NIST Technical Note 1863-2 

Assessment of 

First Generation 

Performance-Based 

Seismic Design 

Methods for 

New Steel Buildings 

Volume 2: 

Special Concentrically 

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.1863-2 
NIST Technical Note 1863-2 

Assessment of First Generation PerformanceBased Seismic Design Methods 

for New Steel Buildings 

Volume 2: Special Concentrically 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.1863-2 

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 1863-2 

Natl. Inst. Stand. Technol. Tech Note 1863-2, 266 pages (February 2015) 

CODEN: NTNOEF 

This publication is available free for charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-2 

 

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 (this report) 

 Volume 3: Eccentrically Braced Frames 

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 ............................................................................................................................. xxiii
 

Executive Summary ................................................................................................................................ xxv
 

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 .......................................................................................... 2-9
 

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

2.4	 SFRS Design ................................................................................................................. 2-13
 

SMF Design...................................................................................................... 2-13
 

SCBF Design.................................................................................................... 2-22
 

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

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

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

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

Analysis Procedures ........................................................................................... 3-6
 

Linear Analysis Procedures................................................................... 3-6
 

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

vii 
   

   

   

   

   

   

   

   

   

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

Nonlinear Analysis Procedures ............................................................. 3-9
 

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 Concentrically Braced Frame ........................................................................................ 3-19
 

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

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

Nonlinear Procedures .......................................................................... 3-32
 

Seismic Assessment Results ............................................................................. 3-44
 

Four-Story Concentrically Braced Frame ........................................... 3-45
 

3.2.2.1.1 Linear Static Procedure ............................................. 3-45
 

3.2.2.1.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-45
 

3.2.2.1.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-46
 

3.2.2.1.2 Linear Dynamic Procedure ........................................ 3-48
 

3.2.2.1.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-48
 

3.2.2.1.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-49
 

3.2.2.1.3 Nonlinear Static Procedure........................................ 3-51
 

3.2.2.1.4 Nonlinear Dynamic Procedure .................................. 3-55
 

Eight-Story Concentrically Braced Frame .......................................... 3-60
 

3.2.2.2.1 Linear Static Procedure ............................................. 3-60
 

3.2.2.2.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-60
 

3.2.2.2.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-62
 

3.2.2.2.2 Linear Dynamic Procedure ........................................ 3-64
 

3.2.2.2.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-64
 

3.2.2.2.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-66
 

3.2.2.2.3 Nonlinear Static Procedure........................................ 3-68
 

3.2.2.2.4 Nonlinear Dynamic Procedure .................................. 3-74
 

Sixteen-Story Concentrically Braced Frame ....................................... 3-79
 

3.2.2.3.1 Linear Static Procedure ............................................. 3-79
 

3.2.2.3.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-79
 

viii 
   

   

   

3.2.2.3.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) ............. 3-82
 

3.2.2.3.2	 Linear Dynamic Procedure ....................................... 3-85
 

3.2.2.3.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-85
 

3.2.2.3.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) ............. 3-88
 

3.2.2.3.3	 Nonlinear Static Procedure ....................................... 3-91
 

3.2.2.3.4 Nonlinear Dynamic Procedure ................................ 3-100
 

Seismic Assessment Discussion ..................................................................... 3-105
 

Linear Assessment Procedures.......................................................... 3-105
 

3.2.3.1.1	 Brace Members ....................................................... 3-105
 

3.2.3.1.2	 Member Cross-section Strength (flexural hinge) and 

Global Strength (member stability) ......................... 3-107
 

3.2.3.1.3 Summary ................................................................. 3-109
 

Nonlinear Assessment Procedures .................................................... 3-110
 

3.2.3.2.1	 Brace Members ....................................................... 3-110
 

3.2.3.2.2	 Member Cross-section Strength (flexural hinge) and 

Global Strength (member stability) ......................... 3-111
 

3.2.3.2.3 Summary ................................................................. 3-112
 

Comparison between Linear and Nonlinear Assessment Results ..... 3-113
 

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
 

Special Concentrically Braced Frame ................................................... 4-6
 

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

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

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

Concentrically Braced Frames .............................................................. 4-8
 

ASCE 7............................................................................................................... 4-9
 

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

Special Concentrically 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-1
 

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

4-Story Special Concentrically Braced Frame .................................................. A-3
 

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

8-Story Special Concentrically Braced Frame .................................................. A-6
 

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

16-Story Special Concentrically 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	 MC4 (Special Moment Frame) .................................. B-4
 

B.1.2.2.2	 MC8 (Special Moment Frame) .................................. B-7
 

B.1.2.2.3 MC16 (Special Moment Frame) .............................. B-10
 

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

B.1.2.3.1	 MC4 (Special Concentrically Braced Frame) .......... B-13
 

B.1.2.3.2	 MC8 (Special Concentrically Braced Frame) .......... B-15
 

B.1.2.3.3	 MC16 (Special Concentrically Braced Frame) ........ B-18
 

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

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

Special Concentrically Braced Frame ............................................................. B-23
 

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

B.4 Example Design Calculations ...................................................................................... B-29
 

Special Concentrically Braced Frame Example .............................................. B-29
 

Member Selection .............................................................................. B-29
 

SCBF Brace........................................................................................ B-30
 

B.4.1.2.1	 Axial Demand .......................................................... B-30
 

A.1.1.1.1	 Axial Strength .......................................................... B-30
 

B.4.1.2.2 Strength Check ......................................................... B-30
 

SCBF Column .................................................................................... B-31
 

B.4.1.3.1	 Axial and Flexural Demand ..................................... B-31
 

B.4.1.3.2	 Axial Strength .......................................................... B-31
 

x 
B.4.1.3.3 Strength Check ..........................................................B-32
 

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

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

SCBF Brace........................................................................................................C-1
 

Axial Demand .......................................................................................C-1
 

Axial Strength .......................................................................................C-1
 

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

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

C.2 Nonlinear Assessment Examples ................................................................................... C-3
 

SCBF Brace........................................................................................................C-3
 

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

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

Acceptance Criteria Check ....................................................................C-4
 

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 ....................................................................... 2-8
 

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) .................................................................................. 3-5
 

Table 3-5. Displacement Multiplier—N-S (SCBF) .................................................................................. 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, SCBF .................................................................... 3-27
 

Table 3-11. NSP General Information, 4-Story SCBF (kip, inch) ......................................................... 3-51
 

Table 3-12. CP NSP Analysis Parameters, 4-Story SCBF BSE-2 CP (kip, inch) .................................. 3-51
 

Table 3-13. LS NSP Analysis Parameters, 4-Story SCBF BSE-1 LS (kip, inch) .................................. 3-51
 

Table 3-14. NSP General Information, 8-Story SCBF (kips, inch) ........................................................ 3-69
 

Table 3-15. CP NSP Analysis Parameters, 8-Story SCBF BSE-2 CP (kip, inch) .................................. 3-69
 

Table 3-16. LS NSP Analysis Parameters, 8-Story SCBF BSE-1 LS (kip, inch) .................................. 3-69
 

Table 3-17. NSP General Information, 16-Story SCBF (kip, inch) ....................................................... 3-92
 

Table 3-18. CP NSP Analysis Parameters, 16-Story SCBF BSE-2 CP (kip, inch) ................................ 3-92
 

Table 3-19. LS NSP Analysis Parameters, 16-Story SCBF BSE-1 LS (kip, inch) ................................ 3-92
 

Table 3-20. Performance Summary of Brace Members (BM) per Frame, Linear Procedures ............. 3-106
 

Table 3-21. Effect of Design and Assessment Provisions on DCRN of a Brace – LS SPL at the BSE-1 

EHL ....................................................................................................................................................... 3-106
 

Table 3-22. Performance Summary of Columns Members (CM) per Frame, Linear Procedures ........ 3-107
 

Table 3-23. BSO Performance Summary of Archetype Buildings, Linear Procedures ....................... 3-109
 

xiii 
Table 3-24. Summary of Base Shears, Linear Procedures (kips) ......................................................... 3-109
 

Table 3-25. Performance Summary of Brace Members (BM) per frame, Nonlinear Procedures ........ 3-110
 

Table 3-26. Performance Summary of Columns Hinges (CH) per frame, Nonlinear Procedures ........ 3-111
 

Table 3-27. Performance Summary of Column Members (CM) per frame, Nonlinear Procedures ..... 3-112
 

Table 3-28. BSO Performance Summary of Archetype Buildings, Nonlinear Procedures .................. 3-112
 

Table 3-29. BSO Performance Summary of Archetype Buildings....................................................... 3-114
 

Table A-1. Ground Motion Records for N-S Direction of MC4 ............................................................. A-3
 

Table A-2. Ground Motion Records for N-S Direction of MC84 ........................................................... A-6
 

Table A-3. Ground Motion Records for N-S Direction of MC16 ........................................................... A-9
 

Table B-1. Wind Forces on MC4 (kips).................................................................................................. B-2
 

Table B-2. Wind Forces on MC8 (kips).................................................................................................. B-2
 

Table B-3. Wind Forces on MC 16 (kips) ............................................................................................... B-2
 

Table B-4. Effect Seismic Weights and Story Gravity Forces, MC4 (kips) ............................................ B-3
 

Table B-5. Effect Seismic Weights and Story Gravity Forces, MC8 (kips) ............................................ B-3
 

Table B-6. Effect Seismic Weights and Story Gravity Forces, MC16 (kips).......................................... B-4
 

Table B-7. Seismic Strength Design Forces, E-W MC4 ......................................................................... B-4
 

Table B-8. Seismic Drift Forces, E-W MC4 ........................................................................................... B-5
 

Table B-9. ASCE 7 Allowable Drift and Stability Verification, E-W MC4 RSA .................................. B-6
 

Table B-10. ASCE 7 Allowable Drift and Stability Verification, E-W MC4 ELF ................................. B-7
 

Table B-11. Seismic Strength Design Forces, E-W MC8 ....................................................................... B-7
 

Table B-12. Seismic Drift Forces, E-W MC8 ......................................................................................... B-8
 

Table B-13. ASCE 7 Allowable Drift and Stability Verification, E-W MC8 RSA ................................ B-9
 

Table B-14. ASCE 7 Allowable Drift and Stability Verification, E-W MC8 ELF ................................. B-9
 

Table B-15. Summary of Seismic Strength Design Forces, E-W MC16 .............................................. B-10
 

Table B-16. Summary of Seismic Drift Forces, E-W MC16 ................................................................ B-11
 

Table B-17. ASCE 7 Allowable Drift and Stability Verification, E-W MC16 RSA ............................ B-12
 

Table B-18. ASCE 7 Allowable Drift and Stability Verification, E-W MC16 RSA ............................ B-13
 

Table B-19. Summary of Seismic Strength Design Forces, N-S MC4 ................................................. B-13
 

Table B-20. Summary of Seismic Drift Forces, N-S MC4 .................................................................... B-14
 

Table B-21. ASCE 7 Allowable Drift and Stability Verification, N-S MC4 RSA ................................ B-15
 

Table B-22. ASCE 7 Allowable Drift and Stability Verification, N-S MC4 ELF ................................ B-15
 

Table B-23. Summary of Seismic Strength Design Forces, N-S MC8 ................................................. B-16
 

Table B-24. Summary of Seismic Drift Forces, N-S MC8 .................................................................... B-16
 

Table B-25. ASCE 7 Allowable Drift and Stability Verification, N-S MC8 RSA ................................ B-18
 

Table B-26. ASCE 7 Allowable Drift and Stability Verification, N-S MC8 ELF ................................ B-18
 

xiv 
Table B-27. Summary of Seismic Strength Design Forces, N-S MC16 ................................................B-18
 

Table B-28. Summary of Seismic Drift Forces, N-S MC16 ..................................................................B-19
 

Table B-29. ASCE 7 Allowable Drift and Stability Verification, N-S MC16 RSA ...............................B-21
 

Table B-30. ASCE 7 Allowable Drift and Stability Verification, N-S MC16 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 (kip, feet) ..................................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 (Using 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. Controlling Load Combinations (kips, feet) .......................................................................B-31
 

xv 
 

xvi
 
List of Figures 

Figure 2-1. Isometric View of MC4 Archetype Building ........................................................................ 2-2
 

Figure 2-2. Isometric View of MC8 Archetype Building ........................................................................ 2-2
 

Figure 2-3. Isometric View of MC16 Archetype Building ...................................................................... 2-3
 

Figure 2-4. Typical Floor Framing Plan, MC4 and MC8 ......................................................................... 2-4
 

Figure 2-5. Typical Floor Framing Plan, MC16 ....................................................................................... 2-4
 

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

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

Figure 2-8. Typical Brace-to-Beam / Column Connection Assembly ................................................... 2-12
 

Figure 2-9. Brace-to-Beam / Column Connection Subassembly Model for Linear Analysis ................ 2-12
 

Figure 2-10. Flow Chart of SMF Design Process .................................................................................. 2-14
 

Figure 2-11. 4-Story SMF Schematic ..................................................................................................... 2-17
 

Figure 2-12. 8-Story SMF Schematic ..................................................................................................... 2-18
 

Figure 2-13. 16-Story SMF Schematic ................................................................................................... 2-20
 

Figure 2-14. Flow Chart of SCBF Design Process ................................................................................. 2-22
 

Figure 2-15. 4-Story SCBF Schematic ................................................................................................... 2-24
 

Figure 2-16. 8-Story SCBF Schematic ................................................................................................... 2-25
 

Figure 2-17. 16-Story SCBF Schematic ................................................................................................. 2-27
 

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
 

 ................................................................................................................................................................. 3-24
 

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 .. 3-25
 

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

Acceptance Criteria ................................................................................................................................. 3-26
 

Figure 3-7. Frame Capacity Schematic (m-factor), LS and CP, 4-Story SCBF ELF ............................. 3-28
 

Figure 3-8. Frame Capacity Schematic (m-factor), LS and CP, 4-Story SCBF RSA ............................ 3-28
 

Figure 3-9. Frame Capacity Schematic (m-factor), LS and CP, 8-Story SCBF ELF ............................. 3-29
 

Figure 3-10. Frame Capacity Schematic (m-factor), LS and CP, 8-Story SCBF RSA .......................... 3-29
 

Figure 3-11. Frame Capacity Schematic (m-factor), LS and CP, 16-Story SCBF ELF ......................... 3-30
 

Figure 3-12. Frame Capacity Schematic (m-factor), LS and CP, 16-Story SCBF RSA ........................ 3-31
 

Figure 3-13. SCBF Brace-to-Beam / Column Subassembly Analytical Schematic ............................... 3-33
 

xvii 
Figure 3-14. PERFORM-3D Brace Calibration ..................................................................................... 3-33
 

Figure 3-15. In-plane Flexural Hinge Yield Surface Model (Including Force-Controlled Response) ... 3-36
 

Figure 3-16. Variation in Acceptance Criteria and Hinge Model for Axial Force ................................. 3-37
 

Figure 3-17. P-M Interaction on Plastic Rotation, LS Acceptance Criteria (Primary Component) ....... 3-38
 

Figure 3-18. P-M Interaction Curve (Section Yield Surface)................................................................. 3-39
 

Figure 3-19. P-M Interaction Curve (Member Instability) ..................................................................... 3-39
 

Figure 3-20. Frame Capacity Schematic (Inelastic), LS and CP, 4-Story SCBF ELF and RSA ............ 3-40
 

Figure 3-21. Frame Capacity Schematic (Inelastic), LS and CP, 8-Story SCBF ELF and RSA ............ 3-41
 

Figure 3-22. Frame Capacity Schematic (Inelastic), LS and CP, 16-Story SCBF ELF ......................... 3-42
 

Figure 3-23. Frame Capacity Schematic (inelastic), LS and CP, 16-Story SCBF RSA ......................... 3-43
 

Figure 3-24. LSP Assessment Results, 4-Story SCBF ELF, BSE-1 LS ................................................. 3-45
 

Figure 3-25. LSP Assessment Results, 4-Story SCBF RSA, BSE-1 LS ................................................ 3-45
 

Figure 3-26. LSP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-1............. 3-46
 

Figure 3-27. LSP Assessment Results, 4-Story SCBF ELF, BSE-2 CP ................................................. 3-47
 

Figure 3-28. LSP Assessment Results, 4-Story SCBF RSA, BSE-2 CP ................................................ 3-47
 

Figure 3-29. LSP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-2............. 3-47
 

Figure 3-30. LDP Assessment Results, 4-Story SCBF ELF, BSE-1 LS ................................................ 3-48
 

Figure 3-31. LDP Assessment Results, 4-Story SCBF RSA, BSE-1 LS ............................................... 3-48
 

Figure 3-32. LDP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-1 ............ 3-49
 

Figure 3-33. LDP Assessment Results, 4-Story SCBF ELF, BSE-2 CP ................................................ 3-50
 

Figure 3-34. LDP Assessment Results, 4-Story SCBF RSA, BSE-2 CP ............................................... 3-50
 

Figure 3-35. LDP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-2 ............ 3-50
 

Figure 3-36. 4-Story SCBF ELF Pushover, BSE-2 ................................................................................ 3-52
 

Figure 3-37. 4-Story SCBF RSA Pushover, BSE-2 ............................................................................... 3-52
 

Figure 3-38. 4-Story SCBF ELF Pushover – Story Drift Ratios – BSE-2 ............................................. 3-53
 

Figure 3-39. 4-Story SCBF RSA Pushover – Story Drift Ratios – BSE-2 ............................................. 3-53
 

Figure 3-40. Schematic of Flexural Actions in Columns, 4-Story SCBF (NSP and NDP) .................... 3-54
 

Figure 3-41. NSP Assessment Results, 4-Story SCBF ELF, BSE-1 LS (+push to left)......................... 3-55
 

Figure 3-42. NSP Assessment Results, 4-Story SCBF RSA, BSE-1 LS (+push to left) ........................ 3-55
 

Figure 3-43. NSP Assessment Results, 4- Story SCBF ELF, BSE-2 CP (+push to left) ....................... 3-55
 

Figure 3-44. NSP Assessment Results, 4-Story SCBF RSA, BSE-2 CP (+push to left) ........................ 3-55
 

Figure 3-45. NDP Assessment Results, Brace Struts, 4-Story SCBF ELF, BSE-1 LS .......................... 3-56
 

Figure 3-46. NDP Assessment Results, Brace Struts, 4-Story SCBF RSA, BSE-1 LS ......................... 3-57
 

Figure 3-47. NDP Assessment Results, Brace Struts, 4-Story SCBF ELF, BSE-2 CP .......................... 3-57
 

Figure 3-48. NDP Assessment Results, Brace Struts, 4-Story SCBF RSA, BSE-2 CP ......................... 3-57
 

xviii 
Figure 3-49. NDP Assessment Results, Column Hinges, 4-Story SCBF ELF, BSE-2 Yield ................ 3-58
 

Figure 3-50. NDP Assessment Results, Column Hinges, 4-Story SCBF RSA, BSE-2 Yield ................ 3-59
 

Figure 3-51. NDP Assessment Results, Column Members, 4-Story SCBF ELF, BSE-2 ...................... 3-59
 

Figure 3-52. NDP Assessment Results, Column Members, 4-Story SCBF RSA, BSE-2 ...................... 3-60
 

Figure 3-53. LSP Assessment Results – 8-Story SCBF ELF – BSE-1 – LS .......................................... 3-61
 

Figure 3-54. LSP Assessment Results, 8-Story SCBF RSA, BSE-1 LS ................................................ 3-61
 

Figure 3-55. LSP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, BSE-1 ............ 3-62
 

Figure 3-56. LSP Assessment Results, 8-Story SCBF ELF, BSE-2 CP ................................................. 3-63
 

Figure 3-57. LSP Assessment Results, 8-Story SCBF RSA, BSE-2 CP ................................................ 3-63
 

Figure 3-58. LSP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, BSE-2 ............ 3-64
 

Figure 3-59. LDP Assessment Results, 8-Story SCBF ELF, BSE-1 LS ................................................ 3-65
 

Figure 3-60. LDP Assessment Results, 8-Story SCBF RSA, BSE-1 LS ............................................... 3-65
 

Figure 3-61. LDP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, BSE-1 ............ 3-66
 

Figure 3-62. LDP Assessment Results, 8-Story SCBF ELF, BSE-2 CP ................................................ 3-67
 

Figure 3-63. LDP Assessment Results, 8-Story SCBF RSA, BSE-2 CP ............................................... 3-67
 

Figure 3-64. LDP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, BSE-2 ............ 3-68
 

Figure 3-65. 8-Story SCBF ELF Pushover, BSE-2 ................................................................................ 3-69
 

Figure 3-66. 8-Story SCBF RSA Pushover, BSE-2 ............................................................................... 3-70
 

Figure 3-67. 8-Story SCBF ELF Pushover – Story Drift Ratios – BSE-2 ............................................. 3-71
 

Figure 3-68. 8-Story SCBF RSA Pushover – Story Drift Ratios – BSE-2 ............................................. 3-71
 

Figure 3-69. Schematic of flexural actions in columns, 08-Story SCBF (NSP and NDP) ..................... 3-72
 

Figure 3-70. NSP Assessment Results, 8-Story SCBF ELF, BSE-1 LS (+push to left) ........................ 3-73
 

Figure 3-71. NSP Assessment Results, 8-Story SCBF RSA, BSE-1 LS (+push to left) ........................ 3-73
 

Figure 3-72. NSP Assessment Results, 8-Story SCBF ELF, BSE-2 CP (+push to left) ........................ 3-73
 

Figure 3-73. NSP Assessment Results, 8- Story SCBF RSA, BSE-2 CP (+push to left)....................... 3-73
 

Figure 3-74. NDP Assessment Results, Brace Struts, 8-Story SCBF ELF, BSE-1 LS .......................... 3-74
 

Figure 3-75. NDP Assessment Results, Brace Struts, 8-Story SCBF RSA, BSE-1 LS ......................... 3-75
 

Figure 3-76. NDP Assessment Results, Brace Struts, 8-Story SCBF ELF, BSE-2 CP .......................... 3-75
 

Figure 3-77. NDP Assessment Results, Brace Struts, 8-Story SCBF RSA, BSE-2 CP ......................... 3-76
 

Figure 3-78. NDP Assessment Results, Column Hinges, 8-Story SCBF ELF, BSE-2 Yield ................ 3-77
 

Figure 3-79. NDP Assessment Results, Column Hinges, 8-Story SCBF RSA, BSE-2 Yield ................ 3-77
 

Figure 3-80. NDP Assessment Results, Column Members, 8-Story SCBF ELF, BSE-2 ...................... 3-78
 

Figure 3-81. NDP Assessment Results, Column Members, 8-Story SCBF RSA, BSE-2 ...................... 3-78
 

Figure 3-82. LSP Assessment Results, 16-Story SCBF ELF, BSE-1 LS ............................................... 3-80
 

Figure 3-83. LSP Assessment Results, 16-Story SCBF RSA, BSE-1 LS .............................................. 3-81
 

xix 
Figure 3-84. LSP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-1........... 3-82
 

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 3-85. LSP Assessment Results, 16-Story SCBF ELF, BSE-2 CP ............................................... 3-83
 

Figure 3-86. LSP Assessment Results, 16-Story SCBF RSA, BSE-2 CP .............................................. 3-84
 

Figure 3-87. LSP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-2........... 3-85
 

Figure 3-88. LDP Assessment Results, 16-Story SCBF ELF, BSE-1 LS .............................................. 3-86
 

Figure 3-89. LDP Assessment Results, 16-Story SCBF RSA, BSE-1 LS ............................................. 3-87
 

Figure 3-90. LDP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-1 .......... 3-88
 

Figure 3-91. LDP Assessment Results, 16-Story SCBF ELF, BSE-2 CP .............................................. 3-89
 

Figure 3-92. LDP Assessment Results, 16-Story SCBF RSA, BSE-2 CP ............................................. 3-90
 

Figure 3-93. LDP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-2......... 3-91
 

Figure 3-94. 16-Story SCBF ELF Pushover, BSE-2 .............................................................................. 3-92
 

Figure 3-95. 16-Story SCBF RSA Pushover, BSE-2 ............................................................................. 3-93
 

Figure 3-96. 16-Story SCBF ELF Pushover – Story Drift Ratios – BSE-2 ........................................... 3-93
 

Figure 3-97. 16-Story SCBF RSA Pushover – Story Drift Ratios – BSE-2 ........................................... 3-94
 

Figure 3-98. Schematic of flexural actions in columns, 16-Story SCBF (NSP and NDP) ..................... 3-95
 

Figure 3-99. NSP Assessment Results, 16-Story SCBF ELF, BSE-1 LS (+push to left)....................... 3-96
 

Figure 3-100. NSP Assessment Results, 16-Story SCBF RSA, BSE-1 LS (+push to left) .................... 3-97
 

Figure 3-101. NSP Assessment Results, 16-Story SCBF ELF, BSE-2 CP (+push to left) .................... 3-98
 

Figure 3-102. NSP Assessment Results, 16-Story SCBF RSA, BSE-2 CP (+push to left).................... 3-99
 

Figure 3-103. NDP Assessment Results, Brace Struts, 16-Story SCBF ELF, BSE-1 LS .................... 3-100
 

Figure 3-104. NDP Assessment Results, Brace Struts, 16-Story SCBF RSA, BSE-1 LS ................... 3-101
 

Figure 3-105. NDP Assessment Results, Brace Struts, 16-Story SCBF ELF, BSE-2 CP .................... 3-101
 

Figure 3-106. NDP Assessment Results, Brace Struts, 16-Story SCBF RSA, BSE-2 CP ................... 3-102
 

Figure 3-107. NDP Assessment Results, Column Hinges, 16-Story SCBF ELF, BSE-2 Yield .......... 3-103
 

Figure 3-108. NDP Assessment Results, Column Hinges, 16-Story SCBF RSA, BSE-2 Yield .......... 3-103
 

Figure 3-109. NDP Assessment Results, Column Members, 16-Story SCBF ELF, BSE-2 ................ 3-104
 

Figure 3-110. NDP Assessment Results, Column Members, 16-Story SCBF RSA, BSE-2 ................ 3-104
 

Figure 3-111. Effect of Design and Assessment Provisions on the DCRN ........................................... 3-107
 

Figure 3-112. NDP Assessment Results, Story Drift Ratios, 8-Story SCBF RSA, BSE-2 CP ............ 3-115
 

Direction of MC4 ..................................................................................................................................... A-4
 

Direction of MC4 ..................................................................................................................................... A-5
 

Direction of MC8 ..................................................................................................................................... A-7
 

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

Direction of MC8 ..................................................................................................................................... A-8
 

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

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

Direction of MC16 ................................................................................................................................. A-10
 

Direction of MC16 ................................................................................................................................. 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
 

xxi 
 

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

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. SCBF Member Sizes, 8-Story RSA ................................................................................. B-29
 

xxii 
 

 

 

 

 

 

 

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 

xxiii 
 

 

 

 

 

 

 

 

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 

xxiv 
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 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. 

