips)

x

(a) Lateral Forces (b) Story Shears 

Figure B-2. Drift Design Lateral Forces and Story Shears 

B-5 
 

 

 

 

 

2

8

Roof 0.0112 0.0136 Roof 11.8 12.1 

0 2 4 6 8 10 12 14 

 RSA

3. 3.5 

 ELF 

7. 6.8 

9.9 9.8 

RSA

 ELF 

0.0162 

0.0163 

0.0163 

0.0177 

0.0177 

0.0179 

0.0198 

4 4 

3 

2 

Floor 

3 0.0202 

Floor 

Allowable Story Drift Ratio, a / h sx 

2 

Base Base 

0.010 0.015 0.020 

Expected Story Drift Ratio, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift Ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-3. Story Drift Ratios and Deflected Shape 

Table B-9 and Table B-10 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and ASCE §12.8.7 for each archetype building design. The 

following formulas were used in these calculations—see ASCE 7, where  is the story drift and  is the 

story drift ratio as defined in ASCE 7. 

C    d xe 

x (B-1) I e 

Cd (B-2)  i x x    1   xe   ( x 1) e  I e 

P  (B-3) PI    x xe ( 1) x e   x i e 2i   Vh C Vh i sx d i sx 

 2i (B-4) 1i 

1   2i 

Table B-9. ASCE 7 Allowable Drift and Stability Verification, E-W ME4 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 418 1091 1.88 168 0.011 0.029 0.028 0.39 0.232 

4 615 2470 2.73 168 0.016 0.065 0.061 0.54 0.168 

3 749 3854 3.39 168 0.020 0.104 0.094 0.63 0.143 

2 911 5257 3.82 216 0.018 0.102 0.093 0.70 0.129 

B-6 
 

 

 

 

 

 

 

 

4 

5 

6 

7 

8 

Table B-10. ASCE 7 Allowable Drift and Stability Verification, E-W ME4 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 488 1095 2.28 168 0.014 0.030 0.030 0.39 0.231 

4 874 2479 3.00 168 0.018 0.051 0.048 0.44 0.208 

3 1088 3877 3.33 168 0.020 0.071 0.066 0.50 0.183 

2 1171 5293 3.51 216 0.016 0.074 0.069 0.53 0.172 

B.1.2.2.2 ME8 (Special Moment Frame) 

Table B-11 and Table B-12 provide the horizontal seismic forces and story shears for each archetype 

building design for the seismic strength analysis and the drift analysis. The data are also graphically 

illustrated in Figure B-4 through Figure B-6. In these tables, Fx represents the seismic forces acting in the 

E-W direction only. The equivalent story forces for the RSA design are backed out from the story shears 

computed via a modal combination procedure. Although not theoretically correct, the forces provide a 

comparison basis for evaluating variations in the vertical distribution. 

Table B-11. Seismic Strength Design Forces, E-W ME8

 RSA ELF Wind (700-Year) 

Level, x Fx 

(kips) 

Vi 

(kips) 

Fx 

(kips) 

Vi 

(kips) 

VELF / 

VRSA 

Fx 

(kips) 

Vi 

(kips) 

Roof 135 135 108 108 1.25 46 46 

8 57 192 108 216 0.89 49 96 

7 39 231 86 302 0.77 48 143 

6 37 268 65 367 0.73 46 190 

5 31 299 47 413 0.72 45 235 

4 26 326 30 444 0.73 43 277 

3 31 357 17 460 0.77 40 318 

2 37 394 7 467 0.84 42 359 

Roof 

0 20 40 60 80 100 120 140 

135 

57 

39 

37 

31 

26 

31 

37 

108 

108 

86 

65 

47 

30 

17 

7 

46 

49 

48 

46 

45 

43 

40 

42 

Lateral Force, F x

 RSA

 ELF

 Wind (700-Year) 

Floor 

Roof 

8 

7 

6 

5 

4 

3 

2 

46 108 135 

0 100 200 300 400 500 600 

192 

231 

268 

299 

326 

357 

394 

394 

216 

302 

367 

413 

444 

460 

467 

467 

96 

143 

190 

235 

277 

318 

359 

359 

RSA

 ELF

 Wind (700-Year) 

Floor Base Base 

 (kips) Story Shear, V x

 (kips)

(a) Lateral Forces (b) Story Shears 

Figure B-4. Strength Design Lateral Forces and Story Shears 

B-7 

2 

3 
 

 

 

 

 

Table B-12. Seismic Drift Forces, E-W ME8

 RSA ELF Wind (10-Year) 

Level, x Fx 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fx 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fx 

(kips) 

Vi 

(kips) 

Roof 66 66 21.48 1.84 0.011 71 71 22.95 2.25 0.013 18 18 

8 28 93 19.64 2.38 0.014 68 139 20.70 2.83 0.017 19 37 

7 19 112 17.26 2.75 0.016 51 190 17.87 2.81 0.017 18 55 

6 18 131 14.52 2.92 0.017 36 226 15.06 3.00 0.018 17 73 

5 15 146 11.59 2.90 0.017 24 250 12.06 3.06 0.018 17 89 

4 13 159 8.69 2.99 0.018 14 264 9.00 3.11 0.019 16 105 

3 15 174 5.70 2.86 0.017 7 271 5.89 2.96 0.018 15 121 

2 18 192 2.84 2.84 0.013 2 273 2.93 2.93 0.014 16 136 

Base 

2 

3 

4 

5 

6 

7 

8 

Roof 66 

28 

19 

18 

15 

13 

15

18 

71 

68 

51 

36 

24 

14 

7 

2 

18 

19 

18 

17 

17 

16 

15 

16 

Floor

RSA

 ELF

 Wind (10-Year) 

Floor Base 

2 

3 

4 

5 

6 

7 

8 

Roof 66 

93 

112 

131 

146 

159 

174 

192 

192 

71 

139 

190 

226 

250 

264 

271 

273 

273 

18 

37 

55 

73 

89 

105 

121 

136 

136 

RSA

 ELF

 Wind (10-Year) 

0 20 40 60 80 0 50 100 150 200 250 

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

Figure B-5. Drift Design Lateral Forces and Story Shears 

B-8 

300 
 

 

 

 

 

 

2 

6 

7 

8 

0.0110 0.0134 Roof Roof 

8 

7 

RSA

 ELF 

0.0142 

0.0132 

0.0132 

0.0136 

0.0136 

0.0163 

0.0174 

0.0173 

0.0178 

0.0170 

0.0168 

0.0167 

0.0179 

0.0182 

0.0185 

0.0176 

Allowable Story Drift Ratio,  / h a sx 

Floor 

6 

5 

4 

3 

2 

Base 

0 4 8 12 16 20 24 

21.5 

19.6 

17.3 

14.5 

11.6 

8.7 

5.7 

2.8 

22.9 

20.7 

17.9 

15.1 

12.1 

9.0 

5.9 

2.9 

RSA

 ELF 

Floor 

5 

4 

3 

Base 

0.000 0.005 0.010 0.015 0.020 

Expected Story Drift Ratio, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-6. Story Drift Ratios and Deflected Shape 

Table B-13 and Table B-14 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and §12.8.7 for each archetype building design. 

Table B-13. ASCE 7 Allowable Drift and Stability Verification, E-W ME8 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 361 1081 1.84 168 0.011 0.033 0.032 0.53 0.172 

8 513 2443 2.38 168 0.014 0.067 0.063 0.68 0.134 

7 619 3815 2.75 168 0.016 0.101 0.092 0.67 0.136 

6 718 5192 2.92 168 0.017 0.126 0.112 0.71 0.128 

5 801 6580 2.90 168 0.017 0.142 0.124 0.62 0.147 

4 872 7973 2.99 168 0.018 0.163 0.140 0.63 0.145 

3 956 9378 2.86 168 0.017 0.167 0.143 0.60 0.151 

2 1055 10807 2.84 216 0.013 0.135 0.119 0.60 0.152 

Table B-14. ASCE 7 Allowable Drift and Stability Verification, E-W ME8 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 392 1083 2.25 168 0.013 0.037 0.036 0.37 0.246 

8 763 2450 2.83 168 0.017 0.054 0.051 0.51 0.180 

7 1043 3835 2.81 168 0.017 0.062 0.058 0.43 0.210 

6 1243 5229 3.00 168 0.018 0.075 0.070 0.48 0.190 

5 1375 6631 3.06 168 0.018 0.088 0.081 0.46 0.199 

4 1453 8038 3.11 168 0.019 0.102 0.093 0.48 0.190 

3 1491 9457 2.96 168 0.018 0.112 0.101 0.47 0.192 

2 1503 10898 2.93 216 0.014 0.098 0.089 0.45 0.200 

B-9 
 

 

 

 

B.1.2.2.3 ME16 (Special Moment Frame) 

Table B-15 and Table B-16 provide the horizontal seismic forces and story shears for each archetype 

building design for the seismic strength analysis and the drift analysis. The data are also graphically 

illustrated in Figure B-7 through Figure B-9. In these tables, Fx represents the seismic forces acting in the 

E-W direction only. The equivalent story forces for the RSA design are backed out from the story shears 

computed via a modal combination procedure. Although not theoretically correct, the forces provide a 

comparison basis for evaluating variations in the vertical distribution. 

