NIST Technical Note 1863-1 

Assessment of 

First Generation 

Performance-Based 

Seismic Design 

Methods for 

New Steel Buildings 

Volume 1: 

Special Moment 

Frames 

John L. Harris III 

Matthew S. Speicher 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-1 
NIST Technical Note 1863-1 

Assessment of First Generation PerformanceBased Seismic Design Methods 

for New Steel Buildings 

Volume 1: Special Moment Frames 

John L. Harris III 

Matthew S. Speicher 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-1 

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 1863-1 

Natl. Inst. Stand. Technol. Tech Note 1863-1, 300 pages (February 2015) 

CODEN: NTNOEF 

This publication is available free for charge from: 

http://dx.doi.org/10.6028/NIST.TN.1863-1 

 

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 (this report) 

 Volume 2: Special Concentrically Braced Frames 

 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 ............................................................................................................................... xxv
 

Executive Summary ............................................................................................................................. xxvii
 

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

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

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

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
 

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

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

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

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

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

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

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

vii 
   

   

   

   

   

   

   

   

   

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

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

3.1.3.2.1 Nonlinear Static Procedure.......................................... 3-9
 

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 Moment Frame .............................................................................................................. 3-19
 

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

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

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

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

Four-Story Moment Frame .................................................................. 3-46
 

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

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

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

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

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

3.2.2.1.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-51
 

3.2.2.1.3 Nonlinear Static Procedure........................................ 3-53
 

3.2.2.1.4 Nonlinear Dynamic Procedure .................................. 3-58
 

Eight-Story Moment Frame................................................................. 3-66
 

3.2.2.2.1 Linear Static Procedure ............................................. 3-66
 

3.2.2.2.1.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-66
 

3.2.2.2.1.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-68
 

3.2.2.2.2 Linear Dynamic Procedure ........................................ 3-70
 

3.2.2.2.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-70
 

3.2.2.2.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) .............. 3-72
 

3.2.2.2.3 Nonlinear Static Procedure........................................ 3-74
 

3.2.2.2.4 Nonlinear Dynamic Procedure .................................. 3-82
 

Sixteen-Story Moment Frame ............................................................. 3-89
 

3.2.2.3.1 Linear Static Procedure ............................................. 3-89
 

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

viii 
   

   

   

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

3.2.2.3.2	 Linear Dynamic Procedure ....................................... 3-95
 

3.2.2.3.2.1 ..... BSE-1 Earthquake Hazard Level (LS BPL) .............. 3-95
 

3.2.2.3.2.2 ..... BSE-2 Earthquake Hazard Level (CP BPL) ............. 3-98
 

3.2.2.3.3	 Nonlinear Static Procedure ..................................... 3-101
 

3.2.2.3.4 Nonlinear Dynamic Procedure ................................ 3-110
 

Seismic Assessment Discussion ..................................................................... 3-117
 

Linear Assessment Procedures.......................................................... 3-117
 

3.2.3.1.1	 Beam-to-Column Connections ................................ 3-117
 

3.2.3.1.2	 Panel Zones ............................................................. 3-119
 

3.2.3.1.3	 Member Cross-section Strength (flexural hinge) and 

Global Strength (member stability) ......................... 3-119
 

3.2.3.1.4 Summary ................................................................. 3-121
 

Nonlinear Assessment Procedures .................................................... 3-122
 

3.2.3.2.1	 Beam-to-Column Connections ................................ 3-122
 

3.2.3.2.2	 Panel Zones ............................................................. 3-123
 

3.2.3.2.3	 Member Cross-section Strength (flexural hinge) and 

Global Strength (member stability) ......................... 3-124
 

3.2.3.2.4 Summary ................................................................. 3-126
 

Comparison between Linear and Nonlinear Assessment Results ..... 3-127
 

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 Moment Frames ........................................................................ 4-6
 

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

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

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

Fully Restrained Moment Frames ......................................................... 4-8
 

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

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

Special Moment Frames ........................................................................ 4-9
 

ix 
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
 

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

4-Story Special Moment Frame ........................................................................ A-3
 

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

8-Story Special Moment Frame ........................................................................ A-6
 

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

16-Story Special Moment 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 Moment Frame Example .................................................................... B-29
 

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

SMF Beam and RBS Beam-to-Column Connection .......................... B-30
 

B.4.1.2.1	 Flexural Demand...................................................... B-30
 

B.4.1.2.2	 Flexural Strength...................................................... B-30
 

B.4.1.2.3	 Fully Restrained Connection .................................... B-31
 

x 
SMF Column .......................................................................................B-31
 

B.4.1.3.1 Axial and Flexural Demand ......................................B-32
 

B.4.1.3.2 Axial Strength ...........................................................B-32
 

B.4.1.3.3 Flexural Strength.......................................................B-33
 

B.4.1.3.4 Strength Check ..........................................................B-33
 

SMF Panel Zone..................................................................................B-34
 

B.4.1.4.1 Shear Demand ...........................................................B-34
 

B.4.1.4.2 Shear Strength ...........................................................B-35
 

B.4.1.4.3 Strength Check ..........................................................B-35
 

SMF Strong-Column / Weak-Beam ....................................................B-36
 

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

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

SMF Frame Beam and RBS Beam-to-Column Connection ...............................C-1
 

Flexural Demand...................................................................................C-1
 

C.1.1.1.1 Frame Beam ................................................................C-1
 

C.1.1.1.2 FR Connection ............................................................C-2
 

Flexural Strength...................................................................................C-2
 

C.1.1.2.1 Beam ...........................................................................C-2
 

C.1.1.2.2 Fully Restrained Connection .......................................C-2
 

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

C.1.1.3.1 Beam ...........................................................................C-3
 

C.1.1.3.2 Fully Restrained Connection .......................................C-3
 

Acceptance Criteria Check ....................................................................C-5
 

C.1.1.4.1 Beam ...........................................................................C-5
 

C.1.1.4.2 Fully Restrained Connection .......................................C-6
 

SMF Column ......................................................................................................C-6
 

Axial Demand .......................................................................................C-7
 

Axial Strength .......................................................................................C-7
 

Flexural Demand...................................................................................C-8
 

Flexural Strength...................................................................................C-8
 

Acceptance Criteria Check ....................................................................C-9
 

SMF Panel Zone.................................................................................................C-9
 

Shear Demand .......................................................................................C-9
 

Shear Strength .......................................................................................C-9
 

xi 
 

Acceptance Criteria .............................................................................. C-9
 

Acceptance Criteria Check ................................................................. C-10
 

C.2 Nonlinear Assessment Examples ................................................................................. C-10
 

SMF Beam....................................................................................................... C-10
 

Deformation Demand ......................................................................... C-10
 

Acceptance Criteria ............................................................................ C-11
 

Acceptance Criteria Check ................................................................. C-12
 

SMF Column ................................................................................................... C-13
 

Axial Demand .................................................................................... C-13
 

Axial Strength .................................................................................... C-13
 

Deformation Demand ......................................................................... C-13
 

Acceptance Criteria ............................................................................ C-13
 

Acceptance Criteria Check ................................................................. C-15
 

SMF Panel Zone.............................................................................................. C-15
 

Deformation Demand ......................................................................... C-16
 

Acceptance Criteria ............................................................................ C-16
 

Acceptance Criteria Check ................................................................. C-16
 

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

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) .................................................................................. 3-6
 

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 Acceptance Criteria for a W24×84 ............................................................................ 3-22
 

Table 3-11. Basic m-factors for Linear Procedures, SMF ...................................................................... 3-26
 

Table 3-12. Plastic Rotation Angles for Improved WUF and Column Hinge for a W18×175 .............. 3-38
 

Table 3-13. NSP General Information, 4-Story SMF (kip, inch) ........................................................... 3-53
 

Table 3-14. NSP Analysis Parameters, 4-Story SMF BSE-2 CP (kip, inch).......................................... 3-53
 

Table 3-15. NSP Analysis Parameters– 4-Story SMF BSE-1 LS (kip, inch) ......................................... 3-53
 

Table 3-16. NSP General Information, 8-Story SMF (kip, inch) ........................................................... 3-75
 

Table 3-17. NSP Analysis Parameters, 8-Story SMF BSE-2 CP (kip, inch).......................................... 3-75
 

Table 3-18. NSP Analysis Parameters– 8-Story SMF BSE-1 LS (kip, inch) ......................................... 3-75
 

Table 3-19. NSP General Information, 16-Story SMF (kip, inch) ....................................................... 3-102
 

Table 3-20. NSP Analysis Parameters, 16-Story SMF BSE-2 CP (kip, inch)...................................... 3-102
 

Table 3-21. NSP Analysis Parameters, 16-Story SMF BSE-1 LS (kip, inch) ...................................... 3-102
 

Table 3-22. Performance Summary of FR Connections (BC) per Frame, Linear Procedures ............. 3-118
 

Table 3-23. Performance Summary of Panel Zones (PZ) per Frame, Linear Procedures .................... 3-119
 

Table 3-24. Performance Summary of Column Members (CM) per Frame, Linear Procedures ......... 3-120
 

xiii 
Table 3-25. BSO Performance Summary of Archetype Buildings, Linear Procedures ....................... 3-121
 

Table 3-26. Summary of Base Shears, Linear Procedures (kips) ......................................................... 3-122
 

Table 3-27. Performance Summary of FR Connections (BC) per Frame, Nonlinear Procedures ........ 3-123
 

Table 3-28. Performance Summary of Panel Zones (PZ) per Frame, Nonlinear Procedures ............... 3-124
 

Table 3-29. Performance Summary of Column Hinges (CH) per Frame, Nonlinear Procedures ........ 3-125
 

Table 3-30. Performance Summary of Column Members (CM) per Frame, Nonlinear Procedures .... 3-126
 

Table 3-31. BSO Performance Summary of Archetype Buildings, Nonlinear Procedures .................. 3-126
 

Table 3-32. BSO Performance Summary of Archetype Buildings....................................................... 3-128
 

Table A-1. Ground Motion Records for E-W Direction of MC4 ............................................................ A-3
 

Table A-2. Ground Motion Records for E-W Direction of MC8 ............................................................ A-6
 

Table A-3. Ground Motion Records for E-W 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
 

xiv 
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
 

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-32
 

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
 

 ................................................................................................................................................................. 3-23
 

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 .. 3-24
 

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

Acceptance Criteria ................................................................................................................................. 3-25
 

Figure 3-7. Frame Capacity Schematic (m-factor), LS and CP, 4-Story SMF ELF ............................... 3-27
 

Figure 3-8. Frame Capacity Schematic (m-factor), LS and CP, 4-Story SMF RSA .............................. 3-27
 

Figure 3-9. Frame Capacity Schematic (m-factor), LS and CP, 8-Story SMF ELF ............................... 3-28
 

Figure 3-10. Frame Capacity Schematic (m-factor), LS and CP, 8-Story SMF RSA ............................ 3-28
 

Figure 3-11. Frame Capacity Schematic (m-factor), LS and CP, 16-Story SMF ELF ........................... 3-29
 

Figure 3-12. Frame Capacity Schematic (m-factor), LS and CP, 16-Story SMF RSA .......................... 3-30
 

Figure 3-13. SMF Beam-to-Column Subassembly Analytical Schematic ............................................. 3-32
 

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

Figure 3-15. PERFORM-3D Panel Zone Calibration ............................................................................ 3-34
 

Figure 3-16. In-plane Flexural Hinge Yield Surface Model (Including Force-Controlled Response) ... 3-36
 

Figure 3-17. Variation in Acceptance Criteria and Hinge Model for Axial Force ................................. 3-36
 

Figure 3-18. P-M Interaction on Plastic Rotation, LS Acceptance Criteria (Primary Component) ....... 3-37
 

Figure 3-19. P-M Interaction Curve (Section Yield Surface)................................................................. 3-38
 

Figure 3-20. P-M Interaction Curve (Member Strength)........................................................................ 3-39
 

Figure 3-21. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 4-Story SMF ELF .................... 3-40
 

Figure 3-22. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 4-Story SMF RSA.................... 3-40
 

Figure 3-23. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 8-Story SMF ELF .................... 3-41
 

Figure 3-24. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 8-Story SMF RSA.................... 3-42
 

Figure 3-25. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 16-Story SMF ELF .................. 3-43
 

Figure 3-26. Frame Capacity Schematic (inelastic), YD, LS and CP, 16-Story SMF RSA ................... 3-44
 

Figure 3-27. LSP Assessment Results, 4-Story SMF ELF, BSE-1 LS ................................................... 3-46
 

Figure 3-28. LSP Assessment Results, 4-Story SMF RSA, BSE-1 LS .................................................. 3-47
 

Figure 3-29. LSP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-1 ........ 3-47
 

Figure 3-30. LSP Assessment Results, 4-Story SMF ELF, BSE-2 CP .................................................. 3-48
 

Figure 3-31. LSP Assessment Results, 4-Story SMF RSA, BSE-2 CP .................................................. 3-48
 

Figure 3-32. LSP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-2 ........ 3-49
 

Figure 3-33. LDP Assessment Results, 4-Story SMF ELF, BSE-1 LS .................................................. 3-50
 

Figure 3-34. LDP Assessment Results, 4-Story SMF RSA, BSE-1 LS ................................................. 3-50
 

Figure 3-35. LDP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-1 ....... 3-51
 

Figure 3-36. LDP Assessment Results, 4-Story SMF ELF, BSE-2 CP .................................................. 3-52
 

Figure 3-37. LDP Assessment Results, 4-Story SMF RSA, BSE-2 CP ................................................. 3-52
 

Figure 3-38. LDP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-2 ....... 3-52
 

Figure 3-39. 4-Story SMF ELF Pushover, BSE-2 .................................................................................. 3-54
 

Figure 3-40. 4-Story SMF RSA Pushover, BSE-2 ................................................................................. 3-54
 

Figure 3-41. 4-Story SMF ELF Pushover – Story Drift Ratios – BSE-2 ............................................... 3-55
 

Figure 3-42. 4-Story SMF RSA Pushover – Story Drift Ratios – BSE-2 ............................................... 3-55
 

Figure 3-43. Schematic of Flexural Actions in Columns, 4-Story SMF (NSP and NDP) ...................... 3-56
 

Figure 3-44. NSP Assessment Results, 4-Story SMF ELF, BSE-1 LS (+push to right) ........................ 3-57
 

Figure 3-45. NSP Assessment Results, 4-Story SMF RSA, BSE-1 LS (+push to right) ....................... 3-57
 

Figure 3-46. NSP Assessment Results, 4-Story SMF ELF, BSE-2 CP (+push to right) ........................ 3-57
 

Figure 3-47. NSP Assessment Results, 4-Story SMF RSA, BSE-2 CP (+push to right) ....................... 3-58
 

Figure 3-48. NDP Assessment Results, Beam Hinges, 4-Story SMF ELF, BSE-1 LS .......................... 3-59
 

xviii 
Figure 3-49. NDP Assessment Results, Beam Hinges, 4-Story SMF RSA, BSE-1 LS ......................... 3-59
 

Figure 3-50. NDP Assessment Results, Beam Hinges, 4-Story SMF ELF, BSE-2 CP .......................... 3-60
 

Figure 3-51. NDP Assessment Results, Beam Hinges, 4-Story SMF RSA, BSE-2 CP ......................... 3-60
 

Figure 3-52. NDP Assessment Results, Column Hinges, 4-Story SMF ELF, BSE-2 CP ...................... 3-61
 

Figure 3-53. NDP Assessment Results, Column Hinges, 4-Story SMF RSA, BSE-2 CP ..................... 3-62
 

Figure 3-54. NDP Assessment Results, Column Hinges, 4-Story SMF ELF, BSE-2 Yield .................. 3-62
 

Figure 3-55. NDP Assessment Results, Column Hinges, 4-Story SMF RSA, BSE-2 Yield ................. 3-63
 

Figure 3-56. NDP Assessment Results, Column Members, 4-Story SMF ELF, BSE-2 CP .................. 3-63
 

Figure 3-57. NDP Assessment Results, Column Members, 4-Story SMF RSA, BSE-2 CP .................. 3-64
 

Figure 3-58. NDP Assessment Results, Panel Zones, 4-Story SMF ELF, BSE-2 CP ............................ 3-65
 

Figure 3-59. NDP Assessment Results, Panel Zones, 4-Story SMF RSA, BSE-2 CP ........................... 3-65
 

Figure 3-60. LSP Assessment Results, 8-Story SMF ELF, BSE-1 LS ................................................... 3-67
 

Figure 3-61. LSP Assessment Results, 8-Story SMF RSA, BSE-1 LS .................................................. 3-67
 

Figure 3-62. LSP Assessment Results, Compression in Exterior Columns, 8-Story SMF, BSE-1 ........ 3-68
 

Figure 3-63. LSP Assessment Results, 8-Story SMF ELF, BSE-2 CP .................................................. 3-69
 

Figure 3-64. LSP Assessment Results, 8-Story SMF RSA, BSE-2 CP .................................................. 3-69
 

Figure 3-65. LSP Assessment Results, Compression in Exterior Columns, 8-Story SMF, BSE-2 ........ 3-70
 

Figure 3-66. LDP Assessment Results, 8-Story SMF ELF, BSE-1 LS .................................................. 3-71
 

Figure 3-67. LDP Assessment Results, 8-Story SMF RSA, BSE-1 LS ................................................. 3-71
 

Figure 3-68. LDP Assessment Results, Compression in Exterior Columns, 8-Story SMF, BSE-1 ....... 3-72
 

Figure 3-69. LDP Assessment Results, 8-Story SMF ELF, BSE-2 CP .................................................. 3-73
 

Figure 3-70. LDP Assessment Results, 8-Story SMF RSA, BSE-2 CP ................................................. 3-73
 

Figure 3-71. LDP Assessment Results, Compression in Exterior Columns, 8-Story SMF, BSE-2 ....... 3-74
 

Figure 3-72. 8-Story SMF ELF Pushover, BSE-2 .................................................................................. 3-75
 

Figure 3-73. 8-Story SMF RSA Pushover, BSE-2 ................................................................................. 3-76
 

Figure 3-74. 8-Story SMF ELF Pushover – Story Drift Ratios – BSE-2 ............................................... 3-76
 

Figure 3-75. 8-Story SMF RSA Pushover – Story Drift Ratios – BSE-2 ............................................... 3-77
 

Figure 3-76. Story Shear Demand to Strength Comparison, ELF .......................................................... 3-78
 

Figure 3-77. Story Shear Demand to Strength Comparison, RSA ......................................................... 3-78
 

Figure 3-78. Schematic of Flexural Actions in Columns, 8-Story SMF (NSP and NDP) ...................... 3-79
 

Figure 3-79. NSP Assessment Results, 8-Story SMF ELF, BSE-1 LS (+push to right) ........................ 3-80
 

Figure 3-80. NSP Assessment Results, 8-Story SMF RSA, BSE-1 LS (+push to right) ....................... 3-80
 

Figure 3-81. NSP Assessment Results, 8-Story SMF ELF, BSE-2 CP (+push to right) ........................ 3-81
 

Figure 3-82. NSP Assessment Results, 8-Story SMF RSA, BSE-2 CP (+push to right) ....................... 3-81
 

Figure 3-83. NDP Assessment Results, Beam Hinges, 8-Story SMF ELF, BSE-1 LS .......................... 3-82
 

xix 
Figure 3-84. NDP Assessment Results, Beam Hinges, 8-Story SMF RSA, BSE-1 LS ......................... 3-83
 

Figure 3-85. NDP Assessment Results, Beam Hinges, 8-Story SMF ELF, BSE-2 CP .......................... 3-83
 

Figure 3-86. NDP Assessment Results, Beam Hinges, 8-Story SMF RSA, BSE-2 CP ......................... 3-84
 

Figure 3-87. NDP Assessment Results, Column Hinges, 8-Story SMF ELF, BSE-2 CP ...................... 3-85
 

Figure 3-88. NDP Assessment Results, Column Hinges, 8-Story SMF RSA, BSE-2 CP ..................... 3-85
 

Figure 3-89. NDP Assessment Results, Column Hinges, 8-Story SMF ELF, BSE-2 Yield .................. 3-86
 

Figure 3-90. NDP Assessment Results, Column Hinges, 8-Story SMF RSA, BSE-2 Yield ................. 3-86
 

Figure 3-91. NDP Assessment Results, Column Members, 8-Story SMF ELF, BSE-2 ........................ 3-87
 

Figure 3-92. NDP Assessment Results, Column Members, 8-Story SMF RSA, BSE-2 ........................ 3-87
 

Figure 3-93. NDP Assessment Results, Panel Zones, 8-Story SMF ELF, BSE-2 CP ............................ 3-88
 

Figure 3-94. NDP Assessment Results, Panel Zones, 8-Story SMF RSA, BSE-2 CP ........................... 3-88
 

Figure 3-95. LSP Assessment Results, 16-Story SMF ELF, BSE-1 LS ................................................. 3-90
 

Figure 3-96. LSP Assessment Results, 16-Story SMF RSA, BSE-1 LS ................................................ 3-91
 

Figure 3-97. LSP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-1 ...... 3-92
 

Figure 3-98. LSP Assessment Results, 16-Story SMF ELF, BSE-2 CP ................................................ 3-93
 

Figure 3-99. LSP Assessment Results, 16-Story SMF RSA, BSE-2 CP ................................................ 3-94
 

Figure 3-100. LSP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-2 .... 3-95
 

Figure 3-101. LDP Assessment Results, 16-Story SMF ELF, BSE-1 LS .............................................. 3-96
 

Figure 3-102. LDP Assessment Results, 16-Story SMF RSA, BSE-1 LS ............................................. 3-97
 

Figure 3-103. LDP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-1 ... 3-98
 

Figure 3-104. LDP Assessment Results, 16-Story SMF ELF, BSE-2 CP .............................................. 3-99
 

Figure 3-105. LDP Assessment Results, 16-Story SMF RSA, BSE-2 CP ........................................... 3-100
 

Figure 3-106. LDP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-2 . 3-101
 

Figure 3-107. 16-Story SMF ELF Pushover, BSE-2 ............................................................................ 3-102
 

Figure 3-108. 16-Story SMF RSA Pushover, BSE-2 ........................................................................... 3-103
 

Figure 3-109. 16-Story SMF ELF Pushover – Story Drift Ratios – BSE-2 ......................................... 3-103
 

Figure 3-110. 16-Story SMF RSA Pushover – Story Drift Ratios – BSE-2 ......................................... 3-104
 

Figure 3-111. Schematic of Flexural Actions in Columns, 16-Story SMF (NSP and NDP) ................ 3-105
 

Figure 3-112. NSP Assessment Results, 16-Story SMF ELF, BSE-1 LS (+push to right) .................. 3-106
 

Figure 3-113. NSP Assessment Results, 16-Story SMF RSA, BSE-1 LS (+push to right) ................. 3-107
 

Figure 3-114. NSP Assessment Results, 16-Story SMF ELF, BSE-2 CP (+push to right) .................. 3-108
 

Figure 3-115. NSP Assessment Results, 16-Story SMF RSA, BSE-2 CP (+push to right) ................. 3-109
 

Figure 3-116. NDP Assessment Results, Beam Hinges, 16-Story SMF ELF, BSE-1 LS .................... 3-110
 

Figure 3-117. NDP Assessment Results, Beam Hinges, 16-Story SMF RSA, BSE-1 LS ................... 3-111
 

Figure 3-118. NDP Assessment Results, Beam Hinges, 16-Story SMF ELF, BSE-2 CP .................... 3-111
 

xx 
Figure 3-119. NDP Assessment Results, Beam Hinges, 16-Story SMF RSA, BSE-2 CP ................... 3-112
 

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

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

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

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

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

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

Figure 3-120. NDP Assessment Results, Column Hinges, 16-Story SMF ELF, BSE-2 CP ................ 3-113
 

Figure 3-121. NDP Assessment Results, Column Hinges, 16-Story SMF RSA, BSE-2 CP ............... 3-113
 

Figure 3-122. NDP Assessment Results, Column Hinges, 16-Story SMF ELF, BSE-2 Yield ............ 3-114
 

Figure 3-123. NDP Assessment Results, Column Hinges, 16-Story SMF RSA, BSE-2 Yield ........... 3-114
 

Figure 3-124. NDP Assessment Results, Column Members, 16-Story SMF ELF, BSE-2 CP ............ 3-115
 

Figure 3-125. NDP Assessment Results, Column Members, 16-Story SMF RSA, BSE-2 CP ............ 3-115
 

Figure 3-126. NDP Assessment Results, Panel Zones, 16-Story SMF ELF, BSE-2 CP ...................... 3-116
 

Figure 3-127. NDP Assessment Results, Panel Zones, 16-Story SMF RSA, BSE-2 CP ..................... 3-116
 

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

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

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

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

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
 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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
 

xxii 
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. SMF Member Sizes, 8-story RSA ..................................................................................... B-29
 

xxiii 
 

xxiv
 
 

 

 

 

 

 

 

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 

xxv 
 

 

 

 

 

 

 

 

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 

xxvi 
Executive Summary 

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

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

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

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

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

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

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

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

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

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

and performance measures of buildings utilizing steel special moment frames (SMF) as the lateral forceresisting system (LFRS). 

A suite of archetype buildings that incorporate SMFs 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. 

xxvii 
To evaluate seismic assessment criteria, each component of the SMFs 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 SMFs 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 Moment 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 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. 

B. Specific Observations for Special Moment Frames: 

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

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

assessment discussion in Chapter 3. 

xxviii 
	 Analytical results based on component-level performances indicate that new SMFs 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 columns and beam-to-column connections. 

	 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 SMFs. 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 beam-to-column connections with a reduced beam section 

(RBS) 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. 

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

41 acceptance criteria. These failures are in beam-columns classified by analysis as “forcecontrolled”, which can be particularly problematic when the columns are located at the base of a 

frame. The results for columns can be enhanced by more mechanistically consistent assessment 

provisions and analytical modeling parameters for columns. Refinement of the relevant interaction 

equations to evaluate specific failure mechanisms could assist by allowing what would be a forcecontrolled column to be classified as “deformation-controlled”. 

	 A significant number of RBS beam-to-column connections, primarily at the exteriors of the frames, 

did not satisfy the ASCE 41 acceptance criteria for the LSP and NDP. Although the nonlinear 

acceptance criteria and detailing recommendations in ASCE 41 were derived from experimental 

test data, the rationale for the quantitative development of the cumulative reduction factors on these 

criteria (i.e., 0.8 multipliers in ASCE 41 §5.4.2.4.3-4) is unclear. The analytical results indicate that 

step function-based cumulative reduction factors can have a significant impact on the performance 

of a SMF. Further, reduction factors for the span-to-depth ratio limitations for beam-to-column 

connections have potentially opposing effects that could impact the results between linear and 

nonlinear assessment procedures. 

	 Assessment results illustrate that panel zones designed per ASCE 7 and its referenced standards, 

including the common practice of upsizing columns to offset the need for doubler plates and/or 

continuity plates, consistently satisfied the ASCE 41 acceptance criteria by a large margin. 

Consequently, the panel zones are deemed stronger than required by ASCE 41. Specifically, 

upsizing columns can impact the strength of panel zones in reference to the balance yield approach 

adopted by ASCE 41 and in turn can influence the performance of the beam-to-column connections. 

	 Components of the SMFs 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 SMF 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 

xxix 
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). 

xxx 
 

 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 moment frames (SMF) as the lateral forceresisting system (LFRS)3 

. 

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

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

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

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

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

 to resist 

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

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

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

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

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

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

analysis procedures prescribed in ASCE 41: 

 Linear Static Procedure (LSP) 

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

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

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

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

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

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

strength. 

1-5
 
 

 Linear Dynamic Procedure (Response Spectrum) (LDP) 

 Nonlinear Static Procedure (NSP) 

 Nonlinear Dynamic Procedure (NDP)
 

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

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

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

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

structural performance objective of an ordinary building5

 in ASCE 7, which is qualitatively defined here as 

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

(MCE) event. 

To evaluate seismic assessment criteria, each component of the SMFs is designated as a primary 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 SMFs designed per ASCE 7 requirements and, in 

turn, evaluated using ASCE 41, 

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

identified by ASCE 41 procedures and performance measures, 

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

extent, ASCE 7), 

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

assessment, and 

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

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

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

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

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

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

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

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

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

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

5 Buildings assigned Risk Category I or II. 

1-6
 
 

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

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

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

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

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

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

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

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

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

Appendix C. 

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

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

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

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

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

1-7
 
 

1-8
 
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 moment frames will be presented in this 

report. Assessment of the braced frames is presented in NIST TN 1863-2: Assessment of First Generation 

Performance-Based Design Methods for New Steel Buildings, Volume 2: Special Concentrically Braced 

Frames (Harris and Speicher 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 is 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 as 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 as 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 modeled) 

Increased joint stiffne ss 

provided by gusset elements 

Column, EIc Column, EIc 

Brace axial stiffness 

computed from 0.9Lwp 

In-pla ne rota tion 

release 

Panel 

Zone 

node 

Rigid End 

Zone, typ. 

Out-of-plane 

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 

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. 

 b 

EI x,c 

Lc G  EI (2-1) x,b

 Lb 

Other relationships can be used to show that G can be computed as function of the in-plane flexural section 

strength, Zx×Fy, independent of the in-plane flexural stiffness, E×Ix. Equation (2-2) shows that the strongaxis plastic section modulus, Zx, is a function of the strong-axis moment of inertia, Ix, and section depth, d. 