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

and performance measures of buildings utilizing steel special concentrically braced frames (SCBF) as the 

lateral force-resisting system (LFRS). 

A suite of archetype buildings that incorporate SCBFs 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. 

xxv 
 

To evaluate seismic assessment criteria, each component of the SCBFs 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 SCBFs 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 Special Concentrically 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 

brace members. Contrary performance results indicate acceptance criteria that need further 

calibration. 

xxvi 
 

B. Specific Observations for Special Concentrically Braced Frames: 

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

the assessment of the SCBFs. 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, dependent on the assessment 

procedure used, that new SCBFs 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 braces and, to a lesser extent, 

the columns. Assessment results for brace members 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 SCBFs. 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 brace members 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 from increasing the 

analytical complexity. Given a properly designed new brace member, the linear procedures will 

result in a maximum DCRN of approximately the ratio of CuTa / T1, which is less than or equal to 

unity. 

	 A significant number of brace members did not satisfy the acceptance criteria for the nonlinear 

procedures. Brace performance is based on high fidelity analytical modeling parameters (except 

for brace fracture); thus, room for brace modeling enhancement is limited, although alternative 

modeling practices could be investigated. Future research should investigate the influence of the 

loading protocol adopted to establish the deterministic acceptance criteria for brace members. 

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

acceptance criteria. 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). Refinement of the relevant interaction equations to evaluate specific failure 

mechanisms could assist by allowing what would be a force-controlled column to be classified as 

“deformation-controlled”. 

	 Components of the SCBFs 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 SCBF 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 

xxvii 
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 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). 

xxviii 
 

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 special concentrically braced frames (SCBF) as the 

lateral force-resisting system (LFRS)3 

. 

A suite of archetype buildings that incorporate SCBFs 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 locations to change brace sizes—every story, two, or four, etc.). 

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 SCBFs 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 SCBFs 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 develop a qualitative 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 special 

concentrically 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 forceresisting 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 2015). 

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 

MC4 

MC8 

4 

8 

150’ = 5 bays 

@ 30’ 

150’ = 5 bays 

@ 30’ 

100’ = 5 bays 

@ 20’ 

100’ = 5 bays 

@ 20’ 

SMF

SMF

 SCBF 

SCBF 

SMF: 3–30-foot bays 

SCBF: 1–20-foot bay inverted ‘V’ 

(Chevron) with HSS braces 

SMF: 3–30-foot bays 

SCBF: 1–20-foot bay two-story X-bracing 

with HSS braces 

MC16 16 150’ = 5 bays 

@ 30’ 

100’ = Varies – 

see Figure 2-5 SMF SCBF 

SMF: 3–30-foot bays 

SCBF: 2–30-foot bays two-story Xbracing with HSS braces 

2-1
 
Figure 2-1. Isometric View of MC4 Archetype Building 

Figure 2-2. Isometric View of MC8 Archetype Building 

2-2
 
Figure 2-3. Isometric View of MC16 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 SCBF Elev. 

Section 2.4.2 

A B C D E F 

1 

2 

3 

4 

5 

6 

W16×26 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

W14×22 W14×22 W14×22 

Note: All non-SFRS beams and girders are composite. 

Figure 2-4. Typical Floor Framing Plan, MC4 and MC8 

5 @ 30'-0" = 150'-0" 

2 @ 30'-0" = 60'-0" 

W14×22 W14×22 W14×22 

W16×26 

W16×26W16×26 

W27×84W27×84 

Sym. About 

Sym.

About 

W16×26 

See SCBF 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 

20'-0" 

40'-0" 

See SMF Elev. 

Section 2.4.1 

Note: All non-SFRS beams and girders are composite. 

Figure 2-5. Typical Floor Framing Plan, MC16 

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 is one archetype building system that is 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 of MC16 (SMF)—this system is shaded in Table 2-4. This frame is 

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 MC4 MC8 MC16 

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) 5172 5136 10618 10527 21782 21649
 

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. 

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

Building MC4 MC8 MC16 

SFRS SCBF SCBF SCBF 

R, Cd, o 6, 5, 2 6, 5, 2 6, 5, 2 

CuTa (seconds) 0.60 0.99 1.64 

ELF Permitted? Yes Yes Yes 

Height Limit (feet) 240 240 240 

Analysis Procedure 

W 1

 (kips) 

Vb

 1 Design (kips) 

Vb

 1 Drift (kips) 

ELF 

5172

857

782

RSA 

5136 

723 

627 

ELF 

10618 

1073 

735 

RSA 

10527 

904 

633 

ELF 

21782 

1326

1089 

RSA 

21649 

1120 

945 

RSA Scaling Factor 3 NA Design = 74 

Drift = 322 NA Design = 92 Drift = 322 NA Design = 76 Drift = 322 

T1

 4 (seconds) 

T2

 4 (seconds) 

T3

 4 (seconds) 

T1

 5 (seconds) 

T1

 6 (seconds) 

Steel Wgt.7 (tons) 

0.67

0.27

0.18

0.67

0.66

13 

 0.72 

 0.28 

 0.19 

 0.72 

 0.71 

12

1.45 

0.48 

0.27 

1.45 

1.43 

28 

1.50 

0.49 

0.28 

1.51 

1.49 

27 

2.08 

0.70 

0.39 

2.09 

2.06 

127

2.14 

0.71 

0.40 

2.14 

2.11 

123 

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. 

2-8
 
 

The difference in the stiffness and strength of the SCBFs provided by the ELF and RSA procedures is 

negligible. This is primarily due to design provisions prescribed in AISC 341 (e.g., minimum width-tothickness ratios for highly ductile braces). 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 

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. 

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. 

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 

2-9
 
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 FR RBS Beam-to-Column Connection Assembly 

In the concentrically braced frames, member ends of the SCBF diagonal braces are rotationally unrestrained 

out-of-plane and restrained in-plane (though design forces do not vary significantly if modeled as 

unrestrained in both planes). Partially rigid end zones are included to capture gusset plate rigidity; the 

tangible length of SCBF diagonal braces is taken equal to 90 percent of the distance between work points 

(W.P.), Lwp. 

The adopted brace-to-beam / column connection in the SCBF allows the beam to rotate near the edge of the 

gusset plate as shown in Figure 2-8—see AISC 341 Figure C-F2.8. The assembly model for linear analysis 

is shown in Figure 2-9. A rotationally unrestrained connection (adjacent to the gusset plate) was selected 

2-10
 
 

 

because ASCE 41 does not prescribe flexural acceptance criteria for beam-to-column connections where a 

brace is present. This approach also provides a seismic design and assessment that does not rely on the 

contribution of non-brace assemblies for stiffness and strength. All other beam-to-column connections are 

simple-type connections (i.e., rotationally unrestrained). 

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. FR RBS Beam-To-Column Connection Subassembly Model for Linear Analysis 

Diagonal braces were analyzed without gravity loads. Thus, two analyses were performed for each 

archetype building: (1) a gravity load-only model with braces removed and (2) a lateral force and gravity 

load model with braces in place. Load effects then were taken from the respective analysis for input into 

load combinations. 

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 

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. 

2-11
 
 

 

 

 

CL Column 

node C Beam L 

C Brace L 

Effective Rotationally 

Unrestrained Connection 

Slab on metal deck 

w/ isolation at connection 

Gusset Plate (shop welded) 

W.P. 

Figure 2-8. Typical Brace-to-Beam / Column Connection Assembly 

Beam, EIb Beam, EIb

Gusset Plate (not modele d) 

Increased joint stiffne ss 

provided by gusset ele ments 

Column, EIc Column, EIc 

Brace axial s tiffnes s 

computed from 0.9Lwp 

In-pla ne rota tion 

release 

Panel 

Zone 

node 

Rigid End 

Zone, typ. 

Out-of-pla ne 

rotation release 

Line Element, 

typ. 

18" 

node 

node 

W.P. 

Figure 2-9. Brace-to-Beam / Column Connection Subassembly Model for Linear Analysis 

2-12 
8

 

 

2.4 SFRS Design 

 SMF Design 

SMF designs are included here to provide the required information of the building for SCBF 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 2-10 

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 = 

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. 

8 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
 
   

   

   

   

   

     

   

   

     

       

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 2-10. 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 beamcolumn 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. 

2-14
 
 

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 L G  c (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 Z x  (2-2) d 

  P   u, min 1.18 1   ,1.0   ZF x c

M p c,  

 Py 

  , y   Pu,   (2-3)  1 Z x,b  min 1.18 1    ,1.0  Z  , M Z  xb F  P   x c 

p b, , y   y 

 d L b c b   G   P   d L u , b c (2-4) min 1.18 1  ,1.0     

 Py  

9 The vertical story strength, Pe,story, is a function of the elastic lateral stiffness of the story. 

2-15
 
 

 

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 c b 1.0 dc 360 18 G    2.52 1.9  P  dL 0.85 d 168 24 u, b c b (2-5) 1.18 1   P   y 

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 2-11 through Figure 2-13. 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). 

2-16
 
 

(a) RSA 

W14×132 W14×132

W14×193 W14×193 

(b) ELF 

W14×159 W14×145

W14×233 W14×257 

Figure 2-11. 4-Story SMF Schematic 

2-17
 
(a) RSA 

W18×175 W18×106

W18×192 W18×192 W18×143 W18×119 

W18×71 W18×55 

Figure 2-12. 8-Story SMF Schematic 

2-18
 
(b) ELF 

Figure 2-12. 8-Story SMF Schematic, Cont’d 

2-19
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 2-13. 16-Story SMF Schematic 

2-20
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 

2-21
 
   

     

     

   

     

   

     

       

 SCBF Design 

For the SCBF designs, seismic strength requirements prescribed in ASCE 7 and seismic compactness 

requirements in AISC 341 controlled brace sizes for all archetype buildings. Section compactness and 

capacity design requirements in AISC 341 §F2.3 (i) and (ii)—exception 2(a) is not considered here— 

governed column and beam sizes. The beams in the 4-story frames are laterally braced per AISC 341 and 

designed for the unbalanced load created by a buckled brace. For the 8- and 16-story frames, except at the 

second floor, beam sizes were maintained at each floor based on the largest required strength (usually at 

the third and fourth floors). The beams on the second floor had an atypical change in required strength 

because of the variation in adjacent story heights. The flowchart in Figure 2-14 illustrates the analysis and 

design process for an SCBF. Additional details on design and construction of special concentrically braced 

frames can be found in NIST GCR 13-917-24: Seismic Design of Steel Special Concentrically Braced 

Frame Systems: A Guide for Practicing Engineers (NIST 2013). 

Strength Analysis

per ASCE 7.

Figure 2-14. Flow Chart of SCBF Design Process 

Design Braces and

Brace

Connections.

Capacity Design

Analysis per AISC

341.

Design Columns

and Beams.

Good?

Drift and Stability

Analysis per

ASCE 7

Verify Design

Story Drift NOGOOD?

Update Member

Sizes

GOOD?

END

Iterate analysis

and design

No Good?

2-22
Wind drift criteria began to influence the 16-story SCBF when two isolated 20-foot two-story braced bays 

were used (as done in the 4- and 8-story archetype buildings). Therefore, a double 30-foot bay configuration 

was adopted to minimize nonseismic force contributions to member selections, as well as to allow seismic 

assessment of longer (potentially slender) braces. 

The Effective Length Method (see AISC 360 §C1) is used for design of the SCBF braces, beams, and 

columns. The effective length factor, K, was conservatively taken as unity for determining the nominal 

compression strength, Pn, of the SCBF members, although a lower value could be justified by analysis. 

Though the gusset plate connections are not fully designed and detailed in this study, a lower value of K 

could have been adopted where the rotational stiffness of the connection can influence the assumed 

boundary conditions of the adjacent braces (out-of-plane buckling controlled design). Hollow structural 

sections (HSS) are used as the diagonal braces in all archetype buildings while keeping face dimensions 

within the adjacent column flange widths. The tangible length of SCBF braces is taken equal to 90 percent 

of the distance between work points, Lwp. Diagonal braces are designed not 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 SCBF 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). 

2-23
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20'-0" 

Sy m. A bou t 

HSS4×4×3/8 

HSS5×5×3/8 

HSS5.5×5.5×3/8 

HSS6×6×1/2 

= Panel Zon e/Gusset Plate 

= Colu mn Splice 

= In-plane mom en t r elease W14×53 W14×13 2

1 

1 2 

2 

3 4 

3 

5 6 

4 

7 8 

W27×10 2 

3 2 

W27×10 2 

W27×11 4 

W27×16 1 

= Out-of-plane mom en t release 

(a) RSA 

20'-0" 

Sym. A bou t 

Roof
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Flo or
 

(ELEV = 18 ft.)
 

Fundam ental Per iods 

T1 = 0.71 sec (Fir st-Order) 

T1 = 0.72 sec (1.0D + 0.25Lo) 

T1 = 0.72 sec (1.2D + 0.25Lo) 

W14×53 W14×13 2

1 

1 2 

2 

3 4 

3 

5 6 

4 

7 8 

W27×12 9 

3 2 

W27×10 2 

W27×14 6 

W27×17 8 

Roof
 

(ELEV = 6 0 ft.)
 

HSS4×4×1/2 

4th Flo or 

(ELEV = 4 6 ft.) 

HSS5×5×3/8 

3rd Flo or 

(ELEV = 3 2 ft.) 

HSS6×6×1/2 

2nd Flo or 

(ELEV = 1 8 ft.) 

HSS6×6×5/8 

= Panel Zon e/Gusset Plate 

= Colu mn Splice 

= In-plane moment release 

= Out-of-plane mom en t release 

(b) ELF 

Fundam ental Per iods 

T1 = 0.66 sec (Fir st-Order) 

T1 = 0.67 sec (1.0D + 0.25Lo) 

T1 = 0.67 sec (1.2D + 0.25Lo) 

Figure 2-15. 4-Story SCBF Schematic 

2-24
 
(a) RSA 

Figure 2-16. 8-Story SCBF Schematic 

2-25
 
(b) ELF 

W14×176 W14×311 W14×132 W14×68 

Figure 2-16. 16-Story SCBF Schematic, Cont’d 

2-26
 
2 @ 30'-0" = 60'-0" 

HSS5×5×3/8 

HSS5.5×5.5×3/8 

HSS6×6×1/2 

HSS6×6×1/2 

HSS6×6×1/2 

HSS6×6×5/8 

HSS7×7×1/2 

HSS8×8×5/8 

Sym. About 

W18×55 

2 

2 3 

4 

5 6 

6 

8 9 

8 

11 12 

4 2 

1 

1 

3 

4 

5 

7 

7 

10 

W18×55 

W16×45 

W18×97 

W18×55 

W16×45 

W18×55 

W16×45 

W18×55 

W16×45 

W18×55 

W16×45 

W18×55 

W16×45 

W18×55 

W16×45 

10 

14 15 

9 

13 

12 

17 18 

11 

16 

14 

20 21 

13 

19 

16 

23 24 

15 

22 

18 

26 27 

17 

25 

20 

29 30 

19 

28 

22 

32 33 

21 

31 

24 

35 36 

23 

34 

26 

38 39 

25 

37 

28 

41 42 

27 

40 

32 

47 48 

31 

46 

30 

44 45 

29 

43 

1 3

2 4 

9 

11

10 12 

17 19

18 20 

25 27

26 28 

33 35

34 36 

41 43

42 44 

49 51

50 52 

57 59

58 60 

5 

6 

7 

8 

13 

14 

15 

16 

21 

22 

23 

24 

29 

30 

31 

32 

37 

38 

39 

40 

45 

46 

47 

48 

53 

54 

55 

56 

61 

62 

63 

64 

= Panel Zone/Gusset Plate 

= Column Splice 

= In-plane moment release 

= Out-of-plane moment release 

(a) RSA 

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 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.)
 

Fundamental Periods
 

T1 = 2.11 sec (First-Order)
 

T1 = 2.14 sec (1.0D + 0.25Lo)
 

T1 = 2.14 sec (1.2D + 0.25Lo)
 

Figure 2-17. 16-Story SCBF Schematic 

2-27
 
(b) ELF 

Figure 2-17. 16-Story SCBF Schematic, Cont’d 

2-28
 
 

Chapter 3 Seismic Assessment 

This chapter presents the results of the seismic assessment of the special concentrically braced frames in 

accordance with ASCE 41. Section 3.1 provides general discussions on the global analysis requirements 

for assessment. Analysis requirements specific to concentrically 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 special concentrically 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-W directions (performance in the N-S 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. 

 SCBF—in-plane and out-of-plane stability of columns (AISC 360) 

 SCBF—adequate flexural strength in the beams and columns (AISC 341) 

ASCE 41 §3.2.10—Overturning: Overturning is not considered for design or seismic assessment of the 

archetype buildings. 

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

 = max / avg 

MC4 MC8 MC16 

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 MC8) - - 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 MC4) 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. 

3-5 
   

 

 

 

 

 

 

 

 

 

 

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

 = max / avg 

MC4 MC8 MC16 

Floor ELF RSA ELF RSA ELF RSA 

Roof ­ ­ ­ ­ 1.088 1.090 

16 ­ ­ ­ ­ 1.088 1.090 

15 ­ ­ ­ ­ 1.088 1.090 

14 ­ ­ ­ ­ 1.088 1.090 

13 ­ ­ ­ ­ 1.089 1.090 

12 ­ ­ ­ ­ 1.089 1.090 

11 ­ ­ ­ ­ 1.089 1.090 

10 ­ ­ ­ ­ 1.089 1.091 

9 (Roof MC8) ­ ­ 1.087 1.091 1.089 1.091 

8 ­ ­ 1.087 1.091 1.089 1.091 

7 ­ ­ 1.088 1.091 1.089 1.091 

6 ­ ­ 1.088 1.092 1.090 1.091 

5 (Roof MC4) 1.093 1.094 1.089 1.092 1.090 1.091 

4 1.094 1.095 1.090 1.093 1.090 1.091 

3 1.094 1.095 1.090 1.093 1.090 1.091 

2 1.094 1.095 1.091 1.093 1.089 1.090 

Values shown to four significant figures are for comparison purposes only.

 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 

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. 

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. 

15 This term is now used in lieu of ‘rehabilitation’. 

3-6
 
 

 

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 MC4 and N-S components of all the 

buildings 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 MC16. 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. 

 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. 

3-7
 
 

 

 

 

 

Table 3-6. Analytical Fundamental Periods (seconds) 

MC4 MC8 MC16 

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 SCBF 0.67 0.72 1.45 1.51 2.09 2.14 

Table 3-7. Empirical Fundamental Periods (seconds) 

MC4 MC8 MC16 

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 SCBF 0.43 0.43 0.71 0.71 1.17 1.17 

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. 

3-8
 
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. 

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 

MC4 MC8 MC16 MC4 MC8 MC16 

Story E-W E-W E-W N-S N-S N-S 

Roof - - - - 2.07 

16 - - - - 1.83 

15 - - - - 1.61 

14 - - - - 1.43 

13 - - 1.29 - - 1.28 

12 - - 1.20 - - 1.17 

11 - - 1.14 - - 1.09 

10 - - 1.09 - - 1.05 

9 (Roof) - 1.98 1.07 - 1.57 1.04 

8 - 1.41 1.07 - 1.31 1.05 

7 - 1.19 1.06 - 1.13 1.07 

6 - 1.10 1.07 - 1.03 1.12 

5 (Roof) 1.45 1.05 1.08 1.07 1.02 1.17 

4 1.10 1.03 1.11 1.01 1.06 1.22 

3 1.01 1.05 1.15 1.00 1.13 1.26 

2 1.06 1.10 1.19 1.02 1.20 1.29 

Table 3-9. Story Shear Ratio – RSA 

Vstor

3.10

2.11

1.65

1.42

1.30

y / Vstory,1st mode 

MC4 MC8 MC16 MC4 MC8 MC16 

Story E-W E-W E-W N-S N-S N-S 

Roof - - - - 2.11 

16 - - - - 1.86 

15 - - - - 1.64 

14 - - - - 1.45 

13 - - - - 1.29 

12 - - 1.22 - - 1.18 

11 - - 1.15 - - 1.10 

10 - - 1.11 - - 1.05 

9 (Roof) - 2.25 1.09 - 1.59 1.04 

8 - 1.50 1.09 - 1.33 1.05 

7 - 1.22 1.09 - 1.14 1.08 

6 - 1.12 1.09 - 1.03 1.13 

5 (Roof) 1.58 1.07 1.11 1.08 1.02 1.18 

4 1.14 1.05 1.15 1.01 1.08 1.24 

3 1.01 1.08 1.21 1.00 1.17 1.28 

2 1.08 1.16 1.26 1.02 1.25 1.31 

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- 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 41 §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; postyield 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- 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 

Q UD G E  Q  Q (ASCE 41 §3.4.2.1.1) (3-2)

Component design actions classified as force-controlled, QUF, are computed by 

Q QE

UF  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  Q UD (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 

Force-controlled: DCR N  QUF [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 200d)). 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. 

Deformation-controlled: 

  plastic elastic 

Total 

UD   y  p AC  Q (3-12)

   pe  ,

DCR N   

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 Concentrically Braced Frame 

Seismic performance assessment of steel concentrically braced frames is performed in accordance with 

ASCE 41 §5.5.2. The concentrically braced frames in the archetype buildings are designed as an SCBF as 

identified in ASCE 7 §12.2 (item B.2 in Table 12.2-1) and AISC 341 §F2. 

 Assessment Methodology 

There are three primary characteristics of each component (i.e., member, connection, etc.) forming the 

mathematical model of the structural system for each assessment method: 

1. Stiffness, ASCE 41 §5.5.2.2 

2. Strength, ASCE 41 §5.5.2.3 

3.	 Acceptance Criteria, ASCE 41 §5.5.2.4, 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: 

 Brace axial force or deformation (compression and tension)17 

	 Beam and column flexural force or deformation at potential plastic hinge zones (section strength) 

	 Column 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 §5.5.2.2.1. 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 beamto-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 §5.5.2.3.2. 

17 Brace connections to adjacent members are force-controlled per ASCE 41 §5.5.2.4.1. 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 compression strength of a brace member, QCE = PCE (= Qy), is computed as Pn from AISC 

360 Chapter E with c = 1.0 and Fye in lieu of Fy. For A992 steel, Fye = 1.1×Fy (see ASCE 41 Table 5-3), 

which corresponds to RyFy in AISC 341. ASCE 41 allows the effective length factor, K, of the brace member 

to be taken as 0.8 for in-plane buckling and 1.0 for out-of-plane buckling, and L is the clear length of the 

brace plus the gusset plate (total length in ASCE 41 §5.5.2.3.2). 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. This total length can underestimate PCE when the 

rotation hinges developed in the brace connections for out-of-plane buckling occur within this total length. 

Research should investigate methods to include gusset plate effects in assessment provisions and develop 

acceptance criteria for brace connections. As a side note, ASCE 41 allows PCE to be governed by local 

buckling (section strength) and does not enforce section compactness requirements similar to AISC 341— 

member slenderness is enforced through the acceptance criteria. 

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 (3-14) 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). 

18 ASCE 41 inadvertently states AISC 341. 

3-20
 
 

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 

a CBF. 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-tobeam/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 §5.5.2.4.2. 

Axial Force in Braces and Brace Connections 

The acceptance criteria for axial tension and compression actions in brace members are provided in ASCE 

41 Table 5-5 and dependent on member slenderness parameter, KL / r, where K can be taken as 0.8 or 1.0, 

as discussed previously, and section configuration (wide-flange, HSS, pipe, etc.). While other provisions 

explicitly use Fye for cross-section slenderness triggers, the member slenderness triggers use Fy to match 

test data. The “slender” brace trigger is nearly that used to delineate between inelastic and elastic flexural 

buckling (i.e., 1.414×) taken from AISC Seismic Provisions (1994) for an ordinary concentrically braced 

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
 
 

frame. The slenderness trigger for “stocky” braces is taken as one-half of that designating a slender brace, 

demarcating inelastic flexural buckling and plastic axial capacity of the brace—stocky braces will have PCE 

close to Pye. The allowable increase in KL / r applied to braces in an SCBF in AISC 341 is not applicable 

in ASCE 41. ASCE 41 does not provide variation in acceptance criteria when local buckling governs the 

expected compression strength, PCE. ASCE 41 should expand the commentary to provide guidance and 

clarification regarding material properties and development of the acceptance criteria for braces in 

compression and tension. 