Table B-15. Summary of Seismic Strength Design Forces, E-W ME16

Level, x 

RSA 

Fx 

(kips) 

Vi 

(kips) 

Fx 

(kips) 

ELF 

Vi 

(kips) 

VELF / VRSA 

Wind (700-Year) 

Fx 

(kips) 

Vi 

(kips) 

Roof 196 196 133 133 1.47 57 57 

16 95 292 144 278 1.05 62 119 

15 54 346 127 405 0.85 61 180 

14 46 391 111 515 0.76 61 241 

13 45 436 95 611 0.71 60 301 

12 41 477 80 691 0.69 59 360 

11 33 510 67 758 0.67 58 417 

10 31 541 55 813 0.67 57 474 

9 33 573 44 857 0.67 56 530 

8 33 607 34 891 0.68 54 584 

7 29 636 26 917 0.69 53 637 

6 26 662 18 935 0.71 51 689 

5 29 691 12 947 0.73 50 738 

4 38 729 7 954 0.76 48 786 

3 44 773 3 957 0.81 45 831 

2 37 810 1 958 0.85 47 878 

Roof 

16 

15 

14 

13 

12 

11 

10 

133 196 Roof 57 

0 50 100 150 200 

196 

95 

54 

46 

45 

41 

33 

31 

33 

33 

29 

26 

29 

38 

44 

37 

133 

144 

127 

111 

95 

80 

67 

55 

44 

34 

26 

18 

12 

7 

3 

1 

57 

62 

61 

61 

60 

59 

58 

57 

56 

54 

53 

51 

50 

48 

45 

47 

RSA

 ELF

 Wind (700-Year) 

Floor 

0 200 400 600 800 1000 

292 

346 

391 

436 

477 

510 

541 

573 

607 

636 

662 

691 

729 

773 

810 

810 

278 

405 

515 

611 

691 

758 

813 

857 

891 

917 

935 

947 

954 

957 

958 

958 

119 

180 

241 

301 

360 

417 

474 

530 

584 

637 

689 

738 

786 

831 

878 

878 

RSA

 ELF

 Wind (700-Year) 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Floor 

9 

8 

7 

6 

5 

4 

3 

Base Base 

Lateral Force, F x (kips) Story Shear, V (kips)

x

(a) Lateral forces (b) Story Shears 

Figure B-7. Strength Design Lateral Forces and Story Shears 

B-10 

2 
 

 

 

 

 

 

 

 

Table B-16. Summary of Seismic Drift Forces, E-W ME16

Level, x Fx 

(kips) 

Vi 

(kips) 

RSA 

x 

(inch) 

i 

(inch)

i / hsx Fx 

(kips) 

Vi 

(kips) 

ELF 

x 

(inch) 

i 

(inch)

i / hsx 

Wind (10-Year) 

Fx 

(kips) 

Vi 

(kips) 

Roof 71 71 29.39 1.28 0.008 52 52 38.12 1.76 0.010 23 23 

16 35 106 28.11 1.69 0.010 56 109 36.36 2.16 0.013 23 46 

15 20 126 26.42 2.00 0.012 50 158 34.20 2.30 0.014 23 69 

14 17 142 24.42 2.02 0.012 43 202 31.89 2.51 0.015 23 91 

13 16 159 22.41 1.89 0.011 37 239 29.39 2.62 0.016 22 114 

12 15 174 20.51 1.99 0.012 31 270 26.77 2.81 0.017 22 136 

11 12 186 18.52 2.09 0.012 26 296 23.96 2.92 0.017 22 157 

10 11 197 16.43 2.10 0.012 21 318 21.05 2.84 0.017 21 178 

9 12 209 14.33 2.04 0.012 17 335 18.21 2.64 0.016 21 199 

8 12 221 12.29 2.07 0.012 13 348 15.57 2.60 0.015 20 219 

7 11 232 10.22 2.07 0.012 10 358 12.97 2.57 0.015 20 239 

6 9 241 8.15 1.94 0.012 7 365 10.40 2.51 0.015 19 258 

5 11 252 6.21 1.75 0.010 5 370 7.89 2.37 0.014 19 277 

4 14 266 4.47 1.67 0.010 3 373 5.52 2.20 0.013 18 295 

3 16 282 2.80 1.49 0.009 1 374 3.32 1.83 0.011 17 311 

2 13 295 1.31 1.31 0.006 0 375 1.49 1.49 0.007 18 329 

8 

9 

71 

35 

20 

17 

16 

15 

12 

11 

12 

12 

11 

9 

11 

14 

16 

13 

52 

56 

50 

43 

37 

31 

26 

21

17 

13 

10 

7 

5 

3 

1 

0 

23 

23 

23 

23 

22 

22 

22 

21 

21 

20 

20 

19 

19 

18 

17 

18 

Floor 

RSA

 ELF

 Wind (10-Year) 

Roof 23 52 71 Roof
 

16
 16 Floor 

15 15
 

14
 14
 

13
 13
 

12
 12
 

11
 11
 

10
 10 

9 

8 

7 7
 

6
 6
 

5
 5
 

4
 4
 

3
 3
 

2
 2 

Base Base 

0 20 40 60 80 0 50 100 150 200 250 300 350 400 

Lateral Force, F x (kips) Story Shear, V (kips) x

(a) Lateral forces (b) Story Shears 

Figure B-8. Drift Design Lateral Forces and Story Shears 

106 

126 

142 

159 

174 

186 

197 

209 

221 

232 

241 

252 

266 

282 

295 

295 

109 

158 

202 

239 

270 

296 

318 

335 

348 

358 

365 

370 

373 

374 

375 

375 

46 

69 

91 

114 

136 

157 

178 

199 

219 

239 

258 

277 

295 

311 

329 

329 

RSA

 ELF

 Wind (10-Year) 

B-11 
 

 

 

 

 

 

5 

6 

7 

8 

12 

13 

14 

15 

16 

0.0076 0.0105 Roof Roof 

16 

15 

14 

0.0100 

0.0119 

0.0120 

0.0113 

0.0119 

0.0125 

0.0125 

0.0122 

0.0123 

0.0123 

0.0116 

0.0104 

0.0099 

0.0089 

0.0061 

0.0061 

0.0128 

0.0137 

0.0149 

0.0156 

0.0167 

0.0174 

0.0169 

0.0157 

0.0155 

0.0153 

0.0150 

0.0141 

0.0131 

0.0109 

0.0069 

0.0069 

 RSA

 ELF 

Allowable Story Drift Ratio, a / h sx 

Floor 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0 5 10 15 20 25 30 35 40 

29.4 

28.1 

26.4 

24.4 

22.4 

20.5 

18.5 

16.4 

14.3 

12.3 

10.2 

8.2 

6.2 

4.5 

2.8 

1.3 

38.1 

36.4 

34.2 

31.9 

29.4 

26.8 

24.0 

21.0 

18.2 

15.6 

13.0 

10.4 

7.9 

5.5 

3.3 

1.5 

 RSA

 ELF 

11 

10 

9

Floor 

4 

3 

2 

Base 

0.000 0.005 0.010 0.015 0.020 

Expected Story Drift Ratio, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-9. Story Drift Ratios and Deflected Shape 

Table B-17 and Table B-18 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and ASCE 7 §12.8.7 for each building design. 

Table B-17. ASCE 7 Allowable Drift and Stability Verification, E-W ME16 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 392 1080 1.28 168 0.008 0.021 0.021 0.52 0.173 

16 583 2444 1.69 168 0.010 0.042 0.040 0.68 0.133 

15 692 3812 2.00 168 0.012 0.066 0.062 0.78 0.116 

14 783 5184 2.02 168 0.012 0.079 0.074 0.81 0.112 

13 874 6570 1.89 168 0.011 0.085 0.078 0.65 0.139 

12 956 7960 1.99 168 0.012 0.099 0.090 0.67 0.137 

11 1022 9355 2.09 168 0.012 0.114 0.102 0.68 0.134 

10 1084 10754 2.10 168 0.012 0.124 0.110 0.68 0.134 

9 1149 12160 2.04 168 0.012 0.129 0.114 0.67 0.135 

8 1216 13570 2.07 168 0.012 0.138 0.121 0.67 0.135 

7 1275 14986 2.07 168 0.012 0.145 0.126 0.68 0.133 

6 1327 16406 1.94 168 0.012 0.143 0.125 0.68 0.134 

5 1386 17837 1.75 168 0.010 0.134 0.118 0.63 0.143 

4 1462 19276 1.67 168 0.010 0.131 0.116 0.61 0.149 

3 1549 20726 1.49 168 0.009 0.118 0.106 0.60 0.150 

2 1622 22207 1.31 216 0.006 0.083 0.077 0.54 0.169 

B-12 
 

 

 

 

 

 

 

Table B-18. ASCE 7 Allowable Drift and Stability Verification, E-W ME16 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 287 1081 1.76 168 0.010 0.040 0.038 0.47 0.194 

16 597 2444 2.16 168 0.013 0.053 0.050 0.61 0.150 

15 870 3822 2.30 168 0.014 0.060 0.057 0.58 0.157 

14 1108 5208 2.51 168 0.015 0.070 0.065 0.64 0.142 

13 1313 6601 2.62 168 0.016 0.078 0.073 0.69 0.131 

12 1486 7997 2.81 168 0.017 0.090 0.082 0.74 0.123 

11 1630 9399 2.92 168 0.017 0.100 0.091 0.78 0.117 

10 1748 10806 2.84 168 0.017 0.104 0.095 0.78 0.116 

9 1843 12221 2.64 168 0.016 0.104 0.094 0.71 0.128 

8 1916 13641 2.60 168 0.015 0.110 0.099 0.69 0.131 

7 1971 15066 2.57 168 0.015 0.117 0.105 0.71 0.127 

6 2010 16496 2.51 168 0.015 0.123 0.109 0.72 0.126 

5 2036 17935 2.37 168 0.014 0.124 0.110 0.75 0.121 

4 2051 19381 2.20 168 0.013 0.124 0.110 0.73 0.125 

3 2058 20843 1.83 168 0.011 0.110 0.099 0.71 0.128 

2 2061 22341 1.49 216 0.007 0.075 0.069 0.59 0.154 

Horizontal Seismic Forces, N-S Direction 

B.1.2.3.1 ME4 (Eccentrically Braced Frame) 

Table B-19 and Table B-20 provide the horizontal seismic forces and story shears for each archetype 

building design for the seismic strength analysis and the drift analysis. The data are also graphically 

illustrated in Figure B-10 through Figure B-12. In these tables, Fy represents the seismic forces acting in 

the N-S direction only. The equivalent story forces for the RSA design are backed out from the story shears 

computed via a modal combination procedure. Although not theoretically correct, the forces provide a 

comparison basis for evaluating variations in the vertical distribution. 