Equation (2-3) rewrites the SCWB equation in AISC 341 (see §E3.4a) for a wide-flange section. 

2I x Zx  (2-2) d 

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

M p c, 

 

 Py 

 

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

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

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 

SCBF designs are included here to provide the required information of the building for SMF designs. 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" 

Sy m. 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 = 60 ft.)
 

HSS4×4×1/2 

4th Flo or 

(ELEV = 46 ft.) 

HSS5×5×3/8 

3rd Flo or 

(ELEV = 32 ft.) 

HSS6×6×1/2 

2nd Floor 

(ELEV = 18 ft.) 

HSS6×6×5/8 

= Panel Zon e/Gusset Plate 

= Colu mn Splice 

= In-plane mom en t release 

= Out-of-plane moment 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
 
W14×176 W14×311 W14×132 W14×68 

(b) ELF 

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

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

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 

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)
 

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 

= Panel Zone/Gusset Plate 

= Column Splice 

= In-plane moment release 

= Out-of-plane moment release 

(a) RSA 

Figure 2-17. 16-Story SCBF Schematic 

2-27
 
2 @ 30'-0" = 60'-0" 

W18×55 

2 

2 3 

4 

5 6 

6 

8 9 

8 

4 2 

1 

1 

3 

4 

5 

7 

7 

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 11 12 13 

14 

15 

16 

9 

11

10 12 

10 

14 15 

12 

9 

13 

11 

16 17 18 21 

22 

23 

24 

17 19

18 20 

14 

20 21 

16 

13 

19 

15 

22 23 24 29 

30 

31 

32 

25 27

26 28 

18 

26 27 

20 

17 

25 

19 

28 29 30 37 

38 

39 

40 

33 35

34 36 

22 

32 33 

24 

21 

31 

23 

34 35 36 45 

46 

47 

48 

41 43

42 44 

26 

38 39 

28 

25 

37 

27 

40 41 42 53 

54 

55 

56 

49 51

50 52 

30 

44 45 

32 

29 

43 

31 

46 47 48 61 

62 

63 

64 

57 59

58 60 

5 

6 

7 

8 

1 3

2 4 

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 = 2.06 sec (First-Order)
 

T1 = 2.08 sec (1.0D + 0.25Lo)
 

T1 = 2.09 sec (1.2D + 0.25Lo)
 

HSS5×5×3/8 

HSS5.5×5.5×3/8 

HSS6×6×1/2 

HSS6×6×5/8 

HSS7×7×1/2 

HSS7×7×1/2 

HSS7×7×1/2 

HSS8×8×5/8 

Sym. About 

= Panel Zone/Gusset Plate 

= Column Splice 

= In-plane moment release 

= Out-of-plane moment release 

(b) ELF 

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

2-28
 
 

 

 Seismic Assessment 

This chapter presents the results of the seismic assessment of the special moment frames in accordance with 

ASCE 41. Section 3.1 provides general discussions on the global analysis requirements for assessment. 

Analysis requirements specific to moment 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 moment 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 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) 

Earthquake Hazard 

Level Earthquake Intensity Structural Performance Level 

Nonstructural 

Performance Level 

Building 

Performance Level 

BSE-1 – §1.6.1.2 2/3×BSE-2 Life Safety (S-3) Not Considered (N-E) Life Safety (3-E) 

BSE-2 – §1.6.1.1 Maximum Considered 

Earthquake (MCE) 

Collapse 

Prevention (S-5) Not Considered (N-E) Collapse Prevention (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 Nonstructural Building Performance Earthquake Intensity Level	 Performance 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 composite shear tab connections and stairs) are not modeled explicitly in the mathematical model. 

This is done to minimize the influence of secondary components on the demands imposed on primary 

components. This will allow assessment results between linear and nonlinear analysis to be compared. 

Performance assessment of these secondary members is outside the scope of this study—though would 

need to be checked in a real retrofit design. In addition, foundation or soil flexibility is not included in the 

analysis. Models for anticipated component inelastic actions in nonlinear assessment procedures include 

both strength and stiffness degradation—discussed subsequently in §3.2. 

ASCE 41 §3.2.3—Configuration: Building irregularities are discussed in ASCE 41 §3.1.3.1. Building 

irregularities defined in ASCE 41 are used only to determine whether the linear procedures are applicable. 

ASCE 41 §3.2.4—Diaphragms: Floor diaphragms are modeled for analysis as semi-rigid membranes (i.e., 

stiff per ASCE 41). The same assumptions adopted in design are maintained for assessment. 

ASCE 41 §3.2.5—P- Effects: Global P- effects are considered in the linear and nonlinear analyses, for 

both static and dynamic. Local P- effects are not addressed either explicitly or implicitly in the analyses. 

ASCE 41 §3.2.6—Soil-Structure Interaction: Soil-Structure Interaction is not considered in the seismic 

assessment of the archetype buildings. 

ASCE 41 §3.2.7—Multidirectional Seismic Effects: The principal axes of the archetype buildings align 

directly with the E-W and N-S directions (performance in the E-W direction is presented in this report). 

Seismic effects are determined by applying the seismic forces independently in each of the two orthogonal 

directions. Per ASCE 41 §3.2.7.1, concurrent seismic effects are addressed in the assessment by combining 

the effects along each principal axes. 

14 Amplification of the accidental torsion, if required, is consistent between ASCE 41 and ASCE 7. 

3-4
 
ASCE 41 §3.2.7—Vertical Seismic Effects: Vertical seismic effects are not considered for seismic 

assessment of the archetype buildings. Masses are input for horizontal accelerations only for dynamic 

analysis. 

ASCE 41 §3.2.8—Gravity Loads: Gravity loads for the linear assessment procedures are applied using the 

following two load combinations (LC). Roof live loads are considered not to be present for seismic analysis. 

There is no snow load acting on the buildings. 

 LC1 = 1.1×(Dead+0.25×Unreduced Floor Live) 

 LC2 = 0.9×Dead 

A P- load combination based on LC1 above is used for the linear assessment analyses; consequently, this 

is conservative for analysis using LC2. 

Both gravity load combinations above are used for the nonlinear static procedure. The average of the two 

combinations (LC1 and LC2) is applied in the nonlinear dynamic procedure. 

 LC3 = 1.0×Dead+0.25×Unreduced Floor Live 

A P- load combination based on LC3 above is used for the nonlinear assessment analyses. 

ASCE 41 §3.2.9—Verification of Design Assumptions: The following design objectives are verified with 

the nonlinear dynamic procedure. 

 SMF—Strong Column Weak Beam (SCWB) (AISC 341) 

 SMF—adequate flexural and shear strength in beam at the face of column (AISC 358) 

 SMF—adequate shear strength at the center of the RBS (AISC 358) 

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

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

archetype buildings. 

 Analysis Procedures 

This section discusses the implementation of the specific analysis procedures prescribed in ASCE 41 §3.3 

in this study. 

Linear Analysis Procedures 

The archetype buildings are modeled and analyzed in ETABS 9.7.4 (CSI 2011a) for the linear analyses. 

The assumptions used in the mathematical model and analysis techniques are the same as those adopted for 

design (see Chapter 2). Modeling and analysis considerations for the linear procedures are outlined in ASCE 

41 §3.2.2 with supplemental information provided in ASCE 41 §3.3.2.2 for the Linear Dynamic Procedure 

(LDP). Gravity loads and load combinations assumed present during the earthquake are computed from 

3-5
 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

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. 

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. 

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. 

3-6
 
 

 

 

ASCE 41 §2.4.1.1 prescribes restrictions on the use of the linear procedures. First, a retrofitted 15 SFRS 

must not contain certain types of structural irregularities where the earthquake demands on the primary 

components of the SFRS fail to comply with the demand capacity ratio (DCR) limitations. 

Q DCR  UD  2.0 (3-1) QCE 

where QUD is the demand on a component due to gravity and earthquake loads and QCE is the expected 

strength of the component. The archetype buildings do not contain any configuration-based in-plane or outof-plane irregularities. Further, a linear analysis procedure must be performed to determine whether a 

building contains a weak story or torsional strength irregularity. Because of plan symmetry and regularity 

of the archetype buildings, there are no torsional irregularities. The required weak story irregularity 

verifications are discussed subsequently in the linear static procedure for each specific system type. 

3.1.3.1.1 Linear Static Procedure 

The Linear Static Procedure (LSP) is outlined in ASCE 41 §3.3.1. The provisions of the LSP closely 

resemble those of the ELF procedure in ASCE 7; as such, no additional analysis details are presented here. 

However, one place where ASCE 7 and ASCE 41 differ is in the determination of the fundamental period, 

T, in the direction being analyzed. ASCE 41 does not place an upper-bound limit on the period used for 

assessment as ASCE 7 does for strength design. In this study, the fundamental periods are determined by 

eigenvalue analysis per ASCE 41 §3.3.1.2.1. 

Further restrictions on the use of the LSP are prescribed in ASCE 41 §2.4.1.2. The LSP cannot be used if 

any of the following occur: 

	 The fundamental period of the building, T, is greater than 3.5×Ts (= 3.5×0.6 = 2.1 seconds in this 

study). This trigger is similar to that used in ASCE 7; however, like ASCE 7, which computation 

method for T to be used in this evaluation is not clear. If the analytical method (ASCE 41 §3.3.1.2.1) 

is used, only the E-W component of the ELF-designed 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. 

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

3-7
 
 

 

 

 

 

	 The building has a non-orthogonal SFRS. In this study, this limitation is not applicable to the 

archetype buildings. 

Regardless of the restrictions on using the LSP, results from applying the LSP to the archetype buildings 

are included for the purpose of seismic performance comparison between the various assessment methods 

in this study. 

Table 3-6. Analytical Fundamental Periods (seconds) 

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. 

Nonlinear Analysis Procedures 

The archetype buildings are modeled and analyzed in PERFORM-3D 5.0.0 (CSI 2011b) for the nonlinear 

procedures. Modeling and analysis considerations for the nonlinear procedures are outlined in ASCE 41 

§3.2.2 with supplemental information provided in ASCE 41 §3.3.3.2 for the Nonlinear Static Procedure 

(NSP) and ASCE 41 §3.3.4.2 for the Nonlinear Dynamic Procedure (NDP). Primary components of the 

SFRS expected to experience inelastic deformations are modeled using a full “backbone” curve that 

includes strength and stiffness (applicable only for the NDP) degradation and residual strength. For this 

study, all nonlinear components are modeled with the anchor points (A to E) bounding the full backbone 

curve as shown in ASCE 41 Figure C2-1 and Figure 5-1—see Figure 3-2. This topic will be discussed 

further in the respective analysis and system-specific sections. 

3-8
 
Gravity loads and corresponding load combination assumed to be present during the earthquake are 

computed from ASCE 41 §3.2.8 as discussed previously. The effective horizontal seismic weights, w, for 

analysis are computed in accordance with ASCE 41 §3.3.1 and are the same as those used for design (see 

Chapter 2). Global P- effects (e.g., B2 in AISC 360 Appendix 8) are addressed in the analysis by using a 

simplified algorithm—see PERFORM-3D User Guide (CSI 2011d). PERFORM-3D does not explicitly 

include local P- effects (e.g., B1 in AISC 360 Appendix 8). Building specific modeling assumptions and 

analysis techniques are described in their respective sections. 

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

3.1.3.2.1 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 

3-9
 
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- effects are directly included in the analysis. Local P- effects are not addressed in the 

analysis. Geometric nonlinearity is assigned to all elements. 

 Number of Steps is taken as 100 and Maximum Number of Events is taken as 1,000. 

 Roof displacement at the center of mass relative to the base is used as the target displacement. The 

reference drift is therefore taken as the roof drift; the maximum allowable drift is taken as 10 

percent. All story drifts are included in the list of Controlled Drifts. 

 See PERFORM-3D User Guide for additional information. 

3.1.3.2.2 Nonlinear Dynamic Procedure 

The Nonlinear Dynamic Procedure (NDP) is outlined in ASCE 41 §3.3.4. The NDP is intended to be the 

most rigorous of all the assessment procedures prescribed, with no limitations placed on types of buildings 

allowed for the assessment because of the intent of capturing the true behavior of the building subjected to 

strong ground motions. 

The mathematical model requirements for use with the NDP are outlined in ASCE 41 §3.2.2 and ASCE 41 

§3.3.4.2, except that the point-in-time gravity load present during strong ground motion is taken as (D + 

SD) + 0.25×Lo,floor, a slight but common alternative to ASCE 41 §3.2.8 (see ASCE 7 §16.2.3). Primary 

components of the SFRS expected to experience inelastic deformations are modeled using full backbone 

curves that include strength and stiffness degradation and residual strength (see ASCE 41 §3.2.2.3 and 

ASCE §3.3.4.2). 

For the NSP, ASCE 41 §5.4.2.2.2 allows using the generalized modeling parameters provided in ASCE 41 

Tables 5-6 and 5-7 to model the full backbone curves of steel components as an alternative to experimental 

calibration. However, for the NDP, ASCE 41 §5.4.2.2.3 requires all component hysteretic behavior be based 

on experimental data unless permitted by the authority have jurisdiction. The benefit of calibrating 

component models with experimental results is that the force-deformation relationship will more accurately 

reflect strength and stiffness degradation, both cyclic and in-cycle—see NIST GCR 10-917-5: Nonlinear 

Structural Analysis for Seismic Design: A Guide for Practicing Engineers (NIST 2010a) and FEMA P440A: Effects of Strength and Stiffness Degradation on Seismic Response (FEMA 2009c). In this study, all 

nonlinear components are modeled with the anchor points (A to E) bounding the full backbone curve as 

shown in Figure 3-2 and quantified in ASCE 41 Tables 5-6 and 5-7. All nonlinear components are calibrated 

based on experimental results to determine cyclic and in-cycle stiffness degradation only; post-yield 

strength increases and strength degradation calibrations from experimental results were not included. 

Component strength at the ultimate deformation, point E on the backbone curve, retains the residual strength 

and does not experience complete strength loss. SFRS-specific modeling approaches are discussed in their 

3-13
 
 

 

 

respective sections. Therefore, the same PERFORM-3D model used in the NSP is also used in the NDP; 

analytical results from the two procedures are thus consistent and directly comparable. Future ASCE 41 

revisions should unify modeling practices for the NSP and NDP, as well as provide supporting data to the 

authority having jurisdiction. Future research should examine the response of these systems with hysteretic 

models calibrated completely to test results, including performing FEMA P695 analyses. 

The nonlinear dynamic analysis algorithm in PERFORM-3D used the following parameters: 

 Damping is taken as three percent of critical for all modes (elastic) and 0.3 percent of critical is 

added as Rayleigh damping (elastic stiffness component only, beta-K) for dynamic analysis. 

Damping computation in PERFORM-3D is not based on the tangent stiffness matrix. All elements 

are assigned a beta-K damping stiffness reduction factor of unity (no reduction). 

 Strength and stiffness degradation are included in the analysis. 

 Global P- effects are directly included in the analysis. Local P- effects are not addressed in the 

analysis. Geometric nonlinearity is assigned to all elements. 

 Maximum Number of Events for each time step is taken as 200. 

 Time steps for analysis are taken as the time step of the input motion, ranging from 0.005 to 0.02 

seconds—see FEMA P695 Appendix A. 

 See PERFORM-3D User Guide for additional information. 

A critical aspect of the NDP is the selection and scaling of input ground motions (free-field motions) which 

is described in ASCE 41 §1.6.2.2. The methodology adopted in this study is discussed in Appendix A. 

In addition to the analysis routine terminating when a solution fails to converge, the routine was also set to 

terminate when an arbitrarily selected roof drift ratio of twenty percent16 is achieved (story drift ratios can 

be higher). While both of these methods are used to indicate and rationalize total or partial collapse of a 

system, the indicator of collapse used in this study is the component demands measured against the 

nonlinear modeling parameters and acceptance criteria. These component limits will typically be reached 

prior to an analysis routine failing to converge or an excessive roof drift is reached. 

 Acceptance Criteria 

This section discusses the implementation of the acceptance criteria in ASCE 41 §3.4. Component actions 

are classified as force-controlled or deformation-controlled depending on the post-elastic behavior of the 

component (see ASCE 41 Table C2-1). Generally speaking, deformation-controlled actions are assigned to 

component actions capable of a ductile response (e.g., moment in a plastic hinge in a compact beam) and 

force-controlled actions are assigned to component actions with limited ductility (e.g., moment in a plastic 

hinge in a column with high axial load). Additionally, a knowledge factor, , is applied to account for 

uncertainties in the framing system and materials. Since the archetype buildings are new construction with 

quality control measures,  is taken as unity in this study to represent new component capacities or actions 

as discussed in ASCE 41 §2.2.2 and ASCE 41 Tables 2-1, 2-2, and 2-3. 

16 This value does not change the qualitative performance result of a component; however, it can influence the mean value of a 

performance response for a set of records. For example, mean values would be slightly larger than if ten percent was selected. 

3-14
 
Linear Procedures 

Acceptance criteria of components for linear assessment procedures are provided as m-factors. The m-factor 

is intended to account for the ductility associated with a specific action and depends on the SPL and 

component type. ASCE 41 Table 5-5 provides the m-factors for steel components for linear assessment 

procedures. Adjustments to the m-factors for member or connection characteristics are detailed in ASCE 

41 Chapter 5. In this study, actions in force-controlled components are assigned m = 1.0 for simplicity and 

computational consistency in developed assessment spreadsheets. It should be noted that ASCE 41 does 

not assign an m-factor to force-controlled components. 

3.1.4.1.1 Calculating Component Assessment Results 

Component forces and deformations obtained by the LSP or LDP are referred to as design actions, QU (e.g., 

flexure in a component). 

Component design actions classified as deformation-controlled, QUD, are computed by 

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 QUF  QG  E (ASCE 41 §3.4.2.1.2) (3-3) C C J 12 

where QG is the action due to gravity loads and QE is the action due to earthquake effects. Elastic forcecontrolled demands from earthquake effects are divided by C1C2 to remove the demand amplification for 

short period structures from non-ductile components (see ASCE 41 §3.3.1). Similarly, the demand is 

divided by J, which is the force-delivery reduction factor and is taken as the minimum demand capacity 

ration (DCR) of the components in the load path delivering force to the component. Alternatively, J can be 

taken as 2.0 when the system is located in a region of a high level of seismicity, independent of EHL. 

However, holding J constant for multiple performance levels (disregarding the change in intensity) is not 

consistent with a capacity design approach, resulting in potentially overly conservative estimates of 

component actions in force-controlled elements at the higher EHL, or vice versa. 

ASCE 41 §3.4.2.2 requires that deformation-controlled and force-controlled actions in primary and 

secondary components satisfy: 

Deformation-controlled: m Q CE  QUD (ASCE 41 §3.4.2.2.1) (3-4) 

Force-controlled:   m Q CL  QUF (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. 

Q DCR Deformation-controlled: DCRN  UD 	 (3-6) m Q CE m

Q Force-controlled: DCR N  UF [with m taken as 1.0] (3-7)   m Q CL 

Nonlinear Procedures 

Acceptance criteria of components for nonlinear assessment procedures are provided as plastic (inelastic) 

deformations dependent on the SPL and component type. ASCE 41 Tables 5-6 and 5-7 provide the plastic 

deformations limits for steel components for nonlinear assessment procedures. Adjustments to the 

acceptance criteria for member or connection characteristics are detailed in ASCE 41 Chapter 5. 

Inelastic deformation parameters in ASCE 41 are provided for steel components in terms of plastic 

deformations rather than total deformations. The choice of whether to use plastic deformations or total 

deformations will depend on what nonlinear component model is adopted for each component action in the 

structural analysis (e.g., moment-curvature hinge or moment-rotation hinge). Consequently, yield and postyield elastic deformations may need to be added to the values given in ASCE 41 to determine the total 

deformation for each SPL. 

In this study, demands on primary components of new buildings are measured against acceptance criteria 

for primary components. ASCE 41 §3.4.3.2 allows primary component demands to be within the 

acceptance criteria for secondary components for the NSP if degradation effects are explicitly modeled—a 

change introduced in FEMA 356. This also includes NDP, although not explicitly stated. This allowance is 

neglected in this study for the following reasons: 

	 Bypassing nonlinear acceptance criteria set for primary components suggests that acceptance 

criteria for primary components for linear and nonlinear assessment procedures are not calibrated. 

In this study, acceptance criteria for primary components are maintained for all assessment methods 

to provide a uniform comparison basis. 

3-16
 
	 There is no technical justification provided in ASCE 41 as to why comprehensive component 

models for primary components, which are required to stabilize the structure after a large 

earthquake, will allow them to deform to the extent given for a secondary component and maintain 

the structural integrity of the system. Analytically speaking, it is debatable if collapse prevention 

can be reliably achieved if a concentrated few SFRS components are deformed past the deformation 

associated with their peak strength and lose a considerable amount of strength and stiffness. 

Available literature has indicated the difficulty in solution convergence in analysis when 

component response is following a negative stiffness branch. Still, some liberties are provided, 

debatably, for existing buildings, but transferring this allowance to new buildings is also of 

debatable validity. Engineering judgment must be applied. Broadly speaking, the function that 

separating existing buildings and new buildings into bins plays in developing a resilient community 

must be clarified. 

	 Reliability issues arise when adopting secondary acceptance criteria for primary components. For 

example, the acceptance criterion of an RBS beam-to-column connection taken as a secondary 

component for the Life Safety SPL is beyond the peak deformation (“a” in Figure 3-2). In ASCE 

41, primary acceptance criteria for the Collapse Prevention SPL generally matches the deformation 

associated with the peak strength of a component. 

	 There is little empirical evidence supporting the acceptance criteria for secondary steel components 

permitted in ASCE 41 §3.4.3.2, other than for beam-to-column connections studied in the SAC 

project (see FEMA 350 series (FEMA 2000a through 2000d)). Experimental tests are rarely 

continued to achieve the peak deformations and the associated reserve strength of a component or 

subassembly after the required loading protocol is complete. 

As a side note, ASCE 41-13 has removed all acceptance criteria for primary components for nonlinear 

assessment. Future research should be conducted to evaluate the systems by measuring demands against 

acceptance criteria for secondary components—which can be done by inspection with the analysis results 

presented in this study. 

3.1.4.2.1 Calculating Component Assessment Results 

Component forces and deformations obtained by the NSP or NDP are referred to as design actions, QU (e.g., 

plastic rotation in a plastic hinge). Component design actions are computed as the action in the member or 

connection at the target displacement for the NSP and as the maximum value for a given earthquake for the 

NDP. Subsequently, a statistical average is computed from the maximum values from the suite of ground 

motions. In specific cases, the maximum value must be coupled with other actions in the component at the 

instant of computation of the maximum response. 

Component design actions classified as deformation-controlled, QUD, are computed by 

QUD  QG QE (ASCE 41 §3.4.3.2.1)	 (3-8) 

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

QUF  QG QE (ASCE 41 §3.4.3.2.3)	 (3-9) 

where QG is the action due to gravity loads (or associated deformation) and QE is the action due to 

earthquake effects (or associated deformations). Superposition of forces or deformations is not applicable 

3-17
 
in a nonlinear analysis; thus, gravity loads are directly applied in the analysis. The above equations are 

numerical interpretations of ASCE 41 §3.4.3.2. They are used in this study to maintain computational 

consistency over the various types of assessment procedures. 

ASCE 41 §3.4.3.2 requires that deformation-controlled and force-controlled actions in primary and 

secondary components satisfy: 

Deformation-controlled: QCE  QUD (ASCE 41 §3.4.2.2.1) (3-10) 

Force-controlled: QCL  QUF (ASCE 41 §3.4.2.2.2) (3-11) 

where QCE is the expected strength or deformation demand of a component, QCL is the lower-bound strength 

of a component, and  is the knowledge factor (taken as unity in this study). ASCE 41 Chapter 5 does not 

explicitly provide a relationship between QCE (or QCL) and Qy on the force-deformation curve. 

The results of the nonlinear assessment procedures are presented in this report as a normalized demand 

capacity ratio, DCRN, where the plastic or total deformation demands are normalized with respect to the 

plastic or total acceptance criteria, modified by  if required. The acceptance criteria verification then 

becomes a unity check similar to that done in modern component design standards (e.g., AISC 360). As 

such, a DCRN value greater than unity indicates that the component does not satisfy the performance criteria 

for a given SPL. This approach is a consistent way to present results over the various types of assessment 

procedures used in this study. 

Deformation-controlled: 

  plastic  elastic Total        y pe p AC  QUD , (3-12) DCR N   

QCE   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 Moment Frame 

Seismic performance assessment of steel moment frames is performed in accordance with ASCE 41 §5.4. 

The moment frames in the archetype buildings are designed with fully restrained (FR) moment connections 

as identified in AISC 360 §B3.6b and as an SMF as identified in ASCE 7 §12.2 (item C.1 in Table 12.2-1) 

and AISC 341 §E3. This designation aligns with that prescribed in ASCE 41 §5.4.2, Fully Restrained 

Moment Frames. The FR beam-to-column moment connection used in each SMF is an RBS as identified 

in AISC 358 Table 2.1 and ASCE 41 Table 5-4. 

 Assessment Methodology 

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

structural model for each assessment method: 

1. Stiffness, ASCE 41 §5.4.2.2 

2. Strength, ASCE 41 §5.4.2.3 

3.	 Acceptance Criteria, ASCE 41 §5.4.2.4, 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 in this study: 

 Beam-to-column connection flexural force or deformation (RBS) 

 Panel zone shear force or deformation 

 Beam and column flexural force or deformation at potential plastic hinge zones (section strength)17
 

 Column axial-moment interaction strength (member strength)
 

 Beam and connection flexure and shear strength (e.g., moment at face of column)
 

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 §5.4.2.2.1. Panel 

zones at the beam-to-column joints are explicitly modeled; ETABS uses the scissor model—see User 

Manual. Explicit joint and connection modeling is not required because the beam-to-column connections 

are classified as FR. However, the stiffness of the frame beams must be modified to account for the reduced 

beam sections within the beam-to-column connections (see Chapter 2). 

17 Beam hinges within the RBS are included in assessment of FR connection (controlling mechanism). 

3-19
 
 

 

Strength 

The strength of all members and connections for linear assessment follow ASCE 41 §5.4.2.3.2. 

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) F F t F F y y w y y 

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). 

Though identified in ASCE 41 §5.4.2.3.2-2, no explicit guidance is provided for computing the expected 

flexural strength, MCE, of a compression member if the axial load demand, 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 where a plastic hinge is anticipated. The term axial strength of a compression member 

is also not well defined (i.e., is it Pye or PCL?). Similarly, 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 selected P-M interaction curve, which will use MCE (or MCL) at P = 0 as the anchor point. 

Further, there is little need to have triggering language based on 10 percent axial load ratio because it 

delineates no physical phenomenon and does not influence computing the yield chord rotation, y. In fact 

18 ASCE 41 inadvertently states AISC 341. 

3-20
 
 

this trigger, it adds complexity, 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 a 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 expected strength, QCE, of a FR beam-tocolumn connection. The RBS beam-to-column connections were designed in accordance with AISC 358. 

As such, the controlling mechanism is the moment at the center of the RBS. It is assumed that the acceptance 

criteria for FR beam-to-column connections (m-factor) translated from results from the SAC project are 

applicable at the face of the column—see below. Therefore, the moment at the face of the column is used 

as the demand, QUD, and the expected flexural strength of the connection, QCE = MCE, is computed as Mp at 

the center of the RBS and projected to the face of the column (this value will always be less than using Mp 

taken at the column face). Alternatively, the demand and acceptance criteria could be adjusted to the hinge 

location (controlling mechanism) and the connection at the face of the column evaluated as force-controlled, 

see ASCE 41 §5.4.2.4.2-4. ASCE 41 should clarify the intent of ASCE 41 Eq. 5-14 and express that is the 

lower-bound strength of the connection evaluated at the column face compared to the expected strength of 

the connection at the hinge location projected to the column face. As noted, AISC 358 design provisions 

for an RBS connection satisfies this criteria. Because the plastic hinge is confined within the RBS and forms 

away from the face of the column, the flexural demand at the center of the RBS should also be used to 

check the plastic hinge as a “beam” hinge. 

Acceptance Criteria 

The acceptance criteria of members and connections for linear assessment follow ASCE 41 §5.4.2.4.2. 

Flexure in Beams and Beam-to-Column 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 

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
 
 

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 full section yielding in shear. These web 

slenderness limits were introduced in FEMA 356 whereas flange limits were introduced in FEMA 273 and 

subsequently modified in FEMA 356 (upper-bound limit was changed from a pure axial compression limit 

to a compression from flexure limit). 

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

using 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 

prevent the unobstructed spread of plasticity. However, because the plastic hinge is forced to develop in a 

prescribed location away from the column face, thus allowing essentially unobstructed spread of plasticity 

within the RBS zone, m-factors for a “beam” should also be used to check the performance of the hinge 

itself. Unless evaluating at the IO performance level, the m-factor for the beam-to-column connection will 

control over the m-factor for flexure in the RBS—see Table 3-10. 

Table 3-10. Basic Acceptance Criteria for a W24×84 

SPL RBS Beam-to-Column 

Connection Beam 

CP 6.2-0.032d = 5.4 8 

LS 4.9-0.025d = 4.3 6 

IO 3.5-0.016d = 3.1 2 

Flexure in Columns and Columns-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 

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

3-22
 
 

 

 

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 

interaction as shown in Figure 3-4 and the flexural demand and strength are taken as MUD and MCE, 

respectively. 