Brace connections are considered force-controlled for axial actions in ASCE 41. 

Flexure in Beams, Beam-to-Column Connections, and Brace Connections 

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). 

Flexural actions in beams in chevron braced frames are considered force-controlled in ASCE 41—this 

component, however, should be evaluated as a column unless permitted otherwise because of the axial load 

ratio (see discussion below on connections). Force-controlled classification in these components is 

consistent with AISC 341 provisions for new buildings. Research on the performance of chevron frames 

that permit beam yielding in combination with brace buckling and yielding could support this as an effective 

assessment option. 

In cases where the expected flexural strength of an unbraced segment is governed by instability (e.g., lateraltorsional 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 

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 

20 This region is also used in AISC 341 to define the protected zone. 

3-22
 
 

 

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 brace connections in a CBF be force-controlled for 

flexural actions. As such, using acceptance criteria applicable for beams to evaluate plastic hinges in beams 

adjacent to a brace connection could be unconservative. It is debatable that these hinges are within the 

connection and therefore should be classified as force-controlled. 

Flexure in Columns and Column-to-Base Connections 

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 

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 

21 Work to develop FEMA 356 was conducted at the same time as the SAC project—see FEMA 350 series. 

3-23
 
 

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 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

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. 

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 9 m M  x CEx 

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) 

3-24
 
E  Fye
 

h 640 4.0  t w Fye 

Wide-Flange Sections 

35% > Group A

 1% > Group B 

12% > AISC HD

 3% > AISC MD 

3.5 

3.0 h 460  tw Fye 

h 400  2.5 t w Fye 

h 418 2.0  t w Fye 

h 300  t 1.5 w Fye h 260  tw Fye 

1.0 

0.5 

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 

F F   50 ksi ye y 

interpolate 

between limits 

	 P hE P      0.125 2.45   1 0.93    c y P tF w y   c y P   AISC HD 

 P hE P E     0.125 0.77 2.93    1.49 P	 P y 

  cy t F w y cy F 	  

	 P hE P      0.125 3.76   1 2.75    c y 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 

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). Columns are designed in accordance with 

capacity design provisions in AISC 341. However, ASCE 41 does not similarly adopt a capacity design 

approach for the assessment of CBF columns and beams as is done for EBF columns and beams (see ASCE 

41 §5.5.3.4.1). 

Shear in Panel Zones 

The acceptance criteria for shear action in panel zones are provided in ASCE 41 Table 5-5. The acceptance 

criteria are not a function of the axial force demand in the panel zone. 

y 

0.0
 

3-25
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 

Demand 

The axial demand, PUD, for the brace is taken as the axial force at the mid-span of the brace. The flexural 

demand, MUD or MUF, and axial force, PUF, for the columns are taken as the moment and axial force at the 

face of the each beam (top and bottom). 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 SCBF for the linear procedures. 

Figure 3-7 through Figure 3-12 provide the load-independent m-factors—taking in to account forcecontrolled and deformation-controlled classifications (force-controlled components are assigned an mfactor of unity, see §3.1.4.1). These figures are referred to herein as “Frame Capacity Schematics.” The two 

3-26 
 

 

 

 

 

 

 

 

 

 

 

 

values given for a column represent the cases when PUF / PCL = 0.2 and 0.5, adjusted for section compactness 

requirements. At PUF / PCL = 0.2 the interaction equation provides the same value when PUF / PCL < 0.2. 

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

Performance Level 

Component - Action LS CP 

Beam - Flexure 

bf 52 h 418 

a)  and 

2t f Fye tw Fye 

6 8 

bf 65 h 640  b)  or 2 3 2t f Fye tw Fye 

c) other lin ear in terpo latio n 

Column - Flexure 

for P UF / P CL < 0.2 

bf 52 h 300  a)  and 6 8 2t F f t F ye w ye 

bf 65 h 460 

b)   or 1.25 2 2t f Fye tw Fye 

c) other lin ear in terpo latio n 

for 0.2 ≤ P UF / P CL ≤ 0.5 

bf 52 h 260  5 P   5 P  9 1   12 1 a)      2t t F f Fye 

 and w ye  3 PCL   3 PCL 

b 65 h 400 f   b) 1.25 1.5 2t f Fye 

or tw Fye 

c) other lin ear in terpo latio n 

Column Panel Zone - S hear 8 11 

Braces - Compres s ion (except EBF) 

KL E 

a) Slender r  4.2 

Fy 

1. W-s hapes 6 8 

2. HSS, pipes , tubes 5 7 

KL E

b) Stocky  2.1 

r Fy 

1. W-s hapes 5 7 

2. HSS, pipes , tubes 4 6 

c) intermediate lin ear in terpo latio n 

Braces - Tens ion (except EBF) 6 8 

3-27
 
 

 

 

 

6, 1.5 5.00 

5.00 

4.88 

4.88 

4.58 

4.58 

4.94 

4.94 

6, 1.5 8, 2 7.00 

7.00 

6.88 

6.88 

6.58 

6.58 

6.94 

6.94 

8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96

(a) Life Safety (b) Collapse Prevention (c) Key 

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

6, 1.5 5.00 

5.00 

4.88 

4.88 

4.69 

4.69 

4 9 .8

4 9 .8

6, 1.5 8, 2 7 0 .0

7 0 .0

6 8 .8

6 8 .8

6 9 .6

6 9 .6

6 9 .8

6 9 .8

8, 2 

Col. Brace 

Brace 

Col. = Column 

Col. 

6, 1.5 6, 1.5 8, 2 8, 2

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-8. Frame Capacity Schematic (m-factor), LS and CP, 4-Story SCBF RSA 

3-28
 
 

 

6, 1.5 

4.88 

4.88 

4.88 

4.88 

4.69 

4.69 

4.69 

4.69 

4.58 

4.58 

4.58 

4.58 

4.34 

4.34 

4.60 

4.60 

6, 1.5 8, 2 

6.88 

6.88 

6.88 

6.88 

6.69 

6.69 

6.69 

6.69 

6.58 

6.58 

6.58 

6.58 

6.34 

6.34 

6.60 

6.60 

8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96 

Col. Brace 

Brace 

Col. = Column 

Col. 

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96 

6, 1.5 6, 1.5 8, 2 8, 2

6, 1.5 6, 1.5 8, 2 8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

6, 1.5 6, 1.5 8, 2 8, 2

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-9. Frame Capacity Schematic (m-factor), LS and CP, 8-Story SCBF ELF 

6, 1.5 

4.88 

4.88 

4.88 

4.88 

4.69 

4.69 

4.69 

4.69 

4.58 

4.58 

4.58 

4.58 

4.34 

4.34 

4.60 

4.60 

6, 1.5 8, 2 

6

8 . .88 

6.88 

6.88 

6.88

6

9 . 6 .69 

6

9 .6 6

9 .6

6.69

6.69

6

8 . 6 .58 

6

8 .5

6 8 .5

6.58

6

0 . 6 .34 

6 4 .3

6 0 .6

6.60

8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96 

5.63, 1.48 5.63, 1.48 7.49, 1.96 7.49, 1.96 

6, 1.5 6, 1.5 8, 2 8, 2

6, 1.5 6, 1.5 8, 2 8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

6, 1.5 6, 1.5 8, 2 8, 2

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-10. Frame Capacity Schematic (m-factor), LS and CP, 8-Story SCBF RSA 

3-29
 
6, 1.5 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

4.88 

4.88 

4.88 

4.88 

4.94 

4.94 

4.94 

4.94 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.41 

4.41 

4.61 

4.61 

6, 1.5 8, 2 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

6.88 

6.88 

6.88 

6.88 

6.94 

6.94 

6.94 

6.94 

6. 06

60 

6.60 

6.60 

6.60

6. 0 .6 6

06 6. 0 .6 6

06 .60

6.60

6. 0 .6 6

06 6. 06

6 0 .6

6.60

6. 1 .6 6

14 6. 14

6 1 .6

6.61

8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

5.63, 1.48 6, 1.5 7.49, 1.96 8, 2 

5.63, 1.48 6, 1.5 7.49, 1.96 8, 2 

5.73, 1.49 6, 1.5 7.64, 1.97 8, 2 

5.73, 1.49 6, 1.5 7.64, 1.97 8, 2 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

Col. Brace 

Brace 

Col. 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

Col. = Column 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 6, 1.5 8, 2 8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-11. Frame Capacity Schematic (m-factor), LS and CP, 16-Story SCBF ELF 

3-30
 
 

6, 1.5 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.94 

4.94 

4.94 

4.94 

4.60 

4.60 

4.60 

4.60 

4.41 

4.41 

4.61 

4.61 

6, 1.5 8, 2 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6. 8 

88 

6.88 

6.88 

6.88

6. 4 .9 6

49 6. 4 .9 6

49 .94

6.94

6. 0 .6 6

06 6. 06

6 0 .6

6.60

6. 1 .6 6

14 6. 14

6 1 .6

6.61

8, 2 

6, 1.5 6, 1.5 8, 2 8, 2 

5.63, 1.48 6, 1.5 7.49, 1.96 8, 2 

5.63, 1.48 6, 1.5 7.49, 1.96 8, 2 

5.73, 1.49 6, 1.5 7.64, 1.97 8, 2 

5.73, 1.49 6, 1.5 7.64, 1.97 8, 2 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

Col. Brace 

Brace 

Col. 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96 

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96

Col. = Column
 

6, 1.5
 5.63, 1.48 8, 2 7.49, 1.96

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96

6, 1.5 5.63, 1.48 8, 2 7.49, 1.96

6, 1.5 6, 1.5 8, 2 8, 2

6, 1.5 6, 1.5 8, 2 8, 2

(a) Life Safety (b) Collapse Prevention (c) Key 

Figure 3-12. Frame Capacity Schematic (m-factor), LS and CP, 16-Story SCBF RSA 

3-31
 
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. 

The stiffnesses of all members and connections for nonlinear assessment follow ASCE 41 §5.5.2.2.2 for 

the NSP and ASCE 41 §5.5.2.2.3 for the NDP. The strength of all members and connections for nonlinear 

assessment follow ASCE 41 §5.5.2.3.3 for the NSP and ASCE 41 §5.5.2.3.4 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 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 3-13 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). 

HSS braces are modeled as single-entity buckling elements (strut) in PERFORM-3D with rigid end zones 

and beam and column modifications to account for brace connection stiffness—discussed above. Axial 

strength and stiffness degradation are modeled based on calibrating the PERFORM-3D MODEL with 

experimental test data (see Figure 3-14—PERFORM-3D response is presented as “Analysis”). The tension 

and compression strength of the brace is taken as TCE and PCE, respectively. Inelastic strain parameters are 

taken from ASCE 41 Table 5-7 and interpolated where required. Brace fracture upon repeated inelastic 

cycles (low-cycle fatigue) is not captured in the hysteretic model or the nonlinear analysis. 

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, 

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 

3-32
 
 

 

maintained. P-M interaction effects on a moment-curvature hinge are included in the analytical model 

(discussed subsequently). 

Figure 3-13. SCBF Brace-to-Beam / Column Subassembly Analytical Schematic 

Elastic Beam, EIb 

Gusset 

Element, 2EIb 

Gusset Plate (not modeled) 

Increased joint stiffness provided 

by gusset elements 

Default 

End Zone 

db/2 

Gusset 

Element, 

2EIc 

Default 

End Zone 

Elastic 

Column, 

EIc 

Elastic 

Column, 

EIc 

18" 

node 

node 

Brace stiffness computed from 

0.9Lwp 

W.P. 

Moment release 

Panel Zone 

Moment-Curvature 

PMM Hinge, typ. 

Elastic 

Column, 

EIc 

Elastic 

Column, 

EIc 

Elastic Beam 

Inelastic Brace Strut 

-60 

-40 

-20 

0 

20 

40 

60 

80 Specimen 5 (Yang and Mahin 2005)

 Test Data

 Analysis 

Axial Force (kips) 

HSS6×6×3/8 

KL / r = 51.9 

-0.02 -0.01 0.00 0.01 0.02 

Axial Strain (in/in) 

Figure 3-14. PERFORM-3D Brace Calibration 

3-33
 
 

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 

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 brace connections in a CBF be force-controlled for all actions. As such, 

using acceptance criteria applicable for beams to evaluate plastic hinges in beams adjacent to a brace 

connection could be unconservative. It is debatable that these hinges are within the connection and therefore 

should be classified as force-controlled. 

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 3-13). 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 

3-34
 
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 (3-15); 

see Figure 3-15, Figure 3-17, and Figure 3-18). 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 3-18. 

 P 

MCEx 1.18 M pe x 1   M (ASCE 41 Equation 5-4) (3-15) , pe x ,  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 (3-16). 

 2   P 

MCEy 1.19 M pe y 1     M (3-16) , pe y ,    P   ye   

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 3-15). 

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 3-15). 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 (3-17) rearranges ASCE 41 Equation 5-12 in terms of the moment 

strength. 

 P  MCE  MCL 1  (from ASCE 41 Equation 5-12) (3-17)  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 3-16, 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 3-16. 

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 3-16, 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 = 

3-35
 
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. 

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 3-15. In-plane Flexural Hinge Yield Surface Model (Including Force-Controlled Response) 

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 

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 

3-36
 
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. 

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 3-16. Variation in Acceptance Criteria and Hinge Model for Axial Force 

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 3-19 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. 

Figure 3-20 through Figure 3-23 provide 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. At PUF / PCL = 0.2, the interaction equation does not provide 

the same value when PUF / PCL < 0.2, as seen for the linear procedures. 

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 3-17. P-M Interaction on Plastic Rotation, LS Acceptance Criteria (Primary Component) 

3-38
Axial Force Ratio (P / P ye ) Axial Force Ratio (

P / P 

ye ) 

1.0 

0.8 

 ASCE 41 In-Plane Yield Surface

 (Eq. 5-4)

0.6 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) 

0.4 

0.2 

0.0 

0.0	 0.2 0.4 0.6 0.8 1.0
 

Moment Ratio (M / M pe )

Figure 3-18. P-M Interaction Curve (Section Yield Surface) 

 

1.0 

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) 0.6 

 ( = 1.75,  = 1.0)

 AISC Out-of-Plane Stability (Cb

 > 1)

 (H1-1, P c = P ne,y )

 PERFORM-3D Out-of-Plane Stability 0.4 

 ( = 1.3,  = 1.0)

 AISC Out-of-Plane Stability (Cb

 > 1)

 (H1-2, P cy = P ne,y )

 PERFORM-3D Out-of-Plane Stability 0.2 ( = 1.0,  = 1.5)

 PERFORM-3D Out-of-Plane Stability (Truncated)

 ( = 2.5,  = 1.25) 

0.0 

0.00	 0.25 0.50 0.75 1.00 1.25 1.50
 

Moment Ratio (M / M pe )

Figure 3-19. P-M Interaction Curve (Member Instability) 

3-39 
 

(a) ELF 

Sym. About 

Column Hinges 

Column Hinges 

Column Hinges 

Column Hinges 

3 2 

Braces 

CP → 560 

LS → 386 

YD → 87 

Braces 

CP → 698 

LS → 489 

YD → 105 

Braces 

CP → 564 

LS → 389 

YD → 88 

Braces 

CP → 360 

LS → 261 

YD → 49 

Roof 

(ELEV = 60 ft.) CP → T=B=5638, 1163 

LS → T=B=4185, 911 

YD → T=B=280, 205 4th Floor 

(ELEV = 46 ft.) CP → T=B=5638, 1163 

LS → T=B=4185, 911 

YD → T=B=280, 205 3rd Floor 

(ELEV = 32 ft.) CP → T=B=4744, 1066 

LS → T=B=3527, 834 

YD → T=B=266, 195 2nd Floor 

(ELEV = 18 ft.) CP → T=B=4744, 1066
 

LS → T=B=3527, 834
 Braces (Tension) YD → T=B=266, 195 CP → 2221 

LS → 1777 

YD → 222 

Braces = Total Strain×105 

Columns = Total Curvature×106 (for P/PCL = 0.2, 0.5) 

CP = Collapse Prevention, LS = Life Safety, YD = Yield 

T = Top Hinge, B = Bottom Hinge 

All values are for Primary Components 

(b) RSA 

Figure 3-20. Frame Capacity Schematic (Inelastic), LS and CP, 4-Story SCBF ELF and RSA 

3-40
 
 

(a) ELF (b) RSA 

Figure 3-21. Frame Capacity Schematic (Inelastic), LS and CP, 8-Story SCBF ELF and RSA 

3-41
 
Figure 3-22. Frame Capacity Schematic (Inelastic), LS and CP, 16-Story SCBF ELF 

3-42 
Figure 3-23. Frame Capacity Schematic (inelastic), LS and CP, 16-Story SCBF RSA 

3-43 
 

Seismic Assessment Results 

The results for the SCBFs 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., braces) 

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. However, ASCE 41 does not provide explicit guidance on performing this 

capacity design analysis22 for a concentrically braced frame, as is done for an eccentrically braced frame in 

ASCE 41 §5.5.3.4. The capacity design procedure in AISC 341 §F2.3 is adopted in this study to determine 

the maximum axial load demands to fulfill ASCE 41 §3.4.2.1.2-1. 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. 

3-44
 
 

Four-Story Concentrically 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 3-24 and Figure 3-25 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 3-26 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. Figure 3-24(b) and Figure 3-25(b) show that 

the frame columns are deformation-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 

0.03 0.03 6.00 6.00 

0.29 0.29 4.77 4.78 

0.23 0.23 5.23 5.24 

0.50 0.50 2.20 2.21 

0.79 

0.79 

0.80 

0.80 

0.58 

0.58 

0.79 

0.79 

5.00 

5.00 

4.88 

4.88 

4.58 

4.58 

4.94 

4.94 

(a) DCRN (b) m-factors (c) Key 

Figure 3-24. LSP Assessment Results, 4-Story SCBF ELF, BSE-1 LS 

0.03 0.03 6.00 6.00 

0.28 0.27 4.89 4.91 

0.09 0.09 5.63 5.63 

0.35 0.34 3.94 3.95 

0.83 

0.83 

0.76 

0.76 

0.79 

0.79 

0.84 

0.84 

5.00 

5.00 

4.88 

4.88 

4.69 

4.69 

4.89 

4.89 

(a) DCRN (b) m-factors (c) Key 

Figure 3-25. LSP Assessment Results, 4-Story SCBF RSA, BSE-1 LS 

3-45
 
 

2 

3 

4 

0 300 600 900 1200 1500 1800 2100 2400 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof Roof Floor 

4 

0 300 600 900 1200 1500 1800 2100 2400 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

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 3-26. LSP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-1 

3.2.2.1.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-27 and Figure 3-28 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 3-29 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. Figure 3-27(b) and Figure 3-28(b) show that 

the frame columns are deformation-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 

3-46
 
 

 

0.03 

0.29 

0.23 

0.49 

0.03 

0.28 

0.09 

0.34 

3 

4 

0

0.03 8.00 8.00 .84 

0.84 

0.85 

0.85 

0.60 

0.60 

0.85 

0.85 

7.00 

7.00 

6.88 

6.88 

6.58 

6.58 

6.94 

6.94 

0.29 6.36 6.38 

0.23 6.96 6.97

0.49 2.93 2.94 

(a) DCRN (b) m-factors (c) Key 

Figure 3-27. LSP Assessment Results, 4-Story SCBF ELF, BSE-2 CP 

0.89 

0.89 

0.81 

0.81 

0.84 

0.84 

0.89 

0.89 

0.03 8.00 

0.27 6.52 

0.09 7.53 

0.34 5.24 

7.00 

7.00 

6.88 

6.88 

6.69 

6.69 

6.89 

6.89 

8.00 

6.55 

7.53 

5.25 

(a) DCRN (b) m-factors (c) Key 

Figure 3-28. LSP Assessment Results, 4-Story SCBF RSA, BSE-2 CP 

Roof Roof 

2 

0 300 600 900 1200 1500 1800 2100 2400 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

P (ASCE 7) u,Omega

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Floor 

2 

Base Base 

Axial Load Demand, P (kips) 

0 300 600 900 1200 1500 1800 2100 2400 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

4 

3 

(a) ELF (b) RSA 

Figure 3-29. LSP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-2 

Floor 

3-47
 
 

 

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 3-30 and Figure 3-31 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 3-32 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. Figure 3-30(b) and Figure 3-31(b) show that 

the frame columns are deformation-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 

0.03 0.03 6.00 6.00 

0.30 0.30 4.67 4.69 

0.24 0.24 5.16 5.17 

0.51 0.51 2.18 2.19 

0.75 

0.75 

0.73 

0.73 

0.52 

0.52 

0.72 

0.72 

5.00 

5.00 

4.88 

4.88 

4.58 

4.58 

4.94 

4.94 

(a) DCRN (b) m-factors (c) Key 

Figure 3-30. LDP Assessment Results, 4-Story SCBF ELF, BSE-1 LS 

0.03 0.03 6.00 6.00 

0.28 0.28 4.81 4.83 

0.09 0.09 5.63 5.63 

0.34 0.34 3.97 3.98 

0.79 

0.79 

0.70 

0.70 

0.73 

0.73 

0.78 

0.78 

5.00 

5.00 

4.88 

4.88 

4.69 

4.69 

4.89 

4.89 

(a) DCRN (b) m-factors (c) Key 

Figure 3-31. LDP Assessment Results, 4-Story SCBF RSA, BSE-1 LS 

3-48
 
 

2 

3 

4 

0 300 600 900 1200 1500 1800 2100 2400 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof Roof Floor 

4 

0 300 600 900 1200 1500 1800 2100 2400 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

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 3-32. LDP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-1 

3.2.2.1.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-33 and Figure 3-34 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 3-35 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. Figure 3-33(b) and Figure 3-34(b) show that 

the frame columns are deformation-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 

3-49
 
 

 

 

0.03 

0.29 

0.24 

0.49 

0.03 

0.28 

0.09 

0.34 

3 

4 

Floor 

0.03 8.00 

0.29 6.23 

0.24 6.87 

0.49 2.90 

0

8.00 .81 

0.81 

0.78 

0.78 

0.54 

0.54 

0.77 

0.77 

7.00 

7.00 

6.88 

6.88 

6.58 

6.58 

6.94 

6.94 

6.25 

6.88 

2.91 

(a) DCRN (b) m-factors (c) Key 

Figure 3-33. LDP Assessment Results, 4-Story SCBF ELF, BSE-2 CP 

0.85 

0.85 

0.74 

0.75 

0.77 

0.77 

0.83 

0.83 

0.03 8.00 

0.28 6.41 

0.09 7.53 

0.34 5.28 

7.00 

7.00 

6.88 

6.88 

6.69 

6.69 

6.89 

6.89 

8.00 

6.44 

7.53 

5.29 

(a) DCRN (b) m-factors (c) Key 

Figure 3-34. LDP Assessment Results, 4-Story SCBF RSA, BSE-2 CP 

Roof Roof

0 300 600 900 1200 1500 1800 2100 2400 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

0 300 600 900 1200 1500 1800 2100 2400 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

P (ASCE 7) u,Omega

P (AISC 341) 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 3-35. LDP Assessment Results, Compression in Ext. Columns, 4-Story SCBF, BSE-2 

3-50
 
 

 

 

 

 

 

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 3-36 and Figure 3-37 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., braces), notated in the figures. Sharp 

points in the curves are a result of the hysteretic model used for the braces not capturing member 

out-of-straightness, which would gradually soften the curves as the buckling strengths are reached. 

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 3-38 and Figure 3-39 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 displacement at the maximum base shear governs d for both the ELF- and 

RSA-designed frames at the BSE-2 EHL whereas the target displacement governs d for both the ELF-and 

RSA-designed frames at the BSE-1 EHL. The change in d between BSE-1 and BSE-2 adds complexity to 

NSP process by changing the pushover variables. 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 SCBF (kip, inch) 

Design T1 K1 y Vy Ke Te h peak Vpeak W Cm C0 

ELF 0.67 710.5 1.6 1104 710.5 0.67 0.94 8.2 2093.5 5172 0.85 1.36 

RSA 0.72 636.2 1.6 1022 636.2 0.72 0.95 6.2 1707.1 5136 0.85 1.36 

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

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 1.34 5.32 1.16 1.05 9.9 1986.8 8.2 0.21 -0.04 -0.01 -0.02 18.07 OK 

RSA 1.25 5.31 1.14 1.00 9.9 1557.4 6.2 0.23 -0.04 -0.01 -0.02 16.50 OK 

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

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.90 3.55 1.09 1.02 6.0 1832.7 6.0 0.23 -0.03 -0.01 -0.01 17.97 OK 

RSA 0.83 3.54 1.08 1.00 6.2 1700.3 6.2 0.23 -0.04 -0.01 -0.02 16.50 OK 

3-51
 
 

 

 

 

 

 

 

 

 

 

Roof Drift Ratio at CoM (%) 

0.0 0.3 0.6 0.8 1.1 1.4 1.7 1.9 2.2 

2200 0.43 

Total Base Shear (Kips) Total Base Shear (Kips) 

Total Base Shear / W Total Base Shear / W 

2000 

0 2 4 6 8 10 12 14 16 

(1.6,1104.0) 

(8.2,2093.5) 

Roof Drift Ratio (%) at Brace Response

Story Buckle CP 

3

Roof (1)0.18 (1)0.46 

 (2)0.25 (3)0.94 

2 (4)0.51 (4)1.40 

1 (3)0.35 (2)0.65 

 ELF (First-Order)

 ELF (Second-Order) 

ELF Idealized Backbone 

0.39 

1800 0.35 

1600 0.31 

1400 0.27 

1200 0.23 

1000 0.19 

800 0.15 

600 0.12 

400 0.08 

200 0.04 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-36. 4-Story SCBF 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 

2200 

0 2 4 6 8 10 12 14 16 

(1.6,1022.0) 

(6.2,1707.1) 

Roof Drift Ratio (%) at Brace Response

Story Buckle CP 

Roof (1)0.21 (1)0.49

3 (4)0.29 (2)0.87

2 (2)0.21 (3)0.93

1 (3)0.22 (4)1.42 

 RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

0.43 

2000 0.39 

1800 0.35 

1600 0.31 

1400 0.27 

1200 0.23 

1000 0.19 

800 0.16 

600 0.12 

400 0.08 

200 0.04 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-37. 4-Story SCBF RSA Pushover, BSE-2 

3-52
 
 

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 SCBF 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 3-39. 4-Story SCBF RSA Pushover – Story Drift Ratios – BSE-2 

3-53
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3-40 illustrates which frame columns 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 3-41 through Figure 3-44 illustrate the DCRN values if greater than unity for the ELFand 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. Nearly all brace axial 

compression actions do not satisfy the LS or CP BPL acceptance criteria. All brace axial tension actions 

satisfy the LS and CP BPL acceptance criteria. Nearly all columns remain essentially elastic at the BSE-2 

EHL; therefore, satisfying the force-controlled lower-bound elastic acceptance criteria where required. The 

hinge that developed in the base column (compression side of the frame) in the ELF-designed frame fails 

the force-controlled criteria at the BSE-2 EHL. 