Table B-19. Seismic Strength Design Forces, N-S ME4 

RSA ELF Wind (700-Year) 

Level, x Fy 

(kips) 

Vi 

(kips) 

Fy 

(kips) 

Vi 

(kips) 

VELF / 

VRSA 

Fy 

(kips) 

Vi 

(kips) 

Roof 138 138 153 153 0.90 52 52 

4 100 238 137 291 0.82 50 103 

3 70 308 89 380 0.81 48 150 

2 51 359 45 425 0.85 50 200 

B-13 
 

 

 

2 

3 

4 

2 

3 

4 

Roof 138 153 Roof 52 

Floor Floor 

0 40 80 120 160 

138 

100 

70 

51 

153 

137 

89 

45 

52 

50 

48 

50 RSA

 ELF

 Wind (700-Year) 

Floor 

0 100 200 300 400 500 

238 

308 

359 

359 

291 

380 

425 

425 

103 

150 

200 

200 

 RSA

 ELF

 Wind (700-Year) 

4 

3 

2 

Base Base 

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

Figure B-10. Strength Design Lateral Forces and Story Shears 

Table B-20. Seismic Drift Forces, N-S ME4

 RSA ELF Wind (10-Year) 

Level, x Fy 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fy 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fy 

(kips) 

Vi 

(kips) 

Roof 120 120 4.35 1.02 0.006 137 137 5.14 1.22 0.007 0.02 22 

4 87 207 3.43 1.15 0.007 120 257 3.92 1.40 0.008 0.02 22 

3 61 268 2.34 1.11 0.007 76 333 2.52 1.24 0.007 0.02 20 

2 44 313 1.25 1.26 0.006 37 370 1.28 1.28 0.006 0.02 21 

22 120 137 Roof Roof 

4 

3 

2 

0 40 80 120 160 

120 

87 

61 

44 

137 

120 

76 

37 

22 

22 

20 

21 RSA

 ELF

 Wind (10-Year) 

Floor 

0 100 200 300 400 

207 

268 

313 

313 

257 

333 

370 

370 

44 

64 

86 

86 

 RSA

 ELF

 Wind (10-Year) 

Base Base 

Lateral Force, F x (kips) Story Shear, V x (kips)

(a) Lateral forces (b) Story Shears 

Figure B-11. Drift Design Lateral Forces and Story Shears 

B-14 
 

 

 

 

 

 

 

2 

Roof 0.0055.0072 Roof 4.4 5.1 

0 2 4 6 

RSA

1.3 1.3 

 ELF 

2.3 2.5 

3.4 3.9 

RSA

0.0059 

0.0059 

 ELF 

0.0065 

0.0065 

0.0058 

0.0058 

0.0083 

0.0074 

4 4 

3

Floor 

Allowable Story Drift Ratio, a / h sx

Floor 

3 

2 

Base Base 

0.000 0.005 0.010 0.015 0.020 

Expected Story Drift Ratio, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift Ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-12. Story Drift Ratios and Deflected Shape 

Table B-21 and Table B-22 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and ASCE §12.8.7 for each archetype building design. 

Table B-21. ASCE 7 Allowable Drift and Stability Verification, N-S ME4 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 480 1085 1.02 168 0.006 0.012 0.012 1.00 0.125 

4 828 2457 1.15 168 0.007 0.019 0.019 1.00 0.125 

3 1073 3834 1.11 168 0.007 0.023 0.023 1.00 0.125 

2 1250 5223 1.26 216 0.006 0.024 0.024 1.00 0.125 

Table B-22. ASCE 7 Allowable Drift and Stability Verification, N-S ME4 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 547 1086 1.22 168 0.007 0.014 0.014 1.00 0.125 

4 1027 2465 1.40 168 0.008 0.020 0.020 1.00 0.125 

3 1333 3851 1.24 168 0.007 0.021 0.021 1.00 0.125 

2 1481 5253 1.28 216 0.006 0.021 0.021 1.00 0.125 

B.1.2.3.2 ME8 (Eccentrically Braced Frame) 

Table B-23 and Table B-24 provide the horizontal seismic forces and story shears for each archetype 

building design for the seismic strength analysis and the drift analysis. The data are also graphically 

illustrated in Figure B-13 through Figure B-15. In these tables, Fy represents the seismic forces acting in 

B-15 
 

 

 

 

 

 

 

 

 

 

 

the N-S direction only. The equivalent story forces for the RSA design are backed out from the story shears 

computed via a modal combination procedure. Although not theoretically correct, the forces provide a 

comparison basis for evaluating variations in the vertical distribution. 

Table B-23. Seismic Strength Design Forces, N-S ME8 

RSA ELF Wind (700-Year) 

Level, x Fy 

(kips) 

Vi 

(kips) 

Fy 

(kips) 

Vi 

(kips) 

VELF / 

VRSA 

Fy 

(kips) 

Vi 

(kips) 

Roof 139 139 118 118 1.18 66 66 

8 76 215 119 237 0.91 68 133 

7 27 242 97 334 0.72 66 199 

6 21 264 75 409 0.64 64 263 

5 35 299 55 464 0.64 62 325 

4 48 347 37 502 0.69 59 385 

3 57 404 22 524 0.77 56 441 

2 45 449 9 533 0.84 59 500 

5 

139 

76 

27 

21 

35 

48 

57 

45 

0

118 

119 

97 

75 

55 

37 

22 

9 

0

66 

68 

66 

64 

62 

59 

56 

59 

0 

Floor 

RSA

 ELF

 Wind (700-Year) 

Floor 

66 118 139 Roof
 

8
 

Roof 

8
 

7
 7
 

6
 6
 

5
 

4
 4
 

3
 3
 

2
 2 

Base Base 

0 40 80 120 160 0 100 200 300 400 500 600 

Lateral Force, F x (kips) Story Shear, V x (kips)

(a) Lateral forces (b) Story Shears 

Figure B-13. Strength Design Lateral Forces and Story Shears 

Table B-24. Seismic Drift Forces, N-S ME8

215 

242 

264 

299 

347 

404 

449 

449 

238 

334 

410 

465 

503 

524 

534 

534 

133 

199 

263 

325 

385 

441 

500 

500 

RSA

 ELF

 Wind (700-Year) 

RSA ELF Wind (10-Year) 

Level, x Fy 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fy 

(kips) 

Vi 

(kips) 

x 

(inch) 

i 

(inch)

i / hsx Fy 

(kips) 

Vi 

(kips) 

Roof 97 97 10.72 1.77 0.011 91 91 13.71 1.94 0.012 0.02 27 

8 53 151 9.15 1.97 0.012 89 180 11.77 2.18 0.013 0.02 27 

7 19 170 7.46 1.83 0.011 69 249 9.59 2.17 0.013 0.02 26 

6 15 185 5.88 1.62 0.010 50 299 7.42 2.00 0.012 0.02 26 

5 25 210 4.43 1.48 0.009 35 334 5.42 1.82 0.011 0.02 25 

4 34 244 3.08 1.25 0.007 21 355 3.60 1.48 0.009 0.02 24 

3 40 284 1.90 1.04 0.006 11 366 2.12 1.14 0.007 0.02 22 

2 31 315 0.89 0.90 0.004 4 370 0.98 0.98 0.005 0.02 24 

B-16 
 

 

 

2 

3 

4 

5 

6 

7 

8 

2 

3 

7 

8 

27 8897 Roof Roof 

8 

0 20 40 60 80 100 

97 

53 

19 

15 

25

34 

40 

31 

88 

85 

65 

47 

32 

20 

10 

3 

27 

27 

27 

26 

25 

24 

23 

24 

RSA

 ELF

 Wind (10-Year) 

Floor 

0 100 200 300 400 

151 

170 

185 

210 

244 

284 

315 

315 

173 

238 

285 

317 

337 

347 

350 

350 

55 

81 

107 

132 

156 

178 

202 

202 

RSA

 ELF

 Wind (10-Year) 

7 

6 

5 

4 

3 

2 

Floor Floor Base Base 

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

Figure B-14. Drift Design Lateral Forces and Story Shears 

Roof 

6 

5 

4 

0.0105 0.0115 Roof 

0.0117 

0.0109 

0.0096 

0.0088 

0.0075 

0.0062 

0.0041 

0.0041 

0.0130 

0.0129 

0.0119 

0.0109 

0.0088 

0.0068 

0.0045 

0.0045 

Allowable

 RSA

 ELF 

Allowable Story Drift Ratio, a / h sx 

Floor 

8 

7 

6 

5 

4 

3 

2 

Base 

0 4 8 12 16 

10.7 

9.1 

7.5 

5.9 

4.4 

3.1 

1.9 

0.9 

13.7 

11.8 

9.6 

7.4 

5.4 

3.6 

2.1 

1.0 

RSA

 ELF 

Base 

0.000 0.005 0.010 0.015 0.020 

Expected Story Drift Ratio, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-15. Story Drift Ratios and Deflected Shape 

Table B-25 and Table B-26 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and ASCE §12.8.7 for each archetype building design. 

B-17 
 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-25. ASCE 7 Allowable Drift and Stability Verification, N-S ME8 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 389 1078 1.77 168 0.011 0.026 0.025 1.00 0.125 

8 603 2439 1.97 168 0.012 0.041 0.039 1.00 0.125 

7 680 3805 1.83 168 0.011 0.053 0.050 1.00 0.125 

6 740 5175 1.62 168 0.010 0.060 0.057 1.00 0.125 

5 839 6555 1.48 168 0.009 0.063 0.059 1.00 0.125 

4 975 7941 1.25 168 0.007 0.057 0.054 1.00 0.125 

3 1134 9333 1.04 168 0.006 0.049 0.047 1.00 0.125 

2 1260 10740 0.90 216 0.004 0.035 0.034 1.00 0.125 

Table B-26. ASCE 7 Allowable Drift and Stability Verification, N-S ME8 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 353 1081 1.94 168 0.012 0.042 0.040 1.00 0.125 

8 693 2446 2.18 168 0.013 0.052 0.050 1.00 0.125 

7 953 3825 2.17 168 0.013 0.058 0.055 1.00 0.125 

6 1142 5211 2.00 168 0.012 0.058 0.055 1.00 0.125 

5 1270 6606 1.82 168 0.011 0.060 0.056 1.00 0.125 

4 1348 8006 1.48 168 0.009 0.055 0.052 1.00 0.125 

3 1388 9411 1.14 168 0.007 0.047 0.045 1.00 0.125 

2 1401 10829 0.98 216 0.005 0.033 0.032 1.00 0.125 

B.1.2.3.3 ME16 (Eccentrically Braced Frame) 

Table B-27 and Table B-28 provide the horizontal seismic forces and story shears for each archetype 

building design for the seismic strength analysis and the drift analysis. The data are also graphically 

illustrated in Figure B-16 through Figure B-18. In these tables, Fy represents the seismic forces acting in 

the N-S direction only. The equivalent story forces for the RSA design are backed out from the story shears 

computed via a modal combination procedure. Although not theoretically correct, the forces provide a 

comparison basis for evaluating variations in the vertical distribution. 