P 0.1  UF  0.2 

PCL 

P M UF UDx  1.0 

2P m M CL x CEx 

P 0.2  UF  0.5 

PCL PUF 

PCL PUF 8  M  UDx    1.0

PCL m M x CEx 9  

PUF 0.5  (m = 1.0)

x PCL 

P M UF UFx  1.0 

P M CL CLx 

P = P ( = 1.0) CL n,AISC

with F = F y yLB mx

MUx 

mM 

_ 

x C x _ Immediate Occupancy

Notes: Life Safety

 Collapse Prevention 1. Knowledge Factor, , taken as unity. 

2. m factors shown are not reduced to reflect compactness requirements or inelastic LTB. 

3. Beam-Column with P / P < 0.1 can be treated as a beam. UF CL

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

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 

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

3-23
 
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. 

 E	 Life Safety 

Fye ASCE 41 Group A Compactness Limit h 640 4.0 t 

F ASCE 41 Group B Compactness Limit w ye AISC 341-10 HD Compactness Limit Wide-Flange Sections AISC 341-10 MD Compactness Limit 35% > Group A

 1% > Group B 

3.5 

P   P P ( 1.0)  0.6 CL n AISC c ,	 ye 12% > AISC HD

3.0 3% > AISC MD F F   50 ksi h 460	 ye y  tw Fye
 

h 400  2.5 t w Fye 

interpolate h 418 2.0 between limits t F 



w ye 

h 300  t 1.5 w Fye h 260  	 P hE P   tw Fye    0.125 2.45   1 0.93    cy P tF w y   c y P   AISC HD   

 1.0  P hE P E   0.125 0.77 2.93    1.49   P tF F P 

P hE P 

 cy w y   cy y

	      0.125 3.76   1 2.75  0.5   cy P tF w y c y P   AISC MD 

 P hE P E     0.125 1.12 2.33    1.49

Width-to-Thickness Ratio, 

h/t 

w 



0.060.12 

    cy P t F w y   P y F  c y 

0.0
 

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 addition to the effect of P-M interaction on the m-factors (which is a section strength issue) for checking 

flexural actions in a column in accordance with ASCE 41 §3.4.2.2, member stability is also checked via 

global interaction equations in accordance with ASCE 41 §5.4.2.4, as shown in Figure 3-4—see projection 

of axial and moment ratios. The discontinuous curve is a result of variable P-M interaction equations, with 

the discontinuity at PUF / PCL = 0.5 being smallest when MCL at PUF = 0 equals Mp, and gets larger as MUD / 

MUF increases. Future efforts should simplify the ASCE 41 interaction curves for consistency and 

applicability, including eliminating Fy,LB for a column that also uses Fye. 

Axial compression action in a column is always force-controlled due to significant reduction in ductility 

because of member and cross-sectional instability. Again, ASCE 41 is rather ambiguous when it comes to 

steel columns. First, there is no guidance on computing MCE for a column. Although ASCE 41 §5.4.2.4.2­

3-24 
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 

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. 



E 

Primary Component Fye 

Life Safety 

P P  0.6 CL ye 

F   F ksi 50

Width-to-Thickness Ratio, 

ye y

h/t 

w 

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 

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 MF columns. 

Shear in Panel Zones 

3-25 
 

 

 

 

 

 

 

 

 

 

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. 

Demand 

The flexural demand, MUD, for the FR beam-to-column connections is taken as the moment at the face of 

the column. The flexural demand, MUD, for the RBS (beam) is taken as the moment at the center of the 

RBS. The flexural demand, MUD or MUF, and axial force, PUF, for the column are taken as the moment and 

axial force at the face of the each beam (top and bottom). 

Table 3-11 summarizes the basic m-factors for the components of the SMF for the linear procedures. Figure 

3-7 through Figure 3-12 provide the load-independent m-factors—taking in to account force-controlled and 

deformation-controlled classifications (force-controlled component actions are assigned an m-factor of 

unity, see §3.1.4.1). These figures are referred to herein as “Frame Capacity Schematics.” 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 provides the same value when PUF / PCL < 0.2. 

Table 3-11. Basic m-factors for Linear Procedures, SMF 

Performance Level 

Component - Action LS CP 

Beam - Flexure 

bf 52 h 418 

a)  and  6 8 2tf F ye tw Fye 

bf 65 h 640  b) 2t 

 or 2 3 f Fye tw Fye 

c) other linear interpolation 

Column - Flexure 

for P UF / P CL < 0.2
 

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

b 65 h 460 

b) f   or 1.25 2 2t f Fye tw Fye 

c) other linear interpolation 

for 0.2 ≤ P UF / P CL ≤ 0.5 

b h 260 

a)  and  f 52  5 P   5 P  9 1   12 1    2t F t f ye w Fye  3 P CL   3 PCL 

bf 65 h 400  b)  1.25 1.5 2t F or f t F ye w ye 

c) other linear interpolation 

Column Panel Zone - S hear 8 11 

RBS - Flexure1 4.9 - 0.025d 6.2 - 0.032d 

1 m -fact ors shall be modified as indicat ed in ASCE 4 1 §5.4.2.2.2, it em 4. 

3-26 
 

 

2.81 2.81 2.82 3.55 3.55 3.56 

5.73, 1.49 7.64, 1.97 

5.73, 1.49 7.64, 1.97 

6, 1.5 8, 2 

6, 1.5 8, 2 

8.00 8.00 

6, 1.5 

2.83 2.83 2.84 

8.00 8.00 

6, 1.5 

2.85 3.56 3.57 

8.00 8.00 

6, 1.5 

2.85 2.85 2.85 

8.00 8.00 

6, 1.5 

11.00 11.00 

8, 2 

11.00 11.00 

3.58 3.58 3.58 3.58 3.58 3.58 

8, 2 

3.60 4.50 4.50

11.00 11.00 

3.60 4.50 4.50 

8, 2 

3.60 3.60 3.60

11.00 11.00 

3.60 3.60 3.60 

8, 2 

Sym. 

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

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

2.81 3.51 3.52 3.55 4.44 4.44 

8.00 8.00 

6, 1.5 

2.81 3.51 3.52 

8.00 8.00 

6, 1.5 

2.81 3.51 3.52 

8.00 8.00 

6, 1.5 

2.81 3.51 3.52 

8.00 8.00 

6, 1.5 

5.63, 1.48 7.49, 1.96

5.63, 1.48 7.49, 1.96

5.63, 1.48 7.49, 1.96

5.63, 1.48 7.49, 1.96 

11.00 11.00 

8, 2 

3.55 4.44 4.44 4.44 4.44

11.00 11.00 

8, 2 

3.55 4.44 4.44 3.55 4.44 4.44 

11.00 11.00 

8, 2 

3.55 4.44 4.44 3.55 4.44 4.44 

11.00 11.00 

8, 2 

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

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

3-27
 
 

2.27 3.54 3.55 2.86 4.48 4.48 

6, 1.5 

8.00 8.00 

6, 1.5 

2.83 3.54 3.55 

8.00 8.00 

6, 1.5 

3.03 3.78 3.79 

8.00 8.00 

6, 1.5 

3.03 3.78 3.79 

8.00 8.00 

6, 1.5 

3.05 3.81 3.81 

8.00 8.00 

6, 1.5 

3.05 3.81 3.81 

8.00 8.00 

6, 1.5 

3.81 3.81 3.81 

8.00 8.00 

6, 1.5 

3.81 3.81 3.81 

8.00 8.00 

6, 1.5 

8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

(a) Life Safety (c) Key 

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

1.95 3.05 3.05 2.47 3.86 3.86 

4.48, 1.42 5.92, 1.84 

4.48, 1.42 5.92, 1.84 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

(b) Collapse Prevention 

Sym. 

11.00 11.00 

8, 2 

3.58 4.48 4.48 

11.00 11.00 

8, 2 

11.00 11.00 

3.82 4.78 4.78 

8, 2 

4.78 

11.00 11.00 

3.82 4.78 

8, 2 

4.81 

11.00 11.00 

3.85 4.81 

8, 2 

11.00 11.00 

3.85 4.81 4.82 

8, 2 

11.00 11.00 

4.81 4.81 4.82 

8, 2 

11.00 11.00 

4.81 4.81 4.82 

8, 2 

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

8.00 8.00 

6, 1.5 

2.44 3.05 3.05 

8.00 8.00 

6, 1.5 

2.83 3.54 3.55 

8.00 8.00 

6, 1.5 

2.83 3.54 3.55 

8.00 8.00 

6, 1.5 

2.86 3.57 3.58 

8.00 8.00 

6, 1.5 

2.86 3.57 3.58 

8.00 8.00 

6, 1.5 

2.87 3.59 3.59 

8.00 8.00 

6, 1.5 

2.87 2.87 2.88 

8.00 8.00 

6, 1.5 

Sym. 

11.00 11.00 

8, 2 

3.08 3.86 3.86 

11.00 11.00 

8, 2 

3.58 4.48 4.48 

11.00 11.00 

8, 2 

3.58 4.48 4.48 

11.00 11.00 

8, 2 

3.61 4.51 4.52 

11.00 11.00 

8, 2 

3.61 4.51 4.52 

11.00 11.00 

8, 2 

3.63 4.54 4.54 

11.00 11.00 

8, 2 

3.63 3.63 3.63 

11.00 11.00 

8, 2 

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

3-28
 
2.31 3.60 3.61 2.91 4.55 4.56 

2.37, 1.31 3.03, 1.62 

2.37, 1.31 3.03, 1.62 

4.13, 1.4 5.44, 1.8 

4.13, 1.4 5.44, 1.8 

4.83, 1.44 6.4, 1.88 

4.83, 1.44 6.4, 1.88 

5.74, 1.49 7.64, 1.97 

5.74, 1.49 7.64, 1.97 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

6, 1.5 8, 2 

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

8.00 8.00 

4.83, 1.44 

2.31 3.60 3.61 2.31 3.60 3.61 

8.00 8.00 

4.83, 1.44 

2.31 3.60 3.61 2.31 3.60 3.61 

8.00 8.00 

6, 1.5 

2.31 3.60 3.61 2.31 3.60 3.61 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.17 3.97 3.97 3.17 3.97 3.97 

8.00 8.00 

6, 1.5 

3.17 3.97 3.97 3.17 3.97 3.97 

8.00 8.00 

6, 1.5 

2.54 3.97 3.97 2.54 3.97 3.97 

8.00 8.00 

6, 1.5 

2.54 3.97 3.97 2.54 3.97 3.97 

8.00 8.00 

6, 1.5 

2.61 4.07 4.07 2.61 4.07 4.07 

8.00 8.00 

6, 1.5 

2.61 4.07 4.07 2.61 4.07 4.07 

8.00 8.00 

6, 1.5 

3.26 4.07 4.07 3.26 4.07 4.07 

8.00 8.00 

6, 1.5 

3.26 4.07 4.07 3.26 4.07 4.07 

8.00 8.00 

6, 1.5 

Sym. 

11.00 11.00 

6.4, 1.88 

2.91 4.55 4.56 2.91 4.55 4.56 

11.00 11.00 

6.4, 1.88 

2.91 4.55 4.56 2.91 4.55 4.56 

11.00 11.00 

8, 2 

2.91 4.55 4.56 2.91 4.55 4.56 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

4.01 5.01 5.02 4.01 5.01 5.02 

11.00 11.00 

8, 2 

4.01 5.01 5.02 4.01 5.01 5.02 

11.00 11.00 

8, 2 

3.21 5.01 5.02 3.21 5.01 5.02 

11.00 11.00 

8, 2 

3.21 5.01 5.02 3.21 5.01 5.02 

11.00 11.00 

8, 2 

3.29 5.14 5.14 3.29 5.14 5.14 

11.00 11.00 

8, 2 

3.29 5.14 5.14 3.29 5.14 5.14 

11.00 11.00 

8, 2 

4.11 5.14 5.14 4.11 5.14 5.14 

11.00 11.00 

8, 2 

4.11 5.14 5.14 4.11 5.14 5.14 

11.00 11.00 

8, 2 

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

3-29
 
2.31 2.88 2.88 2.91 3.64 3.64 

2.37, 1.31 

2.37, 1.31 

4.13, 1.4 

4.13, 1.4 

4.13, 1.4 

4.13, 1.4 

4.91, 1.44 

4.91, 1.44 

5.74, 1.49 

5.74, 1.49 

6, 1.5 

6, 1.5 

6, 1.5 

6, 1.5 

6, 1.5 

6, 1.5 

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

8.00 8.00 

4.83, 1.44 

2.31 3.60 3.61 2.31 3.60 3.61 

8.00 8.00 

4.83, 1.44 

2.31 3.60 3.61 2.31 3.60 3.61 

8.00 8.00 

4.83, 1.44 

2.31 3.60 3.61 2.31 3.60 3.61 

8.00 8.00 

4.83, 1.44 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6, 1.5 

3.17 3.97 3.97 3.17 3.97 3.97 

8.00 8.00 

6, 1.5 

3.17 3.97 3.97 3.17 3.97 3.97 

8.00 8.00 

6, 1.5 

2.54 3.97 3.97 2.54 3.97 3.97 

8.00 8.00 

6, 1.5 

2.54 3.97 3.97 2.54 3.97 3.97 

8.00 8.00 

6, 1.5 

2.61 4.07 4.07 2.61 4.07 4.07 

8.00 8.00 

6, 1.5 

2.61 4.07 4.07 2.61 4.07 4.07 

8.00 8.00 

6, 1.5 

3.26 4.07 4.07 3.26 4.07 4.07 

8.00 8.00 

6, 1.5 

3.26 4.07 4.07

8.00 8.00 

3.26 4.07 4.07 

6, 1.5 

11.00 11.00 

6.4, 1.88 

2.91 4.55 4.56 2.91 4.55 4.56 

11.00 11.00 

6.4, 1.88 

2.91 4.55 4.56 2.91 4.55 4.56 

11.00 11.00 

6.4, 1.88 

2.91 4.55 4.56 2.91 4.55 4.56 

11.00 11.00 

6.4, 1.88 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

3.87 4.84 4.84 3.87 4.84 4.84 

11.00 11.00 

8, 2 

4.01 5.01 5.02 4.01 5.01 5.02 

11.00 11.00 

8, 2 

4.01 5.01 5.02 4.01 5.01 5.02 

11.00 11.00 

8, 2 

3.21 5.01 5.02 3.21 5.01 5.02 

11.00 11.00 

8, 2 

3.21 5.01 5.02 3.21 5.01 5.02 

11.00 11.00 

8, 2 

3.29 5.14 5.14 3.29 5.14 5.14 

11.00 11.00 

8, 2 

3.29 5.14 5.14 3.29 5.14 5.14 

11.00 11.00 

8, 2 

4.11 5.14 5.14 4.11 5.14 5.14 

11.00 11.00 

8, 2 

4.11 5.14 5.14

11.00 11.00 

4.11 5.14 5.14 

8, 2 

3.03, 1.62 

3.03, 1.62 

5.44, 1.8 

5.44, 1.8 

5.44, 1.8 

5.44, 1.8 

6.51, 1.89 

6.51, 1.89 

7.64, 1.97 

7.64, 1.97 

8, 2 

8, 2 

8, 2 

8, 2 

8, 2 

8, 2 

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

3-30
 
Nonlinear Procedures 

This section discusses the three primary component characteristics listed in Section 3.2.1 and computation 

of the demand in the component for the nonlinear assessment procedures. 

Stiffness, Strength, Acceptance Criteria, and Demand 

Component characteristics follow that outlined previously for the linear procedures. Although component 

stiffness is the primary characteristic in linear procedures, component strength is of equal importance in 

nonlinear procedures. 

The stiffnesses of all members and connections for nonlinear assessment follow ASCE 41 §5.4.2.2.2 for 

the NSP and §5.4.2.2.3 for the NDP. The strength of all members and connections for nonlinear assessment 

follow ASCE 41 §5.4.2.3.3 for the NSP and §5.4.2.3.4 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 RBS beam-to-column connection modeled as a 

beam flexural hinge, the column flexural hinge modeled with axial-moment (P-M) interaction, and the panel 

zone modeled using the Krawinkler model (Krawinkler 1978). Figure 3-13 illustrates the analytical model 

of a beam-to-column subassembly for nonlinear assessment procedures. In the figure, Default End Zones 

are modeled with a flexural rigidity factor of two; a higher value 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). 

The acceptance criteria in ASCE 41 for FR beam-to-column connections are derived from the results of the 

SAC project (see FEMA 351 (FEMA 2000b) and FEMA 355D (FEMA 2000c)). Therefore, plastic rotation 

is measured at the column face and the acceptance criteria include all effects inherent in the tested 

assemblies (e.g., panel zone and column yielding). This can be problematic when distinguishing between 

panel zone, beam, and column yielding effects. As the plastic rotation limits specified in ASCE 41 are 

average values for the tested assembly classes, it seems appropriate to separate yielding effects in a 

structural model. Therefore, beam and column hinge components and panel zone yielding components are 

individually modeled for nonlinear analysis in this study. Further, acceptance criteria for RBS beam-tocolumn connections do not address composite action with the floor slab, thus beam properties used in the 

nonlinear analysis model do not include this effect. 

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 

3-31
 
 

model as long as the conversion procedure for all nonlinear model parameters between the two is 

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

(discussed subsequently). 

A 

Reduced beam sections are modeled within the beam member as elastic prismatic beam elements using the 

geometric cross-section properties at the outer two-thirds of the RBS. An MC hinge is placed at the center 

of the RBS with a plastic hinge length equal to the length of the RBS, b. Plastic rotation parameters 

modeling the backbone curve of the FR beam-to-column connection are taken from ASCE 41 Table 5-6. 

These values are converted to plastic curvature and subsequently adjusted from application at the column 

face to the center of the RBS and other FR connection adjustments discussed next. Stiffness and strength 

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”). Intermediate anchor points defining the 

full backbone curve are determined from calibration with experimental test data (see Figure 3-14 and Figure 

3-2). The ultimate flexural strength of the MC hinge is taken as Cpr×MCE in accordance with AISC 358— 

Cpr is defined in AISC 358. 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. 

Inelastic Beam 

Plastic Hinge, lp = b 

Default 

End Zone 

Plastic 

Hinge, lp 

= dc 

Plastic 

Hinge, lp 

= dc 

Default 

End Zone 

Elastic 

Column, 

EIc 

Panel Zone Moment-Curvature Hinge 

(from dummy inelastic beam) 

Elastic Beam, EIb 

SMF Beam-to-Column Subassembly Analytical Schematic 

a b/2

Moment-Curvature 

PMM Hinge 

node 

Figure 3-13. 

Section A-A 

A 

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 

3-32
 
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 RBS. Acceptance criteria for a 

beam hinge should also be used to verify the performance of the plastic hinge in the RBS; however, as 

discussed previously, it will not control unless evaluating the IO SPL. Therefore, this secondary check is 

not performed in this study. 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. 

Specimen DB4 (Engelhardt et al. 1998) 

40000 

 Test Data

 Analysis

Moment at Column Face (kip-in) -10000 

-20000 

-30000 

30000 

20000 

10000 

0 

 Backbone 

W36×194 

-40000 

-8 -6 -4 -2 0 2 4 6 8 

Tip Displacement (inches)

Figure 3-14. PERFORM-3D RBS Calibration 

PERFORM-3D flexural section strength flags (used to verify a design strength at a given location) are 

placed at the column faces and at midspan of the beam to verify acceptable design of the beams and beamto-column connections. Similarly, shear section strength flags are placed at the column faces and at the 

center of the RBS to verify acceptable design of the beam-to-column connections. These section strength 

flags are modified as needed for cross-section geometry, member strengths (does not typically control 

beams), and design-assessment criteria prescribed in ASCE 41. 

Panel zones are explicitly modeled at all beam-to-column joints using the Krawinkler model. This model 

uses the force-deformation relationship intrinsic in the design equations prescribed in AISC 360 (see Figure 

3-15—PERFORM-3D response is presented as “Analysis”). However, the yield stress in the panel zone 

model is taken as 0.55×Fye in ASCE 41 in lieu of 0.6×Fy as used in design. Figure 3-15 shows the range of 

the expected demands on the panel zones (anchored to a shear strain ductility,  / y, of 4). This range is 

small because the probable flexural strength of the connection is used to check the panel zone strength in 

design, and this connection strength is associated with Collapse Prevention (CP) of the beam-to-column 

connection in ASCE 41. Only when an FR connection is strained past the CP level will the panel zone 

deform outside this range; nevertheless, the CP acceptance criteria for a panel zone in ASCE 41 is three 

times a shear strain ductility of 4. 

3-33
 
 

Specimen A-2 (Krawinkler 1971) 

1200 

-1200 

range of applicability 

Difference in Beam Moments, 

M (kip-in) 

 Test Data

 Analysis 

Strength predicted by 

AISC 360-10 Eq. J10-11 

using 0.55F ye 

-32 -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24 28 32 

900 

600 

300 

0 

-300 

-600 

-900 

Shear Strain / Yield Shear Strain,  / y

Figure 3-15. PERFORM-3D Panel Zone Calibration 

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 

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 3-16, Figure 3-18, and Figure 3-19). 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 3-19. 

3-34
 
 P 

MCEx 1.18M 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). 

  P 

2 

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

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 3-16). 

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 3-16). 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 3-17, 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 3-17. 

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 3-17, a plus elastic = DL in PERFORM-3D—see Figure 3-2 for a and DL) do not 

coincide for P / PCL > 0.2. A column hinge with high axial load can reach its peak strength (a plus elastic = 

CP in this case) in regards to the provisions of ASCE 41 yet still be able to maintain its flexural strength. 

In general, column hinges are not expected to be significantly strained; however, demands may affect the 

performance of base hinges, which can have detrimental effects on the system upon loss of strength. More 

detailed information can be found in the PERFORM-3D User Guide (CSI 2011d) and PERFORM-3D 

Components and Elements (CSI 2011c). Lastly, it is of questionable validity to allow a primary column 

3-35
 
 

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 3-16. In-plane Flexural Hinge Yield Surface Model (Including Force-Controlled Response) 

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 3-17. Variation in Acceptance Criteria and Hinge Model for Axial Force 

3-36
 
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 3-18. P-M Interaction on Plastic Rotation, LS Acceptance Criteria (Primary Component) 

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. 

The column-to-base connection is modeled using an FR beam-to-column connection model in PERFORM3D. It is reasonable to adopt an FR connection model (such as an improved welded WUF connection) to 

represent the base connection because doing so will provide a lower-bound estimate of the plastic rotations 

angle compared to that given explicitly for a column hinge, as shown in Table 3-12. Future research is 

needed to develop acceptance criteria and modeling parameters for column-to-base connections, including 

embedded connections. 

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 

3-37
 

 

 

 

 

 

 

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. 

Table 3-12. Plastic Rotation Angles for Improved WUF and Column Hinge for a W18×175 

P = 0 P = 0.1999×PCL P = 0.2×PCL P = 0.5×PCL 

WUF AC 0.041 0.038 0.031 0.0056 

Column AC 0.071 0.065 0.053 0.0097 

Ratio 0.58 0.58 0.58 0.58 

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 

strengths based on the actual unbraced length (i.e., KLx = Lx) is of questionable validity, but so is using the 

design value based on a vertical load-only load combination. Research is needed concerning in-plane 

dynamic instability of inelastic members. 

1.0 

0.8 

Axial Force Ratio (P / P ye ) 

0.6 

0.4 

0.2 

0.0 

0.0 0.2 0.4 0.6 0.8 1.0 

ASCE 41 In-Plane Yield Surface 

(Eq. 5-4)

 AISC In-Plane Yield Surface 

(H1-1, P n = P ye ) 

PERFORM-3D In-Plane Yield Surface 

( = 1.5,  = 1.1) 

Out-of-Plane Yield Surface 

(H1-1, P n = P ye )

 PERFORM-3D Out-of-Plane Yield Surface 

( = 2.5,  = 1.1) 

Moment Ratio (M / M pe ) 

Figure 3-19. P-M Interaction Curve (Section Yield Surface) 

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 

3-38 
 

 

 

 

 

 

 

 

 

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 3-20 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. 

1.0 

0.8 ASCE 41 In-Plane Yield Surface

Axial Force Ratio (P / P ye ) 

0.6 

0.4 

0.2 

0.0 

 (Eq. 5-4)

 AISC In-Plane Stability (Cb

 > 1)

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

 PERFORM-3D In-Plane Stability (Truncated)

 ( = 1.75,  = 1.0)

 AISC Out-of-Plane Stability (Cb

 > 1)

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

 PERFORM-3D Out-of-Plane Stability

 ( = 1.3,  = 1.0)

 AISC Out-of-Plane Stability (Cb

 > 1)

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

 PERFORM-3D Out-of-Plane Stability

 ( = 1.0,  = 1.5)

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

 ( = 2.5,  = 1.25) 

Moment Ratio (M / M pe )

Figure 3-20. P-M Interaction Curve (Member Strength) 

0.00 0.25 0.50 0.75 1.00 1.25 1.50 

Figure 3-21 through Figure 3-26 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. 

3-39
 
 

 

 

Sym. About 

B C D E 

Beam Hinges 

CP → L=R=2535 

LS → L=R=1978 

YD → L=R=197 

Beam Hinges 

CP → L=R=2533 

LS → L=R=1976 

YD → L=R=194 

Beam Hinges 

CP → L=R=2533 

LS → L=R=1976 

YD → L=R=194 

Beam Hinges 

CP → L=2541, R=3117 

LS → L=1986, R=2423 

YD → L=R=207 

Beam Hinges 

CP → L=2535 

LS → L=1978 

YD → L=197 

Beam Hinges 

CP → L=2533 

LS → L=1976 

YD → L=194 

Beam Hinges 

CP → L=2533 

LS → L=1976 

YD → L=194 

Beam Hinges 

CP → L=3117 

LS → L=2423 

YD → L=207 

Column Hinges 

CP → T=B=5816, 1074 

LS → T=B=4440, 843 

YD → T=B=286, 193 

Column Hinges 

CP → T=B=5816, 1074 

LS → T=B=4440, 843 

YD → T=B=286, 193 

Column Hinges 

CP → T=B=5732, 1054 

LS → T=B=4368, 826 

YD → T=B=288, 194 

Column Hinges 

CP → T=B=5732, 1054 

LS → T=B=4368, 826 

YD → T=B=288, 194 

Column Hinges 

CP → T=B=5069, 1018 

LS → T=B=3877, 799 

YD → T=B=272, 183 

Column Hinges 

CP → T=B=5247, 1030 

LS → T=B=4011, 808 

YD → T=B=275, 185 

Column Hinges 

CP → T=B=5069, 1018 

LS → T=B=3877, 799 

YD → T=B=272, 183 

Column Hinges 

CP → T=B=5247, 1030 

LS → T=B=4011, 808 

YD → T=B=275, 185 

RBS Beams = Total Curvature×106 

Panel Zones = Total Shear Strain×106 

Columns = Total Curvature×106 (for P/PCL = 0.0, 0.5) 

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

Roof
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Panel Zones 

CP → 32544 

LS → 24408 

YD → 2712 

L = Left Hinge, R = Right Hinge, T = Top Hinge, B = Bottom Hinge 

All values are for Primary Components 

Figure 3-21. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 4-Story SMF ELF 

Sym. About 

B C D E 

Beam Hinges 

CP → L=2541, R=3117 

LS → L=1986, R=2423 

YD → L=R=207 

Beam Hinges 

CP → L=3117 

LS → L=2423 

YD → L=207 

Column Hinges 

CP → T=B=5722, 1066 

LS → T=B=4357, 834 

YD → T=B=290, 195 

Column Hinges 

CP → T=B=5521, 1068 

LS → T=B=4218, 837 

YD → T=B=281, 189 

Beam Hinges 

CP → L=2541, R=3117 

LS → L=1986, R=2423 

YD → L=R=207 

Beam Hinges 

CP → L=3117 

LS → L=2423 

YD → L=207 

Column Hinges 

CP → T=B=5722, 1066 

LS → T=B=4357, 834 

YD → T=B=290, 195 

Column Hinges 

CP → T=B=5521, 1068 

LS → T=B=4218, 837 

YD → T=B=281, 189 

Beam Hinges 

CP → L=2541, R=3117 

LS → L=1986, R=2423 

YD → L=R=207 

Beam Hinges 

CP → L=3117 

LS → L=2423 

YD → L=207 

Column Hinges 

CP → T=B=5722, 1066 

LS → T=B=4357, 834 

YD → T=B=290, 195 

Column Hinges 

CP → T=B=5521, 1068 

LS → T=B=4218, 837 

YD → T=B=281, 189 

Beam Hinges 

CP → L=2541, R=3117 

LS → L=1986, R=2423 

YD → L=R=207 

Beam Hinges 

CP → L=3117 

LS → L=2423 

YD → L=207 

Column Hinges 

CP → T=B=5722, 1066 

LS → T=B=4357, 834 

YD → T=B=290, 195 

Column Hinges 

CP → T=B=5521, 1068 

LS → T=B=4218, 837 

YD → T=B=281, 189 

RBS Beams = Total Curvature×106 

Panel Zones = Total Shear Strain×106 

Columns = Total Curvature×106 (for P/PCL = 0.0, 0.5) 

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

Roof
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Panel Zones 

CP → 32544 

LS → 24408 

YD → 2712 

L = Left Hinge, R = Right Hinge, T = Top Hinge, B = Bottom Hinge 

All values are for Primary Components 

Figure 3-22. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 4-Story SMF RSA 

3-40
 
Sym. About 

B C D E 

Beam Hinges 

CP → L=3119 

LS → L=2425 

YD → L=207 

Column Hinges 

CP → T=B=3048, 633 

LS → T=B=2344, 505 

YD → T=B=210, 141 

Column Hinges 

CP → T=B=3391, 658 

LS → T=B=2604, 526 

YD → T=B=219, 147 

Beam Hinges 

CP → L=2543, R=3119 

LS → L=1987, R=2425 

YD → L=R=207 

Beam Hinges 

CP → L=2233, R=2741 

LS → L=1743, R=2129 

YD → L=R=176 

Beam Hinges 

CP → L=2226, R=2733 

LS → L=1736, R=2121 

YD → L=R=172 

Beam Hinges 

CP → L=2226, R=2733 

LS → L=1736, R=2121 

YD → L=R=172 

Beam Hinges 

CP → L=R=2733 

LS → L=R=2121 

YD → L=R=172 

Beam Hinges 

CP → L=2733 

LS → L=2121 

YD → L=172 

Beam Hinges 

CP → L=2733 

LS → L=2121 

YD → L=172 

Beam Hinges 

CP → L=2733 

LS → L=2121 

YD → L=172 

Beam Hinges 

CP → L=2733 

LS → L=2121 

YD → L=172 

Beam Hinges 

CP → L=2741 

LS → L=2129 

YD → L=176 

Column Hinges 

CP → T=B=3391, 658 

LS → T=B=2604, 526 

YD → T=B=219, 147 

Column Hinges 

CP → T=B=3468, 664 

LS → T=B=2662, 530 

YD → T=B=221, 148 

Column Hinges 

CP → T=B=3468, 664 

LS → T=B=2662, 530 

YD → T=B=221, 148 

Column Hinges 

CP → T=B=3582, 673 

LS → T=B=2748, 537 

YD → T=B=224, 150 

Column Hinges 

CP → T=B=3582, 673 

LS → T=B=2748, 537 

YD → T=B=224, 150 

Column Hinges 

CP → T=B=3945, 712 

LS → T=B=3024, 569 

YD → T=B=237, 159 

Column Hinges 

CP → T=B=3945, 712 

LS → T=B=3024, 569 

YD → T=B=237, 159 

Column Hinges 

CP → T=B=3048, 633 

LS → T=B=2344, 505 

YD → T=B=210, 141 

Column Hinges 

CP → T=B=3048, 633 

LS → T=B=2344, 505 

YD → T=B=210, 141 

Column Hinges 

CP → T=B=3048, 633 

LS → T=B=2344, 505 

YD → T=B=210, 141 

Column Hinges 

CP → T=B=3134, 639 

LS → T=B=2409, 511 

YD → T=B=212, 143 

Column Hinges 

CP → T=B=3134, 639 

LS → T=B=2409, 511 

YD → T=B=212, 143 

Column Hinges 

CP → T=B=3524, 668 

LS → T=B=2704, 534 

YD → T=B=222, 149 

Column Hinges 

CP → T=B=3524, 668 

LS → T=B=2704, 534 

YD → T=B=222, 149 

Beam Hinges 

CP → L=R=2733 

LS → L=R=2121 

YD → L=R=172 

Beam Hinges 

CP → L=2233, R=2741 

LS → L=1743, R=2129 

YD → L=R=176 

Beam Hinges 

CP → L=2741 

LS → L=2129 

YD → L=176 

Beam Hinges 

CP → L=3119 

LS → L=2425 

YD → L=207 

Beam Hinges 

CP → L=2543, R=3119 

LS → L=1987, R=2425 

YD → L=R=207 

RBS Beams = Total Curvature×106 

Panel Zones = Total Shear Strain×106 

Columns = Total Curvature×106 (for P/PCL = 0.0, 0.5) 

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

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.)
 