3 2 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

Sym. Abou t 

Roof
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

All colum ns are deformationcontrolled (DC) for flexure unless 

indicated as for ce-controlled (FC) 

in figure 

Column is f or ce-co ntro lled for flexur e if 

P > 0.5×PCL, where P is computed at the 

target displacement for the NSP and as 

the maxim um value for the NDP 

Figure 3-40. Schematic of Flexural Actions in Columns, 4-Story SCBF (NSP and NDP) 

3-54
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

3 2 

Roof
 

(ELEV = 60 ft.)
 

4th Fl o or
 

(ELEV = 46 ft.)
 

3rd Flo or
 

(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 

3 2 

Roof
 

(ELEV = 60 ft.)
 

4th Fl o or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Flo or
 

(ELEV = 18 ft.)
 

Figure 3-41. NSP Assessment Results, 4-Story SCBF Figure 3-42. NSP Assessment Results, 4-Story SCBF 

ELF, BSE-1 LS (+push to left) RSA, BSE-1 LS (+push to left)
 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

3 2 

2.02 

Roof
 

(ELEV = 60 ft.)
 

4th Fl o or
 

(ELEV = 46 ft.)
 

3rd Flo or
 

(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 

3 2 

Roof
 

(ELEV = 60 ft.)
 

4th Fl o or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Flo or
 

(ELEV = 18 ft.)
 

Figure 3-43. NSP Assessment Results, 4- Story SCBF Figure 3-44. NSP Assessment Results, 4-Story SCBF 

ELF, BSE-2 CP (+push to left) RSA, 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 3-45 through Figure 3-48 show the performance of the HSS braces at the BSE-1 (LS BPL) and BSE2 (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 from the figures, the ELF-designed frame does not perform 

significantly better than the RSA-designed frame—a corollary of the two frame designs being nearly the 

same. Both designs have braces that do not satisfy the LS or CP BPL acceptance criteria. All braces except 

those in the second story approach being classified as ‘slender’ by ASCE 41 Table 5-7. 

3-55
 
The average ratio of secondary to primary component acceptance criteria for all HSS sections with the 

configuration in this frame is 1.25 for the CP SPL (1.43 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 collapse state when several 

components are strained past the deformation associated with their peak strength—see §3.1.4.2. However, 

brace fracture is not explicitly modeled in the analysis. Therefore, these frames would not solely rely upon 

the resulting moment frame after brace fracture for collapse resistance—see NIST GCR 10-917-8. ASCE 

41 does not provide acceptance criteria for beam-to-column connections once a brace fractures. 

Roof 

4 

Median 

Left Brace 

0 1 2 3 

Right Brace 

0 1 2 3 

Floor ID Floor ID 

Mean 

84th 3 

Mean+1std

 NSP 

LSP 

LDP 

2 

Base 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-45. NDP Assessment Results, Brace Struts, 4-Story SCBF ELF, BSE-1 LS 

Roof 

4 

Median 

Mean 

3 84th 

Mean+1std

 NSP 

LSP 

LDP 2 

Left Brace 

0 1 2 3 

Right Brace 

0 1 2 3 

Base 

DCRN = Total Deformation / Total LS Acceptance Criteria 

3-56 
Figure 3-46. NDP Assessment Results, Brace Struts, 4-Story SCBF RSA, BSE-1 LS 

Roof 

4 

Median 

Mean 

84th 

3 Mean+1std

 NSP 

LSP 

LDP 

2 

Left Brace 

0 1 2 3 4 

Right Brace 

0 1 2 3 4 

Floor ID Floor ID 

Base 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-47. NDP Assessment Results, Brace Struts, 4-Story SCBF ELF, BSE-2 CP 

Roof 

4 Median 

Mean 

84th 

Mean+1std

 NSP 3 

LSP 

LDP 

2 

Left Brace 

0 1 2 3 4 

Right Brace 

0 1 2 3 4 

Base 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-48. NDP Assessment Results, Brace Struts, 4-Story SCBF RSA, BSE-2 CP 

Figure 3-40 (see NSP section) illustrates which flexural actions in the frame columns are force-controlled 

for both the NSP and NDP. Figure 3-49 and Figure 3-50 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. 

3-57
 
 

Figure 3-51 and Figure 3-52 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). However, the 

deformation demands are considerably lower than the primary CP acceptance criteria for a ‘column’. This 

effect 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. 

Still, the exterior base columns in both the ELF- and RSA-designed frames are force-controlled for flexure 

and therefore do not satisfy the lower-bound elastic acceptance criteria at the BSE-2. There is indication 

that other plastic hinges may develop in the columns below stories with highly strained braced. Whether or 

not this is an effect of the column-to-base connection model is not well understood. As illustrated in Figure 

3-40, these columns would be force-controlled for flexure because of high axial load ratios. It does not 

seem justified that force-controlled response be triggered by PUF / PCL in lieu of PUF / Pye, more so when 

PCL is governed by any buckling mode other than in-plane flexural buckling. First, PCL can be controlled by 

flexural buckling about the weak-axis, which is a failure mode that should be treated separately from the 

formation of a plastic hinge from in-plane bending. Second, PCL varies based on the length of a member 

whereas Pye is constant. As a side note, if PUF / Pye were used as the axial force ratio trigger, as was done in 

FEMA 273, base column flexural action would not be classified as force-controlled. ASCE 41-13 took the 

first step in resolving this inconsistency by permitting PUF / PCL to be computed in the plane of bending. 

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 not applicable here because 

the columns are deformation-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. 

Roof 

4 

Col. Line B 

0 1 2 3 4 

Col. Line C 

0 1 2 3 4 

Median 

Mean 

84th 

Mean+1std

3 NSP

 LSP

 LDP 

2 

Base 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-49. NDP Assessment Results, Column Hinges, 4-Story SCBF ELF, BSE-2 Yield 

Floor ID 

3-58
 
Floor ID Floor ID 

Roof Col. Line B Col. Line C

3 

4 Median

Mean

84th

Mean+1std

 NSP

 LSP

 LDP 

2 

01 

Base 

2 3 4 5 6 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

0 1 2 3 4 5 6 

Figure 3-50. NDP Assessment Results, Column Hinges, 4-Story SCBF RSA, BSE-2 Yield 

Roof Col. Line B Col. Line C

4 

Median

Mean

84th 3 Mean+1std

 LSP

 LDP 

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 Result 

(NDP = max of either axis, LSP / LDP = equations from ASCE 41) 

Figure 3-51. NDP Assessment Results, Column Members, 4-Story SCBF ELF, BSE-2 

3-59
 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Base 

2 

3 

4 

Roof Col. Line B 

Floor ID 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Col. Line C 

Median 

Mean 

84th 

Mean+1std

 LSP

 LDP 

DCRN = P-M Interaction Result 

(NDP = max of either axis, LSP / LDP = equations from ASCE 41) 

Figure 3-52. NDP Assessment Results, Column Members, 4-Story SCBF RSA, BSE-2 

Eight-Story Concentrically 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 3-53 and Figure 3-54 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. 

	 Figure 3-55 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. Figure 3-53(b) and Figure 3-54(b) show that 

some frame columns particularly in the lower stories of the frame are force-controlled for flexure and the 

braces tend toward a ‘slender’ classification in ASCE 41 Table 5-5. 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 AISC 341 SCBF column design requirements, as shown in Figure 3-55. 

3-60
 
 

0.08 

0.28 

0.28 

0.55 

0.55 

0.40 

0.40 

0.51 

0.51 

0.54 

0.54 

0.63 

0.63 

0.46 

0.46 

0.60 

0.60 

0.08 6.00 

4.88 

4.88 

4.88 

4.88 

4.58 

4.58 

4.58 

4.58 

4.58 

4.58 

4.58 

4.58 

4.34 

4.34 

4.60 

4.60 

6.00 

0.10 0.10 6.00 6.00 

0.36 0.36 3.53 3.53 

0.38 0.38 3.31 3.31 

0.64 0.64 1.00 1.00 

0.65 0.64 1.00 1.00 

0.53 0.53 1.00 1.00 

0.76 0.76 1.00 1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-53. LSP Assessment Results – 8-Story SCBF ELF – BSE-1 – LS 

0.08 

0.27 

0.27 

0.54 

0.54 

0.59 

0.59 

0.73 

0.73 

0.53 

0.53 

0.60 

0.60 

0.44 

0.44 

0.58 

0.58 

0.08 6.00 

4

8 . .88 

4.88 

4.88 

4.88

4

9 . 4 .69 

4

9 .6 4

9 .6

4.69

4.69

4

8 . 4 .58 

4 8 .5

4 8 .5

4.58

4

0 . 4 .34 

4 4 .3

4 0 .6

4.60

6.00 

0.10 0.10 6.00 6.00 

0.35 0.35 3.62 3.62 

0.37 0.37 3.40 3.41 

0.68 0.68 1.00 1.00 

0.69 0.69 1.00 1.00 

0.57 0.57 1.00 1.00 

0.78 0.78 1.00 1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-54. LSP Assessment Results, 8-Story SCBF RSA, BSE-1 LS 

3-61
 
 

5 

6 

7 

8 

Roof 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

Roof 

Floor 

8 

7 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

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 3-55. LSP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, BSE-1 

3.2.2.2.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

 Figure 3-56 and Figure 3-57 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 3-58 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All brace actions satisfy the CP BPL acceptance criteria. Figure 3-56(b) and Figure 3-57(b) show that most 

frame columns particularly in the lower stories of the frame are force-controlled for flexure and the braces 

tend toward a ‘slender’ classification in ASCE 41 Table 5-5. 

Base columns do not satisfy the CP BPL acceptance criteria using the interaction equation because they are 

designated as force-controlled for flexure because of PUF exceeding 0.5×PCL (see discussion in §3.2.2.1.4). 

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 CP SPL as compared to AISC 341 SCBF column design requirements, as shown in Figure 3-58. 

The axial load changes because J is essentially unchanged between the BSE-1 and BSE-2 analyses— 

contrary to the capacity design philosophy. 

3-62
 
 

0.22 

0.30 

0.30 

0.58 

0.58 

0.42 

0.42 

0.53 

0.53 

0.56 

0.56 

0.66 

0.66 

0.48 

0.48 

0.63 

0.63 

0.22 7.68 

6.88 

6.88 

6.88 

6.88 

6.58 

6.58 

6.58 

6.58 

6.58 

6.58 

6.58 

6.58 

6.34 

6.34 

6.60 

6.60 

7.69 

0.26 0.26 6.96 6.98 

0.50 0.50 2.19 2.19 

0.55 0.55 1.00 1.00 

0.89 0.89 1.00 1.00 

0.90 0.90 1.00 1.00 

0.75 0.74 1.00 1.00 

1.07 1.07 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-56. LSP Assessment Results, 8-Story SCBF ELF, BSE-2 CP 

0.22 

0.29 

0.29 

0.57 

0.57 

0.62 

0.62 

0.77 

0.77 

0.55 

0.55 

0.63 

0.63 

0.45 

0.45 

0.61 

0.61 

0.22 7.71 

6.88 

6.88 

6.88 

6.88 

6

9 . 6 .69 

6

9 .6 6

9 .6

6.69

6.69

6

8 . 6 .58 

6 8 .5

6 8 .5

6.58

6

0 .6 6 .34 

6 4 .3

6 0 .6

6.60

7.71 

0.26 0.25 6.99 7.01 

0.50 0.50 2.14 2.15 

0.54 0.54 1.00 1.00 

0.98 0.98 1.00 1.00 

0.99 0.99 1.00 1.00 

0.82 0.82 1.00 1.00 

1.14 1.14 1.00 1.00

(a) DCRN (b) m-factors (c) Key 

Figure 3-57. LSP Assessment Results, 8-Story SCBF RSA, BSE-2 CP 

3-63
 
 

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 (AISC 341) 

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 (AISC 341) 

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 3-58. LSP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, 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 3-59 and Figure 3-60 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 3-61 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. Figure 3-59(b) and Figure 3-60(b) show that 

the frame columns are deformation-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 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 the least conservative PUF as compared to AISC 341 SCBF column 

design requirements, as shown in Figure 3-61. 

3-64
 
 

0.08 

0.26 

0.26 

0.46 

0.46 

0.31 

0.31 

0.37 

0.37 

0.40 

0.40 

0.47 

0.47 

0.37 

0.37 

0.49 

0.49 

0.08 6.00 

4.88 

4.88 

4.88 

4.88 

4.58 

4.58 

4.58 

4.58 

4.58 

4.58 

4.58 

4.58 

4.34 

4.34 

4.60 

4.60 

6.00 

0.10 0.10 6.00 6.00 

0.30 0.30 4.33 4.33 

0.32 0.32 4.11 4.11 

0.46 0.46 2.44 2.44 

0.47 0.47 2.26 2.26 

0.40 0.40 3.09 3.09 

0.49 0.49 2.49 2.50 

(a) DCRN (b) m-factors (c) Key 

Figure 3-59. LDP Assessment Results, 8-Story SCBF ELF, BSE-1 LS 

0.08 

0.29 

0.29 

0.49 

0.49 

0.47 

0.47 

0.54 

0.54 

0.39 

0.39 

0.46 

0.46 

0.38 

0.38 

0.51 

0.51 

0.08 6.00 

4

8 . .88 

4.88 

4.88 

4.88

4

9 . 4 .69 

4

9 .6 4

9 .6

4.69

4.69

4

8 . 4 .58 

4 8 .5

4 8 .5

4.58

4

0 . 4 .34 

4 4 .3

4 0 .6

4.60

6.00 

0.10 0.10 6.00 6.00 

0.32 0.32 4.15 4.15 

0.33 0.33 3.93 3.93 

0.50 0.50 1.87 1.88 

0.52 0.52 1.68 1.68 

0.43 0.43 2.80 2.80 

0.52 0.52 2.17 2.17 

(a) DCRN (b) m-factors (c) Key 

Figure 3-60. LDP Assessment Results, 8-Story SCBF RSA, BSE-1 LS 

3-65
 
 

 

5 

6 

7 

8 

Roof 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

8 

7 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

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 3-61. LDP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, BSE-1 

3.2.2.2.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-62 and Figure 3-63 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 3-64 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. Figure 3-62(b) and Figure 3-63(b) show that 

most frame columns particularly in the lower stories of the frame are force-controlled for flexure and the 

braces tend toward a ‘slender’ classification in ASCE 41 Table 5-5. 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 the least conservative PUF as compared 

to AISC 341 SCBF column design requirements, as shown in Figure 3-64. 

3-66
 
 

0.22 

0.32 

0.32 

0.54 

0.54 

0.33 

0.33 

0.39 

0.39 

0.42 

0.42 

0.50 

0.50 

0.40 

0.40 

0.55 

0.55 

0.22 7.68 

6.88 

6.88 

6.88 

6.88 

6.58 

6.58 

6.58 

6.58 

6.58 

6.58 

6.58 

6.58 

6.34 

6.34 

6.60 

6.60 

7.68 

0.26 0.26 6.96 6.98 

0.42 0.42 3.65 3.65 

0.44 0.44 3.36 3.36 

0.67 0.67 1.00 1.00 

0.68 0.68 1.00 1.00 

0.58 0.58 1.00 1.00 

0.81 0.81 1.00 1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-62. LDP Assessment Results, 8-Story SCBF ELF, BSE-2 CP 

0.22 

0.31 

0.31 

0.53 

0.53 

0.49 

0.49 

0.57 

0.57 

0.40 

0.40 

0.48 

0.48 

0.39 

0.39 

0.54 

0.54 

0.22 7.68 

6.88 

6.88 

6.88 

6.88 

6

9 . 6 .69 

6

9 .6 6

9 .6

6.69

6.69

6

8 . 6 .58 

6 8 .5

6 8 .5

6.58

6

0 .6 6 .34 

6 4 .3

6 0 .6

6.60

7.69 

0.26 0.26 6.96 6.98 

0.43 0.43 3.56 3.57 

0.44 0.44 3.27 3.28 

0.73 0.73 1.00 1.00 

0.74 0.74 1.00 1.00 

0.63 0.63 1.00 1.00 

0.86 0.86 1.00 1.00 

(a) DCRN (b) m-factors (c) Key 

Figure 3-63. LDP Assessment Results, 8-Story SCBF RSA, BSE-2 CP 

3-67
 
 

5 

6 

7 

8 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof Roof Floor 

8 

7 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

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 3-64. LDP Assessment Results, Compression in Ext. Columns, 8-Story SCBF, 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 3-65 and Figure 3-66 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., braces), notated in the figures. Sharp 

points in the curves are a result of the hysteretic model used for the braces not capturing member 

out-of-straightness, which would gradually soften the curves as the buckling strengths are reached. 

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 3-67 and Figure 3-68 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 the ELF-designed 

frame for both the BSE-1 and BSE-2 EHLs and the RSA-designed frame for the BSE-2 EHL, whereas the 

target displacement governs the RSA-designed frame for the BSE-1 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. 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 

3-68
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 SCBF (kips, inch) 

Design T1 K1 y Vy Ke Te h peak Vpeak W Cm C0 

ELF 1.40 278.8 7.5 2098 279.1 1.40 1.05 11.8 2527.0 10618 1.00 1.41 

RSA 1.45 251.9 7.1 1758 249.1 1.46 1.06 13.0 2068.4 10527 1.00 1.40 

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

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.69 3.50 1.00 1.00 18.7 2214.9 11.8 0.36 -0.09 -0.03 -0.04 8.93 OK 

RSA 0.64 3.85 1.00 1.00 18.8 1986.1 13.0 0.21 -0.10 -0.03 -0.04 8.61 OK 

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

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.46 2.34 1.00 1.00 12.5 2219.9 11.8 0.36 -0.09 -0.03 -0.04 8.93 OK 

RSA 0.43 2.57 1.00 1.00 12.5 2054.8 12.5 0.22 -0.10 -0.03 -0.04 8.62 OK 

Roof Drift Ratio at CoM (%) 

0.0 0.4 0.7 1.1 1.4 1.8 2.2 

2800 0.26 

0 5 10 15 20 25 30 

(7.5,2098.0) 

(11.8,2527.0) 

Roof Drift Ratio (%) for Brace Response

Story Buckle Yield CP-Comp CP-Tens 

8 

7 (3)0.46 

6 

5 (4)0.53 (10)1.70 (4)1.91 

4 (5)0.64 (6)0.74 (3)1.89 

3 (1)0.40 (8)0.80 (1)0.88 

2 (7)0.77 (6)0.74 (2)1.18 

1 (2)0.42 (9)1.08 

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

2400 0.23 

Total Base Shear (Kips) 2000 0.19 

Total Base Shear / 

W

1600
 

1200
 

0.15
 

0.11
 

800 0.08 

400
 0.04
 

0 0.00 

Roof Displacement at CoM (Inches)

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

3-69
 
 

 

 

 

 

 

 

 

 

Roof Drift Ratio at CoM (%) 

0.0 0.4 0.7 1.1 1.4 1.8 2.2 

2800 

0 5 10 15 20 25 30 

(7.1,1758.0) 

(13.0,2068.4) 

Roof Drift Ratio (%) for Brace Response

Story Buckle Yield CP-Comp CP-Tens 

8 

7 (4)0.51 (10)1.54 (3)1.64 

6 (6)0.65 (4)1.77 

5 (1)0.35 (8)0.95 (1)0.70 

4 (5)0.56 (7)0.93 (2)1.09 

3 (2)0.45 (9)0.96 

2 (11)1.79 

1 (3)0.47 

 RSA (First-Order)

 RSA (Second-Order) 

RSA Idealized Backbone 

0.27 

2400 0.23 

Total Base Shear (Kips) 2000 0.19 

1600 0.15 

Total Base Shear / W 

1200
 0.11
 

800
 0.08
 

400
 0.04
 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-66. 8-Story SCBF RSA Pushover, BSE-2 

Figure 3-69 illustrates which frame columns 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. Similar to results from the linear procedures, exterior columns below the mid-height of the 

frame are force-controlled for flexure. 

Figure 3-70 through Figure 3-73 illustrate the DCRN values if greater than unity for the ELF- and RSAdesigned 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. Nearly all brace axial 

compression actions satisfy the LS and CP BPL acceptance criteria. All brace axial tension actions satisfy 

the LS and CP BPL acceptance criteria. Nearly all columns remain essentially elastic at the BSE-2 EHL, 

therefore satisfying the force-controlled lower-bound elastic acceptance criteria where required. The hinge 

that developed in the base column (compression side of the frame) in the ELF-designed frame barely fails 

the force-controlled criteria in compression at the BSE-2 EHL. 

3-70
 
 

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 SCBF 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

 Roof 

Roof Drift Ratio (%)

Figure 3-68. 8-Story SCBF RSA Pushover – Story Drift Ratios – BSE-2 

3-71
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 2 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

Sym. About 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

ELF NDP LS & CP 

ELF NDP LS & CP 

Ro of
 

(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 Flo or
 

(ELEV = 32 ft.)
 

2nd Fl o or
 

(ELEV = 18 ft.)
 

All colum ns are deformationcontrolled (D C) for flexur e unless 

indicated as for ce-controlled (FC) 

in figure 

Colu mn is f or ce-controlled for flex ur e if 

P > 0.5×PCL, where P is computed at the 

target displacement for the NS P and as 

the maxim um value for the NDP 

Figure 3-69. Schematic of flexural actions in columns, 08-Story SCBF (NSP and NDP) 

3-72
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 2 

Roof
 

(ELEV = 116 ft.)
 

8th Floor 

(ELEV = 102 ft.) 

7th Floor 

(ELEV = 88 ft.) 

6th Floor DCRN ≥ 1.0 (ELEV = 74 ft.) 

0.9 ≤ DCRN < 1.0 

5th Floor 

0.8 ≤ DCRN < 0.9 (ELEV = 60 ft.) 

0.7 ≤ DCRN < 0.8 

4th Floor 

DCRN < 0.7 (ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Floor 

(ELEV = 18 ft.) 

Figure 3-70. NSP Assessment Results, 8-Story SCBF Figure 3-71. NSP Assessment Results, 8-Story SCBF 

ELF, BSE-1 LS (+push to left) RSA, BSE-1 LS (+push to left) 

3 2 

1.02 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

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 Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

3 2 

2.79C 

1.69C 

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 Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Figure 3-72. NSP Assessment Results, 8-Story SCBF Figure 3-73. NSP Assessment Results, 8- Story SCBF 

ELF, BSE-2 CP (+push to left) RSA, BSE-2 CP (+push to left)
 

3-73
 
3.2.2.2.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the N-S direction of MC8 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 3-74 through Figure 3-77 show the performance of the HSS braces at the BSE-1 (LS BPL) and BSE2 (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 from the figures, the ELF-designed frame does not perform 

significantly better than the RSA-designed frame—a corollary of the two frame designs being nearly the 

same. Both designs have braces (lower story of the two-story X bracing) that do not satisfy the LS or CP 

BPL acceptance criteria. All braces except those in the second story approach being classified as ‘slender’ 

by ASCE 41 Table 5-7. 

The average ratio of secondary to primary component acceptance criteria for all HSS sections with the 

configuration in this frame is 1.25 for the CP SPL (1.43 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. However, 

brace fracture is not explicitly modeled in the analysis—see §3.2.2.1.3 for more information. 