Table B-27. Seismic Strength Design Forces, N-S ME16 

Level, x 

RSA 

Fy 

(kips) 

Vi 

(kips) 

Fy 

(kips) 

ELF 

Vi 

(kips) 

VELF / VRSA 

Wind (700-Year) 

Fy 

(kips) 

Vi 

(kips) 

Roof 170 170 133 133 1.28 83 83 

16 120 290 144 277 1.04 89 172 

15 56 346 127 405 0.85 88 260 

14 20 365 111 516 0.71 87 347 

13 9 375 96 611 0.61 86 432 

12 14 389 81 692 0.56 85 517 

11 23 412 68 760 0.54 83 600 

10 30 442 55 815 0.54 82 682 

9 32 474 45 860 0.55 80 762 

8 34 508 35 895 0.57 79 841 

7 41 548 26 921 0.60 77 918 

6 50 598 19 939 0.64 75 993 

5 58 657 12 951 0.69 72 1065 

4 62 719 7 959 0.75 70 1135 

3 55 774 4 962 0.80 66 1201 

2 36 810 1 964 0.84 70 1271 

B-18 
 

 

 

 

 

 

 

 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

133170 Roof 83

Roof 

16 

15 

14 

13 

Floor 

0 20 40 60 80 100 120 140 160 180 

170 

120 

56 

20 

9 

14 

23 

30 

32 

34

41 

50 

58 

62 

55 

36 

133 

144 

127 

110 

95 

81 

67 

55 

44 

34 

26 

18 

12 

7 

4 

1 

83 

89 

88 

87 

86 

85 

83 

82 

80 

79 

77 

75 

72 

70 

66 

70 

RSA

 ELF

 Wind (700-Year) 

Floor 

0 200 400 600 800 1000 1200 1400 

290 

346 

365 

375 

389 

412 

442 

474 

508 

548 

598 

657 

719 

774 

810 

810 

277 

405 

516 

611 

692 

760 

815 

860 

895 

921 

939 

951 

959 

962 

964 

964 

172 

260 

347 

432 

517 

600 

682 

762 

841 

918 

993 

1065 

1135 

1201 

1271 

1271 

RSA

 ELF

 Wind (700-Year) 

4 

3 

2 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base Base

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

Figure B-16. Strength Design Lateral Forces and Story Shears 

Table B-28. Summary of Seismic Drift Forces, N-S ME16

Level, x Fy 

(kips) 

Vi 

(kips) 

RSA 

x 

(inch) 

i 

(inch)

i / hsx Fy 

(kips) 

Vi 

(kips) 

ELF 

x 

(inch) 

i 

(inch)

i / hsx 

Wind (10-Year) 

Fy 

(kips) 

Vi 

(kips) 

Roof 99 99 17.56 1.59 0.009 70 70 22.68 1.69 0.010 0.02 34 

16 70 169 16.09 1.72 0.010 76 146 20.99 1.83 0.011 0.02 34 

15 33 202 14.57 1.77 0.011 67 213 19.15 1.89 0.011 0.02 34 

14 12 214 13.02 1.74 0.010 58 271 17.27 1.92 0.011 0.02 34 

13 6 220 11.50 1.65 0.010 50 322 15.34 1.88 0.011 0.02 33 

12 8 228 10.05 1.53 0.009 42 364 13.47 1.82 0.011 0.02 33 

11 14 242 8.70 1.39 0.008 35 400 11.65 1.73 0.010 0.02 32 

10 17 259 7.47 1.28 0.008 29 428 9.93 1.62 0.010 0.02 32 

9 19 278 6.32 1.19 0.007 23 452 8.30 1.52 0.009 0.02 31 

8 20 297 5.26 1.08 0.006 18 470 6.78 1.37 0.008 0.02 30 

7 24 321 4.28 0.98 0.006 13 483 5.41 1.25 0.007 0.02 30 

6 29 350 3.38 0.88 0.005 10 493 4.16 1.12 0.007 0.02 29 

5 34 384 2.56 0.78 0.005 6 499 3.04 0.99 0.006 0.02 28 

4 36 420 1.82 0.70 0.004 4 503 2.06 0.85 0.005 0.02 27 

3 32 453 1.14 0.61 0.004 2 505 1.21 0.67 0.004 0.02 26 

2 21 474 0.54 0.54 0.003 1 505 0.54 0.54 0.002 0.02 27 

B-19 
 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

34 70 99 Roof 99 Roof 

16 

15 

14 

13 

0 20 40 60 80 100 

70 

33 

12 

6 

8 

14 

17 

19 

20 

24 

29

34 

36 

32 

21 

70 

76 

67 

58 

50 

42 

35 

29 

23 

18 

13 

10 

6 

4 

2 

1 

34 

34 

34 

34 

33 

33 

32 

32 

31 

30 

30 

29 

28 

27 

26 

27 

RSA

 ELF

 Wind (10-Year) 

Floor 

169 

202 

214 

220 

228 

242 

259 

278 

297 

321 

350 

384 

420 

453 

474 

474 

146 

213 

271 

322 

364 

400 

428 

452 

470 

483 

493 

499 

503 

505 

505 

505 

68 

102 

136 

169 

202 

234 

266 

297 

327 

357 

386 

414 

441 

467 

494 

494 

RSA

 ELF

 Wind (10-Year) 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Floor Floor 

4 

3 

2 

Base Base 

0 100 200 300 400 500
 

Lateral Force, F x (kips) Story Shear, V (kips) x

(a) Lateral forces (b) Story Shears 

Figure B-17. Drift Design Lateral Forces and Story Shears 

Roof 

16 

15 

14 

13 

12 

11 

10 

9 

8 

Roof 0.0095 0.0101 

0.0102 

0.0105 

0.0104 

0.0099 

0.0091 

0.0083 

0.0076 

0.0071 

0.0064 

0.0058 

0.0053 

0.0046 

0.0042 

0.0036 

0.0025 

0.0025 

0.0109 

0.0112 

0.0114 

0.0112 

0.0108 

0.0103 

0.0097 

0.0090 

0.0082 

0.0074 

0.0067 

0.0059 

0.0050 

0.0040 

0.0025 

0.0025 

RSA

 ELF 

Allowable Story Drift Ratio, a / h sx 

Floor 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0 4 8 12 16 20 24 28 

17.6 

16.1 

14.6 

13.0 

11.5 

10.1 

8.7 

7.5 

6.3 

5.3 

4.3 

3.4 

2.6 

1.8 

1.1 

0.5 

22.7 

21.0 

19.2 

17.3 

15.3 

13.5 

11.7 

9.9 

8.3 

6.8 

5.4 

4.2 

3.0 

2.1 

1.2 

0.5 

RSA

 ELF 

7 

6 

5 

4 

3 

2 

Base 

0.000 0.005 0.010 0.015 0.020 

Expected Story Drift Ratio, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-18. Story Drift Ratios and Deflected Shape 

Table B-29 and Table B-30 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and §12.8.7 for each archetype building design. 

B-20 

600 
 

 

 

 

 

 

 

 

Table B-29. ASCE 7 Allowable Drift and Stability Verification, N-S ME16 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 397 1084 1.59 168 0.009 0.024 0.023 1.00 0.125 

16 677 2452 1.72 168 0.010 0.033 0.032 1.00 0.125 

15 808 3823 1.77 168 0.011 0.044 0.042 1.00 0.125 

14 855 5197 1.74 168 0.010 0.055 0.052 1.00 0.125 

13 878 6585 1.65 168 0.010 0.065 0.061 1.00 0.125 

12 912 7980 1.53 168 0.009 0.070 0.066 1.00 0.125 

11 967 9379 1.39 168 0.008 0.071 0.067 1.00 0.125 

10 1036 10781 1.28 168 0.008 0.071 0.066 1.00 0.125 

9 1110 12190 1.19 168 0.007 0.070 0.065 1.00 0.125 

8 1190 13605 1.08 168 0.006 0.066 0.062 1.00 0.125 

7 1285 15024 0.98 168 0.006 0.063 0.059 1.00 0.125 

6 1401 16447 0.88 168 0.005 0.058 0.054 1.00 0.125 

5 1537 17883 0.78 168 0.005 0.051 0.049 1.00 0.125 

4 1682 19327 0.70 168 0.004 0.046 0.044 1.00 0.125 

3 1810 20779 0.61 168 0.004 0.041 0.039 1.00 0.125 

2 1894 22258 0.54 216 0.003 0.030 0.029 1.00 0.125 

Table B-30. ASCE 7 Allowable Drift and Stability Verification, N-S ME16 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 249 1084 1.69 168 0.010 0.059 0.056 1.00 0.125 

16 517 2452 1.83 168 0.011 0.068 0.064 1.00 0.125 

15 753 3833 1.89 168 0.011 0.074 0.068 1.00 0.125 

14 959 5221 1.92 168 0.011 0.078 0.072 1.00 0.125 

13 1136 6617 1.88 168 0.011 0.081 0.075 1.00 0.125 

12 1286 8018 1.82 168 0.011 0.083 0.077 1.00 0.125 

11 1411 9424 1.73 168 0.010 0.084 0.077 1.00 0.125 

10 1513 10834 1.62 168 0.010 0.083 0.077 1.00 0.125 

9 1595 12252 1.52 168 0.009 0.082 0.076 1.00 0.125 

8 1659 13677 1.37 168 0.008 0.079 0.073 1.00 0.125 

7 1706 15106 1.25 168 0.007 0.076 0.070 1.00 0.125 

6 1740 16542 1.12 168 0.007 0.071 0.067 1.00 0.125 

5 1762 17985 0.99 168 0.006 0.066 0.062 1.00 0.125 

4 1775 19436 0.85 168 0.005 0.058 0.055 1.00 0.125 

3 1782 20899 0.67 168 0.004 0.047 0.045 1.00 0.125 

2 1784 22393 0.54 216 0.002 0.028 0.028 1.00 0.125 

B.2 Horizontal and Vertical Irregularities 

Special Moment Frame 

Table B-31 through Table B-34 provide the results for the horizontal (type 1) and vertical (type 1 and 5) 

irregularity verifications. 