Panel Zones 

CP → T=B=32544 

LS → T=B=24408 

YD → T=B=2712 

L = Left Hinge, R = Right Hinge, T = Top Hinge, B = Bottom Hinge 

All values are for Primary Components 

Figure 3-23. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 8-Story SMF ELF 

3-41
 
Figure 3-24. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 8-Story SMF RSA 

3-42
 
Sym. About 

B C D E 

Beam Hinges 

CP → L=3125 

LS → L=2429 

YD → L=207 

Column Hinges 

CP → T=B=1785, 334 

LS → T=B=1382, 276 

YD → T=B=155, 104 

Beam Hinges 

CP → L=2085, R=3125 

LS → L=1640, R=2429 

YD → L=R=207 

Beam Hinges 

CP → L=1830, R=2747 

LS → L=1437, R=2133 

YD → L=R=176 

Beam Hinges 

CP → L=2445 

LS → L=1899 

YD → L=160 

Beam Hinges 

CP → L=2747 

LS → L=2133 

YD → L=176 

Column Hinges 

CP → T=B=1815, 315 

LS → T=B=145, 280 

YD → T=B=157, 106 

Column Hinges 

CP → T=B=1857, 295 

LS → T=B=1437, 245 

YD → T=B=159, 107 

Column Hinges 

CP → T=B=1904, 252 

LS → T=B=1472, 211 

YD → T=B=161, 108 

Column Hinges 

CP → T=B=1681, 325 

LS → T=B=1302, 269 

YD → T=B=151, 102 

Column Hinges 

CP → T=B=1815, 339 

LS → T=B=1405, 280 

YD → T=B=157, 106 

Beam Hinges 

CP → L=1992, R=2445 

LS → L=1556, R=1899 

YD → L=R=160 

Column Hinges 

CP → T=B=1535, 313 

LS → T=B=1191, 259 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1395, 302 

LS → T=B=1085, 250 

YD → T=B=140, 94 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Column Hinges 

CP → T=B=1571, 316 

LS → T=B=1218, 262 

YD → T=B=147, 99 

Column Hinges 

CP → T=B=1650, 322 

LS → T=B=1279, 267 

YD → T=B=150, 101 

Column Hinges 

CP → T=B=1701, 326 

LS → T=B=1318, 270 

YD → T=B=151, 102 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2445 

LS → L=1899 

YD → L=160 

Beam Hinges 

CP → L=1992, R=2445 

LS → L=1556, R=1899 

YD → L=R=160 

Beam Hinges 

CP → L=2445 

LS → L=1899 

YD → L=160 

Beam Hinges 

CP → L=1992, R=2445 

LS → L=1556, R=1899 

YD → L=R=160 

Beam Hinges 

CP → L=2445 

LS → L=1899 

YD → L=160 

Beam Hinges 

CP → L=1992, R=2445 

LS → L=1556, R=1899 

YD → L=R=160 

Beam Hinges 

CP → L=1830, R=2747 

LS → L=1437, R=2133 

YD → L=R=176 

Beam Hinges 

CP → L=2747 

LS → L=2133 

YD → L=176 

Beam Hinges 

CP → L=3125 

LS → L=2429 

YD → L=207 

Beam Hinges 

CP → L=2085, R=3125 

LS → L=1640, R=2429 

YD → L=R=207 

Column Hinges 

CP → T=B=1681, 325 

LS → T=B=1302, 269 

YD → T=B=151, 102 

Column Hinges 

CP → T=B=1815, 339 

LS → T=B=1405, 280 

YD → T=B=157, 106 

Column Hinges 

CP → T=B=1535, 313 

LS → T=B=1191, 259 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1535, 313 

LS → T=B=1191, 259 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1535, 313 

LS → T=B=1191, 259 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1615, 321 

LS → T=B=1252, 266 

YD → T=B=149, 100 

Column Hinges 

CP → T=B=1785, 334 

LS → T=B=1382, 276 

YD → T=B=155, 104 

Column Hinges 

CP → T=B=1815, 315 

LS → T=B=145, 280 

YD → T=B=157, 106 

Column Hinges 

CP → T=B=1857, 295 

LS → T=B=1437, 245 

YD → T=B=159, 107 

Column Hinges 

CP → T=B=1904, 252 

LS → T=B=1472, 211 

YD → T=B=161, 108 

Column Hinges 

CP → T=B=1395, 302 

LS → T=B=1085, 250 

YD → T=B=140, 94 

Column Hinges 

CP → T=B=1571, 316 

LS → T=B=1218, 262 

YD → T=B=147, 99 

Column Hinges 

CP → T=B=1650, 322 

LS → T=B=1279, 267 

YD → T=B=150, 101 

Column Hinges 

CP → T=B=1701, 326 

LS → T=B=1318, 270 

YD → T=B=151, 102 

RBS Beams = Total Curvature×106 

Panel Zones = Total Shear Strain×106 

Columns = Total Curvature×106 (for P/PCL = 0.0, 0.5) 

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

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.)
 

Panel Zones 

CP → T=B=32544 

LS → T=B=24408 

YD → T=B=2712 

L = Left Hinge, R = Right Hinge, T = Top Hinge, B = Bottom Hinge 

All values are for Primary Components 

Figure 3-25. Frame Capacity Schematic (Inelastic), YD, LS, and CP, 16-Story SMF ELF 

3-43
 
Sym. About 

B C D E 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Column Hinges 

CP → T=B=1719, 323 

LS → T=B=1328, 266 

YD → T=B=155, 104 

Beam Hinges 

CP → L=2085, R=3125 

LS → L=1640, R=2429 

YD → L=R=207 

Beam Hinges 

CP → L=2747 

LS → L=2133 

YD → L=176 

Beam Hinges 

CP → L=3125 

LS → L=2429 

YD → L=207 

Column Hinges 

CP → T=B=1857, 309 

LS → T=B=1437, 255 

YD → T=B=159, 107 

Column Hinges 

CP → T=B=1904, 263 

LS → T=B=1472, 218 

YD → T=B=161, 108 

Column Hinges 

CP → T=B=1815, 357 

LS → T=B=1405, 293 

YD → T=B=157, 106 

Beam Hinges 

CP → L=2237, R=2747 

LS → L=1746, R=2133 

YD → L=R=176 

Beam Hinges 

CP → L=2445 

LS → L=1889 

YD → L=160 

Column Hinges 

CP → T=B=1535, 329 

LS → T=B=1191, 271 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1571, 333 

LS → T=B=1218, 274 

YD → T=B=147, 99 

Beam Hinges 

CP → L=1992, R=2445 

LS → L=1556, R=1889 

YD → L=R=160 

Beam Hinges 

CP → L=1631, R=2445 

LS → L=1281, R=1889 

YD → L=R=160 

Beam Hinges 

CP → L=1462, R=2192 

LS → L=1148, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Beam Hinges 

CP → L=2445 

LS → L=1889 

YD → L=160 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Column Hinges 

CP → T=B=1728, 345 

LS → T=B=1338, 284 

YD → T=B=152, 102 

Column Hinges 

CP → T=B=1785, 351 

LS → T=B=1382, 289 

YD → T=B=155, 104 

Column Hinges 

CP → T=B=1630, 338 

LS → T=B=1264, 278 

YD → T=B=159, 100 

Beam Hinges 

CP → L=1787, R=2192 

LS → L=1395, R=1702 

YD → L=R=144 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Beam Hinges 

CP → L=2747 

LS → L=2133 

YD → L=176 

Beam Hinges 

CP → L=2237, R=2747 

LS → L=1746, R=2133 

YD → L=R=176 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Beam Hinges 

CP → L=2747 

LS → L=2133 

YD → L=176 

Beam Hinges 

CP → L=2237, R=2747 

LS → L=1746, R=2133 

YD → L=R=176 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Beam Hinges 

CP → L=2747 

LS → L=2133 

YD → L=176 

Beam Hinges 

CP → L=2237, R=2747 

LS → L=1746, R=2133 

YD → L=R=176 

Beam Hinges 

CP → L=2085, R=3125 

LS → L=1640, R=2429 

YD → L=R=207 

Beam Hinges 

CP → L=3125 

LS → L=2429 

YD → L=207 

Column Hinges 

CP → T=B=1815, 357 

LS → T=B=1405, 293 

YD → T=B=157, 106 

Beam Hinges 

CP → L=2085, R=3125 

LS → L=1640, R=2429 

YD → L=R=207 

Beam Hinges 

CP → L=3125 

LS → L=2429 

YD → L=207 

Column Hinges 

CP → T=B=1815, 357 

LS → T=B=1405, 293 

YD → T=B=157, 106 

Beam Hinges 

CP → L=2085, R=3125 

LS → L=1640, R=2429 

YD → L=R=207 

Beam Hinges 

CP → L=3125 

LS → L=2429 

YD → L=207 

Column Hinges 

CP → T=B=1815, 357 

LS → T=B=1405, 293 

YD → T=B=157, 106 

Column Hinges 

CP → T=B=1857, 309 

LS → T=B=1437, 255 

YD → T=B=159, 107 

Column Hinges 

CP → T=B=1857, 309 

LS → T=B=1437, 255 

YD → T=B=159, 107 

Column Hinges 

CP → T=B=1857, 309 

LS → T=B=1437, 255 

YD → T=B=159, 107 

Column Hinges 

CP → T=B=1904, 263 

LS → T=B=1472, 218 

YD → T=B=161, 108 

Column Hinges 

CP → T=B=1719, 323 

LS → T=B=1328, 266 

YD → T=B=155, 104 

Column Hinges 

CP → T=B=1630, 338 

LS → T=B=1264, 278 

YD → T=B=159, 100 

Beam Hinges 

CP → L=2445 

LS → L=1889 

YD → L=160 

Beam Hinges 

CP → L=1992, R=2445 

LS → L=1556, R=1889 

YD → L=R=160 

Column Hinges 

CP → T=B=1785, 351 

LS → T=B=1382, 289 

YD → T=B=155, 104 

Column Hinges 

CP → T=B=1630, 338 

LS → T=B=1264, 278 

YD → T=B=159, 100 

Beam Hinges 

CP → L=1631, R=2445 

LS → L=1281, R=1889 

YD → L=R=160 

Beam Hinges 

CP → L=2445 

LS → L=1889 

YD → L=160 

Column Hinges 

CP → T=B=1728, 345 

LS → T=B=1338, 284 

YD → T=B=152, 102 

Column Hinges 

CP → T=B=1630, 338 

LS → T=B=1264, 278 

YD → T=B=159, 100 

Beam Hinges 

CP → L=1462, R=2192 

LS → L=1148, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Beam Hinges 

CP → L=1462, R=2192 

LS → L=1148, R=1702 

YD → L=R=144 

Beam Hinges 

CP → L=2192 

LS → L=1702 

YD → L=144 

Column Hinges 

CP → T=B=1681, 342 

LS → T=B=1302, 281 

YD → T=B=151, 102 

Column Hinges 

CP → T=B=1535, 329 

LS → T=B=1191, 271 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1535, 329 

LS → T=B=1191, 271 

YD → T=B=145, 98 

Column Hinges 

CP → T=B=1535, 329 

LS → T=B=1191, 271 

YD → T=B=145, 98 

RBS Beams = Total Curvature×106 

Panel Zones = Total Shear Strain×106 

Columns = Total Curvature×106 (for P/PCL = 0.0, 0.5) 

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

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.)
 

Panel Zones 

CP → T=B=32544 

LS → T=B=24408 

YD → T=B=2712 

L = Left Hinge, R = Right Hinge, T = Top Hinge, B = Bottom Hinge 

All values are for Primary Components 

Figure 3-26. Frame Capacity Schematic (inelastic), YD, LS and CP, 16-Story SMF RSA 

3-44
 
 

Seismic Assessment Results 

The results for the SMFs 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., beam 

hinges) 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 moment frame, as is done for an eccentrically braced frame in ASCE 

41 §5.5.3.4. The capacity design procedure used in this study models all beam hinges adjacent to columns 

achieving Mpr. Axial force demand estimates from the capacity design procedure prescribed in AISC 341 

for moment frames, which uses 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 §3.2.3.1.4. 

22 ASCE 41 §3.4.2.1.2-1 refers to this type of analysis as a “limit state” analysis. 

3-45
 
 

Four-Story Moment 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 3-27 and Figure 3-28 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 3-29 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 LS BPL acceptance criteria except for the exterior beam-to-column 

connections in the RSA-designed frame on the second and third floors. These connection failures are 

primarily due to reduced m-factors as a result of the FR connection modifiers for panel zone strength and 

clear span-to-depth limitations. Assessment results for the panel zones all remained small compared to 

unity. This suggests that design rules and conventional practice (e.g., increase column sizes to offset the 

use of doubler plates) can produce strong panel zones with regard to ASCE 41 criteria, which can adversely 

affect the beam-to-column connection acceptance criteria. Current steel design practice, however, does not 

enforce a balanced yield condition between a beam hinge and the adjacent panel zone. Moreover, it is not 

logical that the FR connection reduction factors create a step function in performance. The 20 percent 

reduction between the interior connections in the ELF-designed frame on the second and third floors in 

Figure 3-27(b) is due to the change in the average story-height, h, when computing the panel zone 

demands—see ASCE 41 §5.4.2.4.2-4.2. Figure 3-27(b) and Figure 3-28(b) show that the frame columns 

are deformation-controlled for flexure. 

0.53 0.53 0.53 2.81 2.81 2.82 

0.06 5.73

0.11 5.73 

0.13 6.00

0.35 5.60

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

0.14 

0.05

0.16 

0.69 0.69 0.68

0.05 

0.08

0.69 0.69 0.68 

0.23 0.26 

0.08 

0.82 0.65 0.64

0.09

0.27 0.30 

0.82 0.65 0.64 

0.09 

0.88 0.87 0.85

0.18

0.28 0.31 

0.88 0.87 0.85 

0.18 

6.00

8.00 8.00 

6.00 

2.83 2.83 2.84

8.00 8.00 

6.00

2.83 2.83 2.84 

2.85 3.56 3.57

6.00 

6.00

2.85 3.56 3.57 

8.00 8.00 

6.00 

2.85 2.85 2.85

6.00

8.00 8.00 

2.85 2.85 2.85 

6.00 

Figure 3-27. LSP Assessment Results, 4-Story SMF ELF, BSE-1 LS 

3-46
 
 

0.07 

0.12 

0.15 

0.43 

2 

3 

4 

0.55 0.43 0.42 2.81 3.51 3.52 

5.63 

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

0.07

0.15 0.20

0.07 

0.84 0.66 0.64 0.84 0.66 0.64 

0.21 0.27 

0.09

1.05 0.82 0.80

0.09 

1.05 0.82 0.80 

0.25 0.33 

0.11

1.14 0.88 0.85

0.11 

1.14 0.88 0.85 

0.28 0.36 

0.21 

8.00 8.00 

6.00 

2.81 3.51 3.52 2.81 3.51 3.52 

8.00 8.00 

6.00

2.81 3.51 3.52

6.00 

2.81 3.51 3.52 

8.00 8.00 

6.00 

2.81 3.51 3.52 2.81 3.51 3.52 

6.00

8.00 8.00 

6.00 

5.63 

5.63 

4.77 

Figure 3-28. LSP Assessment Results, 4-Story SMF RSA, BSE-1 LS 

Roof Roof

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

P (ASCE 7, AISC 341) u,Omega

Pu,Capacity Design 

PCL (ASCE 41)	 

Floor 

2 

Base Base

4 

Floor

3 

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-29. LSP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-1 

3.2.2.1.1.2 BSE-2 Earthquake Hazard Level (CP 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, 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 3-32 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

3-47
 
 

All component actions satisfy the CP BPL acceptance criteria except for a few beam-to-column connections 

in the ELF- and RSA-designed frames on the second and third floors. As identified previously in 

§3.2.2.1.1.1, these connection failures are primarily due to reduced m-factors as a result of the FR 

connection modifiers for panel zone strength and clear span-to-depth limitations. Assessment results for the 

panel zones all remained small compared to unity—see §3.2.2.1.1.1. Figure 3-30(b) and Figure 3-31(b) 

show that the frame columns are deformation-controlled for flexure. 

0.62 0.62 0.61 3.55 3.55 3.56 

0.06 7.66

0.11 7.66

0.14 8.00

0.40 6.76

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

0.05

0.15 0.17 

0.81 0.80 0.79

0.05 

0.08

0.80 0.79 

0.28 

0.81 

0.25 

0.96 0.76 0.75

0.08 

0.09

0.29 0.33 

0.96 0.76 0.75

0.09 

1.03 1.02 1.00

0.31 0.34 

0.18

1.03 1.02 1.00

0.18 

8.00

11.00 11.00

3.58

8.00 

3.58 3.58

11.00 11.00 

8.00

3.58 3.58 3.58 

3.60

8.00 

4.50 4.50

8.00

3.60 

11.00 11.00 

4.50 4.50 

8.00 

3.60 3.60 3.60

8.00

11.00 11.00 

3.60 3.60 3.60

8.00 

Figure 3-30. LSP Assessment Results, 4-Story SMF ELF, BSE-2 CP 

0.64 0.50 0.49 3.55 4.44 4.44 

0.07 7.53

0.12 7.53

0.15 7.53

0.47 5.76

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

0.07

0.17 0.21 

0.07 

0.99 0.77 0.75 

0.30 

0.99 

0.23 

0.77 0.75 

0.10

1.23

0.10 

1.23 0.96 0.93

0.28 0.36 

0.96 0.93 

0.12

1.34 1.03 0.99

0.12 

1.34 1.03 

0.23

0.30 0.39 

0.23 

11.00 11.00 

8.00 

3.55 4.44 4.44 4.44 4.44

11.00 11.00 

8.00

3.55 

3.55

8.00 

3.55 4.44 4.44

11.00 11.00 

4.44 4.44 

8.00 

3.55 4.44 4.44 3.55 4.44 4.44

8.00

11.00 11.00 

8.00 

Figure 3-31. LSP Assessment Results, 4-Story SMF RSA, BSE-2 CP 

3-48
 
 

2 

3 

4 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41)	 

Roof Roof Floor 

4 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Floor 

3 

2 

Base Base

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-32. LSP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-2 

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 3-33 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-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 3-35 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 LS BPL acceptance criteria. Assessment results for the panel zones all 

remained small compared to unity—see §3.2.2.1.1.1. Figure 3-33(b) and Figure 3-34(b) show that the frame 

columns are deformation-controlled for flexure. 

3-49
 
0.45 0.46 0.45 2.81 2.81 2.82 

0.06 5.73

0.09 5.73

0.12 6.00

0.31 5.89

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

0.05

0.12 0.13 

0.56 0.56 0.55

0.05 

0.07

0.56 0.56 0.55 

0.18 0.21 

0.66 0.53 0.52

0.07 

0.08

0.21 0.24 

0.66 0.53 0.52 

0.08 

0.75 0.74 0.72

0.24 0.27 

0.16

0.75 0.74 0.72 

0.16 

6.00

8.00 8.00 

6.00 

2.83 2.83 2.84

8.00 

6.00

8.00 

2.83 2.83 2.84 

2.85 3.56 3.57

6.00 

6.00

2.85 3.56 3.57 

8.00 8.00 

6.00 

2.85 2.85 2.85

6.00

8.00 8.00 

2.85 2.85 2.85 

6.00 

Figure 3-33. LDP Assessment Results, 4-Story SMF ELF, BSE-1 LS 

0.47 0.37 0.36 2.81 3.51 3.52 

0.06 5.63

0.10 5.63

0.14 5.63

0.38 5.05

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

0.06

0.13 0.17 

0.06 

0.69 0.54 0.53 0.69 0.54 0.53 

0.17 0.22 

0.08

0.85 0.67 0.65

0.08 

0.85 0.67 0.65 

0.20 0.27 

0.10

0.97 0.76 0.73

0.10 

0.97 0.76 0.73 

0.20

0.24 0.30 

0.20 

8.00 8.00 

6.00 

2.81 3.51 3.52 2.81 3.51 3.52 

8.00 8.00 

6.00

2.81 3.51 3.52

6.00 

2.81 3.51 3.52 

8.00 8.00 

6.00 

2.81 3.51 3.52 2.81 3.51 3.52 

6.00

8.00 8.00 

6.00 

Figure 3-34. LDP Assessment Results, 4-Story SMF RSA, BSE-1 LS 

3-50
 
 

2 

3 

4 

Roof Roof 

4 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Floor 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Floor 

3 

2 

Base Base

Axial Load Demand, P (kips)	 Axial Load Demand, P (kips) 

(a) ELF (b) RSA 

Figure 3-35. LDP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-1 

3.2.2.1.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-36 and Figure 3-37 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 3-38 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 except the exterior beam-to-column 

connections in the RSA-designed frame on the second floor. As identified previously in §3.2.2.1.1.1, these 

connection failures are primarily due to reduced m-factors as a result of the FR connection modifiers for 

panel zone strength and clear span-to-depth limitations. Assessment results for the panel zones all remained 

small compared to unity—see §3.2.2.1.1.1. Figure 3-36(b) and Figure 3-37(b) show that the frame columns 

are deformation-controlled for flexure. 

3-51
 
0.06 

0.11 

0.13 

0.37 

0.07 

0.12 

0.15 

0.46 

2 

3 

4 

0.53 0.53 0.52 3.55 3.55 3.56 

7.66 

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

0.05

0.13 0.15 

0.66 0.65 0.65

0.05 

0.08

0.65 

0.23 

0.66 0.65 

0.20 

0.78 0.61 0.61

0.08 

0.09

0.61 

0.26 

0.78 0.61 

0.23 

0.09 

0.88 0.87 0.85

0.18

0.29 

0.88 0.87 

0.26 

0.85 

0.18 

8.00

11.00 11.00

8.00 

3.58 3.58 3.58

8.00

11.00 

3.58 3.58 

11.00 

3.58 

3.60 4.50 4.50

8.00 

4.50 

8.00

4.50 

11.00 11.00

3.60 

3.60

8.00 

3.60 3.60

8.00

3.60 

11.00 

3.60 3.60 

11.00 

8.00 

7.66 

8.00 

7.09 

Figure 3-36. LDP Assessment Results, 4-Story SMF ELF, BSE-2 CP 

0.55 0.43 0.41 3.55 4.44 4.44 

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

0.14 0.18 

0.06 

0.80 0.63 0.61

0.18 

0.09

0.61 

0.24 

0.80 0.63 

0.09 

0.99 0.78 0.75

0.22 

0.75 

0.29 

0.99 0.78 

0.11 

1.14 0.88 0.85 

0.33 

1.14 0.88 

0.26 

0.85 

0.21 

11.00 11.00

8.00

4.44

8.00 

3.55 4.44 4.44 3.55 4.44 

11.00 

8.00

11.00 

8.00 

3.55 4.44 4.44

11.00 

3.55 4.44 

11.00 

4.44 

8.00 

3.55 4.44 4.44 3.55 4.44 

11.00 

4.44 

11.00 

8.00 

7.53 

7.53 

7.53 

6.00 

Figure 3-37. LDP Assessment Results, 4-Story SMF RSA, BSE-2 CP 

Roof Roof 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Floor 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

4 

3 

2 

Base 

Axial Load Demand, P (kips) Axial Load Demand, P (kips) 

Base 

(a) ELF (b) RSA 

Figure 3-38. LDP Assessment Results, Compression in Exterior Columns, 4-Story SMF, BSE-2 

Floor 

3-52
 
 

 

 

 

 

 

 

 

3.2.2.1.3 Nonlinear Static Procedure 

In this section, the following apply: 

	 Table 3-13 through Table 3-15 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-39 and Figure 3-40 illustrate the monotonic pushover curves for the ELF and RSAdesigned frames, respectively, at the BSE-2 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., plastic 

hinges), notated in the figures. The softening of the pushover curve evident at about 12 inches of 

roof displacement for each frame is due to column hinges developing at the base of the frames. 

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 3-41 and Figure 3-42 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, for both BSE-1 and BSE-2, the target displacement governs d for the ELF 

frame whereas the displacement at the maximum base shear governs d for the RSA frame. 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 3-13. NSP General Information, 4-Story SMF (kip, inch) 

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

ELF 1.81 101.1 8.9 891 100.6 1.82 1.09 21.9 967.7 5172 1.00 1.28 

RSA 2.19 67.6 8.4 570 67.7 2.18 1.12 15.3 637.3 5136 1.00 1.28 

Table 3-14. NSP Analysis Parameters, 4-Story SMF BSE-2 CP (kip, inch) 

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

ELF 0.50 2.90 1.00 1.00 20.6 967.7 20.6 0.06 -0.28 -0.01 -0.06 7.61 OK 

RSA 0.43 3.86 1.00 1.00 25.5 579.5 15.3 0.15 -0.20 -0.01 -0.05 9.33 OK 

Table 3-15. NSP Analysis Parameters– 4-Story SMF BSE-1 LS (kip, inch) 

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

ELF 0.33 1.93 1.00 1.00 13.8 945.4 13.8 0.11 -0.18 -0.01 -0.04 9.46 OK 

RSA 0.29 2.57 1.00 1.00 17.0 636.6 15.3 0.15 -0.20 -0.01 -0.05 9.33 OK 

3-53
 
 

 

 

 

 

 

 

 

Roof Drift Ratio at CoM (%) 

0.0 0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.4 5.0 5.6 

1200 

0 4 8 12 16 20 24 28 32 36 40 

(8.9,891.0) 

(20.6,967.7) 

(36.3,534.6) 

ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

Pt. A: 3 hinges reach CP on 1st Floor 

Pt. B: Remaining 3 hinges reach CP on 1st Floor 

Pt. C: 3 hinges reach CP on 2nd Floor C

A 

C 

B 

0.23 

1100 0.21 

1000 0.19 

900 0.17 

800 0.15 

700 0.14 

600 0.12 

500 0.10 

400 0.08 

300 0.06 

200 0.04 

100 0.02 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-39. 4-Story SMF ELF Pushover, BSE-2 

Roof Drift Ratio at CoM (%) 

0.0 0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.4 5.0 5.6 

1200 0.23 

900 

0 4 8 12 16 20 24 28 32 36 40 

(8.4,570.0) 

(15.3,637.3) 

(37.6,342.0) 

D 

Pt. A: 1 hinge reaches CP on 1st Floor 

Pt. B: 1 hinge reaches CP on 1st Floor 

Pt. C: 1 hinge reaches CP on 1st Floor 

Pt. D: 1 hinge reaches CP on 2nd Floor 

RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

A B C 

0.18 

800 0.16 

700 0.14 

1100 0.21 

1000 0.19 

600 0.12 

500 0.10 

400 0.08 

300 0.06 

200 0.04 

100 0.02 

0 0.00 

Roof Displacement at CoM (Inches)

Figure 3-40. 4-Story SMF RSA Pushover, BSE-2 

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

Total Base Shear / W Total Base Shear / W 

3-54
 
 

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 3-41. 4-Story SMF 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 3-42. 4-Story SMF RSA Pushover – Story Drift Ratios – BSE-2 

3-55
 
 

 

 

 

 

 

 

Of particular interest in the pushover curves is the large disparity between the peak base shears developed 

in the ELF- and RSA-designed buildings (RSA / ELF = 637 / 968 = 0.66), a 34 percent change. At first 

glance, this is greater than the 15 percent difference in design base shears allowed by ASCE 7. Upon further 

inspection, it can be reasoned that the primary contribution to this disparity is due to the increase in strength 

provided to the ELF-designed frame to satisfy drift provisions in ASCE 7 (i.e., 15 percent plus additional 

strength)—see NSP discussion in the 8-story results for more information. 