Roof 

8 

7 

6 

Left Brace 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 

Right Brace 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 

Floor ID 

Median 

5 Mean 

84th 

Mean+1std 4 NSP 

LSP 

3 LDP 

2 

Base 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-74. NDP Assessment Results, Brace Struts, 8-Story SCBF ELF, BSE-1 LS 

3-74
 
Floor ID 

Roof 

8 

7 Median

Mean

6 84th

Mean+1std

5 NSP

LSP

LDP 4
 

3
 

2
 

Left Brace Right Brace 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 / Total LS Acceptance Criteria 

Figure 3-75. NDP Assessment Results, Brace Struts, 8-Story SCBF RSA, BSE-1 LS 

 

Roof 

8 

Median

7 Mean

84th

6 Mean+1std

 NSP

Floor ID 

LSP 5 

LDP
 

4
 

3
 

2
 

Left Brace
 Right Brace

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 / Total CP Acceptance Criteria
 

Figure 3-76. NDP Assessment Results, Brace Struts, 8-Story SCBF ELF, BSE-2 CP 

3-75
Roof 

8 Median 

Mean 

7 84th 

Mean+1std

6 NSP 

LSP 

LDP 5
 

4
 

3
 

2
 

Left Brace 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 

Right Brace 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 

Floor ID 

Base 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-77. NDP Assessment Results, Brace Struts, 8-Story SCBF RSA, BSE-2 CP 

Figure 3-69 (see NSP section) illustrates which flexural actions in the frame columns are force-controlled 

for both the NSP and NDP. Figure 3-78 and Figure 3-79 show the curvature ductility demand on the column 

hinges (i.e., section strength) at the BSE-2 EHL—see discussion on column hinge modeling in §3.2.1.2. 

Figure 3-80 and Figure 3-81 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) using the mean 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. However, the deformation demands are considerably lower 

than the primary CP acceptance criteria for a ‘column’. This effect 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. 

Still, the exterior base columns in both the ELF- and RSA-designed frames are force-controlled for flexure 

and therefore do not satisfy the lower-bound elastic acceptance criteria at the BSE-2—see §3.2.2.1.4 for 

additional information and discussion. 

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 most 

of 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 

3-76
 
linear assessment results show similar distributions of demands and location of potential performance 

concerns. 

Roof Col. Line B Col. Line C

8 

7 

Median

6 Mean

84th

Floor ID Floor ID 

Mean+1std

5 NSP

 LSP

4
 LDP
 

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

 

Roof Col. Line B Col. Line C

8
 

7 

Median

Mean

6 84th

Mean+1std

5 NSP

 LSP

 LDP 4 

3 

2 

Base 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

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

 

3-77 
Floor ID Floor ID 

8 

Roof Col. Line B Col. Line C

7 

6 

5 

4 

3 

2 

0.0 

Base 

Figure 3-80. NDP Assessment Results, Column Members, 8-Story SCBF ELF, BSE-2 

0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Result 

(NDP = max of either axis, LSP / LDP = equations from ASCE 41) 

0.0 0.2 0.4 0.6 0.8 1.0 

 

8 

Roof Col. Line B Col. Line C

7 

6 

5 

4 

3 

2 

0.0 

Base 

0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Result 

(NDP = max of either axis, LSP / LDP = equations from ASCE 41) 

0.0 0.2 0.4 0.6 0.8 1.0 

Figure 3-81. NDP Assessment Results, Column Members, 8-Story SCBF RSA, BSE-2 

Median

Mean

84th

Mean+1std

 LSP

 LDP 

1.2 

Median

Mean

84th

Mean+1std

 LSP

 LDP 

1.2 

3-78
Sixteen-Story Concentrically 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 3-82 and Figure 3-83 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 3-84 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. Figure 3-82(b) and Figure 3-83(b) show that 

nearly all exterior frame columns are force-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 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 AISC 

341 SCBF column design requirements, as shown in Figure 3-84. 

3-79
 
 

0.21 

5

4

6 

9 

7 

.

.

2 

5 

0 

.

.

6

5

1 

6 0

5

5

7 

0.25 

3 .

0. 5 . 0

27

55

0.53

0.55 .7

0. .7

06

0 76

0.71

0.50 

8 .

0. 16

0 9 .6

0.58

0.53 

95

0. 76

0 3 .7

0.59

0.48 .5

0. 6 0

60 .65

0.52

0.52 

55

0. 96 0

56 .69

0.55

0.54 .5

0.67

0.69

0.56

0.33 

0 .

0. 74 0 5 .5

0.40

0.04 

0.27 0.07 

0.27 0.06 

0.28 0.08 

0.54 0.08 

0.53 0.09 

0.61 0.06 

0.62 0.06 

0.68 0.07 

0.68 0.07 

0.69 0.07 

0.70 0.08 

0.71 0.09 

0.72 0.10 

0.63 0.08 

0.80 0.11 

(a) DCRN

5.99 

5.06 

4.78 

4.54 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

4.88 

4.88 

4.88 

4.88 

4.94 

4.94 

4.94 

4.94 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.41 

4.41 

4.61 

4.61 

(b) m-factors 

6.00 

6.00 

6.00 

6.00 

6.00 

6.00 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

6.00 

6.00 

(c) Key 

Figure 3-82. LSP Assessment Results, 16-Story SCBF ELF, BSE-1 LS 

3-80
 
 

0.11 

5

3

3 

7 

5 

.

.

4 

9 

4 

.

.

6

5

9 

4 0

5

5

6 

0.24 

2 .

0. 4 . 0

26

54

0.52

0.54 .6

0. .7

95

0 74

0.69

0.49 

7 .

0. 06 0 7 .6

0.57

0.61 

86

0. 47 0

1 .8

0.68

0.69 .7

0. 8 0

84 .89

0.74

0.63 

76

0. 58 0

18 .85

0.67

0.51 .5

0.65

0.67

0.53

0.31 

8 .

0. 64 0 4 .5

0.38

0.04 

0.27 0.07 

0.26 0.06 

0.28 0.08 

0.51 0.08 

0.53 0.09 

0.60 0.06 

0.61 0.06 

0.66 0.07 

0.66 0.08 

0.73 0.08 

0.73 0.08 

0.74 0.09 

0.75 0.10 

0.67 0.08 

0.84 0.11 

(a) DCRN

6.00 

5.09 

4.83 

4.59 

1.57 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.94 

4.94 

4.94 

4.94 

4.60 

4.60 

4.60 

4.60 

4.41 

4.41 

4.61 

4.61 

(b) m-factors 

6.00 

6.00 

6.00 

6.00 

6.00 

6.00 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

6.00 

6.00 

(c) Key 

Figure 3-83. LSP Assessment Results, 16-Story SCBF RSA, BSE-1 LS 

3-81
 
 

 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

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 (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

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 (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

12 

11 

10 

9 

8

Floor 

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 3-84. LSP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-1 

3.2.2.3.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

 Figure 3-85 and Figure 3-86 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 3-87 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All brace actions satisfy the CP BPL acceptance criteria. Figure 3-85(b) and Figure 3-86(b) show that nearly 

all exterior frame columns are force-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 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 AISC 

341 SCBF column design requirements, as shown in Figure 3-87. The axial load, PUF, in Figure 3-84 and 

Figure 3-87 changes because J is essentially unchanged between the BSE-1 and BSE-2 analyses—contrary 

to the capacity design philosophy (compare PUF to Pu,Capacity Design from AISC 341). 

Several exterior frame columns in the ELF- and RSA-designed frames do not satisfy the CP BPL acceptance 

criteria using the interaction equation because they are designated as force-controlled for flexure since PUF 

exceeds 0.5×PCL—see §3.2.2.1.4 for additional information and discussion. 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. 

3-82
 
 

0.26 

5

4

8 

2 

0 

.

.

5 

7 

3 

.

.

7

6

6 

1 

0

5

6 

9 

0.27 .5

0. 9 . 0

29

59

0.56

0.59 .7

0. .8

56

0 81

0.76

0.53 

2 .

0. 56 0 3 .7

0.62

0.57 

36

0. 27 0 8 .7

0.63

0.50 .5

0. 6 0

63 .67

0.55

0.54 

85

0. 27 0

86 .72

0.58

0.56 .5

0.70

0.72

0.58

0.34 

2 .

0. 94 0 7 .5

0.42

0.04 

0.32 0.07 

0.35 0.07 

0.37 0.08 

0.73 0.08 

0.72 0.09 

0.85 0.06 

0.86 0.06 

0.94 0.07 

0.95 0.07 

0.98 0.08 

0.98 0.08 

1.00 0.09

1.01 0.10

0.89 0.08 

1.14 0.11

(a) DCRN

6.94 

5.69 

4.74 

4.42 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

6.88 

6.88 

6.88 

6.88 

6.94 

6.94 

6.94 

6.94 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.41 

6.41 

6.61 

6.61 

(b) m-factors 

8.00 

8.00 

8.00 

8.00 

8.00 

8.00 

7.53 

7.53 

7.53 

7.53 

7.53 

7.53 

7.53 

7.53 

8.00 

8.00 

(c) Key 

Figure 3-85. LSP Assessment Results, 16-Story SCBF ELF, BSE-2 CP 

3-83
 
 

0.26 

5

4

6 

0 

8 

.

.

9 

5 

0 

.

.

7

6

4 

9 0

5

5

8 

0.26 

5 .

0. 7 . 0

28

57

0.55

0.58 .7

0. .7

36

0 79

0.74

0.52 

0 .

0. 36 0 2 .7

0.60

0.64 

27

0. 97 0 6 .8

0.72

0.74 .7

0. 9 0

90 .95

0.79

0.67 

27

0. 09 0

68 .90

0.72

0.54 .5

0.68

0.70

0.56

0.32 

0 .

0. 84

0 6 .5

0.40

0.04 

0.32 0.07 

0.35 0.06 

0.37 0.08 

0.72 0.08 

0.72 0.09 

0.84 0.06 

0.84 0.06 

0.92 0.07 

0.92 0.08 

1.02 0.08

1.02 0.08

1.05 0.09

1.05 0.10

0.94 0.08 

1.19 0.11

(a) DCRN

6.99 

5.75 

4.84 

4.52 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.94 

6.94 

6.94 

6.94 

6.60 

6.60 

6.60 

6.60 

6.41 

6.41 

6.61 

6.61 

(b) m-factors 

8.00 

8.00 

8.00 

8.00 

8.00 

8.00 

7.53 

7.53 

7.53 

7.53 

7.53 

7.53 

7.53 

7.53 

8.00 

8.00 

(c) Key 

Figure 3-86. LSP Assessment Results, 16-Story SCBF RSA, BSE-2 CP 

3-84
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0 2000 4000 6000 8000 10000 12000 14000 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

16 

15 

14 

13 

0 2000 4000 6000 8000 10000 12000 14000 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

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) 

(a) ELF (b) RSA 

Figure 3-87. LSP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, 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 3-88 and Figure 3-89 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 3-90 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. Figure 3-88(b) and Figure 3-89 (b) show that 

nearly all frame columns are deformation-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 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 the least conservative PUF as compared to AISC 341 SCBF column 

design requirements, as shown in Figure 3-90. 

3-85
 
 

0.23 

4

3

0 

6 

3 

.

.

8 

5 

1 

.

.

5

4

2 

7 0

5

5

2 

0.29 

6 .

0. 9 . 0

32

59

0.56

0.53 .6

0. .6

95

0 67

0.62

0.40 

3 .

0. 94 0 2 .5

0.43

0.38 

14

0. 84 0

1 .5

0.41

0.34 .3

0. 4 0

41 .45

0.38

0.40 

44

0. 15 0

74 .51

0.44

0.46 .5

0.53

0.56

0.50

0.33 

9 .

0. 04 0 7 .4

0.39

0.04 

0.29 0.07 

0.27 0.07 

0.29 0.08 

0.48 0.08 

0.49 0.09 

0.51 0.06 

0.52 0.06 

0.52 0.07 

0.54 0.07 

0.50 0.08 

0.51 0.08 

0.51 0.09 

0.51 0.10 

0.45 0.08 

0.54 0.11 

(a) DCRN

5.71 

4.78 

4.72 

4.48 

2.01 

1.79 

1.67 

1.51 

1.56 

1.00 

1.71 

1.61 

1.66 

1.58 

2.38 

1.86 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

4.88 

4.88 

4.88 

4.88 

4.94 

4.94 

4.94 

4.94 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.60 

4.41 

4.41 

4.61 

4.61 

(b) m-factors 

6.00 

6.00 

6.00 

6.00 

6.00 

6.00 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

6.00 

6.00 

(c) Key 

Figure 3-88. LDP Assessment Results, 16-Story SCBF ELF, BSE-1 LS 

3-86
 
 

0.23 

4

3

9 

5 

2 

.

.

4 

2 

8 

.

.

5

4

1 

6 0

5

5

2 

0.29 

6 .

0. 8 . 0

32

58

0.56

0.52 .6

0. .6

85

0 66

0.61

0.39 

2 .

0. 84 0

1 .5

0.42

0.43 

74

0. 35 0 6 .5

0.47

0.49 .5

0. 6 0

58 .62

0.54

0.49 

45

0. 36 0

85 .63

0.54

0.45 .4

0.52

0.55

0.49

0.32 

9 .

0. 04

0 7 .4

0.39

0.04 

0.29 0.07 

0.27 0.06 

0.29 0.08 

0.47 0.08 

0.49 0.09 

0.50 0.06 

0.51 0.07 

0.51 0.07 

0.51 0.08 

0.55 0.08 

0.55 0.09 

0.55 0.09 

0.55 0.10 

0.49 0.08 

0.65 0.11 

(a) DCRN

5.73 

4.80 

4.74 

4.50 

2.08 

1.86 

1.74 

1.58 

1.68 

1.55 

1.00 

1.00 

1.00 

1.00 

1.92 

1.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

5.00 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.88 

4.94 

4.94 

4.94 

4.94 

4.60 

4.60 

4.60 

4.60 

4.41 

4.41 

4.61 

4.61 

(b) m-factors 

6.00 

6.00 

6.00 

6.00 

6.00 

6.00 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

5.63 

6.00 

6.00 

(c) Key 

Figure 3-89. LDP Assessment Results, 16-Story SCBF RSA, BSE-1 LS 

3-87
 
 

 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

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 (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

Roof 

Floor 

16 

15 

14 

13 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 

Axial Load Demand, P (kips) 

PUF (J = Max[min DCR,2]) 

PUF (J = 1) 

Pu,Omega (ASCE 7) 

Pu,Capacity Design (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP) 

12 

11 

10 

9 

8

Floor 

Base 

2 

3 

4 

5 

6 

7 

Base 

2 

3 

4 

5 

6 

7 

Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-90. LDP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-1 

3.2.2.3.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-91 and Figure 3-92 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 3-93 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. Figure 3-91(b) and Figure 3-92 (b) show 

that nearly all exterior frame columns are force-controlled for flexure and the braces tend toward a ‘slender’ 

classification in ASCE 41 Table 5-5. 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 the least conservative PUF as compared to AISC 341 SCBF column 

design requirements, as shown in Figure 3-93. 

3-88
 
 

0.31 

0.34 

0.63 

0.60 

0.57 

0.63 

0.72 

0.66 

0.42 

0.53 

0.55 

0.46 

0.40 

0.51 

0.54 

0.44 

0.35 

0.43 

0.47 

0.40 

0.41 

0.49 

0.53 

0.46 

0.49 

0.55 

0.58 

0.52 

0.34 

0.42 

0.49 

0.41 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

6.88 

6.88 

6.88 

6.88 

6.94 

6.94 

6.94 

6.94 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.60 

6.41 

6.41 

6.61 

6.61 

0.27 0.04 6.72 8.00 

0.33 0.07 5.47 8.00 

0.34 0.07 5.08 8.00 

0.35 0.08 4.76 8.00 

0.63 0.08 1.00 8.00 

0.64 0.09 1.00 8.00 

0.66 0.06 1.00 7.53 

0.67 0.07 1.00 7.53 

0.68 0.07 1.00 7.53 

0.68 0.07 1.00 7.53 

0.66 0.08 1.00 7.53 

0.67 0.08 1.00 7.53 

0.66 0.09 1.00 7.53 

0.67 0.10 1.00 7.53 

0.62 0.08 1.00 8.00 

0.81 0.11 1.00 8.00 

(a) DCRN (b) m-factors 

Figure 3-91. LDP Assessment Results, 16-Story SCBF ELF, BSE-2 CP 

(c) Key 

3-89
 
 

0.31 

0.34 

0.63 

0.60 

0.56 

0.62 

0.71 

0.65 

0.41 

0.52 

0.54 

0.45 

0.46 

0.56 

0.60 

0.50 

0.52 

0.62 

0.66 

0.57 

0.52 

0.62 

0.67 

0.58 

0.47 

0.54 

0.57 

0.51 

0.33 

0.41 

0.49 

0.40 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

7.00 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.88 

6.94 

6.94 

6.94 

6.94 

6.60 

6.60 

6.60 

6.60 

6.41 

6.41 

6.61 

6.61 

0.27 0.04 6.72 8.00 

0.33 0.07 5.47 8.00 

0.34 0.07 5.08 8.00 

0.35 0.08 4.76 8.00 

0.62 0.08 1.00 8.00 

0.63 0.09 1.00 8.00 

0.67 0.06 1.00 7.53 

0.67 0.07 1.00 7.53 

0.67 0.07 1.00 7.53 

0.68 0.08 1.00 7.53 

0.70 0.08 1.00 7.53 

0.70 0.09 1.00 7.53 

0.70 0.09 1.00 7.53 

0.70 0.10 1.00 7.53 

0.68 0.09 1.00 8.00 

0.87 0.11 1.00 8.00 

(a) DCRN (b) m-factors 

Figure 3-92. LDP Assessment Results, 16-Story SCBF RSA, BSE-2 CP 

(c) Key 

3-90
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

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 (AISC 341) 

PCL (ASCE 41) 

P max (NDP) 

P (NSP)	 

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 (AISC 341) 

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 3-93. LDP Assessment Results, Compression in Ext. Columns, 16-Story SCBF, BSE-2 

3.2.2.3.3 Nonlinear Static Procedure 

In this section, the following apply: 

	 Table 3-17 through Table 3-19 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-94 and Figure 3-95 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 (e.g., braces), notated in the figures. Sharp points in the 

curves are a result of the hysteretic model used for the braces not capturing member out-ofstraightness, which would gradually soften the curves as the buckling strengths are reached. Firstorder 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 3-96 and Figure 3-97 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 ELF-designed 

frame for both the BSE-1 and BSE-2 EHLs and the RSA-designed frame for BSE-2 EHL, whereas the 

target displacement governs the RSA-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 

3-91
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 3-17. NSP General Information, 16-Story SCBF (kip, inch) 

Design T1 K1 y Vy Ke Te h peak Vpeak W Cm C0 

ELF 2.03 258.5 9.3 2401 258.6 2.02 1.11 16.8 3363.0 21782 1.00 1.44 

RSA 2.08 243.2 9.4 2292 243.5 2.08 1.11 21.5 2494.9 21649 1.00 1.28 

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

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.45 4.08 1.00 1.00 26.0 2858.7 16.8 0.50 -0.22 -0.03 -0.07 6.59 OK 

RSA 0.45 4.25 1.00 1.00 24.2 2490.7 21.5 0.07 -0.14 -0.03 -0.05 8.62 OK 

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

R ≤ Design Sa R C1 C2 t Vt d 1 2 P- e Rmax Rmax 

ELF 0.30 2.72 1.00 1.00 17.4 3054.8 16.8 0.50 -0.22 -0.03 -0.07 6.59 OK 

RSA 0.30 2.83 1.00 1.00 16.2 2466.9 16.2 0.11 -0.12 -0.03 -0.05 8.71 OK 

Roof Drift Ratio at CoM (%) 

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.5 

Total Base Shear (Kips) 

3600 

3200 

2800 

2400 

2000 

1600 

1200 

800 

400 

0 0.000 

0.018 

0.037 

0.055 

0.073 

0.092 

0.110 

0.129 

0.147 

0.165 

(9.3,2401.0) 

(16.8,3363.0) 

Roof Drift Ratio (%) for Brace Response

Story Buckle Yield CP-Comp CP-Tens 

16 

15 (6-1)0.29 (19-3)0.48 

14 

13 (1-1)0.24 (5-3)0.29 

12 (17-2)0.44 

11 (3-1)0.27 (13-3)0.36 

10 (13-2)0.36 (21-1)0.52 (23-3)0.57 

9 (2-1)0.24 (9-3)0.32 (1-1)0.54 (2-3)0.61 

8 (14-1)0.38 (18-2)0.47 (34-1)1.08 (34-3)1.08 

7 (7-1)0.30 (16-3)0.41 (32-2)0.95 (33-4)1.05 (8-1)1.12 (8-3)1.12 

6 (11-2)0.34 (26-1)0.61 (30-3)0.67 (9-1)1.17 (10-3)1.18 

5 (4-1)0.28 (12-3)0.36 (27-2)0.64 (29-4)0.65 (5-1)0.67 (5-3)0.67 

4 (8-2)0.31 (15-4)0.40 (24-1)0.58 (22-1)0.57 (6-2)0.91 (7-4)0.93 (11-1)1.38 (12-3)1.39 

3 (4-1)0.28 (10-3)0.27 (31-2)0.92 (31-4)0.92 (3-1)0.63 (4-3)0.63 

2 (25-2)0.59 (28-4)0.65 

1 (14-1)0.38 (20-3)0.49 

Total Base Shear / W 

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

0 5 10 15 20 25 30 35 40 

Roof Displacement at CoM (Inches)

Figure 3-94. 16-Story SCBF ELF Pushover, BSE-2 

3-92
 
 

 

 

 

 

 

 

 

 

 

 

 

 

Roof Drift Ratio at CoM (%) 

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.5 

3600
 0.166 

Total Base Shear (Kips) 

Total Base Shear / W 

3200
 

2800
 0.129 

0 5 10 15 20 25 30 35 40 

0.000 

0.018 

0.037 

0.055 

0.111 

0.148 

(9.4,2292.0) 

(21.5,2494.9) 

Roof Drift Ratio (%) for Brace Response

Story Buckle Yield CP-Comp CP-Tens 

16 

15 (10-1)0.32

14 

13 (4-1)0.25 (12-3)0.34

12 

11 (7-1)0.28 (28-3)0.98

10 (14-2)0.36 (23-1)0.57 (27-3)0.73 

9 (3-1)0.23 (11-3)0.32 (25-2)0.62 (26-4)0.65 (6-1)0.59 (7-3)0.72

8 (15-1)0.39 (17-3)0.42 (8-1)0.89 (9-3)0.91

7 (1-1)0.20 (5-3)0.25 (1-1)0.42 (2-3)0.45

6 (5-2)0.25 (9-4)0.31 (20-1)0.52 (18-3)0.50 (3-2)0.54 (4-4)0.56

5 (2-1)0.21 (6-3)0.27 (19-2)0.51 (22-4)0.54 

4 (13-2)0.34 (24-4)0.58

3 (8-1)0.30 (16-3)0.39

2 

1 (21-1)0.53 

 RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

2400
 

2000
 0.092 

1600
 0.074 

1200
 

800
 

400
 

0 

Roof Displacement at CoM (Inches)

Figure 3-95. 16-Story SCBF RSA Pushover, 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 SCBF ELF Pushover – Story Drift Ratios – BSE-2 

3-93
 
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 3-97. 16-Story SCBF RSA Pushover – Story Drift Ratios – BSE-2 

Figure 3-98 illustrates which frame columns 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. Similar to results from the linear procedures, most exterior frame columns are forcecontrolled for flexure. 

Figure 3-99 through Figure 3-102 illustrate the DCRN values if greater than unity for the ELF- and RSAdesigned 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. Nearly all brace axial 

compression actions satisfy the LS and CP BPL acceptance criteria. All brace axial tension actions satisfy 

the LS and CP BPL acceptance criteria. All columns remain essentially elastic at the BSE-2 EHL, therefore 

satisfying the force-controlled lower-bound elastic acceptance criteria where required. 

3-94
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 3 

Sym. About 

ELF NDP LS & CP 

ELF NSP CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RSA NDP LS & CP 

ELF NDP LS & CP 

RSA NDP LS & CP 

ELF NDP LS & CP 

ELF NSP CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

ELF NSP CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RSA NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

2 

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 Flo or
 

(ELEV = 18 ft.)
 

All colum ns are deformation- Column is force-controlled for flexure if 

controlled (DC) fo r flex ur e unless P > 0.5×PCL, where P is computed at the 

indicated as for ce-controlled (FC) target displacement for the NSP and as 

in figure the maxim um value for the NDP 

Figure 3-98. Schematic of flexural actions in columns, 16-Story SCBF (NSP and NDP) 

3-95
 
4 3 2 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

1.38C 

1.08C 

1.09C 

1.03C 

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 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.)
 

Figure 3-99. NSP Assessment Results, 16-Story SCBF ELF, BSE-1 LS (+push to left) 

3-96
 
4 3 2 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

2.31C 

2.06C 

1.23C 

1.11C 

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 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.)
 

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

3-97
 
4 3 2 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

1.14C 

1.10C 

2.78C 

2.64C 

1.75C 

1.67C 

1.39C 

1.08C 

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 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.)
 

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

3-98
 
 

4 3 2 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

1.94C 

1.64C 

2.64C 

2.51C 

4.39C 

4.12C 

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 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.)
 

Figure 3-102. NSP Assessment Results, 16-Story SCBF RSA, BSE-2 CP (+push to left) 

3-99
 
 

3.2.2.3.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the N-S direction of MC16 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 3-103 through Figure 3-106 show the performance of the HSS braces 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 from the figures, the ELF-designed frame does not perform 

significantly better than the RSA-designed frame—a corollary of the two frame designs being nearly the 

same. Both designs have braces (lower story of the two-story X bracing) that do not satisfy the LS or CP 

BPL acceptance criteria. All braces except those in the second story approach being classified as ‘slender’ 

by ASCE 41 Table 5-7. 

The average ratio of secondary to primary component acceptance criteria for all HSS sections with the 

configuration in this frame is 1.25 for the CP SPL (1.43 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. However, 

brace fracture is not explicitly modeled in the analysis—see §3.2.2.1.3 for more information. 