B-21 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-31. Horizontal Irregularity Type 1 (a and b) Verification 

1 max / avg 

ME4 ME8 ME16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof ME16 - - - - 1.015 1.012 

16 - - - - 1.011 1.009 

15 - - - - 1.012 1.008 

14 - - - - 1.011 1.007 

13 - - - - 1.010 1.008 

12 - - - - 1.010 1.007 

11 - - - - 1.009 1.007 

10 - - - - 1.009 1.007 

9 (Roof ME8) - - 1.016 1.011 1.008 1.007 

8 - - 1.013 1.009 1.009 1.007 

7 - - 1.012 1.008 1.008 1.006 

6 - - 1.011 1.007 1.008 1.007 

5 (Roof ME4) 1.007 1.006 1.009 1.006 1.007 1.006 

4 1.006 1.004 1.008 1.005 1.007 1.007 

3 1.005 1.004 1.008 1.006 1.011 1.009 

2 1.004 1.003 1.006 1.004 1.004 1.005 

1. Values include accidental torsion with Ax = 1.0. 

Table B-32. Vertical Irregularity Type 1 (a and b) Verification (Exception 1) 

( / hsx) x / ( / hsx) x+1 1

 ME4 ME8 ME16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof ME16 - - - - - -

16 - ­ - ­ 1.22 1.27 

15 - ­ - ­ 1.07 1.13 

14 - ­ - ­ 1.09 0.97 

13 - ­ - ­ 1.04 0.89 

12 - ­ - ­ 1.07 1.02 

11 - ­ - ­ 1.04 1.02 

10 - ­ - ­ 0.97 0.98 

9 (Roof ME8) - - - - 0.93 0.95 

8 - - 1.26 1.20 0.99 1.00 

7 - - 0.99 1.07 0.99 0.98 

6 - - 1.07 1.02 0.98 0.93 

5 (Roof ME4) - - 1.02 0.95 0.94 0.88 

4 1.32 1.35 1.02 1.00 0.93 0.94 

3 1.11 1.19 0.95 0.94 0.83 0.90 

2 0.82 0.67 0.77 0.60 0.63 0.67 

1.  is taken at the center of mass per ASCE 7 §12.8.6. 

n 

2M , 

V  j1 

prj (B-5) 

y i, h 

h h sx sx 1 h  (B-6) 2 

B-22 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-33. Vertical Irregularity Type 5 (a and b) Verification, ELF (kip, feet) 

MC4 MC8 MC16 

Floor (x) h c Mpr a Vy,x b Vy,x+1 / Vy,x Mpr a Vy,x b Vy,x+1 / Vy,x Mpr a Vy,x b Vy,x+1 / Vy,x 

Roof MC16 7 - - - - - - 491.1 421.0 -

16 14 - - - - - - 491.1 210.5 0.50 

15 14 - - - - - - 951.8 407.9 1.94 

14 14 - - - - - - 951.8 407.9 1.00 

13 14 - - - - - - 1242.1 532.3 1.31 

12 14 - - - - - - 1242.1 532.3 1.00 

11 14 - - - - - - 1242.1 532.3 1.00 

10 14 - - - - - - 1242.1 532.3 1.00 

9 (Roof MC8) 14 / 7 - - - 491.1 421.0 - 1662.3 712.4 1.34 

8 14 - - - 491.1 210.5 0.50 1662.3 712.4 1.00 

7 14 - - - 951.8 407.9 1.94 1662.3 712.4 1.00 

6 14 - - - 951.8 407.9 1.00 1662.3 712.4 1.00 

5 (Roof MC4) 14 / 7 491.1 421.0 - 1161.6 497.8 1.22 1662.3 712.4 1.00 

4 14 679.7 291.3 0.69 1161.6 497.8 1.00 1662.3 712.4 1.00 

3 14 754.6 323.4 1.11 1161.6 497.8 1.00 1662.3 712.4 1.00 

2 16 754.6 283.0 0.88 1161.6 435.6 0.88 1662.3 623.3 0.88 

a. Mpr is for a single beam plastic hinge at the center of the RBS. 

b. Vyx is computed neglecting the plastic moment strength of the adjacent columns. 

c. h is taken as the distance from midheight of a story to mid-height of the story above ( ≠ hsx). 

Table B-34. Vertical Irregularity Type 5 (a and b) Verification, RSA 

MC4 MC8 MC16 

Floor (x) h c Mpr a Vy,x b Vy,x+1 / Vy,x Mpr a Vy,x b Vy,x+1 / Vy,x Mpr a Vy,x b Vy,x+1 / Vy,x 

Roof MC16 7 - - - ­ - ­ 491.1 421.0 -

16 14 - - - ­ - ­ 491.1 210.5 0.50 

15 14 - - - ­ - ­ 491.1 210.5 1.00 

14 14 - - - ­ - ­ 491.1 210.5 1.00 

13 14 - - - ­ - ­ 951.8 407.9 1.94 

12 14 - - - ­ - ­ 951.8 407.9 1.00 

11 14 - - - ­ - ­ 951.8 407.9 1.00 

10 14 - - - ­ - ­ 951.8 407.9 1.00 

9 (Roof MC8) 14 / 7 - - - 358.7 307.5 - 1242.1 532.3 1.31 

8 14 - - - 358.7 153.7 0.50 1242.1 532.3 1.00 

7 14 - - - 491.1 210.5 1.37 1242.1 532.3 1.00 

6 14 - - - 491.1 210.5 1.00 1242.1 532.3 1.00 

5 (Roof MC4) 14 / 7 491.1 421.0 - 679.7 291.3 1.38 1662.3 712.4 1.34 

4 14 491.1 210.5 0.50 679.7 291.3 1.00 1662.3 712.4 1.00 

3 14 491.1 210.5 1.00 754.6 323.4 1.11 1662.3 712.4 1.00 

2 16 491.1 184.2 0.88 754.6 283.0 0.88 1662.3 623.3 0.88 

a. Mpr is for a single beam plastic hinge at the center of the RBS. 

b. Vyx is computed neglecting the plastic moment strength of the adjacent columns. 

c. h is taken as the distance from mid-height of a story to mid-height of the story above ( ≠ hsx).

 Eccentrically Braced Frame 

Table B-35 through Table B-34 provide the results for the horizontal (type 1) and vertical (type 1 and 5) 

irregularity verifications. 

B-23 
 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-35. Horizontal Irregularity Type 1 (a and b) Verification 

a max / avg 

ME4 ME8 ME16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof ME16 - - - - 1.073 1.069 

16 - - - - 1.066 1.066 

15 - - - - 1.065 1.067 

14 - - - - 1.070 1.066 

13 - - - - 1.070 1.067 

12 - - - - 1.069 1.068 

11 - - - - 1.072 1.070 

10 - - - - 1.071 1.068 

9 (Roof 

ME8) - - 1.070 1.073 1.075 1.071 

8 - - 1.067 1.073 1.070 1.069 

7 - - 1.067 1.073 1.074 1.071 

6 - - 1.067 1.074 1.074 1.073 

5 (Roof 

ME4) 1.054 1.064 1.072 1.075 1.076 1.072 

4 1.077 1.075 1.070 1.073 1.075 1.068 

3 1.072 1.079 1.084 1.087 1.129 1.100 

2 1.080 1.081 1.087 1.090 1.161 1.097 

a. Values include accidental torsion with Ax = 1.0. 

Table B-36. Vertical Irregularity Type 1 (a and b) Verification (Exception 1) 

a ( / hsx) x / ( / hsx) x+1 

ME4 ME8 ME16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof ME16 - - - - - -

16 - - - - 1.08 1.08 

15 - - - - 1.03 1.03 

14 - - - - 1.02 0.98 

13 - - - - 0.98 0.95 

12 - - - - 0.97 0.93 

11 - - - - 0.95 0.91 

10 - - - - 0.94 0.92 

9 (Roof ME8) - - - - 0.93 0.93 

8 - - 1.12 1.11 0.91 0.91 

7 - - 1.00 0.93 0.91 0.91 

6 - - 0.92 0.89 0.90 0.90 

5 (Roof ME4) - - 0.91 0.91 0.88 0.88 

4 1.15 1.13 0.81 0.85 0.86 0.90 

3 0.89 0.96 0.77 0.83 0.79 0.87 

2 0.80 0.68 0.67 0.52 0.62 0.70 

a.  is taken at the center of mass per ASCE 7 §12.8.6. 

b V y i,  Vn, lin k hsx (B-7) 

[b = 20 ft. for ME4 and ME8, b = 30 ft. for ME16] 

B-24 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-37. Vertical Irregularity Type 5 (a and b) Verification, ELF (kip, feet) 

ME4 ME8 ME16 

Floor (x) hsx Vn Vy,x a Vy,x+1 / Vy,x Vn Vy,x a Vy,x+1 / Vy,x Vn Vy,x a Vy,x+1 / Vy,x 

Roof ME16 14 - - - - - 128.6 275.6 -

16 14 - - - - - 128.6 275.6 1.00 

15 14 - - - - - 159.2 341.2 1.24 

14 14 - - - - - 159.2 341.2 1.00 

13 14 - - - - - 197.0 422.2 1.24 

12 14 - - - - - 209.3 448.5 1.06 

11 14 - - - - - 240.6 515.5 1.15 

10 14 - - - - - 254.5 545.4 1.06 

9 (Roof ME8) 14 - - - 99.9 142.7 - 269.2 576.8 1.06 

8 14 - - - 121.6 173.6 1.22 304.8 653.2 1.13 

7 14 - - - 154.9 221.3 1.27 304.8 653.2 1.00 

6 14 - - - 197.0 281.5 1.27 304.8 653.2 1.00 

5 (Roof ME4) 14 99.9 142.7 - 209.3 299.0 1.06 304.8 653.2 1.00 

4 14 121.6 173.6 1.22 240.6 343.7 1.15 304.8 653.2 1.00 

3 14 171.5 244.9 1.41 240.6 343.7 1.00 304.8 653.2 1.00 

2 18 237.0 263.4 1.08 304.8 338.7 0.99 371.9 619.9 0.95 

a. Vyx is computed neglecting the plastic moment strength of the adjacent columns. 

Table B-38. Vertical Irregularity Type 5 (a and b) Verification, RSA (kip, feet) 

ME4 ME8 ME16 

Floor (x) hsx Vn Vy,x a Vy,x+1 / Vy,x Vn Vy,x a Vy,x+1 / Vy,x Vn Vy,x a Vy,x+1 / Vy,x 

Roof ME16 14 - - - - - 121.6 260.5 -

16 14 - - - - - 121.6 260.5 1.00 

15 14 - - - - - 121.6 260.5 1.00 

14 14 - - - - - 121.6 260.5 1.00 

13 14 - - - - - 121.6 260.5 1.00 

12 14 - - - - - 154.9 332.0 1.27 

11 14 - - - - - 179.6 384.8 1.16 

10 14 - - - - - 197.0 422.2 1.10 

9 (Roof ME8) 14 - - - 99.9 142.7 - 224.9 482.0 1.14 

8 14 - - - 99.9 142.7 1.00 237.2 508.4 1.05 

7 14 - - - 123.9 177.0 1.24 254.5 545.4 1.07 

6 14 - - - 137.2 195.9 1.11 254.5 545.4 1.00 

5 (Roof ME4) 14 99.9 142.7 - 159.2 227.5 1.16 269.2 576.8 1.06 

4 14 121.6 173.6 1.22 182.4 260.6 1.15 269.2 576.8 1.00 

3 14 154.9 221.3 1.27 197.0 281.5 1.08 269.2 576.8 1.00 

2 18 204.5 227.2 1.03 304.8 338.7 1.20 371.9 619.9 1.07 

a. Vyx is computed neglecting the plastic moment strength of the adjacent columns. 