Figure 3-43 illustrates which frame columns are force-controlled for flexure for both the NSP and NDP; all 

flexural actions are deformation-controlled in these frames. Figure 3-44 through Figure 3-47 illustrate the 

DCRN values if greater than unity for the ELF- and RSA-designed frames at the target displacement for the 

LS BPL at the BSE-1 EHL and CP BPL at the BSE-2 EHL. These figures illustrate demands when the 

system is loaded to the right. The only performance concern observed is the exterior beam-to-column 

connections on the second floor in the RSA-designed frame at the BSE-2. As discussed previously in the 

linear assessment sections, the acceptance criteria of these components are impacted by the FR connection 

modifiers. 

Roof
 

(ELEV = 60 ft.)
 

4th Fl o or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Colu mn is f or ce-controlled for flexur e if 

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

target displacement for the NS P and as 

the maximum value f or the ND P 

Figure 3-43. Schematic of Flexural Actions in Columns, 4-Story SMF (NSP and NDP) 

B C D E Sym. About 

A ll colum ns are deformationcontrolled (DC) for flexur e u nless 

indicated as force-controlled (FC) 

in figur e 

3-56
 
 

 

 

 

Figure 3-44. NSP Assessment Results, 4-Story SMF ELF, BSE-1 LS (+push to right) 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

Roof
 

(ELEV = 60 ft.)
 

4th Floor
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Figure 3-45. NSP Assessment Results, 4-Story SMF RSA, BSE-1 LS (+push to right) 

Figure 3-46. NSP Assessment Results, 4-Story SMF ELF, BSE-2 CP (+push to right) 

3-57
 
 

Figure 3-47. NSP Assessment Results, 4-Story SMF RSA, BSE-2 CP (+push to right) 

3.2.2.1.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the E-W direction of MC4 is shown in Appendix A. For the ELF 

design, the analysis successfully completed for all 14 records at the BSE-1 and BSE-2 EHL. For the RSA 

design, the analysis successfully completed for all 14 records at the BSE-1 EHL; however, four analyses 

did not complete at the BSE-2 EHL due to excessive lateral drift. Maximum axial compression force in the 

exterior column lines from the record set are shown previously in the linear assessment sections. 

Figure 3-48 through Figure 3-51 show the performance of the beam hinges (i.e., beam-to-column 

connections) 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 right) are included in the figures. 

Comparison discussions between the various procedures are addressed subsequently. As is evident from 

the figures, the ELF-designed frame performs better than the RSA-designed frame. Results for the RSAdesigned frame indicate that the exterior beam-to-column connections have difficulty satisfying the CP 

BPL acceptance criteria at the BSE-2 EHL (primarily based on mean response). In contrast to the mean 

response, the median response generally indicates better performance because it is less influenced by large 

deformations resulting from component strength loss potentially resulting in collapse of the system. 

Consequently, the median is potentially a more stable performance metric when analyzing a large number 

of ground motion records, but should be restrained relative to a mean value. 

The average ratio of secondary to primary component acceptance criteria for an RBS beam-to-column 

connection for all W18 sections and deeper is 1.49 for the CP SPL (1.47 for the LS SPL). The figures for 

the RSA-designed frame illustrate that this value is exceeded in the exterior beam-to-column connections 

at the 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. 

3-58
 
Floor ID Floor ID 

Roof 

1-Median

1-Mean

1-84th

4 

1-Mean+1std

2-Median

2-Mean

2-84th

2-Mean+1std

3 1-NSP

 2-NSP

LSP (max)

LDP (max) 

2 

1 = Left Hinge 

2 = Right Hinge 

Base Bay B-C Bay C-D Bay D-E

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-48. NDP Assessment Results, Beam Hinges, 4-Story SMF ELF, BSE-1 LS

Roof 

1 = Left Hinge 

2 = Right Hinge 

1-Median

4 1-Mean

1-84th

1-Mean+1std

2-Median

3 2-Mean

2-84th

2-Mean+1std

 1-NSP

 2-NSP

2 LSP (max)

LDP (max) 

Base Bay B-C Bay C-D Bay D-E

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-49. NDP Assessment Results, Beam Hinges, 4-Story SMF RSA, BSE-1 LS 

3-59
Roof 

4 

2 

3 

1-Median

1-Mean

1-84th

1-Mean+1std

2-Median

2-Mean

2-84th

1 = Left Hinge 

2 = Right Hinge 

2-Mean+1std

 1-NSP

 2-NSP

LSP (max)

LDP (max) 

0.0 

Base 

0.5 1.0 

Bay B-C 

1.5 2.0 0.0 0.5 1.0 1.5 

Bay C-D 

2.0 0.0 0.5 1.0 1.5 

Bay D-E

2.0 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-50. NDP Assessment Results, Beam Hinges, 4-Story SMF ELF, BSE-2 CP 

Roof 

0 

Base 

2 

3 

4 

1 234 

Bay B-C 

01 234 

Bay C-D 

01 234 

1 = Left Hinge 

2 = Right Hinge 

Bay D-E

1-Median

1-Mean

1-84th

1-Mean+1std

2-Median

2-Mean

2-84th

2-Mean+1std

 1-NSP

 2-NSP

LSP (max)

LDP (max) 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-51. NDP Assessment Results, Beam Hinges, 4-Story SMF RSA, BSE-2 CP 

Floor ID Floor ID 

The previous figures for the RSA-designed frame illustrate that the component strengths provided by drift 

control measures in ASCE 7 at 2⁄3×MCER (equal to the BSE-1 here) are not significant enough to overcome 

the demands to satisfy the assessment criteria at the BSE-2 (taken here as MCER). In contrast, the ELFdesigned frame satisfies the assessment criteria at the BSE-2. First, strong panel zones reduce the allowable 

deformations in the acceptance criteria and component model for the exterior beam-to-column connections. 

Second, the increase in hinge demands in the lower floors is attributed primarily to design choices, as drift 

is typically not a primary concern in these regions and thus beam strengths seldom get increased 

3-60
 

significantly. Also contributing to this increase, to a lesser extent, is the distribution of the design forces 

from the MRSA. This effect highlights the change in story demands as column base hinges develop, an 

influence not addressed in elastic design analysis. However, a secondary design analysis to address the 

effects of “pinned” column bases could be conducted—not done in this study. 

Figure 3-43 (see NSP section) illustrates which flexural actions in the frame columns are force-controlled 

for both the NSP and NDP; all flexural actions are deformation-controlled in these frames. Figure 3-52 and 

Figure 3-53 show the performance of the column hinges for the CP BPL criteria at the BSE-2 EHL (LS 

BPL for the BSE-1 is not shown). Column hinges at the base experience inelastic strain demands (yield 

corresponds to a DCRN ≈ 0.15 in the figures). However, the deformation demands are considerably lower 

than the primary CP acceptance criteria. 

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 applicable here because the columns 

are also 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. 

0.0 0.2 0.4 0.6 0.8 1.0 

Base 

2 

3 

4 

Roof 

DCRN for the LSP and 

LDP are based on 

interaction equations. 

All columns are 

deformation-controlled 

for flexure 

Col. Line B 

Floor ID 

0.0 0.2 0.4 0.6 0.8 1.0 

Col. Line C 

0.0 0.2 0.4 0.6 0.8 1.0 

Col. Line D 

0.0 0.2 0.4 0.6 0.8 1.0 

Col. Line E 

Median 

Mean 

84th 

Mean+1std

 NSP 

LSP (max) 

LDP (max) 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-52. NDP Assessment Results, Column Hinges, 4-Story SMF ELF, BSE-2 CP 

3-61
 
Roof Col. Line B Col. Line C Col. Line E

All columns are 

Col. Line D 

DCRN for the LSP and deformation-controlled 4 

LDP are based on for flexural actions. 

interaction equations. 

Floor ID 

Median

3 Mean

84th

Mean+1std

 NSP

2 LSP (max)

LDP (max) 

Base 

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-53. NDP Assessment Results, Column Hinges, 4-Story SMF RSA, BSE-2 CP 

Figure 3-54 and Figure 3-55 show the curvature ductility demand of the column hinges (i.e., section 

strength) at the BSE-2 EHL. Figure 3-56 and Figure 3-57 show the elastic member strength interaction 

results at the BSE-2 EHL. The results indicate that the columns in the ELF- and RSA-designed frames 

satisfy the intended lower-bound acceptance criteria. 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

Median 4 

Mean All columns are 84th

deformation-controlled Mean+1std

Floor ID 

 NSP

3
 

for flexural actions. 

LSP

 LDP 

2 

Base 

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 

DCRN = Total Deformation / Total YD Acceptance Criteria 

Figure 3-54. NDP Assessment Results, Column Hinges, 4-Story SMF ELF, BSE-2 Yield 

3-62 
Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

4 All columns are 

deformation-controlled Median

Mean for flexural actions. 

Floor ID Floor ID 

84th

Mean+1std 3 

 NSP

 LSP

 LDP 

2 

Base 

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 
 

DCRN = Total Deformation / Total YD Acceptance Criteria
 

Figure 3-55. NDP Assessment Results, Column Hinges, 4-Story SMF RSA, BSE-2 Yield 

All columns are deformation-controlled for flexure 

Roof Col. Line B Col. Line C Col. Line D Col. Line E

Median

4
 Mean

84th

Mean+1std

 LSP

 LDP 

3 

2 

Base 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 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 Interation Result 

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

Figure 3-56. NDP Assessment Results, Column Members, 4-Story SMF ELF, BSE-2 CP 

3-63
All columns are deformation-controlled for flexure 

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 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Col. Line D 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Col. Line E 

Median 

Mean 

84th 

Mean+1std

 LSP

 LDP 

DCRN = P-M Interation Result
 

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

Figure 3-57. NDP Assessment Results, Column Members, 4-Story SMF RSA, BSE-2 CP 

Figure 3-58 and Figure 3-59 show the performance of the panel zones for the CP BPL criteria at the BSE2 EHL (LS BPL for the BSE-1 is not shown). The deformation demands are significantly lower than the 

CP acceptance criteria. Converting the results to total deformation / yield deformation indicates that the 

demands for the BSE-2 are consistently less than 4×y. These results illustrate that the panel zones are 

stronger than required by the assessment criteria, which may be the result of designing panel zones for the 

probable connection strength in lieu of the nominal yield strength (i.e., My) as recommended in FEMA 350. 

Also, upsizing column sizes to offset the need for doubler plates increases the shear strength of the panel 

zones. Future research should investigate alternative design procedures for panel zones as well as the 

variation in performance if columns sizes were not increased and doubler plates were added. This research 

would include the variation in the performance of column base hinges or column-to-base connections. 

3-64
 
Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

4 

Median

Mean

84th

Mean+1std

 NSP

Floor ID Floor ID 

LSP (max)

LDP (max) 3 

2 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-58. NDP Assessment Results, Panel Zones, 4-Story SMF ELF, BSE-2 CP 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

Median

Mean

4 84th

Mean+1std

 NSP

LSP (max)

LDP (max) 3 

2 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-59. NDP Assessment Results, Panel Zones, 4-Story SMF RSA, BSE-2 CP 

3-65 
Eight-Story Moment 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 3-60 and Figure 3-61 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 3-62 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column and panel zone component actions satisfy the LS BPL acceptance criteria except for 

the exterior beam-to-column connections in the RSA-designed frame on the third through sixth floors. 

These connection failures are primarily due to reduced m-factors as a result of the FR connection modifiers 

for panel zone strength and clear span-to-depth limitations. The 20 percent reduction between the interior 

connections in the RSA-designed frame on the second and third floors in Figure 3-61(b) is due to the change 

in the average story-height, h, when computing the panel zone demands—see ASCE 41 §5.4.2.4.2-4.2. 

These figures illustrate that drift and stability control in ASCE 7 provides a significant amount of member 

overstrength so that beam-to-column connections in the ELF-designed frame easily satisfy the LS BPL 

acceptance criteria. Assessment results for the panel zones all remained small compared to unity—see 

§3.2.2.1.1.1. 

Several columns do not satisfy the LS BPL acceptance criteria using the interaction equation because they 

are designated as force-controlled for flexure since PUF exceeds 0.5×PCL. Force-controlled designation can 

be particularly problematic for base columns where plastic hinges are expected to form. 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; interior columns are not applicable 

because PE is essentially zero. This approach produces the least conservative PUF as compared to AISC 341 

SMF column design requirements and the fully yielded system as prescribed in ASCE 41 §3.4.2.1.2-1, as 

shown in Figure 3-62. 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. ASCE 41-13 took the first step in resolving this 

inconsistency by permitting PUF / PCL to be computed in the plane of bending. 

3-66
 
0.54 0.36 0.39 2.27 3.54 3.55 

0.13 

0.40 

0.16 

0.35 

0.39 

0.51 

0.56 

1.48 

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

0.07

0.13 0.17

0.07 

0.66 0.54 0.57

0.11

0.17 0.22

0.66 0.54 

0.11 

0.62 0.50 0.54

0.10

0.22 0.23 

0.62 0.50 

0.70 0.57 0.59

0.10 

0.70 0.57 

0.23 0.25 

0.59 

0.12

0.70 0.56

0.12 

0.70 0.56 0.58

0.13

0.58 

0.24 0.27 

0.13 

0.74 0.59 0.60

0.28 

0.14

0.59 

0.24 

0.74 

0.14 

0.61 0.59 0.59 0.61 0.59 

0.22 

0.59 

0.15

0.27 

0.56

0.15 

0.59 0.57

0.36

0.22 0.26 

0.59 0.57 0.56

0.36 

8.00 8.00

6.00 

2.83 3.54 3.55

8.00 8.00 

6.00 

3.03 3.78 3.79 

8.00 8.00

6.00 

3.03 3.78 3.79

8.00 8.00 

6.00 

8.00 

3.05 3.81 3.81

8.00 

6.00 

3.05 3.81 3.81

8.00 8.00 

6.00 

8.00 

3.81 3.81 3.81

8.00 

6.00 

3.81 

8.00 8.00 

3.81 3.81 

5.64 

6.00 

4.24 

6.00 

4.70 

4.23 

2.95 

2.39 

1.00 

Figure 3-60. LSP Assessment Results, 8-Story SMF ELF, BSE-1 LS 

0.76 0.52 0.56 1.95 3.05 3.05 

0.16 5.86

0.58 2.43 

1.13 1.00

1.39 1.00

0.60 2.47

1.07 1.00

0.48 3.06

1.00 1.46 

(a) DCRN (b) m-factors 

0.16 0.19 

0.08 

0.93 0.78 0.80

0.12

0.22 0.26

0.93 0.78 0.80 

0.12 

0.99 0.81 0.83 0.99 0.81 0.83 

0.27 0.34 

0.14 

1.120.90 0.92 0.90 0.92 

0.29 0.37 

0.17

1.07 0.86 0.88

0.17 

1.07 0.86 0.88 

0.33 0.37 

0.15 

1.080.86 0.88 0.86 0.88 

0.32 0.36 

0.18 

1.05 0.79 0.76

0.22 

1.05 0.79 0.76 

0.35 

0.28

1.00 0.92 0.85

0.28 

1.00 0.92 0.85 

0.47

0.20 0.32 

0.47 

8.00 8.00 

6.00 

2.44 3.05 3.05 

8.00 8.00

6.00 

2.83 3.54 3.55 

8.00 8.00 

6.00 

2.83 3.54 3.55 

8.00 8.00 

6.00 

2.86 3.57 3.58 

8.00 8.00 

6.00 

2.86 3.57 3.58 

8.00 8.00

6.00 

2.87 3.59 3.59 

8.00 8.00 

5.76 

2.87 2.87 2.88 

8.00 8.00

4.59 

(c) Key 

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

3-67
 
 

 

5 

6 

7 

8 

Roof 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof 

0 300 600 900 1200 1500 1800 2100 

Floor 

8 

7 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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 3-62. LSP Assessment Results, Compression in Exterior Columns, 8-Story SMF, BSE-1 

3.2.2.2.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-63 and Figure 3-64 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 3-65 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column and panel zone component actions satisfy the CP BPL acceptance criteria except for 

the beam-to-column connections in the RSA-designed frame on the second through eighth floors. As 

identified previously, in §3.2.2.2.1.1these connection failures are primarily due to reduced m-factors as a 

result of the FR connection modifiers for panel zone strength and clear span-to-depth limitations. 

Assessment results for the panel zones all remained small compared to unity—see §3.2.2.1.1.1. 

Several 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 previous discussion 

in §3.2.2.2.1.1). Further, comparing Figure 3-62 and Figure 3-65 illustrates that adopting a constant J factor 

of 2.0 for both performance levels is inconsistent with the intent of capacity design because of the change 

in the variation between PUF and PCapacity Design in the figures. Although a column can satisfy the criteria for 

BSE-1, it may fail the criteria for BSE-2 because of an overly conservative value for PUF. Consequently, J 

should vary between performance levels for consistency. 

3-68
 
0.63 0.42 0.45 2.86 4.48 4.48 

0.14 

0.48 

0.30 

0.44 

0.50 

0.74 

1.08 

2.06 

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

0.08

0.14 0.18 

0.08 

0.78 0.63 0.66 0.78 0.63 0.66 

0.19 0.24 

0.11 

0.73 0.59 0.63 0.73 0.59 0.63 

0.24 0.25 

0.11

0.70

0.11 

0.82 0.66 0.70 

0.25 0.27 

0.82 0.66 

0.12 

0.83 0.66 0.68

0.30 

0.14

0.83 0.66 0.68 

0.26 

0.14 

0.88 0.69 0.71

0.15

0.88 0.69 0.71 

0.27 0.30 

0.15 

0.72 0.69 0.69

0.16

0.72 0.69 0.69 

0.24 0.30 

0.16 

0.70 0.67 0.66 0.70 0.67 0.66 

0.24 0.29 

0.38 

11.00 11.00

8.00 

3.58 4.48 4.48

11.00 11.00 

8.00 

4.78 

11.00 

3.82 4.78 

11.00 

8.00 

3.82 4.78 4.78

11.00 11.00 

8.00 

11.00 

3.85 4.81 4.81

11.00 

8.00 

3.85 4.81 4.82

11.00 11.00 

8.00 

11.00 

4.81 4.81 4.82

11.00 

8.00 

4.81 

11.00 11.00 

4.81 4.82 

7.47 

8.00 

4.72 

7.33 

5.07 

4.20 

2.00 

1.00 

1.00 

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

0.89 0.60 0.64 2.47 3.86 3.86 

0.17 7.82

0.66 2.64 

1.41 1.00

1.72 1.00

0.77 2.02

1.34 1.00

0.58 2.80

1.00 1.89 

(a) DCRN (b) m-factors 

0.18 0.21 

0.09 

1.090.89 0.93 0.89 0.93 

0.13

0.25 0.29 

0.13 

1.17 0.94 0.97 0.94 0.97

0.37 

1.17 

0.29 

0.16 

1.32 1.061.08 

0.31 0.40 

1.32 

0.19

1.26 1.01 1.04

0.19 

0.36 0.40 

1.26 1.01 1.04

0.16

1.27

0.16 

1.27 1.01 1.03 

0.35 0.39 

0.19

1.23

0.19 

1.23 0.93 0.89 0.93 0.89 

0.24 0.39 

0.29

1.17 1.08 0.99

0.29 

1.17 1.08 

0.22 0.35 

0.49 

11.00 11.00 

8.00 

3.86 3.86 

11.00 

3.08 

11.00 

8.00 

4.48 4.48 

11.00 

3.58 

11.00 

8.00 

4.48 4.48 

11.00 11.00 

3.58 

8.00 

11.00 11.00 

3.61 4.51 4.52

8.00 

3.61 4.51 4.52 

11.00 11.00 

8.00 

3.63 4.54 4.54 

11.00 11.00 

7.66 

3.63 3.63 3.63

11.00 11.00 

6.10 

(c) Key 

Figure 3-64. LSP Assessment Results, 8-Story SMF RSA, BSE-2 CP 

3-69
 
 

5 

6 

7 

8 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof Roof 

0 300 600 900 1200 1500 1800 2100 

Floor 

8 

7 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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 3-65. LSP Assessment Results, Compression in Exterior Columns, 8-Story SMF, 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 3-66 and Figure 3-67 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 3-68 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column connection and panel zone component actions satisfy the LS BPL for the ELF- and 

RSA-designed frames. Assessment results for the panel zones all remained small compared to unity—see 

§3.2.2.1.1.1. 

Several columns do not satisfy the LS BPL acceptance criteria using the interaction equation as they are 

designated as force-controlled for flexure because of PUF exceeding 0.5×PCL (see previous discussion in 

§3.2.2.2.1.1). 

3-70
 
0.47 0.32 0.33 2.27 3.54 3.55 

0.12 

0.37 

0.13 

0.30 

0.33 

0.42 

0.45 

1.28 

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

0.11 0.14 

0.06 

0.54 0.45 0.45 0.54 0.45 0.45 

0.13 0.17 

0.10 

0.46 0.38 0.40 0.46 0.38 0.40 

0.16 0.17 

0.08

0.43

0.08 

0.50 0.41 0.43 

0.17 0.18 

0.50 0.41 

0.10 

0.52 0.41 0.43

0.20 

0.11

0.52 0.41 0.43 

0.17 

0.11 

0.57 0.45 0.46

0.13

0.57 0.45 0.46 

0.19 0.21 

0.13 

0.49 0.48 0.47 0.49 0.48 0.47 

0.18 0.22 

0.14 

0.50 0.48 0.47

0.34

0.50 0.48 0.47 

0.18 0.22 

0.34 

8.00 8.00

6.00 

2.83 3.54 3.55

8.00 8.00 

6.00 

3.78 

8.00 

3.03 3.79 

8.00 

6.00 

3.03 3.78 3.79

8.00 8.00 

6.00 

8.00 

3.05 3.81 3.81

8.00 

6.00 

3.05 3.81 3.81

8.00 8.00 

6.00 

8.00 

3.81 3.81 3.81

8.00 

6.00 

3.81 

8.00 8.00 

3.81 3.81 

5.66 

6.00 

4.49 

6.00 

5.17 

4.85 

3.78 

3.33 

1.00 

Figure 3-66. LDP Assessment Results, 8-Story SMF ELF, BSE-1 LS 

0.71 0.49 0.50 1.95 3.05 3.05 

0.15 5.86

0.52 2.58 

0.68 1.83 

1.18 1.00

0.48 3.22

0.66 1.81

0.40 3.84

0.84 1.78

(a) DCRN (b) m-factors 

0.15 0.18 

0.07 

0.78 0.66 0.67

0.10

0.18 0.21 

0.78 0.66 0.67 

0.10 

0.75 0.61 0.62 0.75 0.61 0.62 

0.19 0.25 

0.12 

0.82 0.66 0.67 0.82 0.66 0.67 

0.21 0.26

0.15 

0.78 0.63 0.64

0.24 

0.13

0.78 0.63 0.64 

0.27 

0.13 

0.81 0.65 0.66 0.81 0.65 0.66 

0.24 0.27 

0.16

0.83 0.63 0.60

0.16 

0.83 0.63 0.60 

0.17 0.28 

0.27

0.84 0.77 0.71

0.27 

0.84 0.77 0.71 

0.17 0.27 

0.45 

8.00 8.00 

6.00 

2.44 3.05 3.05 

8.00 8.00 

6.00 

2.83 3.54 3.55 

8.00 8.00 

6.00 

2.83 3.54 3.55 

8.00 8.00

6.00 

8.00 8.00 

2.86 3.57 3.58

6.00 

2.86 3.57 3.58 

8.00 8.00 

6.00 

2.87 3.59 3.59 

8.00 8.00 

5.77 

2.87 2.87 2.88 

8.00 8.00 

4.56 

(c) Key 

Figure 3-67. LDP Assessment Results, 8-Story SMF RSA, BSE-1 LS 

3-71
 
 

 

 

5 

6 

7 

8 

Roof 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof 

0 300 600 900 1200 1500 1800 2100 

Floor 

8 

7 

0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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 3-68. LDP Assessment Results, Compression in Exterior Columns, 8-Story SMF, BSE-1 

3.2.2.2.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-69 and Figure 3-70 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 3-71 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column connection and panel zone component actions satisfy the CP BPL for the ELF- and 

RSA-designed frames. Assessment results for the panel zones all remained small compared to unity—see 

§3.2.2.1.1.1. 

Several columns do not satisfy the CP BPL acceptance criteria using the interaction equation as they are 

designated as force-controlled for flexure because of PUF exceeding 0.5×PCL (see previous discussion in 

§3.2.2.2.1.1). 

3-72
 
0.58 0.38 0.40 2.86 4.48 4.48 

0.13 

0.44 

0.25 

0.36 

0.40 

0.52 

0.58 

1.77 

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

0.12 0.16 

0.07 

0.64 0.52 0.54

0.19 

0.64 0.52 

0.15 

0.11

0.54 0.44 0.47

0.11 

0.54 0.44 0.47 

0.17 0.18 

0.09 

0.60 0.48 0.51

0.18 0.20 

0.11

0.60 0.48 0.51 

0.62 0.49 0.50

0.11 

0.12

0.62 0.49 0.50 

0.19 0.22 

0.12 

0.67 0.53 0.54 0.67 0.53 0.54 

0.20 0.23 

0.13 

0.58 0.56 0.55 0.58 0.56 0.55 

0.20 0.24 

0.14 

0.59 0.57 0.55

0.35

0.59 0.57 0.55 

0.20 0.24 

0.35 

11.00 11.00

8.00 

3.58 4.48 4.48

11.00 11.00 

8.00 

4.78 

11.00 

3.82 4.78 

11.00 

8.00 

3.82 4.78 4.78

11.00 11.00 

8.00 

11.00 

3.85 4.81 4.81

11.00 

8.00 

3.85 4.81 4.82

11.00 11.00 

8.00 

11.00 

4.81 4.81 4.82

11.00 

8.00 

11.00 

4.81 4.81 4.82

11.00 

7.50 

8.00 

5.14 

7.83 

6.02 

5.43 

3.67 

2.88 

1.00 

Figure 3-69. LDP Assessment Results, 8-Story SMF ELF, BSE-2 CP 

0.83 0.56 0.58 2.47 3.86 3.86 

0.16 7.82

0.61 2.79 

1.29 1.00

1.53 1.00

0.59 3.12

1.14 1.00

0.48 3.96

1.00 1.72 

(a) DCRN (b) m-factors 

0.08

0.16 0.19 

0.08 

0.91 0.75 0.77

0.11

0.77 

0.23 

0.91 0.75 

0.20 

0.11 

0.88 0.71 0.73 0.88 0.71 

0.21 

0.73 

0.27 

0.13 

0.96 0.77 0.78 0.96 0.77 

0.22 

0.78 

0.16

0.29 

0.16 

0.92 0.74 0.76 0.92 

0.29 

0.74 

0.14

0.26 

0.76 

0.14 

0.95 0.76 0.77 0.95 0.76 

0.26 

0.77 

0.29 

0.17

0.98 0.74

0.17 

0.70

0.19 

0.98 0.74 0.70 

0.30 

0.28 

0.98 0.90 0.83

0.29 

0.98 0.90 

0.19 

0.83 

0.47 

11.00 11.00

8.00 

3.08 3.86 

11.00 

3.86 

11.00 

8.00 

3.58 4.48 

11.00 

4.48 

11.00 

8.00 

3.58 4.48 

11.00 

4.48 

11.00 

8.00 

3.61 4.52 

11.00 11.00 

4.51 

8.00 

4.52 

11.00 

3.61 4.51 

11.00 

8.00 

4.54 

11.00 11.00

3.63 4.54 

7.67 

3.63 3.63 

11.00 

3.63 

11.00 

6.05 

(c) Key 

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

3-73
 
PUF (J = Max

PUF (J = 1)

Pmax (NDP)

P (NSP)

Pu,Omega (A

Pu,Capacity Design

PCL

5 

6 

Roof Roof 

8 8 

7 7 

[min DCR,2]) 

SCE 7, AISC 341)

 (ASCE 41) 

Floor 

0 300 600 900 1200 1500 1800 2100 0 300 600 900 1200 1500 1800 2100 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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

3.2.2.2.3 Nonlinear Static Procedure 

In this section, the following apply: 

	 Table 3-16 through Table 3-18 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-72 and Figure 3-73 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., plastic hinges), notated in the figures. The softening 

of the pushover curve evident at about 20 inches of roof displacement for each frame is due to 

column hinges developing at the base of the frames. 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 3-74 and Figure 3-75 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 for both the BSE-1 and BSE-2 EHLs, the displacement at the maximum base 

shear governs d for both the ELF- and RSA-designed frames. Axial compression force in the exterior 

columns at the target displacement are shown previously in the linear assessment sections. Results indicate 

that the NSP generally results in a lower estimate of the axial force demands compared to the other methods 

used in this study. This is partly because the fundamental mode-based lateral force distribution does not 

adequately capture higher mode effects. Also, the target displacement at the roof computed based on 

fundamental mode properties may underestimate the story demands in the upper stories. 