Roof 

16 

15 

14 

Median 13 

Mean 12 

84th 

11 Mean+1std

Left Brace 

0 1 2 3 4 

Right Brace 

0 1 2 3 4 

Floor ID 

10 NSP 

9 LSP 

8 LDP 

7 

6 

5 

4 

3 

2 

Base 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-103. NDP Assessment Results, Brace Struts, 16-Story SCBF ELF, BSE-1 LS 

3-100
 
Floor ID Floor ID 

Roof 

16 

15 

14 

13 

12 Median

10 

11 Mean

84th

Mean+1std

9 NSP

8 LSP

7 LDP 

6 

5 

4 

3 

Base 

2 Left Brace Right Brace

01 2 3 4 01 2 3 4 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-104. NDP Assessment Results, Brace Struts, 16-Story SCBF RSA, BSE-1 LS

 

Roof 

16 

15 

14 

13 

12 Median

11 Mean

10 84th

Mean+1std 9 

 NSP 8 LSP

7 LDP 

6 

5 

4 

3 

2 Left Brace Right Brace

Base 

012 3 4 012 34 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-105. NDP Assessment Results, Brace Struts, 16-Story SCBF ELF, BSE-2 CP 

3-101
Floor ID 

Roof 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

Left Brace 

0 1 2 3 4 5 

Right Brace 

0 1 2 3 4 5 

Median 

Mean 

84th 

Mean+1std

 NSP 

LSP 

LDP 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-106. NDP Assessment Results, Brace Struts, 16-Story SCBF RSA, BSE-2 CP 

Figure 3-98 (see NSP section) illustrates which flexural actions in the frame columns are force-controlled 

for both the NSP and NDP. Figure 3-107 and Figure 3-108 show the curvature ductility demand on the 

column hinges (i.e., section strength) at the BSE-2 EHL—see discussion on column hinge modeling in 

§3.2.1.2. Figure 3-109 and Figure 3-110 show the elastic member strength interaction results at the BSE-2 

EHL—see discussion on column strength modeling in §3.2.1.2. These figures illustrate that linear analysis 

has difficulty assessing columns that support components that experience significant strength loss quickly 

as common for a brace in compression. 

Column hinges at the base above the brace connection experience inelastic strain demands (yield 

corresponds to a DCRN = 1 in the figures) using the mean 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. However, the deformation demands are considerably lower 

than the primary CP acceptance criteria for a ‘column’. This effect 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. 

Still, the exterior base columns in both the ELF- and RSA-designed frames are force-controlled for flexure 

and therefore do not satisfy the lower-bound elastic acceptance criteria at the BSE-2—see §3.2.2.1.4 for 

additional information and discussion. 

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 not applicable here because 

most of the exterior frame columns are force-controlled for flexure in the linear assessment procedures. 

3-102
 
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. 

Roof 

16 Col. Line B Col. Line C Col. Line D

15 

14 

13 

12 Median

11 Mean

 84th 10 

Floor ID Floor ID 

 Mean+1std

9 NSP

8 LSP

7 LDP 

6 

5 

4 

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 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 3-107. NDP Assessment Results, Column Hinges, 16-Story SCBF ELF, BSE-2 Yield 

 

16 

Roof 

Col. Line B Col. Line C Col. Line D

15 

14 

13 Median

12 Mean

11 84th

10 Mean+1std

9 NSP

7 

8 LSP

 LDP 

6 

5 

4 

3 

2 

Base 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 

DCRN = Total Deformation / Yield Deformation at P / PCL = 0.2 

Figure 3-108. NDP Assessment Results, Column Hinges, 16-Story SCBF RSA, BSE-2 Yield 

3-103
16 

Roof Col. Line B Col. Line C Col. Line D

15 

14 

13 

12 Median

11 Mean

10 84th

9 Mean+1std

7 

8 LSP

 LDP 

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 0.0 0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Result 

(NDP = max of either axis, LSP / LDP = equations from ASCE 41) 

Figure 3-109. NDP Assessment Results, Column Members, 16-Story SCBF ELF, BSE-2 

 

16 

Roof 

Col. Line B Col. Line C Col. Line D

15 

14 

13 

12 Median

11 Mean

9 

10 84th

Mean+1std

 LSP

8 LDP 

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 0.0 0.2 0.4 0.6 0.8 1.0 1.2 

DCRN = P-M Interaction Result 

(NDP = max of either axis, LSP / LDP = equations from ASCE 41) 

Figure 3-110. NDP Assessment Results, Column Members, 16-Story SCBF RSA, BSE-2 

Floor ID Floor ID 

3-104
 

Seismic Assessment Discussion 

The discussion in this section focuses on the following component design actions: 

 Brace axial force (compression and tension)23 

 Beam and column flexure within anticipated plastic hinge zones (section strength) 

 Column axial-moment interaction strength (e.g., 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 §5.5.2.5). 

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 assessment does not allow the analysis to account for post-yield strength and deformation 

capacity of a gusset-type connection or for its influence on the performance of adjacent members once a 

brace fractures. 

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 Assessment Procedures 

The following discusses the analytical results for the noted components from the linear procedures for each 

archetype building. 

3.2.3.1.1 Brace Members 

Table 3-20 provides a summary of the performance of the brace members for each linear assessment 

procedure and each BPL. Brace members consistently satisfy the performance criteria for the LS and CP 

BPL for both linear procedures. 

23 Brace connections to adjacent members are force-controlled per ASCE 41 §5.5.2.4.1. 

3-105
 
Table 3-20. 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 

As a side note, Table 3-21 summarizes the effects of design (AISC 360) and assessment (ASCE 41) 

provisions on the DCRN for a brace member at 2⁄3×MCER for the LS BPL. On the component capacity side, 

the axial compression strength prescribed in ASCE 41, PCE, and AISC 360, Pn, have the same underlying 

equation; differences arise when using nominal versus expected material properties and a strength reduction 

factor, c = 0.9, resulting in a capacity ratio (ASCE 41 / AISC 360) ranging from 1.2 to 1.4 depending on 

KL / r for the axis of buckling. 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 braces 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 while ASCE 7 divides the elastic demand by R (= 6 for an SCBF). 

The m-factor ranges from 4.26 to 4.88 (see ASCE 41 Table 5-5) because HSS braces with slenderness 

values in the “inelastic” bucking range were considered in this discussion. Thus, for a brace member 

designed per ASCE 7 and its referenced standards whose nominal strength exactly equals the demand from 

ASCE 7, the corresponding DCRN for the linear assessment will be less than or equal to 1.03, as illustrated 

in Figure 3-111. This value increases to 1.09 for the CP SPL at the BSE-2. 

Table 3-21. Effect of Design and Assessment Provisions on DCRN of a Brace – LS SPL at the BSE-1 EHL 

Demand Capacity Effect on DCRN 

a) ASCE 41 Sa at T = Tanalysis 1 1 4.26 to 4.88 m      0.658 FF ye e P CE F ye g A        

 

# 1.0 1.23 to 1.41 

1.19 to 1.38 

DCRN

 

1.03  DCRN 

b) ASCE 7 and 

AISC 341 

Sa at T = 

min(Tanalysis, CuTa) 1 1 6 R    0.9 0.658 FF y e cn P F y g A     

Ratio (a / b) a / b ≤ 1.0 a / b ≤ 1.23 to 1.41 

Given: 4.71 K L r E F  y

a / b ≤ 1.19 to 1.38 

Assuming CuTa and Tanalysis are both on the descending branch of the response spectrum (but less the TL 

defined in ASCE 7), the following can be observed: 

S a ASCE , 41 S D1 T analysis  C T  ua (3-18) S , 7 CT T  S a ASCE D 1 u a  analysis 

As an example, the ELF-designed MC8 shows a reduction in the demand of 34 percent (0.99 / 1.5 = 0.66 

from Table 2-5) from that using CuTa. This reduction aligns well with the DCRN values observed in the LSP 

results, see Figure 3-53. Inversely, if the brace exactly satisfied the ASCE 41 assessment criteria, the design 

demand would be equal to approximately 1.5 times the nominal design strength—clearly larger than what 

would be comfortably accepted in practice. 

3-106
 
 

 

65 70 75 80 85 90 95 100 

0.9 

1.0 

1.1 

1.2 

1.3 

1.4 

1.5

 capacity ratio (ASCE 41 / AISC 360)

 demand ratio (ASCE 41 / ASCE 7)

 demand ratio / capacity ratio 

Comparison Ratio 

Slenderness Parameter, KL/r 

Figure 3-111. Effect of Design and Assessment Provisions on the DCRN

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. 

Table 3-22. Performance Summary of Columns 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 

16-Story 

ELF 

RSA 

ELF 

RSA 

All CM Pass 

All CM Pass 

All BC Pass 

All BC Pass 

Ext CM Fail (2) 

13% 

Ext CM Fail (2) 

13% 

Ext CM Fail (6) 

19% 

Ext CM Fail (10) 

31% 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

All CM Pass 

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, principally for the CP BPL using the 

3-107
 
 

LSP. These members are all force-controlled for both axial force and flexure because PUF exceeds 

0.5×PCL—generally associated with weak-axis flexural buckling. As such, MUF and MCL are used in the 

interaction equation (ASCE 41 Equation 5-12). Determination of MUF is subject to the same limitations as 

PUF (see sections on assessment results). As noted previously, the force distribution used in the LSP directly 

contributes to the increased column forces. However, generally speaking, the estimated axial load demands 

in the columns are the least conservative approximations, as compared to more rigorous analysis procedures 

(see the axial load figures (e.g., Figure 3-64)). Nonetheless, there are many columns that pass the forcecontrolled assessment criteria. It is unclear whether certain upper story columns fail by member instability 

or section hinging because of the adopted interaction equation in ASCE 41. Additionally, it is difficult to 

assess column failures with interaction results slightly over 1.0 due to the uncertainties in the analysis 

procedures and conservatisms in the assessment provisions. However, the axial load demands computed 

using ASCE 41 §3.4.2.1.2-2 are generally less than those determined using a capacity design approach (e.g., 

AISC 341 §F2.3) or the NDP. 

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-tobase 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. 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 

column-to-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 discussed previously, it is of debatable validity that force-controlled response be triggered with PUF / 

PCL in lieu of PUF / Pye, as was done in FEMA 273. The interaction equation in ASCE 41 used for the case 

of out-of-plane instability and in-plane flexure is also debatable; ASCE 41 would benefit from following 

AISC 360 in this regard (see AISC 360 §H1.3). ASCE 41 would also 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. The columns in the 4-story frames are somewhat oversized from that required 

from analysis to satisfy section compactness requirements in AISC 341, and therefore, the columns 

efficiently satisfy the acceptance criteria, regardless of estimation of PCL. All the frame columns in the 4­

story frames are deformation-controlled for flexure. As a side note, there is also considerably less scatter in 

the axial load demands in the columns from the various approximation methods. 

3-108
 
 

 

 

 

 

 

 

 

 

 

3.2.3.1.3 Summary 

Table 3-23 summarizes the performance of the archetype buildings in reference to the BSO for both linear 

procedures. Table 3-24 provides the base shears computed with the linear assessment procedures. All 

frames satisfy the seismic performance objective using the LDP, but only the 4-story frames satisfy the 

criteria using the LSP. Column performance (primarily at the base) controls the overall assessment of the 

SCBF frames for the LSP. However, in this analytical context, base column failure due to flexural action 

(plastic hinge) in an SCBF is not necessarily detrimental to the overall structural performance unless total 

strength loss of adjacent braces occurs. As noted above, additional research is needed on assessment criteria 

for columns. 

Table 3-23. BSO Performance Summary of Archetype Buildings, Linear Procedures 

Archetype Design BM

LSP 

CM Conn. Design BM

LDP 

CM Conn. 

4-Story 

8-Story 

16-Story 

ELF 

RSA 

ELF 

RSA 

ELF 

RSA 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Fail 

Fail 

Fail 

Fail 

NA 

NA 

NA

NA

NA

NA

ELF 

RSA 

ELF 

RSA 

ELF 

RSA 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

NA 

NA 

NA 

NA 

NA 

NA 

The assessment results from the LSP and LDP illustrate that, on average, the ELF-designed SCBF performs 

only slightly better than the RSA-designed SCBF for all archetype buildings—a corollary of the two frame 

designs being nearly the same. This can be attributed to the slight increase in 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. Further, section compactness requirements in AISC 341 resulted 

in minor variations in member sizes during design. 

Table 3-24. Summary of Base Shears, Linear Procedures (kips) 

MC4 MC8 MC16 

EHL Routine ELF RSA ELF RSA ELF RSA 

LSP 4409 4044 4403 4196 6283 6070 

BSE-1 LDP 3999 3760 3654 3998 5778 5666 

Ratio 0.91 0.93 0.83 0.95 0.92 0.93 

LSP 6614 6067 6604 6293 9425 9105 

BSE-2 LDP 5999 5640 5848 5697 8667 8499 

Ratio 0.91 0.93 0.89 0.91 0.92 0.93 

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. 

3-109
 
Analytical results based on component-level performances obtained from the LDP suggest that special 

concentrically braced frames designed in accordance with ASCE 7 and its referenced standards can achieve 

the selected seismic performance objective of an existing building intended to be equivalent to a new 

building. Conversely, results from the LSP provide a contrary inference based on the performance of the 

columns, a result that can be enhanced by more mechanistically consistent column provisions and analytical 

modeling parameters. 

Nonlinear Assessment 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 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 Brace Members 

Table 3-25 provides a summary of the performance of the brace members 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 braces 

consistently do not satisfy the performance criteria for the LS and CP BPL for both nonlinear procedures. 

Although the median response is biased less 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 braces than that given by the NSP. 

Table 3-25. Performance Summary of Brace Members (BM) per frame, Nonlinear Procedures 

Archetype Design 

LS

NSP 

CP 

NDP 

(based on mean response of record set) 

LS CP 

4-Story 

ELF 

RSA 

BM Fail (2) 

25% 

BM Fail (1) 

13% 

BM Fail (3) 

38% 

BM Fail (3) 

38% 

BM Fail (6) 

75% 

BM Fail (8) 

100% 

BM Fail (7) 

88% 

BM Fail (8) 

100% 

8-Story 

ELF 

RSA 

BM Fail (1) 

6% 

BM Fail (1) 

6% 

BM Fail (2) 

13% 

BM Fail (2) 

13% 

BM Fail (4) 

25% 

BM Fail (6) 

38% 

BM Fail (6) 

38% 

BM Fail (8) 

50% 

16-Story 

ELF 

RSA 

BM Fail (4) 

6% 

BM Fail (4) 

6% 

BM Fail (8) 

13% 

BM Fail (6) 

9% 

BM Fail (14) 

22% 

BM Fail (12) 

19% 

BM Fail (17) 

27% 

BM Fail (16) 

25% 

The distribution of brace failures identified by the nonlinear procedures illustrates the effect that design 

choices can have on frame performance. For example, the variation in failures between alternating stories 

is due to maintaining the brace size over two stories. Similarly, the location of the failures indicated by the 

3-110
 
 

NSP highlights variations between the force distributions used in assessment and that used for design. 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. 

3.2.3.2.2 Member Cross-section Strength (flexural hinge) and Global Strength (member stability) 

Table 3-26 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 the frames 

consistently fail the performance criteria. These failures are a corollary of the column-to-base connection 

assumptions adopted for analysis and the modeling parameters for P-M hinges in ASCE 41 (see linear 

discussion above for information). However, while the mean response of the record set indicates column 

hinging at the base, the median response does not (recall that all analyses completed). 

Table 3-26. Performance Summary of Columns 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 

--­

--­

CH Fail (2) 

13% 

All CH Pass 

--­

--­

CH Fail (2) 

13% 

CH Fail (2) 

13% 

8-Story 

ELF

RSA 

--­

--­

CH Fail (2) 

6% 

All CH Pass 

--­

--­

CH Fail (2) 

6% 

CH Fail (2) 

6% 

16-Story 

ELF 

RSA 

--­

--­

All CH Pass 

All CH Pass 

--­

--­

CH Fail (3) 

3% 

CH Fail (3) 

3% 

These exterior column members that fail the criteria are force-controlled for both axial force and flexure 

due to P exceeding 0.5×PCL for the NSP and NDP. 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. 

3-111
 
 

Table 3-27 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. It is mechanistically 

inconsistent to adjust material properties between section strength and member stability for a given column 

(i.e., hinge uses Pye and member uses PCL). 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 in-plane 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 wide-flanged 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 3-27. 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 SCBF columns (most are force-controlled) except at the base 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. 

3.2.3.2.3 Summary 

Table 3-28 summarizes the performance of the archetype buildings in reference to the BSO for both 

nonlinear procedures. Brace member 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. As noted above, additional research is needed 

on assessment criteria for brace connections and columns. In the end, none of the designed frames satisfy 

the seismic performance objective using the NSP (not considering results from the LDP where required) or 

the NDP. 

Table 3-28. BSO Performance Summary of Archetype Buildings, Nonlinear Procedures 

Archetype Design 

BM 

NSP 

CH CM 

Design 

NDP 

(based on mean response of record set) 

BM CH CM 

4-Story 

ELF 

RSA

Fail 

Fail 

Fail 

Pass 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass 

Fail Fail Pass 

8-Story ELF 

RSA

Fail 

Fail 

Fail 

Pass 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass 

Fail Fail Pass 

16-Story 

ELF 

RSA

Fail 

Fail 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass 

Fail Fail Pass 

3-112
 
The assessment results from the NSP and NDP illustrate that, on average, the ELF-designed SCBF does 

not perform significantly better than the RSA-designed SCBF for all archetype buildings—a corollary of 

the two frame designs being nearly the same. This result can be attributed to the slight increase in 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. Further, section compactness requirements 

in AISC 341 resulted in minor variations in member sizes during design. 

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 strut-type brace members. 

Analytical results based on component-level performances obtained from the NSP and NDP suggest that 

special concentrically 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 braces and, to a lesser extent, 

the columns. The results for the columns can be enhanced by more mechanistically consistent column 

provisions and analytical modeling parameters. The results for the braces provide a contrary inference to 

that provided for the linear procedures. However, brace performance is based on high fidelity analytical 

modeling parameters (except for brace fracture) thus room for brace model enhancement is limited, 

although alternative modeling practices could be investigated. 

Comparison between Linear and Nonlinear Assessment Results 

Table 3-29 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. No tangible 

consistency is evident in the global performance rating of the frames among the various assessment 

procedures. However, not all component performance failures align between the procedures, as discussed 

previously (e.g., brace members). The conservatism of the linear procedures is also apparent, as expected. 

3-113
 
 

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 

brace members 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 3-29. 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 

Pass 

Fail 

Fail 

Fail 

Fail 

16-Story 

ELF 

RSA 

Fail 

Fail 

Pass 

Pass 

Fail 

Fail 

Fail 

Fail 

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 

brace members 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. 

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 diagonal braces. 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 brace members while the nonlinear procedures illustrate that the braces fail 

the acceptance criteria. 

3-114
 
For observation purposes only, Figure 3-112 illustrates the story drift ratios (normalized to two percent) for 

the RSA-designed frame at the BSE-2 EHL from the NDP. Evaluating drift ratios against Figure 3-77 shows 

that some braces are failing the CP criteria prior to achieving a two percent story drift ratio. 

Roof 

 Median

 Mean

8 84th

 Mean+1Std

7 Drift Ratio 

6 

0 1 2 3 

Floor ID 

5 

4 

3 

2 

Base 

Drift Ratio / 0.02

Figure 3-112. NDP Assessment Results, Story Drift Ratios, 8-Story SCBF RSA, BSE-2 CP 

The columns that failed the acceptance criteria are typically force-controlled due to high axial loads, a result 

of using P / PCL in lieu of P / Pye to model flexural hinge strength and trigger force-controlled response. In 

comparison to the results from the NDP, the linear procedures produced conservative estimates of poor 

performance. On average, the linear procedures slightly overestimate the axial force demand in the exterior 

columns. Although there is general agreement between the procedures on which members may pose a risk, 

the results from the NDP illustrate that the column hinges can satisfy the performance criteria if the hinges 

were not force-controlled using PCL, which is generally governed by out-of-plane flexural buckling. 

Enhancements to the assessment of beam-columns could consider using a dual assessment criterion that 

evaluates stability and flexural hinging separately (as is done for the NDP in this study). Noting the number 

of force-controlled columns (assuming PCL is appropriate), ASCE 41 could impose a capacity design 

philosophy for a CBF similar to that prescribed for an EBF to simplify and clarify the process. As such, an 

SCBF designed in accordance with AISC 341 would pass the assessment criteria in ASCE 41 by default. 

The failure of the SCBF 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, which went undetected during the (linear) design process and the ensuing linear 

performance assessment. 

3-115
 

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 special concentrically braced frames (SCBF) as the 

lateral force-resisting system (LFRS). 

A suite of archetype buildings that incorporate SCBFs 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 SCBFs 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 SCBFs 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. 

4-5
 
 

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

brace members. Contrary performance results indicate acceptance criteria that need further 

calibration. 

Special Concentrically Braced Frame 

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

the assessment of the SCBFs. 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, dependent on the assessment 

procedure used, that new SCBFs 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 braces and, to a lesser extent, 

the columns. Assessment results for brace members 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 SCBFs. 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 brace members 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 from increasing the 

analytical complexity. Given a properly designed new brace member, the linear procedures will 

result in a maximum DCRN value for a primary component of approximately the ratio of CuTa / T1, 

which is less than or equal to unity. 

	 A significant number of brace members did not satisfy the acceptance criteria for the nonlinear 

procedures. Brace performance is based on high fidelity analytical modeling parameters (except 

for brace fracture); thus, room for brace modeling enhancement is limited, although alternative 

modeling practices could be investigated. Research should investigate the influence of the loading 

protocol adopted to establish the deterministic acceptance criteria for brace members. 

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

acceptance criteria. 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). Refinement of the relevant interaction equations to evaluate specific failure 

mechanisms could assist by allowing what would be a force-controlled column to be classified as 

“deformation-controlled”. 

	 Components of the SCBFs 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 

4-6
 
(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 SCBF 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 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. 

4-7
 
	 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 

diagonal brace members in the MC8 buildings. Even if secondary component criteria were 

implemented, the DCRN values still indicate unsatisfactory performance in the several floors. The 

primary acceptance 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. 

Concentrically Braced Frames 

The following items are considerations for future studies to enhance ASCE 41 assessment provisions for 

concentrically braced frames: 

 Research should critically examine the applicability of the generalized modeling parameters for 

strut-type braces for use in the nonlinear procedures. 

 Research should investigate the correlation between acceptance criteria for the linear and nonlinear 

procedures. This effort can include alternative modeling strategies for brace members. 

	 Research should investigate the influence of the loading protocol adopted to establish the 

deterministic acceptance criteria for strut-type brace members. Similarly, the influence of total 

brace fracture on the acceptance criteria can be included. ASCE 41-13 partly addressed this issue 

in revised acceptance criteria for braces in tension. However, acceptance criteria for braces in 

compression always governed the assessment in this study. A supplementary analysis performed 

on the RSA-designed MC8 using the revised ASCE 41-13 criteria indicated no change in the 

governing DCRN value. 

	 Research should investigate the use of acceptance criteria and modeling parameters for brace 

connections. Guidance is needed concerning modeling parameters for beam-to-column connections 

strengths and acceptance criteria once the adjacent brace(s) experience total strength loss from 

fracture. 

	 Research is needed to develop acceptance criteria and modeling parameters for column / brace-tobase connections, including embedded connections. 

4-8
 
	 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: 

	 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 

Special Concentrically Braced Frames 

The following items are considerations for future studies to enhance AISC 341 provisions of special 

concentrically braced frames: 

	 The design adopted for the archetype buildings indicate that there is minor variation in member 

sizes when using either the ELF procedure or the RSA to determine required member strengths. 

This is primarily due to section compactness requirements. 

	 The axial load demands on the columns determined from the NDP are consistently greater than that 

determined using the system overstrength factor (i.e., ASCE 7) and less than that determined from 

the capacity analysis prescribed in AISC 341 §F2.3. As such, results indicate that the capacity 

design procedure in AISC 341 does well in setting the required member strength. Research should 

investigate whether a 0.88 factor, as allowed for an EBF—see AISC 341 §F3.3, or similar concept 

is applicable for an SCBF. Similarly, the use of the overstrength factor to compute required axial 

strengths should be disregarded since it can be highly unconservative. AISC 341 can provide more 

guidance on how to perform this analysis as well as how to incorporate the flexural demand that 

can exist in beams and columns after brace fracture. 