B.3 SMF AISC Frame Stability (Effective Length Method) 

Table B-39 through Table B-44 provide the results from AISC 360, appendix 7 Effective Length Method 

verifications. 

B-25 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B-39. AISC 360 Frame Stability (Effective Length Method), 4-Story SMF ELF (kip, inch) 

a b Pstory H H L Rm Pe story B2 

1314 2.24 499.9 168 0.954 35716 1.04 

2936 2.92 897.8 168 0.954 49223 1.06 

4574 3.21 1120.0 168 0.954 55854 1.09 

6235 3.38 1208.0 216 0.954 73615 1.09 

1. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

2. H and H are determined from a first-order static analysis using ASCE 7 §12.8.6. 

Table B-40. AISC 360 Frame Stability (Effective Length Method), 4-Story SMF RSA (kip, inch) 

a b Pstory H H L Rm Pe story B2 

1309 2.51 435.5 168 0.954 27764 1.05 

2925 3.50 765.8 168 0.954 35055 1.09 

4547 3.97 938.0 168 0.954 37806 1.14 

6192 4.13 999.6 216 0.954 49870 1.14 

1. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

2. H and H are determined from a first-order static analysis using ASCE 7 §12.8.6. 

Table B-41. AISC 360 Frame Stability (Effective Length Method), 8-Story SMF ELF (kip, inch) 

a b Pstory H H L Rm Pe story B2 

1300 2.15 392.5 168 0.954 29312 1.05 

2901 2.68 764.5 168 0.954 45678 1.07 

4525 2.64 1045.2 168 0.954 63361 1.08 

6158 2.79 1244.9 168 0.954 71414 1.09 

7803 2.81 1377.1 168 0.954 78453 1.11 

9452 2.83 1455.0 168 0.954 82282 1.13 

11115 2.68 1493.0 168 0.954 89151 1.14 

12806 2.66 1505.3 216 0.954 116595 1.12 

1. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

2. H and H are determined from a first-order static analysis using ASCE 7 §12.8.6. 

Table B-42. AISC 360 Frame Stability (Effective Length Method), 8-Story SMF RSA (kip, inch) 

a b Pstory H H L Rm Pe story B2 

1297 5.76 665.9 168 0.954 18506 1.08 

2893 7.62 1297.1 168 0.954 27284 1.12 

4501 8.56 1770.7 168 0.954 33134 1.16 

6114 8.74 2107.1 168 0.954 38612 1.19 

7741 8.11 2330.3 168 0.954 46054 1.20 

9373 7.72 2462.1 168 0.954 51065 1.22 

11021 6.83 2526.7 168 0.954 59299 1.23 

12697 6.44 2547.5 216 0.954 81474 1.18 

1. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

2. H and H are determined from a first-order static analysis using ASCE 7 §12.8.6. 

B-26 
 

 

 

 

 

 

 

 

 

 

Table B-43. AISC 360 Frame Stability (Effective Length Method), 16-Story SMF ELF (kip, inch) 

Pstory a H b H L Rm Pe story B2 

1297 1.62 278.1 168 0.954 27566 1.05 

2895 1.97 578.3 168 0.954 47016 1.07 

4509 2.09 843.4 168 0.954 64592 1.08 

6133 2.26 1073.9 168 0.954 76131 1.09 

7766 2.34 1272.1 168 0.954 86953 1.10 

9403 2.49 1439.8 168 0.954 92517 1.11 

11046 2.57 1579.7 168 0.954 98355 1.13 

12695 2.50 1694.0 168 0.954 108744 1.13 

14355 2.31 1785.7 168 0.954 123781 1.13 

16020 2.27 1856.8 168 0.954 131214 1.14 

17691 2.24 1909.9 168 0.954 136851 1.15 

19369 2.18 1947.6 168 0.954 143441 1.16 

21056 2.05 1972.5 168 0.954 154360 1.16 

22754 1.91 1987.2 168 0.954 167096 1.16 

24469 1.60 1994.5 168 0.954 199929 1.14 

26227 1.32 1996.8 216 0.954 311432 1.09 

1. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

2. H and H are determined from a first-order static analysis using ASCE 7 §12.8.6. 

Table B-44. AISC 360 Frame Stability (Effective Length Method), 16-Story SMF RSA (kip, inch) 

Pstory a H b H L Rm Pe story B2 

1296 2.83 390.9 168 0.954 22100 1.06 

2893 3.88 812.9 168 0.954 33576 1.09 

4496 4.75 1182.8 168 0.954 39868 1.13 

6105 4.89 1503.8 168 0.954 49305 1.14 

7728 4.56 1781.0 168 0.954 62558 1.14 

9358 4.71 2015.7 168 0.954 68592 1.16 

10993 4.83 2211.3 168 0.954 73302 1.18 

12634 4.73 2371.3 168 0.954 80383 1.19 

14282 4.45 2499.2 168 0.954 90046 1.19 

15936 4.34 2598.5 168 0.954 95899 1.20 

17595 4.17 2672.7 168 0.954 102632 1.21 

19260 3.78 2725.3 168 0.954 115496 1.20 

20939 3.25 2760.2 168 0.954 136170 1.18 

22627 2.94 2780.8 168 0.954 151337 1.18 

24328 2.50 2790.8 168 0.954 178505 1.16 

26067 2.16 2794.1 216 0.954 267012 1.11 

1. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

2. H and H are determined from a first-order static analysis using ASCE 7 §12.8.6 

Table B-45. Adjusted Effective Length Factors – 4-Story SMF 

ELF RSA 

Story K2x (note a) K2x (note a) K2x (note a) K2x (note a) 

Exterior Interior Exterior Interior 

4 2.23 2.98 2.46 3.08 

3 2.44 3.26 2.99 3.74 

2 2.54 3.37 3.08 3.86 

1 2.42 3.21 2.58 3.23 

a. x designates in-plane buckling about x-axis as depicted in AISC 360 Part 1. 

B-27 
 

 

 

 

 

Table B-46. Adjusted Effective Length Factors – 8-Story SMF 

ELF RSA 

Story K2x (note a) K2x (note a) K2x (note a) K2x (note a) 

Exterior Interior Exterior Interior 

8 2.18 2.75 2.59 2.74 

7 2.12 2.67 2.61 2.76 

6 2.09 2.80 2.26 3.21 

5 2.04 2.74 2.16 3.08 

4 2.04 2.88 2.20 3.38 

3 1.99 2.81 2.27 3.48 

2 2.09 3.21 2.44 3.82 

1 2.03 3.11 2.24 3.51 

a. x designates in-plane buckling about x-axis as depicted in AISC 360 Part 1. 

Table B-47. Adjusted Effective Length Factors – 16-Story SMF 

ELF RSA 

Story K2x (note a) K2x (note a) K2x (note a) K2x (note a) 

Exterior Interior Exterior Interior 

16 3.09 2.46 2.51 2.64 

15 3.33 2.65 2.41 2.53 

14 2.66 2.80 2.11 2.73 

13 2.46 2.59 2.02 2.61 

12 2.29 2.52 2.17 2.66 

11 2.20 2.43 2.29 2.81 

10 2.05 2.49 2.11 2.90 

9 2.01 2.43 2.05 2.81 

8 1.97 2.70 2.21 2.89 

7 2.07 2.84 2.32 3.04 

6 2.03 3.21 2.22 3.43 

5 1.97 3.12 2.09 3.22 

4 2.08 3.21 2.88 3.11 

3 2.07 3.20 3.79 4.09 

2 2.69 3.25 3.48 4.20 

1 2.62 3.17 2.62 3.17 

a. x designates in-plane buckling about x-axis as depicted in AISC 360 Part 1. 

B.4 Eccentrically Braced Frame Plastic Link Rotation 

Figure B-19 through Figure B-21 illustrate the design link rotation angles for the 4-, 8-, and 16-story frames, 

respectively. The links in the 8- and 16-story frames have high link rotation demands in the upper stories 

using the approach prescribed by the code. Research (Richards and Thompson 2009) has shown how current 

procedures based on elastic analysis can overestimate the expected link rotation angle, as compared to 

results from a nonlinear analysis. Further, included in the figures for comparison is the acceptance criterion 

for the Life Safety SPL for link rotation angle from ASCE 41; note that the seismic hazard for BSE-1 given 

the BSO criteria and design per ASCE 7 are identical at maximum demand (i.e., 2⁄3×MCER). 