Figure 3-72 also includes a curve representing the force-displacement response if the column base hinges 

did not develop, such as for the case when columns are oversized. In this case, the target displacement 

3-74
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

controls d and P- would be zero (or even positive). The second-order curves shown in the figure illustrate 

the potential sensitivity of NSP results when base column hinges develop in moment frames—including 

the effect of modeling parameters used for the hinges. Furthermore, the NSP is not permitted for assessment 

of the E-W direction of MC8 for the RSA-designed frame since R > Rmax for the BSE-2 EHL—results are 

provided here only for performance comparison between systems. However, the ratio of R / Rmax (= 1.01) 

would likely be acceptable in practice. 

Table 3-16. NSP General Information, 8-Story SMF (kip, inch) 

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

ELF 2.79 76.9 13.7 1050 76.9 2.79 1.15 19.1 1116.9 10618 1.00 1.32 

RSA 3.60 41.5 14.9 623 41.7 3.59 1.19 26.3 664.8 10527 1.00 1.33 

Table 3-17. NSP Analysis Parameters, 8-Story SMF BSE-2 CP (kip, inch) 

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

ELF 0.33 3.37 1.00 1.00 33.5 1092.3 19.1 0.16 -0.25 -0.02 -0.07 6.88 OK 

RSA 0.26 4.35 1.00 1.00 43.3 593.2 26.3 0.09 -0.31 -0.10 -0.14 4.31 R > Rmax 

Table 3-18. NSP Analysis Parameters– 8-Story SMF BSE-1 LS (kip, inch) 

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

ELF 0.22 2.25 1.00 1.00 22.4 1113.0 19.1 0.16 -0.25 -0.02 -0.07 6.88 OK 

RSA 0.17 2.90 1.00 1.00 28.8 660.7 26.3 0.09 -0.31 -0.10 -0.14 4.31 OK 

Roof Drift Ratio at CoM (%) 

0.0 0.4 0.7 1.1 1.4 1.8 2.2 2.5 2.9 3.2 3.6 

1600 0.15 

1400 0.13 

800 

0 5 10 15 20 25 30 35 40 45 50 

(13.7,1050.0) 

(19.1,1116.9) 

(44.9,630.0) 

Pt. A: Ext. column base hinge reaches CP, followed

 by 2 hinges reach CP on 1st Floor 

Pt. B: Remaining 4 hinges reach CP on 1st Floor

 2 hinges reach CP on 2nd Floor 

Pt. C: Remaining column hinges reach CP 

Roof Displacement at CoM (Inches) 

A 

B 

C

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone

 ELF (First-Order) No Column Hinges

 ELF (Second-Order) No Column Hinges 

0.08 

Total Base Shear (Kips) 1200 0.11 

Total Base Shear / W 

1000 0.09 

600 0.06 

400 0.04 

200 0.02 

0 0.00 

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

3-75
 
 

 

Roof Drift Ratio at CoM (%) 

0.0 0.4 0.7 1.1 1.4 1.8 2.2 2.5 2.9 3.2 3.6 

1600 0.15 

Story Drift Ratio (%) Total Base Shear (Kips) 

Total Base Shear / W 

1400 

1200 

0 5 10 15 20 25 30 35 40 45 50 

(14.9,623.0) 

(26.3,664.8) 

(48.6,373.8) 

Pt. A: Ext. column base hinge reaches CP 

Pt. B: Ext. hinges (2) reach CP on both 

1st and 2nd Floor 

Pt. C: Ext. hinges (2) reach CP on 3rd Floor 

 RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

A 

B 

C 

0.11 

1000 0.09 

800 0.08 

0.13 

600 0.06 

400 0.04 

200 0.02 

0 0.00 

Roof Displacement at CoM (Inches)

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

3.0% 

2.5% 

2.0% 

1.5% 

1.0% 

0.5% 

0.0% 

0.0% 0.5% 1.0% 1.5% 2.0% 

1st Story

 2nd Story

 3rd Story

 4th Story

 5th Story

 6th Story

 7th Story

 8th Story

 Roof 

Roof Drift Ratio (%)

Figure 3-74. 8-Story SMF ELF Pushover – Story Drift Ratios – BSE-2 

3-76
 
 

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 3-75. 8-Story SMF RSA Pushover – Story Drift Ratios – BSE-2 

Of particular interest in the pushover curves is the large disparity between the peak base shears developed 

in the ELF- and RSA-designed buildings (RSA / ELF = 665 / 1117 = 0.6), a 40 percent change. At first 

glance, this is greater than the 15 percent difference in design base shears allowed by ASCE 7. Upon further 

inspection, it can be reasoned that the primary contribution to this disparity is due to the increase in strength 

provided to the ELF-designed frame to satisfy drift provisions in ASCE 7 (i.e., 15 percent plus additional 

strength). To a lesser extent, the distribution of the lateral forces in the NSP do not coincide with the 

allocation of the story shear yield strengths (as shown in Figure 3-76 and Figure 3-77), which results in 

capping the base shear if the initial story mechanism develops above the first story (as is the case for the 

RSA-designed frame). The oval in these figures illustrates the first floor to develop its defined yield 

strength, Vy, and the color-code for the expected plastic hinges match that provided in Figure 3-79. 

Figure 3-78 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. As shown in the figure, the force-controlled columns do not align between the two frames— 

the axial load ratios, P / PCL, for the exterior base columns are 0.58 and 0.48 for the ELF- and RSA-designed 

frames, respectively (0.26 and 0.64 at the fifth story). This illustrates the sensitivity of results due to 

variations between the non-adaptive loading profile in the NSP and that used for design. Figure 3-79 

through Figure 3-82 illustrate the DCRN values if greater than unity for the ELF- and RSA-designed frames 

at the target displacement for the LS BPL at the BSE-1 EHL and CP BPL at the BSE-2 EHL. These figures 

illustrate the demands when the system is loaded to the right. All component actions for the beam-to-column 

connections and panel zones satisfy the LS and CP BPL acceptance criteria at the target displacements. 

However, assuming deformation-controlled flexural actions, the exterior base column hinge for both frames 

fail the CP BPL primary acceptance criteria. This is a corollary to a column plastic hinge model (section 

3-77
 
 

 

 

strength) being a function of PCL (based on member stability) and not Pye (based on section strength), as 

well as the adopted P-M interaction equation (see previous discussion on nonlinear model). This also 

indicates that this may be the first hinge to experience significant strength loss (P / PCL = 0.28 for gravity 

loads alone—see summary section for calculations). As it is an exterior base column, this could be 

detrimental to the performance of the system. 

Roof Expected Story Strength, V
 

or 

Building: MC8 

SFRS: SMF (E-W) 

Design: ELF 

1st Mode Lateral Force Distribution

 1st Mode Lateral Force Distribution

 (at First Expected Story Strength)

 Design Lateral Force Distribution 

First Expected 

Story Strength 

0 200 400 600 800 1000 1200
 

y

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base
 

Floor ID Floor ID 

Story Shear (kips) 

(a) story shear comparison (b) mechanism schematic 

Figure 3-76. Story Shear Demand to Strength Comparison, ELF 

Roof 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base
 

Expected Story Strength, V
 

or 

First Expected Story Strength 

1st Mode Lateral Force Distribution

 1st Mode Lateral Force Distribution

 (at First Expected Story Strength)

 Design Lateral Force Distribution 

Building: MC8 

SFRS: SMF (E-W) 

Design: RSA 

y

0 200 400 600 800 1000 1200
 

Story Shear (kips)
 

(a) story shear comparison (b) mechanism schematic 

Figure 3-77. Story Shear Demand to Strength Comparison, RSA 

3-78
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Several exterior columns, including those at the base of the ELF-designed frame, are force-controlled for 

flexure at the target displacements. Force-controlled base columns are problematic for a region that is 

expected to experience inelastic strain demands. Therefore, the acceptance criterion for these flexural 

actions is based on the force-controlled lower-bound elastic P-M interaction (ASCE 41 Equation 5-12). As 

discussed previously, variations in P-M interaction curves add complexity to nonlinear flexural hinge 

model. Essentially, a nonlinear hinge based on the expected yield surface of the section must be 

accompanied by another model that can measure the lower-bound strength of the member (one for each 

axis of buckling). For simplicity, failing of the acceptance criteria (without computing interaction values) 

is self-evident because of the development of plastic hinges in the frame columns. Because plastic hinges 

have developed in the base columns in the ELF-design frame, flexural actions therefore do not satisfy the 

intended elastic acceptance criteria. Conversely, the force-controlled columns in the RSA frame satisfy the 

intended elastic acceptance criteria—member stability would still need to be verified. 

B C D E 

ELF NDP LS & CP 

ELF NSP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

All colum ns are deformationcontrolled (DC) for flexure unless 

indicated as for ce-controlled (FC) 

in figur e 

Sym. About 

Roof
 

(ELEV = 116 ft.)
 

8th Floor 

(ELEV = 102 ft.) 

7th Floor 

(ELEV = 88 ft.) 

6th Floor 

(ELEV = 74 ft.) 

5th Floor 

(ELEV = 60 ft.) 

4th Floor 

(ELEV = 46 ft.) 

3rd Flo or 

(ELEV = 32 ft.) 

2nd Flo or 

(ELEV = 18 ft.) 

Column is f or ce-controlled for flexur e if 

P > 0.5×PCL, wher e P is computed at the 

target displacement for the NSP and as 

the maxim um value f or the NDP 

Figure 3-78. Schematic of Flexural Actions in Columns, 8-Story SMF (NSP and NDP) 

3-79
 
 

 

 

 

 

 

 

 

 

 

 

 

B C D E 

Roof 

2.45 4.01 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

(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.) 

(< 1.0 if DC) (< 1.0 if DC) 

Figure 3-79. NSP Assessment Results, 8-Story SMF ELF, BSE-1 LS (+push to right) 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

1.26 

Roof
 

(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.)
 

Figure 3-80. NSP Assessment Results, 8-Story SMF RSA, BSE-1 LS (+push to right) 

3-80
 
 

 

 

 

 

 

 

 

 

 

 

 

B C D E 

Roof 

6.42 9.43 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

(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.) 

(< 1.0 if DC) (2.11 if DC) 

Figure 3-81. NSP Assessment Results, 8-Story SMF ELF, BSE-2 CP (+push to right) 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

2.38 

Roof
 

(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.)
 

Figure 3-82. NSP Assessment Results, 8-Story SMF RSA, BSE-2 CP (+push to right) 

3-81
 
3.2.2.2.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the E-W direction of MC8 is shown in Appendix A. For the ELF 

design, the analysis successfully completed for all 14 records at the BSE-1 EHL; however, three analyses 

did not complete at the BSE-2 EHL because of excessive lateral drift or solution non-convergence. For the 

RSA design, the analysis successfully completed for 12 records at the BSE-1 EHL; however, nine analyses 

did not complete at the BSE-2 EHL because of excessive lateral drift or solution non-convergence. 

Maximum axial compression force in the exterior column lines from the record set are shown previously in 

the linear assessment sections. 

Figure 3-83 through Figure 3-86 show the performance of the beam hinges (i.e., beam-to-column 

connections) 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 right) are included in the figures. 

Comparison discussions between the various procedures are addressed subsequently. As is evident from 

the figures, the ELF-designed frame performs better than the RSA–designed frame. Results for the RSAdesigned frame indicate that the beam-to-column connections have difficulty satisfying the CP BPL 

acceptance criteria at the BSE-2 EHL (primarily based on mean response). In contrast to the mean response, 

the median response indicates better performance at all stories 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. Further, there is a strong 

probability that system response is triggered by the performance of the exterior base column hinges—see 

previous discussion in NSP section. 

Roof 1-Median 

1-Mean 

8 1-84th 

1-Mean+1std 

7 2-Median 

2-Mean 

6 2-84th 

2-Mean+1std

Floor ID 

 1-NSP

5 2-NSP 

LSP (max) 

4 LDP (max) 

3 1 = Left Hinge 

2 = Right Hinge 

2 

Base 

Bay B-C Bay C-D Bay D-E 

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-83. NDP Assessment Results, Beam Hinges, 8-Story SMF ELF, BSE-1 LS 

3-82
 
6 

7 

8 

Roof 1 = Left Hinge 

2 = Right Hinge 

1-Median

1-Mean

1-84th

1-Mean+1std

2-Median

2-Mean

2-84th

2-Mean+1std

Floor ID 

4 

5 

 1-NSP

 2-NSP

LSP (max)

LDP (max) 

3 

0 

Base 

2 

1 2 3 4 5 6 7 8 

Bay B-C 

DCRN = Total Deformation / Total LS Acceptance Criteria 

0 1 2 3 4 5 6 7 8 

Bay C-D 

0123456 

Bay D-E

78 

Figure 3-84. NDP Assessment Results, Beam Hinges, 8-Story SMF RSA, BSE-1 LS 

The average ratio of secondary to primary component acceptance criteria for an RBS beam-to-column 

connection for all W18 sections and deeper is 1.49 for the CP SPL (1.47 for the LS SPL). The figures for 

the both frames illustrate that this value is exceeded in the beam-to-column connections at the BSE-2 EHL. 

This highlights the rapid progression towards a collapse state when several components are strained past 

the deformation associated with their peak strength—see §3.1.4.2. 

Roof 

1 = Left Hinge 1-Median

8 

2 = Right Hinge 1-Mean

1-84th

1-Mean+1std

7 2-Median

2-Mean

6 2-84th

2-Mean+1std

Floor ID 

4 

5 

 1-NSP

 2-NSP

LSP (max)

LDP (max) 

3 

2 

Base Bay B-C Bay C-D Bay D-E

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-85. NDP Assessment Results, Beam Hinges, 8-Story SMF ELF, BSE-2 CP 

 

3-83
6 

7 

8 

Roof 

1 = Left Hinge 

2 = Right Hinge 

1-Median

1-Mean

1-84th

1-Mean+1std

2-Median

2-Mean

2-84th

2-Mean+1std

Floor ID 

4 

5 

 1-NSP

 2-NSP

LSP (max)

LDP (max) 

3 

0 

Base 

2 

2 4 6 8 10 12 14 

Bay B-C 

DCRN = Total Deformation / Total CP Acceptance Criteria 

0 2 4 6 8 10 12 14 

Bay C-D 

0 2 4 6 8 10 

Bay D-E

12 14 

Figure 3-86. NDP Assessment Results, Beam Hinges, 8-Story SMF RSA, BSE-2 CP 

The previous figures illustrate for both frames that the component strengths provided by drift and stability 

control measures in ASCE 7 at 2⁄3×MCER (equal to the BSE-1 here) are not significant enough to overcome 

the demands to satisfy the assessment criteria at the BSE-2 (taken here as MCER). First, strong panel zones 

reduce the allowable deformations in the acceptance criteria and component model for the exterior beamto-column connections. Second, base hinge modeling could have a drastic effect on the performance of the 

beam-to-column connections. This further highlights the change in story demands as column base hinges 

develop, an influence not addressed in elastic design analysis. However, a secondary design analysis to 

address the effects of “pinned” column bases could be conducted—not done in this study. 

Figure 3-78 (see NSP section) illustrates which flexural actions in the frame columns are force-controlled 

for both the NSP and NDP. Figure 3-87 and Figure 3-88 show the performance of the column hinges for 

the CP BPL criteria for the BSE-2 assuming deformation-controlled flexural actions (LS BPL for the BSE1 is not shown). Column hinges at the base experience inelastic strain demands (yield corresponds to a 

DCRN ≈ 0.15 in the figures). The deformation demands in these hinges are considerably higher than the CP 

primary acceptance criteria, indicating a significant performance concern of the frame columns and the 

SFRS. Similarly, the exterior base columns in the ELF-designed frame are force-controlled for flexure and 

therefore do not satisfy the lower-bound elastic acceptance criteria at the BSE-2 EHL. Moreover, the 

columns in the RSA-designed frame on the fifth floor do not satisfy the acceptance criteria because they 

are also force-controlled. 

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 columns are force-controlled for flexure in the linear assessment procedures. Though there is a 

fundamental difference in how the DCRN is computed for the linear and nonlinear procedures, the linear 

assessment results show similar distributions of demands and location of potential performance concerns. 

3-84 
Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

6 

7 

8 

DCRN for the LSP and 

LDP are based on 

interaction equations. 

See LSP and LDP 

for force-controlled 

columns. 

Floor ID Floor ID 

Median

5 Mean

84th

4 Mean+1std

 NSP

3 LSP (max)

LDP (max)
 

2 

Base 

0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-87. NDP Assessment Results, Column Hinges, 8-Story SMF ELF, BSE-2 CP 

 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

8 

DCRN for the LSP and See LSP and LDP 

7 LDP are based on for force-controlled 

interaction equations. columns. 

6 

5 Median

Mean

84th

4 Mean+1std

 NSP

3 LSP (max)

LDP (max) 

2 

Base 

02 46 8 10 02 468 10 02 468 10 02 46 8 10 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-88. NDP Assessment Results, Column Hinges, 8-Story SMF RSA, BSE-2 CP 

Figure 3-89 and Figure 3-90 show the curvature ductility demand of the column hinges (i.e., section 

strength) at the BSE-2 EHL. Figure 3-91 and Figure 3-92 show the elastic member strength interaction 

results at the BSE-2 EHL. The results indicate that the columns above the base in the ELF-designed frame 

satisfy the intended lower-bound acceptance criteria whereas the columns in the RSA-designed frame 

consistently do not satisfy these acceptance criteria—a result of the large number of analyses that did not 

complete. 

3-85 
6 

7 

8 

Roof 

Col. Line B 

See LSP and LDP 

for force-controlled 

columns. 

Col. Line C 

See NSP for 

force-controlled 

columns. 

Col. Line D Col. Line E

Median

Mean

84th

Mean+1std

 NSP

 LSP

Floor ID 

5 

LDP 

4 

3 

2 

0 

Base 

Figure 3-89. NDP Assessment Results, Column Hinges, 8-Story SMF ELF, BSE-2 Yield 

2 4 6 8 10 12 14 

DCRN = Total Deformation / Total YD Acceptance Criteria 

0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 

 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

7 

8 See LSP and LDP 

for force-controlled 

columns. 

See NSP for 

force-controlled 

columns. 

Median

Mean

84th

Mean+1std

 NSP

6 LSP

Floor ID

5 

LDP 

4 

3 

2 

0 

Base 

5 10 15 20 25 30 

DCRN = Total Deformation / Total YD Acceptance Criteria 

0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 

Figure 3-90. NDP Assessment Results, Column Hinges, 8-Story SMF RSA, BSE-2 Yield 

3-86
Roof Col. Line B Col. Line C Col. Line D Col. Line E

See LSP and LDP 8 

for force-controlled 

7 columns. 

See NSP for 

6 

Floor ID 

force-controlled 

columns. 5 

Median

Mean 4 

84th

Mean+1std

3 LSP

 LDP
 

2
 

Base 

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 

DCRN = P-M Interation Result 

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

Figure 3-91. NDP Assessment Results, Column Members, 8-Story SMF ELF, BSE-2 

 

Roof Col. Line B Col. Line C Col. Line D Col. Line E

8 See LSP and LDP 

for force-controlled 

7 columns. 

6 See NSP for 

Floor ID

force-controlled 

5 columns. 

4 Median

Mean

3 84th

Mean+1std

 LSP

2 LDP 

Base 

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 

DCRN = P-M Interation Result 

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

Figure 3-92. NDP Assessment Results, Column Members, 8-Story SMF RSA, BSE-2 

Figure 3-93 and Figure 3-94 show the performance of the panel zones for the CP BPL criteria at the BSE2 EHL (LS BPL for the BSE-1 is not shown). The deformation demands are significantly lower than the 

CP acceptance criteria. Converting the results to shear ductility (total deformation / yield deformation, y) 

indicates that the demands for the BSE-2 are consistently less than 4×y. These results illustrate that the 

panel zones are stronger than required by the assessment criteria—see discussion in the 4-story NDP 

section. There is one outlier at the interior panel zones on the third floor in the RSA-designed frame. First, 

3-87
the first hinges to form are on the third floor. Second, the mean results are biased toward the collapse state 

of the frame for a given record—a result of the large number of analyses that did not complete. 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E

8 

7 Median

Mean

6 84th

Floor ID Floor ID 

Mean+1std

 NSP 5 

LSP

LDP 

4 

3 

2 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-93. NDP Assessment Results, Panel Zones, 8-Story SMF ELF, BSE-2 CP 

Roof Col. Line B Col. Line C Col. Line D Col. Line E

8
 

7 Median

Mean

6 84th

Mean+1std

5 NSP

LSP

LDP 4 

3 

2 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 0 1 2 3 0 1 2 3 0.0 0.2 0.4 0.6 0.8 1.0
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-94. NDP Assessment Results, Panel Zones, 8-Story SMF RSA, BSE-2 CP 

 

3-88 
Sixteen-Story Moment 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 3-95 and Figure 3-96 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 3-97 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column and panel zone component actions satisfy the LS BPL acceptance criteria except for 

the exterior beam-to-column connections in the RSA-designed frame on the 14th floor. These connection 

failures are primarily due to reduced m-factors as a result of the FR connection modifiers for panel zone 

strength and clear span-to-depth limitations. These figures illustrate that drift and stability control in ASCE 

7 provides a significant amount of member overstrength so that beam-to-column connections in the ELFdesigned frame easily satisfy the LS BPL acceptance criteria. Assessment results for the panel zones all 

remained small compared to unity—see §3.2.2.1.1.1. 

Several exterior frame columns in the RSA-designed frame do not satisfy the LS BPL acceptance criteria 

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

0.5×PCL—see §3.2.2.2.1 for more discussion. 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; interior columns are not applicable because PE is essentially zero. This approach 

produces the least conservative PUF as compared to AISC 341 SMF column design requirements and the 

fully yielded system as prescribed in ASCE 41 §3.4.2.1.2-1, as shown in Figure 3-97. 

3-89
 
0.42 0.34 0.43 2.31 2.88 2.88 

0.08 4.01 

0.14 4.01 

0.30 3.77 

0.43 2.79 

0.52 2.41 

0.90 1.00 

0.51 2.67 

0.69 1.52 

0.52 2.45 

0.76 1.00 

0.60 1.72 

0.81 1.00 

0.55 2.04 

0.76 1.00 

0.38 3.89 

0.55 2.92 

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

0.07 0.12 

0.06 

0.60 0.39 0.46 

0.09 0.14 

0.10 

0.47 0.38 0.47 

0.14 0.18 

0.08 

0.55 0.44 0.53 

0.16 0.20 

0.09 

0.55 0.44 0.54 

0.18 0.21 

0.10 

0.61 0.49 0.58 

0.19 0.22 

0.12 

0.68 0.53 0.61 

0.20 0.24 

0.13 

0.70 0.54 0.61 

0.20 0.24 

0.15 

0.18 0.24 

0.82 0.49 0.54 

0.15 

0.82 0.49 0.53 

0.18 0.24 

0.26 

0.69 0.50 0.53 

0.16 0.24 

0.28 

0.69 0.50 0.52 

0.15 0.24 

0.30 

0.72 0.52 0.53 

0.12 0.20 

0.27 

0.70 0.51 0.50 

0.11 0.19 

0.29 

0.17 

0.67 0.47 0.44 

0.06 

0.30 

0.05 0.13 

0.56 0.39 0.35 

0.39 

Sym. 

8.00 8.00 

6.00

2.31 3.60 3.61

6.00 

2.31 3.60 3.61 

8.00 8.00 

6.00 

3.07 3.83 3.84 3.07 3.83 3.84 

6.00 

8.00 8.00 

6.00 

3.07 3.83 3.84 3.07 3.83 3.84 

8.00 8.00 

6.00 

3.17 3.97 3.97

8.00 8.00 

3.17 3.97 3.97 

6.00 

3.17 3.97 3.97 3.17 3.97 3.97 

6.00 

8.00 8.00 

6.00 

3.17 3.97 3.97 3.17 3.97 3.97 

8.00 8.00 

6.00 

3.17 3.97 3.97

8.00 8.00 

3.17 3.97 3.97 

6.00 

2.61 4.07 4.07 2.61 4.07 4.07 

6.00 

8.00 8.00 

6.00 

2.61 4.07 4.07 2.61 4.07 4.07 

8.00 8.00 

5.84 

3.26 4.07 4.07

8.00 8.00 

3.26 4.07 4.07 

5.56 

3.26 4.07 4.07 3.26 4.07 4.07 

5.29 

8.00 8.00 

5.29 

3.26 4.07 4.07 3.26 4.07 4.07 

8.00 8.00 

5.70 

3.26 4.07 4.07

8.00 8.00 

3.26 4.07 4.07 

5.49 

3.26 4.07 4.07 3.26 4.07 4.07 

5.31 

8.00 8.00 

5.31 

3.26 4.07 4.07 3.26 4.07 4.07 

4.67 

8.00 8.00 

4.67 

Figure 3-95. LSP Assessment Results, 16-Story SMF ELF, BSE-1 LS 

3-90
 
 

0.44 0.37 0.48 2.31 2.88 2.88 

0.08 

0.16 

0.29 

0.43 

0.58 

0.96 

0.55 

0.89 

0.86 

0.96 

0.91 

1.05 

0.88 

0.95 

0.73 

1.15 

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

0.07

0.07 0.13 

0.67 0.45 0.53

0.07 

0.11

0.67 0.45 0.53 

0.11 0.17 

0.11 

0.97 0.62 0.69

0.15

0.12 0.22 

0.97 0.62 0.69 

0.15 

1.13 0.71 0.78

0.32

0.14 0.25 

1.13 0.71 0.78 

0.32 

0.74 0.59 0.68

0.12

0.21 0.27 

0.74 0.59 0.68 

0.76 0.62 0.72

0.12 

0.13

0.22 0.27 

0.76 0.62 0.72 

0.13 

0.83 0.67 0.75

0.15

0.23 0.29 

0.83 0.67 0.75 

0.15 

0.86 0.68 0.76

0.28

0.23 0.29 

0.86 0.68 0.76 

0.78 0.62 0.69

0.28 

0.25

0.23 0.28 

0.78 0.62 0.69 

0.25 

0.77 0.61 0.68

0.28

0.23 0.27 

0.77 0.61 0.68 

0.28 

0.99 0.61 0.66

0.31

0.20 0.26 

0.99 0.61 0.66 

0.95 0.59 0.62

0.31 

0.35

0.19 0.25 

0.95 0.59 0.62 

0.35 

0.82 0.51 0.55

0.27

0.17 0.20 

0.82 0.51 0.55 

0.27 

0.76 0.47 0.50

0.29

0.15 0.18 

0.76 0.47 0.50 

0.59 0.44 0.44

0.29 

0.31

0.10 0.16 

0.59 0.44 0.44 

0.31 

0.51 0.37 0.36

0.41

0.08 0.13 

0.51 0.37 0.36 

0.41 

6.00

8.00 8.00 

6.00 

2.31 3.60 3.61

6.00 

8.00 8.00 

2.31 3.60 3.61 

6.00 

2.31 3.60 3.61

6.00 

8.00 8.00 

2.31 3.60 3.61 

6.00 

2.31 3.60 3.61

4.55 

8.00 8.00 

2.31 3.60 3.61 

4.55 

3.07 3.83 3.84

6.00

8.00 8.00 

3.07 3.83 3.84 

3.07 3.83 3.84

6.00 

6.00 

8.00 8.00 

3.07 3.83 3.84 

6.00 

3.07 3.83 3.84

6.00 

8.00 8.00 

3.07 3.83 3.84 

6.00 

3.07 3.83 3.84

5.80

8.00 8.00 

3.07 3.83 3.84 

3.17 3.97 3.97

5.80 

5.96 

8.00 8.00 

3.17 3.97 3.97 

5.96 

3.17 3.97 3.97

5.60 

8.00 8.00 

3.17 3.97 3.97 

5.60 

2.54 3.97 3.97

5.26

8.00 8.00 

2.54 3.97 3.97 

2.54 3.97 3.97

5.26 

4.93 

8.00 8.00 

2.54 3.97 3.97 

4.93 

2.61 4.07 4.07

5.64 

8.00 8.00 

2.61 4.07 4.07 

5.64 

2.61 4.07 4.07

5.38

8.00 8.00 

2.61 4.07 4.07 

3.26 4.07 4.07

5.38 

5.15 

8.00 8.00 

3.26 4.07 4.07 

5.15 

3.26 4.07 4.07

4.46 

8.00 8.00 

3.26 4.07 4.07 

4.46 

Sym. 