4-9
 
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 Special Concentrically Braced Frame 

Table A-1 summarizes the 14 strong motion records used for the nonlinear dynamic procedure (NDP) for 

the N-S direction of MC4 special concentrically braced frame (SCBF). 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 MC4 

ID EQ No. Event Name Station Comp.1 Error2 BSE-2 

Scaling3 

BSE-1 

Scaling3 Step4

 Time5 

1 40 Chi-Chi, Taiwan TCU045 2 6 1.853 1.236 0.005 90 

2 35 Cape Mendocino Rio Dell Overpass 1 9 2.005 1.337 0.020 36 

3 9 Imperial Valley Delta 1 9 2.543 1.695 0.010 100 

4 31 Superstition Hills El Centro Imp. Co. 1 9 2.301 1.534 0.005 40 

5 4 Northridge Canyon Country-WLC 2 11 1.469 0.980 0.010 20 

6 17 Kocaeli, Turkey Duzce 1 11 2.256 1.504 0.005 28 

7 7 Hector Mine Hector 1 13 3.719 2.479 0.010 46 

8 34 Superstition Hills Poe Road (temp) 2 14 2.807 1.871 0.010 23 

9 21 Landers Yermo Fire Station 1 15 3.024 2.016 0.020 44 

10 15 Kobe, Japan Shin-Osaka 1 15 2.811 1.874 0.010 41 

11 20 Kocaeli, Turkey Arcelik 2 15 6.796 4.531 0.005 30 

12 6 Duzce, Turkey Bolu 2 15 1.172 0.781 0.010 56 

13 28 Loma Prieta Gilroy Array #3 2 16 2.689 1.793 0.005 40 

14 44 Friuli, Italy Tolmezzo 2 16 1.878 1.252 0.005 37 

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 4 

 Code Code

 121422 121422

 120611 120611

Original EQ 121321

 121211 3 

Scaled EQ 121321

 121211

Spectral Acceleration (g) 

 120122

2 120811

 120521

 121222

 120911

 120721

 120822

 120412

1 121712

 121022

 Average 

Spectral Acceleration (g) 

 120122

 120811

 120521

 121222

 120911 2 120721

 120822

 120412

 121712

 121022 1 Average 

01 

0 

2 3 

Period (sec)

4 5 6 01 

0 

2 3 

Period (sec)

4 5 6 

2 

Scaled Average Spectrum 

Spectral Acceleration (g) 

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 MC4 

A-4 
2 2 3 

EQ 1 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

 121321 Scaled

 121321 Unscaled 

 Code 1 1 120611 Scaled 121422 Scaled 120611 Unscaled 121422 Unscaled 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 3 

EQ 4 EQ 5 EQ 6 

2 

1 

 Code

 121211 Scaled

 121211 Unscaled 

2 

1 

 Code

 120122 Scaled

 120122 Unscaled 

2 

1 

 Code

 120811 Scaled

 120811 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 2 

EQ 7 EQ 8 EQ 9 

2 

1 

 Code

 120521 Scaled

 120521 Unscaled 

2 

 Code

 121222 Scaled

 121222 Unscaled 

1 

 Code

1 120911 Scaled

 120911 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 2 

EQ 10 EQ 11 EQ 12 

2 

1 

 Code

 120721 Scaled

 120721 Unscaled 

2 

1 

 Code

 120822 Scaled

 120822 Unscaled 

 Code

 120412 Scaled 1 120412 Unscaled 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

2 4 

EQ 13 3 EQ 14 

Spectral Acceleration (g) 

 Code

 121712 Scaled 1 121712 Unscaled 

Spectral Acceleration (g) 

 Code

 121022 Scaled 2 121022 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 MC4 

A-5 
 

 

 

 

 

 

 

 

 

 

 

A.4 Eight-Story Archetype Building 

8-Story Special Concentrically Braced Frame 

Table A-2 summarizes the 14 strong motion records used for the NDP for the N-S direction of MC8 (SCBF). 

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 and BSE-2 for the ELF and RSA design. 

Table A-2. Ground Motion Records for N-S Direction of MC84 

I BSE-2 BSE-1 EQ No. Event Name Station Comp.1

 Error2 Step4 Time5 

D Scaling3 Scaling3 

1 34 Superstition Poe Road (temp) 2 20 3.023 2.015 0.010 23 

Hills 

2 31 Superstition El Centro Imp. Co. 1 24 2.504 1.669 0.005 40 

Hills 

3 37 Chi-Chi, Taiwan CHY101 1 25 2.223 1.482 0.005 90 

4 10 Imperial Valley Delta 2 25 2.165 1.443 0.010 100 

5 20 Kocaeli, Turkey Arcelik 2 29 6.379 4.253 0.005 30 

6 17 Kocaeli, Turkey Duzce 1 29 2.385 1.590 0.005 28 

7 16 Kobe, Japan Shin-Osaka 2 33 2.799 1.866 0.010 41 

8 5 Duzce, Turkey Bolu 1 33 1.714 1.143 0.010 56 

9 12 Imperial Valley El Centro Array #11 2 35 3.678 2.452 0.005 40 

10 35 Cape Mendocino Rio Dell Overpass 1 35 2.049 1.366 0.020 36 

11 28 Loma Prieta Gilroy Array #3 2 35 1.831 1.221 0.005 40 

12 22 Landers Yermo Fire Station 2 38 3.808 2.539 0.020 44 

13 3 Northridge Canyon Country-WLC 1 38 1.774 1.183 0.010 20 

14 2 Northridge Beverly Hills - Mulhol 2 38 1.102 0.735 0.010 30 

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 6 

 Code Code

 121222 121222

 121211 121211 5 121411 Scaled EQ 121411 Original EQ 120612 120612

Spectral Acceleration (g) 

 120822

Spectral Acceleration (g) 

 120822

2 120811 4 120811

 120722

 120411

 120622

 121321

 121022

 120912

 120722

 120411

 120622 3 121321

 121022

 120912

2 120121

 120112

 Average 

1 

1 120121

 120112

 Average 

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-3. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S Direction of MC8 

A-7 
3 3 2 

EQ 1 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) 

2 

 Code Code

1 121411 Scaled

 121411 Unscaled 

 Code

 121222 Scaled

 121222 Unscaled 

 121211 Scaled

 121211 Unscaled 

1 1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 3 

EQ 4 EQ 5 EQ 6 

2 

1 

 Code

 120612 Scaled

 120612 Unscaled 

2 

1 

 Code

 120822 Scaled

 120822 Unscaled 

2 

1 

 Code

 120811 Scaled

 120811 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

2 4 5 

EQ 7 3 EQ 8 4 EQ 9 

3 

 Code

 120622 Scaled

 120622 Unscaled 

2 

1 

 Code

 Code 120411 Scaled

1 120722 Scaled

 120722 Unscaled 

2 120411 Unscaled 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 3 

EQ 10 EQ 11 EQ 12 

2 

1 

 Code

 121321 Scaled

 121321 Unscaled 

2 

1 

 Code

 121022 Scaled

 121022 Unscaled 

2 

1 

 Code

 120912 Scaled

 120912 Unscaled 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

3 3 

EQ 13 EQ 14 

Spectral Acceleration (g) 2 

1 

 Code

 120121 Scaled

 120121 Unscaled 

Spectral Acceleration (g) 2 

 Code

 120112 Scaled

 120112 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 MC8 

A-8 
 

 

 

 

 

 

 

 

 

 

A.5 Sixteen-Story Archetype Building 

16-Story Special Concentrically Braced Frame 

Table A-3 summarizes the 14 strong motion records used for the NDP for the N-S direction of MC16 

(SCBF). 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 and RSA design. 

Table A-3. Ground Motion Records for N-S Direction of MC16 

ID EQ No. Event Name Station Comp. 1 Error2 BSE-2 

Scaling3 

BSE-1 

Scaling3 Step4

 Time5 

1 34 Superstition Hills Poe Road (temp) 2 28 2.987 1.991 0.010 23 

2 12 Imperial Valley El Centro Array #11 2 28 4.059 2.706 0.005 40 

3 5 Duzce, Turkey Bolu 1 35 2.005 1.337 0.010 56 

4 31 Superstition Hills El Centro Imp. Co. 1 38 2.805 1.870 0.005 40 

5 10 Imperial Valley Delta 2 38 2.410 1.606 0.010 100 

6 20 Kocaeli, Turkey Arcelik 2 41 5.844 3.896 0.005 30 

7 15 Kobe, Japan Shin-Osaka 1 43 3.023 2.015 0.010 41 

8 17 Kocaeli, Turkey Duzce 1 43 2.480 1.653 0.005 28 

9 28 Loma Prieta Gilroy Array #3 2 44 2.036 1.358 0.005 40 

10 22 Landers Yermo Fire Station 2 47 4.553 3.035 0.020 44 

11 3 Northridge Canyon Country-WLC 1 51 2.163 1.442 0.010 20 

12 38 Chi-Chi, Taiwan CHY101 2 52 1.183 0.789 0.005 90 

13 39 Chi-Chi, Taiwan TCU045 1 53 4.848 3.232 0.005 90 

14 30 Manjil, Iran Abbar 2 54 1.316 0.877 0.020 54 

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

 121222 121222

 120622 6 120622

Original EQ 120411

 121211

Scaled EQ 120411

 121211

5

Spectral Acceleration (g) 

 120612

2 120822

 120721

 120811

 121022

 120912

 120121

 121412

1 121421

 121112

 Average 

Spectral Acceleration (g) 

 120612

 120822

 120721

4 120811

 121022

 120912

3 120121

 121412

 121421

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-5. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for N-S Direction of MC16 

A-10 
3 6 5 

5 

EQ 1 EQ 2 4 EQ 3 

2 4 

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

3 120622 Scaled

 120622 Unscaled 

2 

 Code

 120411 Scaled

 120411 Unscaled 

 Code

 121222 Scaled

 121222 Unscaled 2 

1 

1 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 3 

EQ 4 EQ 5 EQ 6 

2 

1 

 Code

 121211 Scaled

 121211 Unscaled 

2 

1 

 Code

 120612 Scaled

 120612 Unscaled 

2 

1 

 Code

 120822 Scaled

 120822 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 3 

EQ 7 EQ 8 EQ 9 

2 

1 

 Code

 120721 Scaled

 120721 Unscaled 

2 

1 

 Code

 120811 Scaled

 120811 Unscaled 

2 

1 

 Code

 121022 Scaled

 121022 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 2 

EQ 10 EQ 11 EQ 12 

2 

1 

 Code

 120912 Scaled

 120912 Unscaled 

2 

1 

 Code

 120121 Scaled

 120121 Unscaled 

 Code

 121412 Scaled 1 121412 Unscaled 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

7 3 

6 

EQ 13 EQ 14 

Spectral Acceleration (g) 5 

4 Code

 121421 Scaled

 121421 Unscaled 

3 

2 

1 

Spectral Acceleration (g) 2 

 Code

 121112 Scaled

 121112 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 MC16 

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 example calculations for the strength design of a few specific members and 

components: 

 SCBF brace 

 SCBF 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 MC4 (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 MC8 (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 63.44 44.19 63.33 18.47 27.03 18.00 27.03 

8 102 49.32 63.10 45.43 62.89 18.55 26.74 17.64 26.74 

7 88 47.98 61.52 44.20 61.31 18.05 26.07 17.16 26.07 

6 74 46.48 59.75 42.81 59.54 17.49 25.32 16.62 25.32 

5 60 44.76 57.72 41.23 57.52 16.84 24.46 16.00 24.46 

4 46 42.72 55.31 39.35 55.12 16.07 23.44 15.28 23.44 

3 32 40.18 52.31 37.01 52.13 15.12 22.17 14.37 22.17 

2 18 41.88 55.02 38.58 54.83 15.76 23.32 14.98 23.32 

Base 0 359.49 468.19 332.81 466.67 136.35 198.54 130.04 198.54 

Table B-3. Wind Forces on MC 16 (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 77.60 55.35 77.48 22.58 32.73 22.22 32.73 

16 214 62.23 78.96 59.41 78.72 23.22 32.81 22.50 32.81 

15 200 61.44 78.03 58.66 77.80 22.93 32.42 22.22 32.42 

14 186 60.61 77.06 57.86 76.83 22.62 32.02 21.92 32.02 

13 172 59.74 76.04 57.03 75.81 22.29 31.59 21.60 31.59 

12 158 58.81 74.95 56.14 74.73 21.95 31.14 21.27 31.14 

11 144 57.82 73.79 55.20 73.58 21.58 30.66 20.91 30.66 

10 130 56.76 72.55 54.19 72.34 21.18 30.15 20.53 30.15 

9 116 55.62 71.21 53.10 71.00 20.76 29.59 20.11 29.59 

8 102 54.37 69.75 51.91 69.54 20.29 28.98 19.66 28.98 

7 88 53.00 68.14 50.60 67.94 19.78 28.31 19.16 28.31 

6 74 51.46 66.33 49.12 66.13 19.20 27.56 18.61 27.56 

5 60 49.69 64.26 47.44 64.07 18.54 26.70 17.97 26.70 

4 46 47.60 61.81 45.44 61.62 17.76 25.68 17.21 25.68 

3 32 44.98 58.74 42.94 58.57 16.79 24.41 16.26 24.41 

2 18 47.26 62.28 45.12 62.09 17.64 25.88 17.09 25.88 

Base 0 878.18 1131.51 839.50 1128.26 329.11 470.62 319.23 470.62 

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, MC4 (kips) 

RSA ELF 

Level, x wx 

1 Pstory 

2 Px 

3 wx 1 Pstory 

2 Px

 3 

Roof 1091 1309 1091 1095 1314 1095 

4 1339 2925 2470 1345 2936 2479 

3 1346 4547 3854 1359 4574 3877 

2 1364 6192 5257 1377 6235 5293 

Total 5140 ­ - 5176 ­ -

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, MC8 (kips) 

RSA ELF 

Level, x wx 

1 Pstory 

2 Px 

3 wx 1 Pstory 

2 Px

 3 

Roof 1081 1297 1081 1084 1300 1083 

8 1324 2893 2443 1328 2901 2450 

7 1333 4501 3815 1346 4525 3835 

6 1338 6114 5192 1355 6158 5229 

5 1349 7741 6580 1364 7803 6631 

4 1353 9373 7973 1368 9452 8038 

3 1367 11021 9378 1380 11115 9457 

2 1390 12697 10807 1402 12806 10898 

Total 10536 - - 10627 - -

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, MC16 (kips) 

RSA ELF 

Level, x wx

 1 Pstory 

2 Px 

3 wx 1 Pstory 

2 Px 

3 

Roof 1083 1296 1080 1083 1297 1081 

16 1327 2893 2444 1327 2895 2444 

15 1332 4496 3812 1342 4509 3822 

14 1337 6105 5184 1349 6133 5208 

13 1349 7728 6570 1357 7766 6601 

12 1354 9358 7960 1360 9403 7997 

11 1359 10993 9355 1366 11046 9399 

10 1363 12634 10754 1370 12695 10806 

9 1370 14282 12160 1379 14355 12221 

8 1374 15936 13570 1384 16020 13641 

7 1379 17595 14986 1389 17691 15066 

6 1384 19260 16406 1394 19369 16496 

5 1395 20939 17837 1402 21056 17935 

4 1403 22627 19276 1410 22754 19381 

3 1414 24328 20726 1425 24469 20843 

2 1445 26067 22207 1462 26227 22341 

Total 21667 - - 21800 - -

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 MC4 (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 MC4 

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 

2 

3 

4 

138145 Roof 36 

Floor Floor 

Roof 

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 (kips)

x

(a) Lateral Forces (b) Story Shears 

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

Table B-8. Seismic Drift Forces, E-W MC4 

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) 

Floor 

0 50 100 150 200 250 

112 

136 

166 

166 

159 

198 

213 

213 

29 

42 

55 

55 

RSA

 ELF

 Wind (10-Year) 

4 

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 

4 

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 

3 

2 

Floor 

3

Floor 

0.0202 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   x e   ( 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 MC4 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 MC4 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 MC8 (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 MC8

 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 

108 135 Roof 46 Roof 

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) 

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 

 RSA

 ELF

 Wind (700-Year) 

Floor 

8 

7 

6 

5 

4 

3 

2 

Floor Base Base 

Lateral Force, F x (kips) Story Shear, V (kips)

x

(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 MC8

 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 

0 20 40 60 80 

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 

18 6671 

Lateral Force, F x (kips) (kips)

0 50 100 150 200 250 300 

Base 

2 

3 

4 

5 

6 

7 

8 

Roof 

93 

112 

131 

146 

159 

174 

192 

192 

139 

190 

226 

250 

264 

271 

273 

273 

37 

55 

73 

89 

105 

121 

136 

136 

Story Shear, V x

 RSA

 ELF

 Wind (10-Year) 

(a) Lateral forces (b) Story Shears 

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

B-8 
 

 

 

 

 

 

5 

6 

7 

8 

0.0110 0.0134 Roof Roof 

8 

7 

4 

3 

2 

Base 

0.0142 

0.0163 

0.0174 

0.0173 

0.0178 

0.0170 

0.0132 

0.0132 

0.0168 

0.0167 

0.0179 

0.0182 

0.0185 

0.0176 

0.0136 

0.0136 

RSA

 ELF 

Allowable Story Drift Ratio, a / h sx 

Floor 

6 

5 

4 

3 

2 

Base 

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 

0.000 0.005 0.010 0.015 0.020 0 4 8 12 16 20 24 

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 MC8 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 MC8 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 

Floor 

B-9 
 

 

 

 

B.1.2.2.3 MC16 (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 MC16

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 

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 

133 196 Roof 57 

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 

2 

Base Base 

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

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

B-10 
 

 

 

 

 

 

 

 

Table B-16. Summary of Seismic Drift Forces, E-W MC16 

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 x

 (kips)

(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 

10 

11 

12 

13 

14 

15 

16 

0.0076 0.0105 Roof Roof 

16 

15 

14 

13 

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 

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 

Floor

9 

8 

7 

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 MC16 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 MC16 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 MC4 (Special Concentrically 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. Summary of Seismic Strength Design Forces, N-S MC4 

RSA ELF Wind (700-Year) 

Level, x Fy 

(kips) 

Vi 

(kips) 

Fy 

(kips) 

Vi 

(kips) 

VELF / 

VRSA 

Fy 

(kips) 

Vi 

(kips) 

Roof 261 261 293 293 0.89 36 36 

4 219 480 272 565 0.85 35 72 

3 153 633 188 753 0.84 33 105 

2 91 723 104 857 0.84 34 139 

B-13 
 

 

 

2 

3 

4 

2 

3 

4 

Roof 261 293 Roof 52 

Floor Floor 

0 40 80 120 160 200 240 280 320 

261 

219 

153 

91 

293 

272 

188 

104 

52 

50 

48 

50 RSA

 ELF

 Wind (700-Year) 

Floor 

0 100 200 300 400 500 600 700 800 900 

480 

633 

723 

723 

565 

753 

857 

857 

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. Summary of Seismic Drift Forces, N-S MC4

 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 226 226 4.88 1.02 0.006 270 270 5.41 1.20 0.007 15 15 

4 190 416 3.85 1.22 0.007 249 519 4.21 1.51 0.009 14 29 

3 132 549 2.63 1.28 0.008 170 689 2.70 1.31 0.008 13 42 

2 78 627 1.35 1.35 0.006 93 782 1.39 1.39 0.006 14 55 

Roof 226 270 Roof 22 

0 40 80 120 160 200 240 280 

226 

190 

132 

78 

270 

249 

170 

93 

22 

22 

20 

21 RSA

 ELF

 Wind (10-Year) 

Floor 

0 100 200 300 400 500 600 700 800 

416 

549 

627 

627 

519 

689 

782 

782 

44 

64 

86 

86 

 RSA

 ELF

 Wind (10-Year) 

4 

3 

2 

Base Base 

Lateral Force, F x (kips) Story Shear, V (kips)

x

(a) Lateral forces (b) Story Shears 

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

B-14 
 

 

 

 

 

 

0.0071 0.0061 Roof Roof 4.9 5.4 

0.000 0.005 0.010 0.015 0.020 0 2 4 6 

Expected Story Drift Ratio,  / h x 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 MC4 RSA 

RSA

1.4 1.4 

 ELF 

2.6 2.7 

3.9 4.2 

Allowable Story Drift Ratio, a / h sx 

Floor 

RSA

0.0065 

0.0065 

 ELF 

0.0073 

0.0076 

0.0063 

0.0063 

0.0090 

0.0078 

4 4

3 

2 

3

Floor 

2 

Base Base 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 1130 1091 1.02 168 0.006 0.006 0.006 1.00 0.100 

4 2082 2470 1.22 168 0.007 0.009 0.009 1.00 0.100 

3 2743 3854 1.28 168 0.008 0.011 0.011 1.00 0.100 

2 3135 5257 1.35 216 0.006 0.010 0.010 1.00 0.100 

Table B-22. ASCE 7 Allowable Drift and Stability Verification, N-S MC4 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 1351 1095 1.20 168 0.007 0.006 0.006 1.00 0.100 

4 2597 2479 1.51 168 0.009 0.009 0.008 1.00 0.100 

3 3446 3877 1.31 168 0.008 0.009 0.009 1.00 0.100 

2 3909 5293 1.39 216 0.006 0.009 0.009 1.00 0.100 

B.1.2.3.2 MC8 (Special Concentrically 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. Summary of Seismic Strength Design Forces, N-S MC8 

RSA ELF Wind (700-Year) 

Level, x Fy 

(kips) 

Vi 

(kips) 

Fy 

(kips) 

Vi 

(kips) 

VELF / 

VRSA 

Fy 

(kips) 

Vi 

(kips) 

Roof 239 239 216 216 1.11 46 46 

8 174 414 225 441 0.94 49 96 

7 94 508 190 631 0.80 48 143 

6 59 566 154 785 0.72 46 190 

5 70 636 119 904 0.70 45 235 

4 93 729 86 990 0.74 43 277 

3 100 829 55 1045 0.79 40 318 

2 76 904 27 1073 0.84 42 359 

Roof 

8 

7 

6 

216239 239 Roof 63 

0 40 80 120 160 200 240 

174 

94 

59 

70 

93 

100 

76 

216 

225 

190 

154 

119 

86 

55 

27 

63 

63 

62 

60 

58 

55 

52 

55 

 RSA

 ELF

 Wind (700-Year) 

Floor 

0 200 400 600 800 1000 1200 

414 

508 

566 

636 

729 

829 

904 

904 

441 

631 

785 

904 

990 

1045 

1073 

1073 

127 

188 

248 

306 

361 

413 

468 

468 

RSA

 ELF

 Wind (700-Year) 8 

7 

6 

5 

4 

3 

2 

Floor

5 

4 

3 

2 

Base Base 

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. Summary of Seismic Drift Forces, N-S MC8

 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 168 168 10.93 1.51 0.009 161 161 14.59 2.03 0.012 18 18 

8 122 290 9.42 1.62 0.010 163 324 12.56 2.23 0.013 19 37 

7 66 356 7.79 1.68 0.010 133 458 10.33 2.17 0.013 18 55 

6 41 397 6.12 1.54 0.009 104 562 8.16 1.99 0.012 17 73 

5 49 446 4.58 1.37 0.008 77 638 6.17 2.00 0.012 17 89 

4 65 511 3.20 1.10 0.007 52 690 4.17 1.57 0.009 16 105 

3 70 581 2.11 1.04 0.006 31 721 2.60 1.39 0.008 15 121 

2 53 633 1.06 1.06 0.005 13 735 1.22 1.22 0.006 16 136 

B-16 
 

 

2 

3 

4 

5 

6 

7 

8 

2 

3 

4 

5 

6 

7 

8 

Roof 27 168 Roof 161 

8
 

7
 

0 20 40 60 80 100 120 140 160 180 

168 

122 

66 

41 

49 

65 

70 

53 

161 

163 

133 

104 

77 

52 

31 

13 

27 

27 

26 

25 

24 

23 

22 

23 

 RSA

 ELF

 Wind (10-Year) 

Floor 

0 100 200 300 400 500 600 700 800 

290 

356 

397 

446 

511 

581 

633 

633 

324 

458 

562 

638 

690 

721 

735 

735 

54 

80 

105 

130 

153 

175 

199 

199 

RSA

 ELF

 Wind (10-Year) 

6
 

5
 

4
 

3
 

2
 

Floor Floor Base Base 

Lateral Force, F x (kips) Story Shear, V (kips)

x

(a) Lateral forces (b) Story Shears 

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

0.0090 0.0121 Roof 

0.000 0.005 0.010 0.015 0.020 

0.0097 

0.0100 

0.0092 

0.0082 

0.0065 

0.0062 

0.0049 

0.0049 

0.0133 

0.0129 

0.0118 

0.0119 

0.0093 

0.0083 

0.0056 

0.0056 

 RSA

 ELF 

Allowable Story Drift Ratio, a / h sx 

Floor 

Roof 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base 

10.9 

9.4 

7.8 

6.1 

4.6 

3.2 

2.1 

1.1 

14.6 

12.6 

10.3 

8.2 

6.2 

4.2 

2.6 

1.2 

 RSA

 ELF 

Base 

0 4 8 12 16
 

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 MC8 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 838 1081 1.51 168 0.009 0.012 0.011 1.00 0.100 

8 1449 2443 1.62 168 0.010 0.016 0.016 1.00 0.100 

7 1778 3815 1.68 168 0.010 0.021 0.021 1.00 0.100 

6 1985 5192 1.54 168 0.009 0.024 0.023 1.00 0.100 

5 2229 6580 1.37 168 0.008 0.024 0.024 1.00 0.100 

4 2555 7973 1.10 168 0.007 0.020 0.020 1.00 0.100 

3 2903 9378 1.04 168 0.006 0.020 0.020 1.00 0.100 

2 3167 10807 1.06 216 0.005 0.017 0.017 1.00 0.100 

Table B-26. ASCE 7 Allowable Drift and Stability Verification, N-S MC8 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 805 1083 2.03 168 0.012 0.016 0.016 1.00 0.100 

8 1622 2450 2.23 168 0.013 0.020 0.020 1.00 0.100 

7 2288 3835 2.17 168 0.013 0.022 0.021 1.00 0.100 

6 2808 5229 1.99 168 0.012 0.022 0.022 1.00 0.100 

5 3192 6631 2.00 168 0.012 0.025 0.024 1.00 0.100 

4 3452 8038 1.57 168 0.009 0.022 0.021 1.00 0.100 

3 3606 9457 1.39 168 0.008 0.022 0.021 1.00 0.100 

2 3673 10898 1.22 216 0.006 0.017 0.016 1.00 0.100 

B.1.2.3.3 MC16 (Special Concentrically 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. Summary of Seismic Strength Design Forces, N-S MC16 