B-28 
 

 

 

 

 

 

 

 

 

 

 

2 

3 

4 

Floor 

Table B-48. 4-Story EBF ELF, Shear Link Parameters 

Floor Link 

Member 

e 

(inch) 

1.6Mp/Vp 

(inch) eVp/Mp 

Demand-to-Capacity Ratio 

(DCR) 

EQ Wind 

Plastic Story 

Drift, xp,s

(inch)

Link 

Rotation 

Angle 

(rad) 

Roof W14X26 30 32.2 1.49 0.64 0.19 0.91 0.043 

4 W14X38 30 40.5 1.19 1.00 0.29 1.05 0.050 

3 W16X50 30 42.9 1.12 0.93 0.29 0.93 0.044 

2 W16X89 30 59.1 0.81 0.97 0.35 0.96 0.036 

Table B-49. 4-Story EBF RSA, Shear Link Parameters 

Floor Link 

Member 

e 

(inch) 

1.6Mp/Vp 

(inch) eVp/Mp 

Demand-to-Capacity Ratio 

(DCR) 

EQ Wind 

Plastic Story 

Drift, xp,s

(inch)

Link 

Rotation 

Angle 

(rad) 

Roof W14X26 30 32.2 1.49 0.58 0.19 0.77 0.036 

4 W14X38 30 40.5 1.19 0.83 0.29 0.86 0.041 

3 W16X45 30 42.5 1.13 0.84 0.33 0.83 0.040 

2 W16X77 30 58.7 0.82 0.96 0.41 0.73 0.027 

1.22 Roof Roof 1.02 

0.0 0.5 1.0 1.5 2.0 

1.15 

1.11 

0.98 

1.40 

1.24 

1.28 

RSA

 ELF 

Floor

Life Safety (LS) Acceptance Criteria

(per ASCE 41 Table 5-6) 

Design - ELF 

Design - RSA 

Allowable Rotation Angle

(per AISC 341 Section F3.4a) 

0.00 0.02 0.04 0.06 0.08 0.10 0.12 

4 

3 

2 

Base Base 

Design Story Drift, x (inch) Plastic Link Rotation Angle (radians) 

(a) design story drift at center of mass (b) plastic rotation of link beams 

Figure B-19. Link Rotation Angle, 4-Story EBF ELF and RSA 

B-29 
 

 

 

 

 

 

 

 

 

2 

3 

4 

5 

6 

Floor 

Table B-50. 8-Story EBF ELF, Shear Link Parameters 

Demand-to-Capacity Ratio Plastic Link 

Floor Link 

Member 

e 

(inch) 

1.6Mp/Vp 

(inch) eVp/Mp 

EQ

(DCR) 

 Wind 

Story 

Drift, xp,s

(inch)

Rotation 

Angle 

(rad) 

Roof W14X26 30 32.2 1.49 0.50 0.21 1.45 0.069 

8 W14X38 30 40.5 1.19 0.82 0.35 1.63 0.078 

7 W16X45 30 42.5 1.13 0.91 0.41 1.63 0.078 

6 W18X55 30 45.5 1.06 0.87 0.43 1.50 0.071 

5 W18X60 30 47.0 1.02 0.93 0.49 1.37 0.065 

4 W21X57 30 42.9 1.12 0.88 0.52 1.11 0.053 

3 W21X57 30 42.9 1.12 0.92 0.59 0.85 0.041 

2 W21X83 30 51.4 0.93 0.95 0.67 0.73 0.027 

Table B-51. 8-Story EBF RSA, Shear Link Parameters 

Demand-to-Capacity Ratio Plastic Link 

Floor Link 

Member 

e 

(inch) 

1.6Mp/Vp 

(inch) eVp/Mp 

EQ

(DCR) 

 Wind 

Story 

Drift, xp,s

(inch)

Rotation 

Angle 

(rad) 

Roof W14X26 30 32.2 1.49 0.59 0.22 1.33 0.063 

8 W14X26 30 32.2 1.49 0.92 0.44 1.47 0.070 

7 W16X31 30 34.9 1.38 0.84 0.53 1.37 0.065 

6 W16X40 30 42.6 1.13 0.84 0.63 1.21 0.058 

5 W18X40 30 39.4 1.22 0.81 0.68 1.11 0.053 

4 W18X46 30 39.8 1.21 0.81 0.69 0.94 0.045 

3 W18X55 30 45.5 1.06 0.87 0.73 0.78 0.037 

2 W21X83 30 51.4 0.93 0.80 0.68 0.52 0.019 

1.94 Roof Roof 1.77 

0.0 0.5 1.0 1.5 2.0 2.5 

1.97 

1.83 

1.62 

1.48 

1.25 

1.04 

0.70 

2.18 

2.17 

2.00 

1.82 

1.48 

1.14 

0.98 

RSA

 ELF 

Floor

Life Safety (LS) Acceptance Criteria

(per ASCE 41 Table 5-6) 

 Design - ELF

 Design - RSA 

Allowable Rotation Angle

(per AISC 341 Section F3.4a) 

0.00 0.02 0.04 0.06 0.08 0.10 0.12 

8 

7 

8 

7 

6 

5 

4 

3 

2 

Base Base 

Design Story Drift, x (inch) Plastic Link Rotation Angle (radians)

(a) design story drift at center of mass (b) plastic rotation of link beams 

Figure B-20. Link Rotation Angle, 8-Story EBF ELF and RSA 

B-30 
 

 

 

 

 

 

 

 

 

 

Table B-52. 16-Story EBF ELF, Shear Link Parameters 

Demand-to-Capacity Ratio Plastic Link 

Floor Link 

Member 

e 

(inch) 

1.6Mp/Vp 

(inch) eVp/Mp 

EQ

(DCR) 

 Wind 

Story 

Drift, xp,s

(inch)

Rotation 

Angle 

(rad) 

Roof W14X48 39 48.8 1.28 0.27 0.13 1.27 0.070 

16 W14X48 39 48.8 1.28 0.56 0.28 1.37 0.076 

15 W18X40 39 39.4 1.58 0.66 0.35 1.42 0.078 

14 W18X40 39 39.4 1.58 0.84 0.46 1.44 0.079 

13 W18X55 39 45.5 1.37 0.80 0.46 1.41 0.077 

12 W18X60 39 47.0 1.33 0.85 0.51 1.36 0.075 

11 W21X57 39 42.9 1.45 0.82 0.53 1.29 0.071 

10 W21X68 39 50.3 1.24 0.83 0.56 1.22 0.067 

9 W21X73 39 51.1 1.22 0.82 0.59 1.14 0.062 

8 W21X83 39 51.4 1.21 0.76 0.57 1.03 0.057 

7 W21X83 39 51.4 1.21 0.78 0.62 0.94 0.051 

6 W21X83 39 51.4 1.21 0.79 0.67 0.84 0.046 

5 W21X83 39 51.4 1.21 0.80 0.72 0.74 0.041 

4 W21X83 39 51.4 1.21 0.81 0.77 0.64 0.035 

3 W21X83 39 51.4 1.21 0.81 0.81 0.50 0.028 

2 W24X103 39 60.2 1.04 0.86 0.91 0.40 0.017 

Table B-53. 16-Story EBF RSA, Shear Link Parameters 

Demand-to-Capacity Ratio Plastic Link 

Floor Link 

Member 

e 

(inch) 

1.6Mp/Vp 

(inch) eVp/Mp 

EQ

(DCR) 

 Wind 

Story 

Drift, xp,s

(inch)

Rotation 

Angle 

(rad) 

Roof W14X38 39 40.5 1.54 0.40 0.17 1.19 0.066 

16 W14X38 39 40.5 1.54 0.69 0.34 1.29 0.071 

15 W14X38 39 40.5 1.54 0.87 0.52 1.33 0.073 

14 W14X38 39 40.5 1.54 0.94 0.69 1.31 0.072 

13 W14X38 39 40.5 1.54 0.99 0.86 1.24 0.068 

12 W16X45 39 42.5 1.47 0.84 0.81 1.15 0.063 

11 W18X50 39 45.0 1.39 0.80 0.82 1.04 0.057 

10 W18X55 39 45.5 1.37 0.78 0.84 0.96 0.053 

9 W21X50 39 39.1 1.59 0.73 0.83 0.89 0.049 

8 W21X62 39 48.6 1.29 0.76 0.86 0.81 0.044 

7 W21X68 39 50.3 1.24 0.77 0.86 0.74 0.040 

6 W21X68 39 50.3 1.24 0.83 0.92 0.66 0.036 

5 W21X73 39 51.1 1.22 0.86 0.93 0.59 0.032 

4 W21X73 39 51.1 1.22 0.93 0.98 0.52 0.029 

3 W21X73 39 51.1 1.22 0.99 1.01 0.45 0.025 

2 W24X103 39 60.2 1.04 0.90 0.93 0.41 0.017 

B-31 
 

 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

1.69 Roof Roof 1.59 

16
 

15
 

16
 

15
 

14
 

Floor 

0.0 0.5 1.0 1.5 2.0 

1.72 

1.77 

1.74 

1.65 

1.53 

1.39 

1.28 

1.19 

1.08 

0.98 

0.88 

0.78 

0.70 

0.61 

0.54 

1.83 

1.89 

1.92 

1.88 

1.82 

1.73 

1.62 

1.52 

1.37 

1.25 

1.12 

0.99 

0.85 

0.67 

0.54 

RSA

 ELF 

Floor

Life Safety (LS) Acceptance Criteria

(per ASCE 41 Table 5-6) 

Design - ELF 

Design - RSA 

Allowable Rotation Angle

(per AISC 341 Section F3.4a) 

0.00 0.02 0.04 0.06 0.08 0.10 0.12 

Plastic Link Rotation Angle (radians) 

4
 

3
 

2
 

13
 

12
 

11
 

10
 

9
 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base Base
 

Design Story Drift, x (inch)

(a) design story drift at center of mass (b) plastic rotation of link beams 

Figure B-21. Link Rotation Angle, 16-Story EBF ELF and RSA 

B-32 
B.5 Example Design Calculations 

The examples presented detail the strength design calculations for the following members and components 

of each SFRS for the RSA-designed 8-story buildings (ME8): 

 EBF shear link, ME8 RSA 

 EBF brace, ME8 RSA 

 EBF column, ME8 RSA 

Example calculations for components of the SMF can be found in Volume 1 (Harris and Speicher 2015a). 

Example calculations of columns and braces (ductile) can also be found in Volume 2 (Harris and Speicher 

2015b). 

Eccentrically Braced Frame Example 

Member Selection 

After several design and analysis iterations, the final member sizes are shown in Figure B-22. 

Figure B-22. EBF member sizes, 8-story RSA 

B-33 
 

EBF Link Beam 

The second floor link beam along grid line 1 between grid lines B and C is selected for this example (see 

circled elements in Figure B-22): 

 W21×83 

 e = 30 in 

 A992 Steel: Fy = 50 ksi, Ry = 1.1, E = 29000 ksi, G = 11200 ksi 

B.5.1.2.1 Shear Demand 

Based on the controlling load combination from ASCE 7, the demand on the link is as follows: 

Vu = 247 kips (governed by seismic) 

B.5.1.2.2 Shear Strength 

Check to see if the link is short. 

M  F Z  50 196    9800 kip-in. p y x 

A d t t  21.4  2 0.835 0.515 10.16 lw   2 f w  	 in.2 

V  0.6 F A  0.6   50 10.25   305 kips p y 	 lw 

M p	  9800 

e  30	 1.6 1.6  51.4  the link is short. Vp	 



 305 

The nominal design shear strength of the link is determined by AISC 341 §F3.5b: 

 V   V  0.9 305    275 kips vn v p 

B.5.1.2.3	 Strength Check 

V 247 u 	  0.89 1.0  OK 

Vn 275 

B.5.1.2.4 Link Rotation Angle Verification 

The allowable plastic rotation angle for a short link beam in accordance with AISC 341 is 0.08 radians.
 