4.01 

4.01 

3.84 

2.97 

1.85 

1.00 

2.17 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

Figure 3-96. LSP Assessment Results, 16-Story SMF RSA, BSE-1 LS 

3-91
 
 

 

 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0 1000 2000 3000 4000 5000 6000 7000 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof 

Floor 

16 

15 

14 

13 

0 1000 2000 3000 4000 5000 

Axial Load Demand, P (kips) 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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 3-97. LSP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-1 

3.2.2.3.1.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-98 and Figure 3-99 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 3-100 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column and panel zone component actions satisfy the CP BPL acceptance criteria except for 

several exterior beam-to-column connections in the RSA design on several floors. These connection failures 

are due to reduced m-factors as a result of the FR connection modifiers for panel zone strength and clear 

span-to-depth limitations. Assessment results for the panel zones all remained small compared to unity— 

see §3.2.2.1.1.1. 

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 §3.2.2.2.1 for more discussion. Further, comparing Figure 3-97 and Figure 3-100 

illustrates that adopting a constant J factor of 2.0 for both performance levels is inconsistent with the intent 

of capacity design because of the change in the variation between PUF and PCapacity Design in the figures—see 

§3.2.2.2.1 for more discussion. 

3-92
 
 

0.49 0.39 0.50 2.91 3.64 3.64
 

0.09
 

0.15
 

0.35
 

0.53
 

0.71
 

1.19
 

0.97
 

1.17
 

0.93
 

1.02
 

0.97
 

1.09
 

0.91
 

1.02
 

0.51
 

1.29
 

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

0.07

0.08 0.13 

0.07 

0.70 0.44 0.53 0.44 0.53

0.16 

0.70 

0.10

0.10 

0.10 

0.56 0.45 0.55 0.56 

0.15 

0.45 0.55 

0.20 

0.09

0.65

0.09 

0.65 0.51 0.62

0.10

0.17 0.21 

0.51 0.62 

0.10 

0.65 0.52 0.63 0.65 0.52 0.63

0.11

0.19 0.23 

0.72 

0.11 

0.72 0.57 0.68 0.57 0.68

0.24 

0.13

0.21 

0.13 

0.80 0.62 0.72 0.62 0.72

0.26 

0.80 

0.22 

0.14

0.83 0.64 0.72

0.14 

0.83 0.64 0.72

0.22 0.26 

0.17

0.97 0.58 0.64

0.17 

0.97 0.58 0.64

0.25

0.20 0.27 

0.97 0.57 0.63

0.25 

0.97 0.57 

0.28

0.19 

0.63 

0.26 

0.28 

0.81 0.59 0.62 0.59 0.62

0.26 

0.81 

0.17 

0.30

0.82 0.59 0.61

0.30 

0.82 0.59 0.61

0.17 0.26 

0.33

0.85

0.33 

0.85 0.62 0.63

0.28

0.13 0.22 

0.62 0.63 

0.28 

0.82 0.60 0.59

0.13 0.20 

0.82 0.60 0.59

0.30

0.79

0.30 

0.79 0.56 0.52

0.07 0.18 

0.56 0.52 

0.31

0.66 0.46 0.41

0.31 

0.66 0.46 0.41

0.41

0.05 0.14 

0.41 

11.00 11.00

8.00

2.91 4.55 4.56

8.00 

2.91 4.55 4.56

11.00 11.00 

8.00

3.87

8.00 

3.87 4.84 4.84

8.00

11.00 11.00 

4.84 4.84 

8.00 

3.87 4.84 4.84

11.00 11.00 

3.87 4.84 4.84

8.00 

4.01 5.01 5.02

11.00 11.00 

5.01 

8.00

4.01 5.02

4.01

8.00 

4.01 5.01 5.02

8.00

11.00 11.00 

5.01 5.02 

8.00 

4.01 5.01 5.02

11.00 11.00 

4.01 5.01 5.02

8.00 

4.01 5.01 5.02

11.00 11.00 

5.01 

8.00

4.01 5.02

3.29

8.00 

3.29 5.14 5.14

7.94

11.00 11.00 

5.14 5.14 

7.94 

3.29 5.14 5.14

11.00 11.00 

3.29 5.14 5.14

7.51 

4.11 5.14 5.14

11.00 11.00 

5.14 

7.14

4.11 5.14

4.11

7.14 

4.11 5.14 5.14

6.79

11.00 11.00 

5.14 5.14 

6.79 

4.11 5.14 5.14

11.00 11.00 

4.11 5.14 5.14

7.39 

4.11 5.14 5.14

11.00 11.00 

5.14 

7.13

4.11 5.14

4.11

7.13 

4.11 5.14 5.14

6.92

11.00 11.00 

5.14 5.14 

6.92 

4.11 5.14 5.14 4.11 5.14 5.14

6.09

11.00 11.00 

6.09 

5.48
 

5.48
 

4.50
 

2.91
 

1.90
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

3.24
 

1.00
 

Figure 3-98. LSP Assessment Results, 16-Story SMF ELF, BSE-2 CP 

3-93
 
 

0.51 0.42 0.55 2.91 3.64 3.64
 

0.09
 

0.33
 

0.34
 

0.52
 

0.98
 

1.28
 

1.00
 

1.20
 

1.15
 

1.28
 

1.22
 

1.42
 

1.18
 

1.27
 

0.98
 

1.59
 

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

0.07

0.08 0.14 

0.79 0.51 0.62

0.07 

0.12

0.51 0.62 

0.19 

0.79 

0.12 

1.15 0.72 0.80

0.12 

0.16

0.13 0.25 

1.15 0.72 0.80

1.33 0.83 0.91

0.16 

0.34

0.15 0.27 

1.33 0.83 0.91

0.88 0.80

0.34 

0.69

0.13

0.88 

0.23 0.30 

0.69 

0.90 0.73 0.85

0.13 

0.14

0.24 0.30 

0.90 0.73 0.85

0.99 0.78 0.88

0.14 

0.16

0.25 0.32 

0.99 0.78 0.88

1.02 0.89

0.16 

0.80

0.30

1.02 

0.25 0.32 

0.80 

0.92 0.72 0.82

0.30 

0.27

0.25 0.30 

0.92 0.72 0.82

0.91 0.72 0.80

0.27 

0.30

0.25 0.29 

0.91 0.72 0.80

1.17 0.78

0.30 

0.72

0.33

1.17 

0.22 0.29 

0.72 

1.12 0.69 0.73

0.33 

0.38

0.20 0.27 

1.12 0.69 0.73

0.97 0.60 0.64

0.38 

0.29

0.18 0.22 

0.97 0.60 0.64

0.90 0.59

0.29 

0.56

0.31

0.90 

0.16 0.20 

0.56 

0.69 0.52 0.51

0.31 

0.33

0.11 0.17 

0.69 0.52 0.51

0.60 0.44 0.42

0.33 

0.44

0.09 0.14 

0.60 0.44 0.42

0.44 

8.00

11.00 11.00

2.91 4.55 4.56

8.00 

8.00

11.00 11.00 

2.91 4.55 4.56

2.91 4.55 4.56

8.00 

8.00

11.00 11.00 

2.91 4.55 4.56

2.91 4.55 4.56

8.00 

5.91

11.00 11.00 

2.91 4.55 4.56

3.87 4.84

5.91 

4.84

8.00

3.87 

11.00 11.00 

4.84 

3.87 4.84 4.84

8.00 

8.00

11.00 11.00 

3.87 4.84 4.84

3.87 4.84 4.84

8.00 

8.00

11.00 11.00 

3.87 4.84 4.84

3.87 4.84

8.00 

4.84

7.52

3.87 

11.00 11.00 

4.84 

4.01 5.01 5.02

7.52 

7.74

11.00 11.00 

4.01 5.01 5.02

4.01 5.01 5.02

7.74 

7.21

11.00 11.00 

4.01 5.01 5.02

3.21 5.02

7.21 

5.01

6.74

3.21 

11.00 11.00 

5.01 

3.21 5.01 5.02

6.74 

6.28

11.00 11.00 

3.21 5.01 5.02

3.29 5.14 5.14

6.28 

7.28

11.00 11.00 

3.29 5.14 5.14

3.29 5.14

7.28 

5.14

6.93

3.29 

11.00 11.00 

5.14 

4.11 5.14 5.14

6.93 

6.64

11.00 11.00 

4.11 5.14 5.14

4.11 5.14 5.14

6.64 

5.70

11.00 11.00 

4.11 5.14 5.14

5.70 

5.48
 

3.02
 

4.63
 

3.24
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

1.00
 

Figure 3-99. LSP Assessment Results, 16-Story SMF RSA, BSE-2 CP 

3-94
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0 1000 2000 3000 4000 5000 6000 7000 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof 

Floor 

16 

15 

14 

13 

0 1000 2000 3000 4000 5000 

Axial Load Demand, P (kips) 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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 3-100. LSP Assessment Results, Compression in Exterior Columns, 16-Story SMF, 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 3-101 and Figure 3-102 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 3-103 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column connection, panel zone, and column component actions satisfy the LS BPL for the 

ELF- and RSA- designed frames. Contrary to the LSP results, all exterior frame columns in the ELFdesigned frame are deformation-controlled for flexural action for the LDP, whereas only a few more are 

deformation-controlled for the RSA-designed frame. Assessment results for the panel zones all remained 

small compared to unity—see §3.2.2.1.1.1. 

3-95
 
 

0.50 0.41 0.43 2.31 2.88 2.88 

0.09 

0.15 

0.28 

0.40 

0.45 

0.60 

0.42 

0.51 

0.41 

0.48 

0.45 

0.52 

0.42 

0.47 

0.30 

0.42 

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

0.06

0.08 0.13 

0.06 

0.63 0.41 0.43 0.63 0.41 0.43 

0.10

0.09 0.13 

0.10 

0.42 0.34 0.39 0.42 0.34 0.39 

0.12 0.15 

0.07

0.43 0.36 0.41

0.07 

0.43 0.36 0.41 

0.09

0.12 0.15 

0.09 

0.41 0.34 0.39 0.41 0.34 0.39 

0.09

0.13 0.15 

0.44 0.36 0.41

0.09 

0.44 0.36 0.41 

0.10

0.14 0.16 

0.10 

0.48 0.38 0.43 0.48 0.38 0.43 

0.14 0.16 

0.11

0.49 0.38 0.43

0.11 

0.49 0.38 0.43 

0.14 0.16 

0.13

0.58 0.35 0.38

0.13 

0.58 0.35 0.38 

0.13

0.13 0.17 

0.59 0.35 0.38

0.13 

0.59 0.35 0.38 

0.24

0.13 0.17 

0.24 

0.50 0.37 0.38 0.50 0.37 0.38 

0.11 0.17 

0.26

0.52 0.38 0.38

0.26 

0.52 0.38 0.38 

0.11 0.17 

0.28

0.56 0.40 0.40

0.28 

0.56 0.40 0.40 

0.25

0.09 0.15 

0.25 

0.56 0.40 0.40

0.09 0.15 

0.56 0.40 0.40 

0.27

0.56 0.39 0.36

0.27 

0.56 0.39 0.36 

0.05 0.14 

0.28

0.48 0.33 0.30

0.28 

0.48 0.33 0.30 

0.37

0.04 0.11 

0.37 

8.00 8.00 

6.00

2.31 3.60 3.61

6.00 

2.31 3.60 3.61 

8.00 8.00 

6.00

3.07 3.83 3.84

6.00 

3.07 3.83 3.84 

6.00

8.00 8.00 

6.00 

3.07 3.83 3.84

8.00 8.00 

3.07 3.83 3.84 

6.00 

3.17 3.97 3.97

8.00 8.00 

6.00

3.17 3.97 3.97 

3.17 3.97 3.97

6.00 

3.17 3.97 3.97 

6.00

8.00 8.00 

6.00 

3.17 3.97 3.97

8.00 8.00 

3.17 3.97 3.97 

6.00 

3.17 3.97 3.97

8.00 8.00 

6.00

3.17 3.97 3.97 

2.61 4.07 4.07

6.00 

2.61 4.07 4.07 

6.00

8.00 8.00 

6.00 

2.61 4.07 4.07

8.00 8.00 

2.61 4.07 4.07 

5.97 

3.26 4.07 4.07

8.00 8.00 

5.69

3.26 4.07 4.07 

3.26 4.07 4.07

5.69 

3.26 4.07 4.07 

5.42

8.00 8.00 

5.42 

3.26 4.07 4.07

8.00 8.00 

3.26 4.07 4.07 

5.80 

3.26 4.07 4.07

8.00 8.00 

5.58

3.26 4.07 4.07 

3.26 4.07 4.07

5.58 

3.26 4.07 4.07 

5.37

8.00 8.00 

5.37 

3.26 4.07 4.07 3.26 4.07 4.07 

4.69

8.00 8.00 

4.69 

4.01 

4.01 

3.79 

2.94 

2.78 

1.72 

3.42 

2.53 

3.50 

2.70 

3.02 

2.31 

3.34 

2.78 

4.85 

4.05 

Figure 3-101. LDP Assessment Results, 16-Story SMF ELF, BSE-1 LS 

3-96
 
 

0.51 0.43 0.46 2.31 2.88 2.88 

0.09 

0.16 

0.28 

0.41 

0.51 

0.81 

0.45 

0.55 

0.56 

0.77 

0.61 

0.83 

0.61 

0.76 

0.47 

0.97 

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

0.07

0.09 0.13 

0.69 0.46 0.49

0.07 

0.11

0.69 0.46 0.49 

0.10 0.16 

0.86 0.56 0.57

0.11 

0.14

0.10 0.19 

0.86 0.56 0.57 

0.90 0.58 0.60

0.14 

0.30

0.10 0.19 

0.90 0.58 0.60 

0.55 0.45 0.49

0.30 

0.10

0.55 0.45 0.49 

0.16 0.20 

0.55 0.45 0.51

0.10 

0.12

0.16 0.19 

0.55 0.45 0.51 

0.58 0.47 0.52

0.12 

0.13

0.16 0.20 

0.58 0.47 0.52 

0.60 0.48 0.52

0.13 

0.25

0.60 0.48 0.52 

0.16 0.20 

0.54 0.43 0.48

0.25 

0.14

0.16 0.19 

0.54 0.43 0.48 

0.54 0.44 0.48

0.14 

0.26

0.16 0.19 

0.54 0.44 0.48 

0.71 0.45 0.47

0.26 

0.28

0.71 0.45 0.47 

0.14 0.19 

0.70 0.44 0.45

0.28 

0.32

0.14 0.18 

0.70 0.44 0.45 

0.62 0.39 0.41

0.32 

0.25

0.12 0.15 

0.62 0.39 0.41 

0.60 0.37 0.39

0.25 

0.27

0.60 0.37 0.39 

0.12 0.14 

0.49 0.36 0.36

0.27 

0.29

0.08 0.13 

0.49 0.36 0.36 

0.44 0.32 0.30

0.29 

0.38

0.07 0.11 

0.44 0.32 0.30 

0.38 

6.00

8.00 8.00 

2.31 3.60 3.61

6.00 

6.00

8.00 8.00 

2.31 3.60 3.61 

2.31 3.60 3.61

6.00 

6.00

8.00 8.00 

2.31 3.60 3.61 

2.31 3.60 3.61

6.00 

4.60

8.00 8.00 

2.31 3.60 3.61 

3.07 3.83 3.84

4.60 

6.00

3.07 3.83 3.84 

8.00 8.00 

3.07 3.83 3.84

6.00 

6.00

8.00 8.00 

3.07 3.83 3.84 

3.07 3.83 3.84

6.00 

6.00

8.00 8.00 

3.07 3.83 3.84 

3.07 3.83 3.84

6.00 

5.91

3.07 3.83 3.84 

8.00 8.00 

3.17 3.97 3.97

5.91 

6.00

8.00 8.00 

3.17 3.97 3.97 

3.17 3.97 3.97

6.00 

5.73

8.00 8.00 

3.17 3.97 3.97 

2.54 3.97 3.97

5.73 

5.40

2.54 3.97 3.97 

8.00 8.00 

2.54 3.97 3.97

5.40 

5.07

8.00 8.00 

2.54 3.97 3.97 

2.61 4.07 4.07

5.07 

5.76

8.00 8.00 

2.61 4.07 4.07 

2.61 4.07 4.07

5.76 

5.50

2.61 4.07 4.07 

8.00 8.00 

3.26 4.07 4.07

5.50 

5.27

8.00 8.00 

3.26 4.07 4.07 

3.26 4.07 4.07

5.27 

4.58

8.00 8.00 

3.26 4.07 4.07 

4.58 

4.01 

4.01 

3.85 

3.07 

2.16 

1.00 

2.81 

2.06 

1.96 

1.00 

1.60 

1.00 

1.51 

1.00 

2.78 

1.00 

Figure 3-102. LDP Assessment Results, 16-Story SMF RSA, BSE-1 LS 

3-97
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

0 1000 2000 3000 4000 5000 6000 7000 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof Roof Floor 

16 

15 

14 

13 

0 1000 2000 3000 4000 5000 

Axial Load Demand, P (kips) 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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) 

(a) ELF (b) RSA 

Figure 3-103. LDP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-1 

3.2.2.3.2.2 BSE-2 Earthquake Hazard Level (CP BPL) 

In this section, the following apply: 

	 Figure 3-104 and Figure 3-105 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 3-106 provides the maximum axial compression demands, PUF, in the exterior column lines 

for various analysis methods and the column capacity, PCL. 

All beam-to-column and panel zone component actions satisfy the CP BPL acceptance criteria except for 

several exterior beam-to-column connections in the RSA- designed frame in the upper floors. As identified 

previously in §3.2.2.3.1.1, these connection failures are primarily due to reduced m-factors as a result of 

the FR connection modifiers for panel zone strength and clear span-to-depth limitations. Assessment results 

for the panel zones all remained small compared to unity—see §3.2.2.1.1.1. 

Several exterior frame columns in the 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 §3.2.2.2.1 for more discussion. 

3-98
 
 

0.58 0.46 0.50 2.91 3.64 3.64 

0.09 

0.32 

0.33 

0.48 

0.56 

0.97 

0.52 

0.92 

0.52 

0.82 

0.59 

0.85 

0.54 

0.80 

0.38 

0.55 

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

0.09 0.14 

0.07 

0.73 0.47 0.50

0.15 

0.73 0.47 

0.09 

0.11

0.50 

0.11 

0.50 0.40 0.45

0.16 

0.50 0.40 

0.13 

0.07 

0.51 0.41 0.47

0.13 

0.09

0.47 

0.16 

0.51 0.41 

0.09 

0.49 0.39 0.46

0.16 

0.49 0.39 

0.14 

0.10 

0.52 0.42 0.48

0.17 

0.52 0.42 

0.15 

0.11 

0.57 0.44 0.50 0.57 0.44 

0.15 

0.50 

0.18 

0.12

0.58 0.45

0.12 

0.58 0.45 0.50

0.15 

0.50 

0.18 

0.14

0.68 0.41 0.45

0.14 

0.18 

0.68 0.41 

0.14 

0.14

0.45 

0.69 0.41 0.45

0.14 

0.18 

0.25

0.69 0.41 0.45 

0.14 

0.25 

0.59 0.43 0.45 0.59 0.43 

0.12 

0.45 

0.19 

0.27

0.61 0.45

0.27 

0.61 0.45 0.45

0.12 

0.45 

0.19 

0.30 

0.66 0.48 0.48

0.10 

0.26

0.48 

0.17 

0.66 0.48 

0.26 

0.65 0.48 0.47

0.16 

0.65 0.48 

0.10 

0.28 

0.65 0.46 0.42

0.15 

0.65 0.46 

0.06 

0.30

0.56 0.39 0.35

0.30 

0.12 

0.56 0.39 

0.04 

0.39

0.35 

0.39 

11.00 11.00 

8.00

2.91 4.55

8.00 

2.91 4.55 4.56

11.00 

4.56 

11.00 

8.00 

3.87 4.84 4.84

11.00 

8.00

4.84 

11.00 

3.87 4.84 

8.00 

3.87 4.84 4.84

11.00 

3.87 4.84 

11.00 

8.00 

4.01 5.01 5.02

11.00 

8.00

4.01 5.01 

11.00 

8.00 

4.01 5.01 5.02

11.00 

8.00

5.02 

11.00 

4.01 5.01 

8.00 

4.01 5.01 5.02

11.00 

4.01 5.01 

11.00 

8.00 

4.01 5.01 5.02

11.00 

8.00

4.01 5.01 

11.00 

8.00 

3.29 5.14 5.14

11.00 

8.00

5.14 

11.00 

3.29 5.14 

8.00 

3.29 5.14 5.14

11.00 

3.29 5.14 

11.00 

7.78 

4.11 5.14 5.14

11.00 

7.41

4.11 5.14 

11.00 

7.41 

4.11 5.14 5.14

11.00 

7.05

5.14 

11.00 

4.11 5.14 

7.05 

4.11 5.14 5.14

11.00 

4.11 5.14 

11.00 

7.59 

4.11 5.14 5.14

11.00 

7.31

4.11 5.14 

11.00 

7.31 

4.11 5.14 5.14

11.00 

7.04

5.14 

11.00 

4.11 5.14 

7.04 

4.11 5.14 5.14

11.00 

4.11 5.14 

11.00 

6.14

5.14 

6.14 

5.48 

3.02 

4.55 

3.19 

2.65 

1.00 

3.22 

1.00 

3.14 

1.00 

2.28 

1.00 

2.72 

1.00 

5.15 

3.83 

Figure 3-104. LDP Assessment Results, 16-Story SMF ELF, BSE-2 CP 

3-99
 
 

0.60 0.49 0.53 2.91 3.64 3.64 

0.10 

0.32 

0.33 

0.49 

0.64 

1.04 

0.56 

0.95 

0.90 

0.99 

0.94 

1.09 

0.91 

0.99 

0.77 

1.31 

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

0.07

0.09 0.15 

0.82 0.53 0.57

0.07 

0.11

0.57 

0.17 

0.82 0.53 

0.11 

1.02 0.64 0.67

0.11 

0.14

0.67 

0.20 

1.02 0.64 

0.11 

1.07 0.67 0.70

0.14 

0.32

1.07 0.67 

0.11 

0.70 

0.21 

0.65 0.52

0.32 

0.58

0.21 

0.11

0.65 0.52 

0.17 

0.58 

0.65 0.53 0.60

0.11 

0.12

0.60 

0.21 

0.65 0.53 

0.17 

0.69 0.55 0.61

0.12 

0.14

0.69 0.55 

0.17 

0.61 

0.22 

0.71 0.56

0.14 

0.61

0.22 

0.26

0.71 0.56 

0.17 

0.61 

0.64 0.51 0.56

0.26 

0.24

0.56 

0.21 

0.64 0.51 

0.17 

0.64 0.51 0.56

0.24 

0.27

0.64 0.51 

0.17 

0.56 

0.20 

0.84 0.52

0.27 

0.56

0.20 

0.30

0.84 0.52 

0.16 

0.56 

0.83 0.51 0.53

0.30 

0.33

0.53 

0.20 

0.83 0.51 

0.15 

0.74 0.46 0.48

0.33 

0.26

0.74 0.46 

0.14 

0.48 

0.17 

0.71 0.44

0.26 

0.46

0.15 

0.28

0.71 0.44 

0.13 

0.46 

0.58 0.43 0.42

0.28 

0.30

0.42 

0.14 

0.58 0.43 

0.09 

0.51 0.38 0.36

0.30 

0.41

0.36 

0.12 

0.51 0.38 

0.07 

0.41 

8.00

11.00 11.00

2.91 4.55 4.56

8.00 

8.00

4.56 

11.00 

2.91 4.55 

11.00 

2.91 4.55 4.56

8.00 

8.00

4.56 

11.00 

2.91 4.55 

11.00 

2.91 4.55 4.56

8.00 

6.02

2.91 4.55 

11.00 

4.56 

11.00 

3.87 4.84

6.02 

4.84

11.00 

8.00

3.87 4.84 

11.00 

4.84 

3.87 4.84 4.84

8.00 

8.00

4.84 

11.00 

3.87 4.84 

11.00 

3.87 4.84 4.84

8.00 

8.00

3.87 4.84 

11.00 

4.84 

11.00 

3.87 4.84

8.00 

4.84

11.00 

7.74

3.87 4.84 

11.00 

4.84 

4.01 5.01 5.02

7.74 

7.96

5.02 

11.00 

4.01 5.01 

11.00 

4.01 5.01 5.02

7.96 

7.47

4.01 5.01 

11.00 

5.02 

11.00 

3.21 5.01

7.47 

5.02

11.00 

7.02

3.21 5.01 

11.00 

5.02 

3.21 5.01 5.02

7.02 

6.58

5.02 

11.00 

3.21 5.01 

11.00 

3.29 5.14 5.14

6.58 

7.52

3.29 5.14 

11.00 

5.14 

11.00 

3.29 5.14

7.52 

5.14

11.00 

7.18

3.29 5.14 

11.00 

5.14 

4.11 5.14 5.14

7.18 

6.88

5.14 

11.00 

4.11 5.14 

11.00 

4.11 5.14 5.14

6.88 

5.94

5.14 

11.00 

4.11 5.14 

11.00 

5.94 

5.48 

3.00 

4.66 

3.45 

1.97 

1.00 

2.62 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

Figure 3-105. LDP Assessment Results, 16-Story SMF RSA, BSE-2 CP 

3-100
 
 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Roof 

0 1000 2000 3000 4000 5000 6000 7000 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

Roof 

Floor 

16 

15 

14 

13 

0 1000 2000 3000 4000 5000 

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

PUF (J = 1) 

P max (NDP) 

P (NSP) 

Pu,Omega (ASCE 7, AISC 341) 

Pu,Capacity Design 

PCL (ASCE 41) 

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 3-106. LDP Assessment Results, Compression in Exterior Columns, 16-Story SMF, BSE-2 

3.2.2.3.3 Nonlinear Static Procedure 

In this section, the following apply: 

	 Table 3-19 through Table 3-21 provide the computed NSP analysis and assessment parameters in 

accordance with ASCE 41 §3.3.3. 

	 Figure 3-107 and Figure 3-108 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., plastic hinges), notated in the figures. The softening 

of the pushover curve evident at about 30 inches of roof displacement for each frame is due to 

column hinges developing at the base of the frames. 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 3-109 and Figure 3-110 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 target displacement governs d for the ELF-designed frame for both BSE-1 

and BSE-2 and the RSA-designed frame for BSE-1, whereas the displacement at the maximum base shear 

governs the RSA-designed frame for BSE-2. 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 show decreased values for Rmax between BSE-1 and BSE-2. 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 of the fundamental modebased lateral force distribution not capturing higher mode effects. Also, the target displacement at the roof 

computed based on fundamental mode properties may underestimate the story demands in the upper stories. 

3-101
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3-19. NSP General Information, 16-Story SMF (kip, inch) 

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

ELF 4.12 64.0 24.6 1571 63.8 4.13 1.21 62.3 1617.0 21782 1.00 1.29 

RSA 4.67 45.5 25.8 1177 45.6 4.66 1.23 41.1 1203.6 21649 1.00 1.36 

Table 3-20. NSP Analysis Parameters, 16-Story SMF BSE-2 CP (kip, inch) 

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

ELF 0.22 3.04 1.00 1.00 47.4 1617.0 47.4 0.03 -0.45 0.00 -0.09 6.58 OK 

RSA 0.20 3.60 1.00 1.00 56.7 1196.3 41.1 0.04 -0.34 -0.02 -0.08 7.09 OK 

 Table 3-21. NSP Analysis Parameters, 16-Story SMF BSE-1 LS (kip, inch) 

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

ELF 0.15 2.03 1.00 1.00 31.6 1581.9 31.6 0.02 -0.25 0.00 -0.05 10.53 OK 

RSA 0.13 2.40 1.00 1.00 37.8 1202.9 37.8 0.05 -0.31 -0.02 -0.07 7.54 OK 

Roof Drift Ratio at CoM (%) 

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.6 2.7 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

0.000 

0.009 

0.018 

0.028 

0.037 

0.046 

0.055 

0.064 

0.073 

0.083 

0.092 

0.101 

(24.6,1571.0) 

(47.4,1617.0) 

(71.0,942.6) D 

Pt. A: Ext. hinges (2) reach CP on both

 6th and 7th Floor 

Pt. B: Ext. hinges (2) reach CP on 5th Floor 

Pt. C: Ext. hinges (2) reach CP on 8th Floor 

Pt. D: Remaining hinges reach CP on both

 6th and 7th Floor 

Total Base Shear / 

W

Total Base Shear (Kips) 

 ELF (First-Order)

 ELF (Second-Order)

 ELF Idealized Backbone 

A 

B 

C 

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 

Roof Displacement at CoM (Inches)

Figure 3-107. 16-Story SMF ELF Pushover, BSE-2 

3-102
 
 

 

 

 

 

 

 

Roof Drift Ratio at CoM (%) 

0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.6 2.7 

2200 0.102 

Total Base Shear (Kips) 

Total Base Shear / W 

2000 

1600 

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 

(25.8,1177.0) 

(41.1,1203.6) 

(73.5,706.2) 

C 

Pt. A: Ext. hinges (2) reach CP on 7th Floor 

Pt. B: Ext. hinges (2) reach CP on both 

8th and 9th Floor 

Pt. C: Ext. hinges (2) reach CP on 10th Floor 

Pt. D: Remaining hinges reach CP on both 

8th and 9th Floor 

 RSA (First-Order)

 RSA (Second-Order)

 RSA Idealized Backbone 

A 

B 

D 

0.074 

1400 0.065 

0.092 

1800 0.083 

1200 0.055 

1000 0.046 

800 0.037 

600 0.028 

400 0.018 

200 0.009 

0 0.000 

Roof Displacement at CoM (Inches)

Figure 3-108. 16-Story SMF 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 3-109. 16-Story SMF ELF Pushover – Story Drift Ratios – BSE-2 

3-103
 
 

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 3-110. 16-Story SMF RSA Pushover – Story Drift Ratios – BSE-2 

Of particular interest in the pushover curves is the large disparity between the peak base shears developed 

in the ELF- and RSA-designed buildings (RSA / ELF = 1204 / 1617 = 0.74), a 26 percent change. At first 

glance, this is greater than the 15 percent difference in design base shears allowed by ASCE 7. Upon further 

inspection, it can be reasoned that the primary contribution to this disparity is due to the increase in strength 

provided to the ELF-designed frame to satisfy drift provisions in ASCE 7 (i.e., 15 percent plus additional 

strength). See NSP discussion in the 8-story results for more information. 