Level, x 

RSA 

Fy 

(kips) 

Vi 

(kips) 

Fy 

(kips) 

ELF 

Vi 

(kips) 

VELF / VRSA 

Wind (700-Year) 

Fy 

(kips) 

Vi 

(kips) 

Roof 190 190 159 159 1.19 57 57 

16 172 362 177 336 1.08 62 119 

15 115 477 161 497 0.96 61 180 

14 73 550 144 641 0.86 61 241 

13 45 595 128 769 0.77 60 301 

12 33 628 112 881 0.71 59 360 

11 31 658 98 979 0.67 58 417 

10 33 692 83 1062 0.65 57 474 

9 41 733 70 1132 0.65 56 530 

8 50 783 57 1190 0.66 54 584 

7 58 841 46 1235 0.68 53 637 

6 66 907 35 1270 0.71 51 689 

5 68 975 25 1296 0.75 50 738 

4 62 1037 17 1312 0.79 48 786 

3 50 1087 10 1322 0.82 45 831 

2 33 1120 4 1326 0.84 47 878 

B-18 
 

 

 

 

 

 

 

8 

9 

190 

172 

115 

73 

45 

33 

31 

33 

41 

50 

58 

66

68 

62

50 

33 

159 

177 

161 

144 

128 

112 

98 

83 

70 

57 

46 

35 

25 

17 

10 

4 

78 

79 

78 

77 

76 

75 

74 

73 

71 

70 

68 

66 

64 

62 

59 

62 

Floor 

RSA

 ELF

 Wind (700-Year) 

Roof 159190 Roof 78
 

16
 16
 

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 40 80 120 160 200 0 200 400 600 800 1000 1200 1400 

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 Floor 

Table B-28. Summary of Seismic Drift Forces, N-S MC16

362 

477 

550 

595 

628 

658 

692 

733 

783 

841 

907 

975 

1037 

1087 

1120 

1120 

336 

497 

641 

769 

881 

979 

1062 

1132 

1190 

1235 

1270 

1296 

1312 

1322 

1326 

1326 

157 

235 

312 

388 

463 

536 

609 

680 

750 

818 

884 

949 

1010 

1069 

1132 

1132 

RSA

 ELF

 Wind (700-Year) 

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 160 160 16.00 1.01 0.006 142 142 24.43 1.53 0.009 23 23 

16 145 305 15.00 1.15 0.007 155 296 22.90 1.78 0.011 23 46 

15 97 402 13.84 1.21 0.007 139 435 21.12 1.91 0.011 23 69 

14 62 464 12.63 1.23 0.007 122 557 19.20 1.99 0.012 23 91 

13 38 502 11.41 1.12 0.007 107 664 17.21 1.89 0.011 22 114 

12 28 530 10.29 1.08 0.006 92 757 15.32 1.82 0.011 22 136 

11 26 555 9.21 1.08 0.006 78 835 13.50 1.74 0.010 22 157 

10 28 584 8.13 1.05 0.006 65 900 11.76 1.65 0.010 21 178 

9 35 619 7.08 1.05 0.006 54 954 10.11 1.63 0.010 21 199 

8 42 661 6.03 1.01 0.006 43 997 8.48 1.53 0.009 20 219 

7 49 710 5.02 0.93 0.006 33 1030 6.95 1.48 0.009 20 239 

6 55 766 4.09 0.89 0.005 24 1054 5.47 1.36 0.008 19 258 

5 57 823 3.20 0.91 0.005 17 1071 4.11 1.29 0.008 19 277 

4 53 875 2.29 0.84 0.005 10 1082 2.82 1.11 0.007 18 295 

3 42 917 1.45 0.69 0.004 6 1087 1.71 0.86 0.005 17 311 

2 28 945 0.76 0.76 0.004 2 1089 0.84 0.84 0.004 18 329 

B-19 
 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 33 142 160 Roof 

16 

15 

14 

Floor Floor 

0 40 80 120 160 

160 

145 

97 

62 

38 

28 

26 

28 

35 

42 

49 

55 

57 

53 

42 

28 

142 

155 

139 

122 

107 

92 

78 

65 

54 

43 

33 

24 

17 

10 

6 

2 

33 

33 

32 

32 

32 

31 

31 

30 

30 

29 

28 

28 

27 

26 

24 

26 

 RSA

 ELF

 Wind (10-Year) 

Floor 

0 200 400 600 800 1000 1200 

305 

402 

464 

502 

530 

555 

584 

619 

661 

710 

766 

823 

875 

917 

945 

945 

296 

435 

557 

664 

757 

835 

900 

954 

997 

1030 

1054 

1071 

1082 

1087 

1089 

1089 

66 

98 

130 

162 

193 

223 

254 

283 

312 

340 

368 

395 

420 

445 

471 

471 

RSA

 ELF

 Wind (10-Year) 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

4 

3 

2 

Base Base 

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

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

0.0060 0.0091 

0.000 0.005 0.010 0.015 0.020 

Base 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0.0069 

0.0072 

0.0073 

0.0067 

0.0064 

0.0064 

0.0062 

0.0063 

0.0060 

0.0055 

0.0053 

0.0054 

0.0050 

0.0041 

0.0035 

0.0035 

0.0106 

0.0114 

0.0119 

0.0112 

0.0108 

0.0104 

0.0098 

0.0097 

0.0091 

0.0088 

0.0081 

0.0077 

0.0066 

0.0051 

0.0039 

0.0039 

RSA

 ELF 

Allowable Story Drift Ratio,  / h 

Roof 16.0 

15.0 

13.8 

12.6 

11.4 

10.3 

9.2 

8.1 

7.1 

6.0 

5.0 

4.1 

3.2 

2.3 

1.5 

0.8 

22.9 

21.1 

19.2 

17.2 

15.3 

13.5 

11.8 

10.1 

8.5 

6.9 

5.5 

4.1 

2.8 

1.7 

0.8 

RSA

 ELF 

a sx 

Floor 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0 4 8 12 16 20 

Expected Floor Displacement,  (inch) Expected Story Drift Ratio, x

 / h sx x

(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 

24 

24.4 
 

 

 

 

 

 

 

Table B-29. ASCE 7 Allowable Drift and Stability Verification, N-S MC16 RSA 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 800 1080 1.01 168 0.006 0.008 0.008 1.00 0.100 

16 1524 2444 1.15 168 0.007 0.011 0.011 1.00 0.100 

15 2010 3812 1.21 168 0.007 0.014 0.013 1.00 0.100 

14 2320 5184 1.23 168 0.007 0.016 0.016 1.00 0.100 

13 2508 6570 1.12 168 0.007 0.017 0.017 1.00 0.100 

12 2646 7960 1.08 168 0.006 0.019 0.019 1.00 0.100 

11 2775 9355 1.08 168 0.006 0.022 0.021 1.00 0.100 

10 2916 10754 1.05 168 0.006 0.023 0.022 1.00 0.100 

9 3090 12160 1.05 168 0.006 0.025 0.024 1.00 0.100 

8 3302 13570 1.01 168 0.006 0.025 0.024 1.00 0.100 

7 3548 14986 0.93 168 0.006 0.023 0.023 1.00 0.100 

6 3824 16406 0.89 168 0.005 0.023 0.022 1.00 0.100 

5 4109 17837 0.91 168 0.005 0.023 0.023 1.00 0.100 

4 4372 19276 0.84 168 0.005 0.022 0.021 1.00 0.100 

3 4581 20726 0.69 168 0.004 0.019 0.018 1.00 0.100 

2 4721 22207 0.76 216 0.004 0.017 0.016 1.00 0.100 

Table B-30. ASCE 7 Allowable Drift and Stability Verification, N-S MC16 ELF 

Level, x Vi × Cd Px i hsx i / hsx 2i i i max,i

(kips) (kips) (inch) (inch) 

ROOF 706 1080 1.52 168 0.009 0.014 0.014 1.00 0.100 

16 1479 2444 1.78 168 0.011 0.017 0.017 1.00 0.100 

15 2170 3821 1.91 168 0.011 0.020 0.020 1.00 0.100 

14 2782 5206 1.99 168 0.012 0.022 0.022 1.00 0.100 

13 3316 6598 1.88 168 0.011 0.022 0.022 1.00 0.100 

12 3775 7994 1.82 168 0.011 0.023 0.022 1.00 0.100 

11 4167 9396 1.74 168 0.010 0.023 0.023 1.00 0.100 

10 4493 10802 1.65 168 0.010 0.024 0.023 1.00 0.100 

9 4762 12217 1.63 168 0.010 0.025 0.024 1.00 0.100 

8 4975 13636 1.53 168 0.009 0.025 0.024 1.00 0.100 

7 5140 15061 1.47 168 0.009 0.026 0.025 1.00 0.100 

6 5261 16491 1.36 168 0.008 0.025 0.025 1.00 0.100 

5 5345 17929 1.29 168 0.008 0.026 0.025 1.00 0.100 

4 5398 19375 1.11 168 0.007 0.024 0.023 1.00 0.100 

3 5425 20836 0.86 168 0.005 0.020 0.019 1.00 0.100 

2 5435 22334 0.84 216 0.004 0.016 0.016 1.00 0.100 

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 

MC4 MC8 MC16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof - - - - 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 - - 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 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

 MC4 MC8 MC16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof - - - - - -

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 - ­ - ­ 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 - - 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Mpr j , 

j1 (B-5) V 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 (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 - - - ­ - ­ 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). 

Special Concentrically Braced Frame 

Table B-35 through Table B-38 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 

MC4 MC8 MC16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof MC16 - - - - 1.097 1.100 

16 - - - - 1.073 1.071 

15 - - - - 1.072 1.086 

14 - - - - 1.079 1.075 

13 - - - - 1.077 1.083 

12 - - - - 1.073 1.073 

11 - - - - 1.089 1.089 

10 - - - - 1.063 1.073 

9 (Roof MC8) - - 1.079 1.084 1.098 1.094 

8 - - 1.081 1.086 1.060 1.070 

7 - - 1.073 1.077 1.102 1.097 

6 - - 1.073 1.082 1.057 1.060 

5 (Roof MC4) 1.078 1.096 1.084 1.083 1.103 1.105 

4 1.071 1.056 1.069 1.075 1.059 1.056 

3 1.040 1.064 1.089 1.091 1.127 1.129 

2 1.044 1.045 1.076 1.078 1.077 1.080 

a. Values include accidental torsion with Ax = 1.0. 

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

( / hsx) x / ( / hsx) x+1 a

 MC4 MC8 MC16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof - - - - - -

16 ­ ­ ­ ­ 1.17 1.20 

15 ­ ­ ­ ­ 1.07 1.08 

14 ­ ­ ­ ­ 1.04 1.02 

13 ­ ­ ­ ­ 0.95 0.91 

12 ­ ­ ­ ­ 0.97 0.94 

11 ­ ­ ­ ­ 0.96 1.00 

10 ­ ­ ­ ­ 0.95 0.94 

9 ­ ­ ­ ­ 0.99 0.99 

8 ­ ­ 1.10 1.11 0.94 0.93 

7 ­ ­ 0.97 1.03 0.96 0.91 

6 ­ ­ 0.92 0.91 0.92 0.93 

5 ­ ­ 1.00 0.88 0.95 1.01 

4 1.26 1.14 0.79 0.77 0.86 0.91 

3 0.87 1.02 0.88 0.93 0.78 0.82 

2 0.83 0.63 0.68 0.61 0.76 0.85 

a.  is taken at the center of mass per ASCE 7 §12.8.6. 

Vy i,  P ,  Pbr T  b br C , 

b 2 

2 2      h   sx 2 (B-7) 

[b = 20 ft. for MC4 and MC8, b = 30 ft. for MC16] 

B-24 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

 MC4 MC8 MC16 

Floor (x) hsx Pbr,C a Pbr,T b Vy,x 

Vy,x+1 / 

Vy,x 

Pbr,C a Pbr,T b Vy,x 

Vy,x+1 / 

Vy,x 

Pbr,C a Pbr,T b Vy,x 

Vy,x+1 / 

Vy,x 

Roof MC16 14 - - ­ ­ ­ ­ ­ ­ 99.4 255.9 259.7 -

16 14 - - ­ ­ ­ ­ ­ ­ 99.4 255.9 259.7 1.00 

15 14 - - ­ ­ ­ ­ ­ ­ 132.7 284.8 305.3 1.18 

14 14 - - ­ ­ ­ ­ ­ ­ 132.7 284.8 305.3 1.00 

13 14 - - ­ ­ ­ ­ ­ ­ 207.5 403.2 446.5 1.46 

12 14 - - ­ ­ ­ ­ ­ ­ 207.5 403.2 446.5 1.00 

11 14 - - ­ ­ ­ ­ ­ ­ 240.2 484.4 529.7 1.19 

10 14 - - ­ ­ ­ ­ ­ ­ 240.2 484.4 529.7 1.00 

9 (Roof MC8) 14 - - - - 131.7 255.9 225.3 - 297.9 480.2 568.9 1.07 

8 14 - - ­ ­ 131.7 255.9 225.3 1.00 297.9 480.2 568.9 1.00 

7 14 - - ­ ­ 252.8 403.2 381.3 1.69 297.9 480.2 568.9 1.00 

6 14 - - ­ ­ 252.8 403.2 381.3 1.00 297.9 480.2 568.9 1.00 

5 (Roof MC4) 14 78.3 249.2 190.4 - 252.8 403.2 381.3 1.00 297.9 480.2 568.9 1.00 

4 14 131.7 255.9 225.3 1.18 252.8 403.2 381.3 1.00 297.9 480.2 568.9 1.00 

3 14 252.8 403.2 381.3 1.69 343.3 480.2 478.7 1.26 469.2 679.0 839.4 1.48 

2 18 239.0 484.4 351.3 0.92 296.9 480.2 377.4 0.79 419.4 679.0 703.1 0.84 

a. Design compression strength. 

b. Design tension strength. 

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

MC4 MC8 MC16 

Floor (x) hsx Pbr,C a Pbr,T b Vy,x 

Vy,x+1 / 

Vy,x 

Pbr,C a Pbr,T b Vy,x 

Vy,x+1 / 

Vy,x 

Pbr,C a Pbr,T b Vy,x 

Vy,x+1 / 

Vy,x 

Roof MC16 14 - - ­ ­ ­ ­ ­ ­ 99.4 255.9 259.7 -

16 14 - - ­ ­ ­ ­ ­ ­ 99.4 255.9 259.7 1.00 

15 14 - - ­ ­ ­ ­ ­ ­ 132.7 284.8 305.3 1.18 

14 14 - - ­ ­ ­ ­ ­ ­ 132.7 284.8 305.3 1.00 

13 14 - - ­ ­ ­ ­ ­ ­ 207.5 403.2 446.5 1.46 

12 14 - - ­ ­ ­ ­ ­ ­ 207.5 403.2 446.5 1.00 

11 14 - - ­ ­ ­ ­ ­ ­ 207.5 403.2 446.5 1.00 

10 14 - - ­ ­ ­ ­ ­ ­ 207.5 403.2 446.5 1.00 

9 (Roof MC8) 14 - - - - 131.7 255.9 225.3 - 207.5 403.2 446.5 1.00 

8 14 - - ­ ­ 131.7 255.9 225.3 1.00 207.5 403.2 446.5 1.00 

7 14 - - ­ ­ 166.5 284.8 262.3 1.16 240.2 484.4 529.7 1.19 

6 14 - - ­ ­ 166.5 284.8 262.3 1.00 240.2 484.4 529.7 1.00 

5 (Roof MC4) 14 67.6 197.9 154.3 - 252.8 403.2 381.3 1.45 297.9 480.2 568.9 1.07 

4 14 131.7 255.9 225.3 1.46 252.8 403.2 381.3 1.00 297.9 480.2 568.9 1.00 

3 14 166.5 284.8 262.3 1.16 343.3 480.2 478.7 1.26 469.2 679.0 839.4 1.48 

2 18 206.6 403.2 296.1 1.13 296.9 480.2 377.4 0.79 419.4 679.0 703.1 0.84 

a. Design compression strength 

b. Design tension strength. 

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 

a. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

b. 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 

a. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

b. 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 

a. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

b. 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 

a. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

b. 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 

a. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

b. 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 

a. Pstory is computed from 1.2×Dead + 0.25×Floor Live. 

b. 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-28 
 

B.4 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 (MC8): 

 SCBF brace, MC8 RSA 

 SCBF column, MC8 RSA 

Example calculations for components of the SMF can be found in Volume 1 (Harris and Speicher 2015).

 Special Concentrically Braced Frame Example 

Member Selection 

After several design and analysis iterations, the final member sizes are shown in Figure B-19. 

20'-0" 

W18×46 

2 

4 

6 

8 

= Panel Zone/Gusset Plate 

= Column Splice 

3 2 

1 

1 

2 

3 

3 

5 

4 

7 

W16×31 

W18×60 

W16×31 

W16×31 

W18×46 

W18×46 

W18×46 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

9 10

11 

12 

12 

13 

14 

1

14 

5 

16 

5 

6 

7 

8 

16 

11 

13 

15 

Sym. About 

Roof
 

(ELEV = 116 ft.)
 

8th Floor HSS5×5×3/8 (ELEV = 102 ft.) 

7th Floor 

(ELEV = 88 ft.) 

6th Floor HSS5.5×5.5×3/8 (ELEV = 74 ft.) 

5th Floor 

(ELEV = 60 ft.) 

4th Floor HSS6×6×1/2 (ELEV = 46 ft.) 

3rd Floor 

(ELEV = 32 ft.) 

2nd Floor HSS7×7×1/2 (ELEV = 18 ft.) 

Fundamental Periods
 

T1 = 1.49 sec (First-Order)
 

= In-plane moment release T1 = 1.50 sec (1.0D + 0.25Lo) 

= Out-of-plane moment release T1 = 1.51 sec (1.2D + 0.25Lo) 

Figure B-19. SCBF Member Sizes, 8-Story RSA 

B-29 
 

SCBF Brace 

The first story brace along grid line A between grid lines 2 and 3 was selected for this example (see circled 

elements in Figure B-19): 

 HSS 7×7×1/2 

 Lwp = 247 in, Lbr ≈ 0.9×Lwp = 222 in
 

 A500 Gr. B, Fy = 46 ksi, Ry = 1.4, E = 29000 ksi, G = 11200 ksi
 

B.4.1.2.1 Axial Demand 

The axial compression force in the brace is (assuming braces do not carry gravity loads): 

P  PG  P  0 265  265 kips u	 E 

There is no significant moment in the brace. 

A.1.1.1.1 Axial Strength 

The axial compression strength of the brace is calculated per AISC 360 §E3—weak-axis (y) governs. 

P ,  AF n y 	 g cry ,

KL yy y F 1.0(222) 46   3.36  4.71 

ry	 E 2.63 29000
 

2 E 2 29000  F    40.0 ksi e y, 2 2

 KL  1.0(222) 
  y y     r	   2.63   y	 

	 FF 

 y e y,   F ,  0.658 y  28.4 ksi cr y  

F 

 P	 

,  0.9 11.6 24.8    0.9 330    297 kips c ny

B.4.1.2.2	 Strength Check 

P u 265   0.89 1.0OK
 

c ny  P 297 , 

B-30 
 

 

 

 

SCBF Column 

The first story column along grid line 3 was selected for this example (see circled elements in Figure B-19): 

 W14×283 

 hsx = 216 in, Lclear=197.4 in 

 A992 Steel: Fy = 50 ksi, Ry = 1.1, E = 29000 ksi, G = 11200 ksi 

B.4.1.3.1 Axial and Flexural Demand 

The demands in the column from the controlling load combinations from ASCE 7 are presented in Table 

B-48—maximum/minimum values for an individual action displayed with bolded text. 

Table B-48. Controlling Load Combinations (kips, feet) 

LC Index Pu,A Pu,B Mu,A,x Mu,B,x Max/Min Action 

179 602.97 602.97 222.35 45.65 Pu,min 

133 -1108.72 -1102.21 -224.11 -42.20 Pu,max 

179 599.72 602.97 222.35 45.65 Mu,A,min 

133 -1108.72 -1102.21 -224.11 -42.20 Mu,A,max 

123 414.63 421.14 221.69 46.93 Mu,B,min 

189 -923.63 -920.38 -223.46 -43.48 Mu,B,max 

Pr = 1109 kips and Mr,x = 224 kip-ft.—from the load combination selected for this example (#133 in Table 

B-48). 

The SCBF column design is also governed by the capacity design requirements specified in AISC 341 

§F2.3. AISC 341 §F2.3, exception (1) permits flexural forces resulting from seismic drift of the frame to 

be neglected. 

P,  2841 kips r CD 

B.4.1.3.2 Axial Strength 

The axial compression strength of the column is calculated per AISC 360 §E3—weak-axis (y) governs. 

P  A F n y cr y ,	 g ,

KL F y y 	 y 1.0(216) 50   2.15  4.71 

ry	 E 4.17 29000
 

2 E 2 29000  F   106.7 ksi e y, 2 2

 KL  1.0(216) 
  yy    	   4.17   ry	 

B-31 
 F F y e y,   50 106.7  F ,  

0.658  y 50  41.1 ksi cr y	 F  0.658    
 

 P ,  0.9 83.3 41.1    0.9 3423    3081 kips c ny

B.4.1.3.3	 Strength Check 

P , 2841 r CD   0.92 1.0OK 

 P	 3081 c ny ,

The P-M interaction values from AISC 360 Equation H1-1(a) and Equation H1-2 are 0.42 and 0.48, 

respectively. 

B-32 
 

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 (MC8): 

 SCBF brace, MC8 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) 

 SCBF Brace 

The first story brace along grid line A between grid lines 2 and 3 was selected for this example (see circled 

elements in Figure B-19): 

 HSS 7×7×1/2 

 Lwp = 247 in, Lbr ≈ 0.9×Lwp = 222 in 

 A500 Gr. B, Fy,LB = Fy = 46 ksi, Fye = 64.4 ksi, E = 29000 ksi, G = 11154 ksi 

Axial Demand 

The axial compression force in the brace is (assuming braces do not carry gravity loads): 

PE 1.0Ey  0.3 Ex 1353 kips 

PUD  PG  PE  0 1353 1353 kips 

Axial Strength 

Per ASCE 41 §5.5.2.3, the expected axial compression strength is computed as Pn from AISC 360-05 §E3 

with c =1 and Fye. 

C-1 
 

P  P  A F CE n y ,	 g cr y ,

KL y y ye F 1.0(222) 64.4   3.98  4.71 

ry	 E 2.63 29000
 

2 E 2 29000  F    40.0 ksi e y, 2 2

 KL  1.0(222) 
  yy     ry   2.63   

 F
 F 

 ye e y ,   F ,  0.658 cr y	 F ye  32.8 ksi  

PCE 11.6 32.8    381 kips → Pye = 11.6(64.4) = 747 kips
 

Acceptance Criteria 

The m-factor for a brace in compression is based on the slenderness of the member and the section type 

(HSS): 

E KL E 2.1  52.7   84.6  4.2 105.5 

Fy r Fy 

Note that ASCE 41 defines Fy,LB and Fye, but does not define Fy as a material strength. 

Therefore, linear interpolation gives the following: 

7  684.6  52.73  m  6	  6.60 105.5  52.73 

Acceptance Criteria Check 

The brace acceptance criteria check is: 

DCR P 1353 DCR	   UD   0.54 1.0 N m mP CE 6.60 381 

Therefore, the brace satisfies the CP BPL acceptance criteria at the BSE-2 EHL. 

 

C-2 
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 

 SCBF Brace 

The first story brace along grid line A between grid lines 2 and 3 was selected for this example (see circled 

elements in Figure B-19): 

 HSS 7×7×1/2 

 Lwp = 247 in, Lbr ≈ 0.9Lwp = 222 in. 

 A500 Gr. B, Fy,LB = Fy = 46 ksi, Fye=64.4 ksi, E = 29000 ksi, G = 11200 ksi 

The demands for the SCBF are taken from the median value of the record set from the NDP. 

Deformation Demand 

The brace demand in terms of axial compressive deformation is: 

 1.69 in. UD

Acceptance Criteria 

The acceptance criteria in terms of plastic axial deformation are given in ASCE 41 Table 5-7. To compare 

against the strain results coming from PERFORM-3D, the plastic deformation is converted to total axial 

deformation. 

E KL E 2.1  52.8   84.4  4.2 105.5 

Fy r Fy 

Therefore, linear interpolation gives 

105.5  84.4   21.1   ,  6 c 7 c  7 c  6 c 7 c  7   c c p AC    6.6  105.5  52.8   52.7 

c is the axial deformation at expected buckling (flexural): 

PCE 11.6 32.8    381 kips (see Linear Assessment calculations above)

C-3 
 

 

PL 381 222   CE br     0.252 in. → PCE ≈ 0.5Pye, assume elastic cross-section response c AE 11.6 29000  
 

 ,    in. p AC 6.6 0.252 1.66 

    1.66  0.38 0.252 1.76 in. total AC p AC , ,   c  

where  is the reduction in elastic deformation due to strength loss at the acceptance criterion. 

Acceptance Criteria Check 

The brace acceptance criteria check is: 

 1.69 DCR  UD   0.96 1.0

  1.0 1.76 N 

total AC ,  

Therefore, the brace satisfies the CP BPL acceptance criteria at the BSE-2 EHL. 

C-4 
 

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