B-34 
 

 

 

 

3     0.75(0.7)  0.52 in. (see Chapter 2) xp s , x 4 

L  xp s , 20(12) 0.52  p  b   0.019 rad. (see Chapter 2) e hsx 30 216 

EBF Brace 

The first story brace along grid line 1 between grid lines B and C was selected for this example (see circled 

elements in Figure B-22): 

 HSS 9×9×5/8 

 L = 213 in 

 A500 Gr. B, Fy = 46 ksi, Ry = 1.4, E = 29000 ksi, G = 11200 ksi 

B.5.1.3.1 Axial and Flexure Demand 

The demands in the brace from the controlling load combinations from ASCE 7 are presented in Table 

B-54—maximum/minimum values for an individual action displayed with bolded text. 

Table B-54. Controlling Load Combinations (kips, feet) 

LC Index Pu,A Pu,B Mu,A,x Mu,B,x Max/Min Action 

179 295.39 295.39 27.58 33.66 Pu,min 

133 -333.61 -332.20 -31.38 -31.39 Pu,max 

179 294.68 295.39 27.58 33.66 Mu,A,min 

133 -333.61 -332.20 -31.38 -31.39 Mu,A,max 

123 278.92 280.34 26.15 34.70 Mu,B,min 

189 -317.85 -317.14 -29.95 -32.42 Mu,B,max 

Pr = 334 kips and Mr,x = 32 kip-ft.—from the load combination selected for this example (#133 in Table). 

The flexural demand contribution to the P-M interaction verification is small (≤ 10%) compared to the axial 

demand contribution. Therefore, P-M interaction is neglected in this example for brevity. 

EBF brace design is also governed by the capacity design requirements specified in AISC 341 §F3.3. AISC 

341 §F3.3, exception (2) permits flexural forces resulting from seismic drift of the frame to be neglected. 

Pr,CD = 564 kips 

B.5.1.3.2 Axial Strength 

The axial compression strength of the brace is calculated per AISC 360 §E3—weak-axis (y) governs. 

P  A F n y cr y , g ,

B-35 
 

 

 

 

KL yy y F 1.0(213) 46   2.50  4.71 

ry	 E 3.40 29000
 

2 E 2 29000  F    72.9 ksi e y, 2 2

 KL  1.0(213) 
  yy    	   3.40   ry	 

	 FF 

 y e y,   F ,  0.658 cr y	 F y  35.4 ksi  

c n y P	 

,  0.9 18.7 35.4    0.9 660    595 kips

B.5.1.3.3	 Strength Check 

P , 564 r CD   0.95 1.0 OK 

 P	 595 c ny ,

EBF Column 

The first story column along grid line 3 was selected for this example (see circled elements in Figure B-22): 

 W14×145
 

 hsx = 216 in, Lclear=197.4 in
 

 A992 Steel: Fy = 50 ksi, Ry = 1.1, E = 29000 ksi, G = 11200 ksi
 

B.5.1.4.1 Axial and Flexural Demand 

The demands in the column from the controlling load combinations from ASCE 7 are presented in Table 

B-55—maximum/minimum values for an individual action displayed with bolded text. 

Table B-55. Controlling Load Combinations (kips, feet) 

LC Index Pu,A Pu,B Mu,A,x Mu,B,x Max/Min Action 

179 528.58 528.58 101.33 43.23 Pu,min 

133 -987.68 -984.39 -112.00 -22.81 Pu,max 

179 526.93 528.58 101.33 43.23 Mu,A,min 

133 -987.68 -984.39 -112.00 -22.81 Mu,A,max 

123 358.95 362.24 97.43 50.68 Mu,B,min 

189 -819.70 -818.06 -108.11 -30.27 Mu,B,max 

Pr = 988 kips and Mr,x = 112 kip-ft.—from the load combination selected for this example (#133 in Table 

B-55). 

B-36 
The flexural demand contribution to the P-M interaction verification is small (≤ 10%) compared to the axial 

demand contribution. Therefore, P-M interaction is neglected in this example for brevity. 

EBF column design is also governed by the capacity design requirements specified in AISC 341 §F3.3. 

AISC 341 §F3.3, exception (2) permits flexural forces resulting from seismic drift of the frame to be 

neglected. AISC 341 §F3.3 exception (1) permits demands to be multiplied by 0.88 for columns in frames 

over three stories. 

P r C 	   1468 kips , D	 0.88 1668 

B.5.1.4.2 Axial Strength 

The axial compression strength of the column is calculated per AISC 360 §E3—weak-axis (y) governs. 

P ,  AF n y 	 g	 cry ,

KL F y y 	 y 1.0(216) 50   2.25  4.71 

ry	 E 3.98 29000
 

2 E 2 29000  F    97.18 ksi e y, 2 2

 KL  1.0(216) 
  yy     r	   3.98   y	 

	 F F y e y,   50 97.18  F	 ,  

0.658 y 50  40.3 ksi cr y	 F  0.658    
 

 P	 

,  0.9 42.7  40.3   0.9 1721   1549
 kips c ny

B.5.1.4.3	 Strength Check 

P r C, D 1468   0.95 1.0 OK 

 P	 1549 c ny ,

B-37 

Appendix C Example Assessment Calculations 

The examples presented in this appendix detail the assessment calculations for the following primary 

members and connections of each SFRS for the RSA-designed 8-story buildings (ME8): 

 EBF shear link, ME8 RSA 

Linear assessment example calculations are provided in C.1, and examples for the nonlinear assessment 

example calculations are provided in C.2. 

C.1 Linear Assessment Examples 

The following example provides guidance to how the linear assessment calculations were conducted in 

this study. Linear assessment of the selected components is performed for the following criteria: 

 Linear Dynamic Procedure (LDP) 

 Collapse Prevention (CP) Building Performance Level (BPL) for the BSE-2 Earthquake Hazard 

Level (EHL) 

 EBF Link 

The second floor link along grid line 1 between grid lines B and C is selected for this example (see circled 

elements in Figure B-22): 

 W21×83 

 e = 30 in 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi 

Shear Demand 

Based on the controlling load combination, the demand on the link is as follows: 

VUD VG VE 1705 kips 

Shear Strength 

The flexural and shear strength of the link beam is determined per ASCE 41 §5.5.3.3.2. 

CE  x M M 55 196  kip-in. pe  F Z ye   10776 

C-1 
 

CE  0.6 F A V w     335 ye 0.6 55 10.16  kips 

Aw  d t  2 f tw 10.16 in.2 

MCE 10776 

e  30 1.6  1.6  51.5 in. 

VCE 335 

Acceptance Criteria 

The m-factor is taken from ASCE 41 Table 5-5 (Primary Component). 

MCE e 1.6 →   m 13

VCE 

Acceptance Criteria Check 

The link acceptance criteria check is: 

DCR VUD 1705 DCR     0.39 1.0 N m mV CE 13 335  

Therefore, the link beam satisfies the CP BPL acceptance criteria at the BSE-2 EHL. 

C.2 Nonlinear Assessment Examples 

The following example provides guidance to how the nonlinear assessment calculations were conducted 

in this study. Nonlinear assessment of the selected components is performed for the following criteria: 

 Nonlinear Dynamic Procedure (NDP) or Nonlinear Static Procedure (NSP) 

 Median value of the record set is used for the NDP 

 Collapse Prevention Building Performance Level for the BSE-2 EHL 

 EBF Link 

The second floor link along grid line 1 between grid lines B and C is selected for this example (see circled 

elements in Figure B-22): 

 W21×83 

 e = 30 in. 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi 

The demands for the EBF beam are taken from the median value of the record set from the NDP. 

C-2 
 

Deformation Demand 

The demand is given in terms of plastic shear strain of the link beam is: 

    0.125 rad. UD p 

Acceptance Criteria 

The acceptance criteria in terms of plastic shear strain are given in ASCE 41 Table 5-6. 

MCE 10776 

e  30 1.6 1.6  51.5 

VCE 335 

    0.14 rad. p AC , , p AC 

Acceptance Criteria Check 

The link acceptance criteria check is: 

 p 0.125 DCR    0.89 1.0
 

p AC   N  1.0 0.14 , 

Therefore, the link satisfies the CP BPL acceptance criteria at the BSE-2 EHL. 

C-3 
C-4 
 

Appendix D References 

AISC (1989). Specification for Structural Steel Buildings: Allowable Stress Design and Plastic Design. 

American Institute of Steel Construction, Chicago, IL. 

AISC (1999). Wide-Flange Column Stiffening at Moment Connections – Design Guide 13. American 

Institute of Steel Construction, Chicago, IL. 

AISC (2002). Seismic Provisions for Structural Steel Buildings – ANSI/AISC 341-02. American Institute 

of Steel Construction, Chicago, IL. 

AISC (2005). Specification for Structural Steel Buildings – ANSI/AISC 360-05. American Institute of Steel 

Construction, Chicago, IL. 

AISC (2010a). Specification for Structural Steel Buildings – ANSI/AISC 360-10. American Institute of 

Steel Construction, Chicago, IL. 

AISC (2010b). Seismic Provisions for Structural Steel Buildings – ANSI/AISC 341-10. American Institute 

of Steel Construction, Chicago, IL. 

AISC (2010c). Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic 

Applications – ANSI/AISC 358-10. American Institute of Steel Construction, Construction, Chicago, IL. 

AISC (2013). Stability Design of Steel Buildings – Design Guide 28. American Institute of Steel 

Construction, Chicago, IL. 

ASCE (2005). Minimum Design Loads for Buildings and Other Structures – ASCE/SEI 7-05. American 

Society of Civil Engineers, Reston, VA. 

ASCE (2006). Seismic Rehabilitation of Existing Buildings – ASCE/SEI 41-06. American Society of Civil 

Engineers, Reston, VA. 

ASCE (2010). Minimum Design Loads for Buildings and Other Structures – ASCE/SEI 7-10. American 

Society of Civil Engineers, Reston, VA. 

ASCE (2014). Seismic Evaluation and Retrofit of Existing Buildings – ASCE/SEI 41-13. American Society 

of Civil Engineers, Reston, VA. 

ASCE (2016). Minimum Design Loads for Buildings and Other Structures – ASCE/SEI 7-16. American 

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D-1 
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