Figure 3-111 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. As shown in the figure, the force-controlled columns do not align between the two frames— 

the axial load ratios for the exterior base columns are 0.39 and 0.59 for the ELF- and RSA-designed frames, 

respectively. This illustrates the sensitivity of results due to variations between the non-adaptive loading 

profile in the NSP and that used for design. Figure 3-112 through Figure 3-115 illustrate the DCRN values 

if greater than unity for the ELF- and RSA-designed frames at the target displacement for the LS BPL at 

the BSE-1 EHL and CP BPL at the BSE-2 EHL. These figures illustrate the demands when the system is 

loaded to the right. All component actions for the beam-to-column connections, columns (assuming 

deformation-controlled), and panel zones satisfy the LS and CP BPL acceptance criteria at the target 

displacements for both designs. 

Several exterior columns, including those at the base of the frame for the RSA-designed frame, are forcecontrolled for flexure at the target displacement. Force-controlled base columns are problematic for a region 

that is expected to experience inelastic strain demands. Therefore, the acceptance criterion for these flexural 

actions is based on the force-controlled lower-bound elastic P-M interaction (ASCE 41 Equation 5-12). As 

discussed previously, variations in P-M interaction curves add complexity to nonlinear flexural hinge 

3-104
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

model. Essentially, a nonlinear hinge based on the expected yield surface of the section must be 

accompanied by another model that can measure the lower-bound strength of the member (one for each 

axis of buckling). For simplicity, failing of the acceptance criteria (without computing interaction values) 

is self-evident because of the development of plastic hinges in the frame columns. Because plastic hinges 

have developed in the base columns in the ELF-design frame, flexural actions therefore do not satisfy the 

intended elastic acceptance criteria. Conversely, the force-controlled columns in the RSA frame satisfy the 

intended elastic acceptance criteria; however, member stability would still need to be verified. 

B C D E Sym. Abou t 

ELF NDP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

RS A NDP LS & CP 

RS A NS P C P 

ELF NDP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

ELF NSP LS & CP 

RS A NS P LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

ELF NDP LS & CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

RS A NDP CP 

RS A NDP LS & CP 

RS A NS P LS & CP 

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 Flo or
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

All colum ns are deformation- Column is force-controlled for flexure if 

controlled (DC) for flexur e unless P > 0.5×PCL, where P is computed at the 

indicated as force-controlled (FC) target displacement for the NS P and as 

in figure the maximum value for the NDP 

Figure 3-111. Schematic of Flexural Actions in Columns, 16-Story SMF (NSP and NDP) 

3-105
 
 

 

 

 

 

 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

Roof
 

(ELEV = 228 ft.)
 

16th Flo or
 

(ELEV = 214 ft.)
 

15th Flo or
 

(ELEV = 200 ft.)
 

14th Flo or
 

(ELEV = 186 ft.)
 

13th Flo or
 

(ELEV = 172 ft.)
 

12th Flo or
 

(ELEV = 158 ft.)
 

11th Flo or
 

(ELEV = 144 ft.)
 

10th Flo or
 

(ELEV = 130 ft.)
 

9th Flo or
 

(ELEV = 116 ft.)
 

8th Flo or
 

(ELEV = 102 ft.)
 

7th Flo or
 

(ELEV = 88 ft.)
 

6th Flo or
 

(ELEV = 74 ft.)
 

5th Flo or
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Figure 3-112. NSP Assessment Results, 16-Story SMF ELF, BSE-1 LS (+push to right) 

3-106
 
 

 

 

 

 

 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

Roof
 

(ELEV = 228 ft.)
 

16th Flo or
 

(ELEV = 214 ft.)
 

15th Flo or
 

(ELEV = 200 ft.)
 

14th Flo or
 

(ELEV = 186 ft.)
 

13th Flo or
 

(ELEV = 172 ft.)
 

12th Flo or
 

(ELEV = 158 ft.)
 

11th Flo or
 

(ELEV = 144 ft.)
 

10th Flo or
 

(ELEV = 130 ft.)
 

9th Flo or
 

(ELEV = 116 ft.)
 

8th Flo or
 

(ELEV = 102 ft.)
 

7th Flo or
 

(ELEV = 88 ft.)
 

6th Flo or
 

(ELEV = 74 ft.)
 

5th Flo or
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Figure 3-113. NSP Assessment Results, 16-Story SMF RSA, BSE-1 LS (+push to right) 

3-107
 
 

 

 

 

 

 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

Roof
 

(ELEV = 228 ft.)
 

16th Flo or
 

(ELEV = 214 ft.)
 

15th Flo or
 

(ELEV = 200 ft.)
 

14th Flo or
 

(ELEV = 186 ft.)
 

13th Flo or
 

(ELEV = 172 ft.)
 

12th Flo or
 

(ELEV = 158 ft.)
 

11th Flo or
 

(ELEV = 144 ft.)
 

10th Flo or
 

(ELEV = 130 ft.)
 

9th Flo or
 

(ELEV = 116 ft.)
 

8th Flo or
 

(ELEV = 102 ft.)
 

7th Flo or
 

(ELEV = 88 ft.)
 

6th Flo or
 

(ELEV = 74 ft.)
 

5th Flo or
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Figure 3-114. NSP Assessment Results, 16-Story SMF ELF, BSE-2 CP (+push to right) 

3-108
 
 

 

 

 

 

 

 

DCRN ≥ 1.0 

0.9 ≤ DCRN < 1.0 

0.8 ≤ DCRN < 0.9 

0.7 ≤ DCRN < 0.8 

DCRN < 0.7 

B C D E 

Roof
 

(ELEV = 228 ft.)
 

16th Flo or
 

(ELEV = 214 ft.)
 

15th Flo or
 

(ELEV = 200 ft.)
 

14th Flo or
 

(ELEV = 186 ft.)
 

13th Flo or
 

(ELEV = 172 ft.)
 

12th Flo or
 

(ELEV = 158 ft.)
 

11th Flo or
 

(ELEV = 144 ft.)
 

10th Flo or
 

(ELEV = 130 ft.)
 

9th Flo or
 

(ELEV = 116 ft.)
 

8th Flo or
 

(ELEV = 102 ft.)
 

7th Flo or
 

(ELEV = 88 ft.)
 

6th Flo or
 

(ELEV = 74 ft.)
 

5th Flo or
 

(ELEV = 60 ft.)
 

4th Flo or
 

(ELEV = 46 ft.)
 

3rd Floor
 

(ELEV = 32 ft.)
 

2nd Floor
 

(ELEV = 18 ft.)
 

Figure 3-115. NSP Assessment Results, 16-Story SMF RSA, BSE-2 CP (+push to right) 

3-109
 
3.2.2.3.4 Nonlinear Dynamic Procedure 

The earthquake record set used to assess the E-W direction of MC16 is shown in Appendix A. For the ELF 

design, the analysis successfully completed for all 14 records at the BSE-1 and BSE-2 EHL. For the RSA 

design, the analysis successfully completed for all 14 records for the BSE-1 EHL; however, four analyses 

did not complete at the BSE-2 EHL because of excessive lateral drift or solution non-convergence. 

Maximum axial compression force in the exterior column lines from the record set are shown previously in 

the linear assessment sections. 

Figure 3-116 through Figure 3-119 show the performance of the beam hinges (i.e., beam-to-column 

connections) 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 right) are included in the figures. 

Comparison discussions between the various procedures are addressed subsequently. As is evident from 

the figures, the ELF–designed frame performs better than the RSA-designed frame; however, recall that the 

ELF procedure is not permitted in this case. Results of the RSA-designed frame indicate that the beam-tocolumn connections have difficulty satisfying the CP BPL acceptance criteria at the BSE-2 EHL (based on 

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. 

The average ratio of secondary to primary component acceptance criteria for an RBS beam-to-column 

connection for all W18 sections and deeper is 1.49 for the CP SPL (1.47 for the LS SPL). The figures for 

the RSA-designed frame illustrate that this value is exceeded in the beam-to-column connections at the 

BSE-2 EHL. This highlights the rapid progression towards a collapse state when several components are 

strained past the deformation associated with their peak strength—see §3.1.4.2. 

Roof
 

16
 1-Median

15 1-Mean

 1-84th 14 

 1-Mean+1std 13 2-Median

12 2-Mean

11 2-84th

Floor ID 

10 2-Mean+1std

9 1-NSP

8 2-NSP

6 

7 LSP (max)

 LDP (max) 

4 

5 1 = Left Hinge 

2 = Right Hinge 

3 

Base 

2 Bay B-C Bay C-D Bay D-E

0.0	 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-116. NDP Assessment Results, Beam Hinges, 16-Story SMF ELF, BSE-1 LS 

3-110
 
11 

12 

13 

14 

15 

16 

Roof 

1 = Left Hinge 

2 = Right Hinge 

 1-Median

 1-Mean

Floor ID Floor ID 

10 1-84th

9 1-Mean+1std

8 2-Median

7 2-Mean

 2-84th 6 

 2-Mean+1std 5 1-NSP

4 2-NSP

3 LSP (max)

2 LDP (max) Bay B-C Bay C-D Bay D-E

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 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 

DCRN = Total Deformation / Total LS Acceptance Criteria 

Figure 3-117. NDP Assessment Results, Beam Hinges, 16-Story SMF RSA, BSE-1 LS 

Roof 1-Median

16 1-Mean

15 1-84th

14 1-Mean+1std

13 2-Median

11 

12 2-Mean

 2-84th

 2-Mean+1std

10 1-NSP

9 2-NSP

8 LSP (max)

7 LDP (max) 

4 

5 

6 1 = Left Hinge 

2 = Right Hinge 

3 

Base 

2 Bay B-C Bay C-D Bay D-E

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 = Total Deformation / Total CP Acceptance Criteria 

Figure 3-118. NDP Assessment Results, Beam Hinges, 16-Story SMF ELF, BSE-2 CP 

3-111 
Roof 

16 

15 

14 

13 

12 

11 

10 

 1-Median

 1-Mean

 1-84th

 1-Mean+1std

 2-Median

 2-Mean

 2-84th

 2-Mean+1std

Floor ID 

7 

8 

9 1-NSP

 2-NSP

 LSP (max)

 LDP (max) 

6 

4 

5 1 = Left Hinge 

2 = Right Hinge 

3 

Base 

2 Bay B-C Bay C-D Bay D-E

012 34 56 7 0 123 4 567 01 23 4 5 67 

DCRN = Total Deformation / Total CP Acceptance Criteria 

Figure 3-119. NDP Assessment Results, Beam Hinges, 16-Story SMF RSA, BSE-2 CP 

The previous figures illustrate for the RSA-designed frame that the component strengths provided by drift 

and stability control measures in ASCE 7 at 2⁄3×MCER (equal to the BSE-1 here) are not significant enough 

to overcome the demands to satisfy the assessment criteria at the BSE-2 (taken here as MCER). First, strong 

panel zones reduce the allowable deformations in the acceptance criteria and component model for the 

exterior beam-to-column connections. Second, base hinge modeling could have a drastic effect on the 

performance of the beam-to-column connections. This further highlights the change in story demands as 

column base hinges develop, an influence not addressed in elastic design analysis. In contrast, the results 

indicate that the ELF-designed frame satisfies the criteria by a considerable margin. 

Figure 3-111 (see NSP section) illustrates which flexural actions in the frame columns are force-controlled 

for both the NSP and NDP. Figure 3-120 and Figure 3-121 show the performance of the column hinges for 

the CP BPL criteria at the BSE-2 EHL assuming deformation-controlled flexural actions (LS BPL for the 

BSE-1 is not shown unless assessment at BSE-2 illustrates performance concerns). Column hinges at the 

base experience inelastic strain demands (yield corresponds to a DCRN ≈ 0.15 in the figures). Mean response 

results also indicate column hinges develop up the height of the frame. However, this phenomenon is more 

likely associated to the number of collapses rather than a trigger mechanism initiating a structural collapse; 

median results may be a more stable metric in this case. Similarly, the exterior base columns in the RSA 

frame are force-controlled for flexure. 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 columns are force-controlled for flexure in the linear 

assessment procedures. Though there is a fundamental difference in how the DCRN is computed for the 

linear and nonlinear procedures, the linear assessment results show similar distributions of demands and 

location of potential performance concerns. 

3-112
15 

16 

Roof 

11 

12 

13 

14 

Col. Line B Col. Line C 

DCRN for the LSP and 

LDP are based on 

interaction equations. 

Col. Line D 

See LSP and LDP 

for force-controlled 

columns. 

Col. Line E

Median

Mean

84th

Mean+1std

 NSP

LSP

Floor ID 

10 LDP 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4	 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 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 = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-120. NDP Assessment Results, Column Hinges, 16-Story SMF ELF, BSE-2 CP 

 

16 

Roof Col. Line B Col. Line C Col. Line D Col. Line E

15 DCRN for the LSP and See LSP and LDP 

14 LDP are based on for force-controlled 

12 

13 interaction equations. columns. 

11 Median

Floor ID 

Mean

84th

10 

9 

Mean+1std 8 

 NSP

7 LSP

6 LDP 

5
 

4
 

3
 

2
 

Base 

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-121. NDP Assessment Results, Column Hinges, 16-Story SMF RSA, BSE-2 CP 

 

Figure 3-122 and Figure 3-123 show the curvature ductility demand of the column hinges (i.e., section 

strength) at the BSE-2 EHL. Figure 3-124 and Figure 3-125 show the elastic member strength interaction 

results at the BSE-2 EHL. The results indicate that the columns above the base in the ELF-designed frame 

satisfy the intended lower-bound acceptance criteria whereas the columns in the RSA-designed frame 

consistently do not satisfy these acceptance criteria—a result of the number of analyses that did not 

complete. 

3-113
Roof 

Col. Line B Col. Line C Col. Line D Col. Line E 16
 

15
 

14
 

Median 13 See LSP and LDP See NSP for Mean 12 for force-controlled force-controlled 84th

11 columns. Mean+1std columns. 

Floor ID 

10 NSP

9 LSP

8
 LDP
 

7
 

6
 

5
 

4
 

3
 

2
 

Base 

0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 
 

DCRN = Total Deformation / Total YD Acceptance Criteria
 

Figure 3-122. NDP Assessment Results, Column Hinges, 16-Story SMF ELF, BSE-2 Yield 

 

See LSP and LDP for force-controlled columns. See NSP for force-controlled columns. 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E 16
 

15
 

14
 

13
 

12
 

11
 

Floor ID 

10 

9 

8 

6 

7 Median

Mean

84th

5 Mean+1std

4 NSP

3 LSP

2 LDP 

Base 

0 1 2 3 4 5 6 7 01 23 4 5 6 7 01 2 3 4 5 6 7 0 1 2 3 4 56 7 

Total Deformation / Total YD Acceptance Criteria 

Figure 3-123. NDP Assessment Results, Column Hinges, 16-Story SMF RSA, BSE-2 Yield 

3-114 
11 

12 

13 

14 

15 

16 

Roof Col. Line B Col. Line C Col. Line D 

See LSP and LDP 

for force-controlled 

columns. 

See NSP for 

Col. Line E

Floor ID Floor ID 

force-controlled 10
 

9
 columns.
 

8
 Median 7 Mean

6 84th

5 Mean+1std

4 LSP

3
 LDP 

2 

Base 

0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 

DCRN = P-M Interation Result 

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

Figure 3-124. NDP Assessment Results, Column Members, 16-Story SMF ELF, BSE-2 CP 

Roof Col. Line B Col. Line C Col. Line D Col. Line E 16
 

15
 See LSP and LDP 

14 for force-controlled 

13 columns. 

12
 

11
 See NSP for 

10 force-controlled 

9 columns. 

8 

Median 7 

Mean 6 84th

5 Mean+1std

4 LSP

3 LDP 

2 

Base 

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 

DCRN = P-M Interation Result 

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

Figure 3-125. NDP Assessment Results, Column Members, 16-Story SMF RSA, BSE-2 CP 

Figure 3-126 and Figure 3-127 show the performance of the panel zones for the CP BPL criteria at the BSE2 (LS BPL for the BSE-1 is not shown). The deformation demands are significantly lower than the CP 

acceptance criteria. Converting the results to total deformation / yield deformation indicates that the 

demands for the BSE-2 are consistently less than 4×y. These results illustrate that the panel zones are 

stronger than required by the assessment criteria—see discussion in the 4-story NDP section. 

3-115 
11 

12 

13 

14 

15 

16 

Roof Col. Line B Col. Line C Col. Line D Col. Line E

Median

Mean

84th

Floor ID Floor ID 

10 Mean+1std

9 NSP

8
 LSP

7
 LDP 

6 

5 

4 

3 

2 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-126. NDP Assessment Results, Panel Zones, 16-Story SMF ELF, BSE-2 CP 

Roof 

Col. Line B Col. Line C Col. Line D Col. Line E 16
 

15
 

14
 

13
 Median

12 Mean

11 84th

Mean+1std

9 

10 

 NSP

LSP 8 

LDP 7
 

6
 

5
 

4
 

3
 

2
 

Base 

0.0	 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
 

DCRN = Total Deformation / Total CP Acceptance Criteria
 

Figure 3-127. NDP Assessment Results, Panel Zones, 16-Story SMF RSA, BSE-2 CP 

 

3-116
 

Seismic Assessment Discussion 

The discussion in this section focuses on the following component design actions: 

 Beam-to-column connection flexure (e.g., RBS) 

 Panel zone shear 

 Beam and column flexure within anticipated plastic hinge zones (section strength)23 

 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 §5.4.2.5). 

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. 

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. 

As noted previously, the LSP cannot be used to assess the E-W component of MC16. This assessment is 

included for comparison purposes and the results are shown as shaded in the tables in this section. 

3.2.3.1.1 Beam-to-Column Connections 

Table 3-22 provides a summary of the performance of the FR beam-to-column connections (RBS) 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. The results indicate that the RSAdesigned frame has difficulty satisfying the acceptance criteria when using the LSP for both the LS and CP 

BPL whereas only the 4-story ELF-designed frame fails the CP BPL. In contrast, the performance of both 

23 Beam hinges within the RBS are included in assessment of Type FR connection (controlling mechanism). 

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frames improves when using the LDP, although the 4- and 16-story RSA-designed frames fail the CP BPL 

acceptance criteria by a slight margin. 

Table 3-22. Performance Summary of FR Connections (BC) per Frame, Linear Procedures 

Archetype Design LSP

LS CP LS 

LDP 

CP 

4-Story 

ELF 

RSA 

All BC Pass 

Ext. BC Fail (4) 

Int. BC Pass 

17% 

Ext. BC Fail (2) 

Int. BC Fail (2) 

17% 

Ext. BC Fail (4) 

Int. BC Fail (2) 

25% 

All BC Pass 

All BC Pass 

All BC Pass 

Ext. BC Fail (2) 

Int. BC Pass 

8% 

ELF All BC Pass All BC Pass All BC Pass All BC Pass 

8-Story 

RSA 

Ext. BC Fail (8) 

Int. BC Pass 

17% 

Ext. BC Fail (14) 

Int. BC Fail (14) 

58% 

All BC Pass All BC Pass 

ELF All BC Pass All BC Pass All BC Pass All BC Pass 

16-Story 

RSA 

Ext. BC Fail (2) 

Int. BC Pass 

Ext. BC Fail (10) 

Int. BC Pass All BC Pass 

Ext. BC Fail (4) 

Int. BC Pass 

2% 10% 4% 

Performance failures are generally increased by reduced acceptance criteria (i.e., m-factors) attributed to 

panel zones strength, connection detailing, and span-to-depth ratio, Lc / db. Section compactness 

requirements in ASCE 41 match that required for design of highly ductile elements in AISC 341—except 

ASCE 41 uses expected in lieu of nominal material properties. As such, section compactness generally will 

not trigger a reduction in new building designs. However, continuity plates in one-sided connections 

designed in accordance with AISC 341 and AISC 360 can trigger a reduction if tcf < bbf / 7 with tcp ≥ tbf / 2, 

but also tcp < tbf. Further, AISC 358 requires that Lc / db ≥ 7 for an RBS beam-to-column connection in an 

SMF, but ASCE 41 requires a reduction in acceptance criteria when Lc / db > 10. Additionally, increasing 

column sizes to offset the need for doubler plates can be problematic with regards to connection 

performance (assuming adjacent beams are not similarly increased). Nonetheless, it is debatable if reduction 

factors based on (cumulative) step functions are appropriate for components expected to experience 

inelastic straining. Further research is needed to justify the fixed reductions to acceptance criteria for beamto-column connections. The commentary for ASCE 41 should reference FEMA 355D (FEMA 2000c) in 

lieu of FEMA 355F (FEMA 2000d) for connection detailing recommendations. 

The results for the 16-story archetype buildings indicate that drift and strength control (via stability 

verification) in ASCE 7 provides a significant amount of member overstrength so that beam-to-column 

connections more easily satisfy the acceptance criteria (compared to the 8-story which was primarily drift 

controlled). 

The easiest retrofit option for these frames is to increase the flexural strength (and hinge strength in the 

beam) of the distressed connections so to offset any reductions due to panel zone strength and continuity 

plates (see Rehabilitation Strategies in ASCE 41 §2.5). However, this may adversely affect the performance 

of other components of the frame (e.g., columns). In terms of ASCE 41 assessment performance, using 

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doubler plates in lieu of upsizing the columns and keeping the beam span-to-depth ratio less than 10 (but 

greater than 7 if using linear procedures or 8 if using nonlinear procedures) may be more effective. 

Additional cost-benefit analyses are needed to validate the seismic performance of an SMF with these 

constraints (assuming performance metrics and analysis are reflective of realistic conditions). 

3.2.3.1.2 Panel Zones 

Table 3-23 provides a summary of the performance of the panel zones for each linear assessment procedure 

and each BPL. The results indicate that the panel zones consistently satisfy the performance criteria for the 

LS and CP BPL for both procedures. The DCRN values all remained low, 0.1–0.3, indicating that panel 

zone design based on the probable connection strength, Mpr, as well as conventional practice (e.g., increase 

column sizes to offset the need for doubler plates) may tend toward producing strong panel zones under 

ASCE 41. As noted above, this can adversely affect the beam-to-column connection acceptance criteria. 

Table 3-23. Performance Summary of Panel Zones (PZ) per Frame, Linear Procedures 

Archetype Design LS

LSP

 CP LS 

LDP 

CP 

4-Story ELF 

RSA 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

8-Story ELF 

RSA 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

16-Story ELF 

RSA 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

All PZ Pass 

Take for example a one-sided connection where a W24×76 beam frames to a W18×106 column. The ratio 

of shear in the panel zone at the probable flexural strength of the connection to shear yielding of the panel 

zone is conservatively 0.98 (see Equation (3-18)) and increase to 1.07 when using 0.55Fy for Vy. This 

indicates that the panel zone may not yield until the connection approaches its peak strength, generally 

associated with CP. Research (FEMA 350 (FEMA 2000a)) has suggested that a balanced yield condition 

between beam hinge and adjacent panel zone can increase the inelastic deformation capacity of a 

connection. This condition has been adopted in ASCE 41. Current steel design practice in accordance with 

AISC 341 does not impose a balanced yield condition. 

 CZ 1.1F   pr x y  

V  0.95db  (3-18) pr   594    0.98

V 0.6 1.1  F dt  605 y y c wc 

3.2.3.1.3 Member Cross-section Strength (flexural hinge) and Global Strength (member stability) 

Table 3-24 provides a summary of the performance of the column members for each linear assessment 

procedure and each BPL. Hinges in beam members that are part of the beam-to-column connection are 

discussed above and not addressed in this section. 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 

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option for a column can be challenging because understanding and isolating the failure mechanism of the 

column can be difficult. 

Table 3-24. Performance Summary of Column Members (CM) per Frame, Linear Procedures 

Archetype Design LSP

LS CP LS 

LDP 

CP 

ELF All CM Pass All CM Pass All CM Pass All CM Pass 

4-Story 

RSA All CM Pass All CM Pass All CM Pass All CM Pass 

ELF 

Ext. CM Fail (2) 

Int. CM Pass 

Ext. CM Fail (4) 

Int. CM Pass 

Ext. CM Fail (2) 

Int. CM Pass 

Ext. CM Fail (2) 

Int. CM Pass 

8-Story 

RSA 

6% 

Ext. CM Fail (8) 

Int. CM Pass 

13% 

Ext. CM Fail (8) 

Int. CM Pass 

6% 

Ext. CM Fail (2) 

Int. CM Pass 

6% 

Ext. CM Fail (8) 

Int. CM Pass 

25% 25% 6% 25% 

ELF All CM Pass 

Ext. CM Fail (12) 

Int. CM Pass All CM Pass All CM Pass 

16-Story 

RSA 

Ext. CM Fail (4) 

Int. CM Pass 

19% 

Ext. CM Fail (20) 

Int. CM Pass All CM Pass 

Ext. CM Fail (6) 

Int. CM Pass 

6% 31% 9% 

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. 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). There 

are columns where the force-controlled requirement does not result in a performance failure (e.g., some 16­

story SMF columns). 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 3-71). Exterior base columns in these frames consistently fail the acceptance 

criteria. This result is problematic because flexure hinges are expected to develop at the base of these 

columns. ASCE 41 does not provide guidance on how to assess column-to-base connections similar to 

beam-to-column connections. 

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 

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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. 

3.2.3.1.4 Summary 

Table 3-25 summarizes the performance of the archetype buildings in reference to the BSO for both linear 

procedures. Table 3-26 provides the base shears computed with the linear assessment procedures. Column 

performance (primarily at the base) from both assessment procedures controls the overall assessment of the 

SMF frames. Base column failure in this analytical context is more detrimental to the overall structural 

performance than beam-to-column connection performance. As noted above, additional research is needed 

concerning assessment criteria for beam-to-column connections and columns. The qualitative ratings are 

assigned primarily based on the performance of the column members and a few cases coupled with the 

performance of the beam-to-column connections. In the end, the 4- and 16-story ELF-designed frames 

satisfy the seismic performance objective only using the LDP (recall from Chapter 2 that the ELF procedure 

is not permitted for design of the 16-story SMF). 

Table 3-25. BSO Performance Summary of Archetype Buildings, Linear Procedures 

LSP Archetype Design BC CM PZ 

ELF Fail Pass Pass 4-Story RSA Fail Pass Pass 

ELF Pass Fail Pass 8-Story RSA Fail Fail Pass 

ELF Pass Fail 16-Story RSA Fail Fail 

Pass 

Pass 

Design BC 

LDP 

CM PZ 

ELF Pass Pass Pass 

RSA Fail Pass Pass 

ELF Pass Fail Pass 

RSA Pass Fail Pass 

ELF Pass Pass Pass 

RSA Fail Fail Pass 

The assessment results from the LSP and LDP illustrate that, on average, the ELF-designed SMF performs 

better than the RSA-designed SMF for all archetype buildings. This can be attributed to the increased 

strength and stiffness provided to the ELF-designed frames (see Table 2-4) by differences in the ELF and 

RSA procedures, including associated scaling provisions, in ASCE 7. 

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 

3-121
 
 

 

 

 

 

 

 

 

of column forces in the taller frames. This can be problematic for beam-columns due to the lower-bound 

estimate of compressive strength, PCL. 

Table 3-26. Summary of Base Shears, Linear Procedures (kips) 

4-Story 8-Story 16-Story 

EHL Routine ELF RSA ELF RSA ELF RSA 

LSP 1696 1380 2176 1646 2977 2574 

BSE-1 LDP 1585 1334 1974 1545 2710 2382 

Ratio 0.93 0.97 0.91 0.94 0.91 0.93 

LSP 2545 2070 3264 2470 4466 3862 

BSE-2 LDP 2377 2000 2996 2318 4065 3573 

Ratio 0.93 0.97 0.92 0.94 0.91 0.93 

Analytical results based on component-level performances obtained from the LSP and LDP suggest that 

special moment frames designed in accordance with ASCE 7 and its referenced standards have difficulty 

achieving the selected seismic performance objective of an existing building intended to be equivalent to a 

new building. This notion is driven by the performance of the columns and beam-to-column connections. 

The results for the columns can be enhanced by more mechanistically consistent column provisions and 

analytical modeling parameters. Although the acceptance criteria for a connection are derived from a highly 

vetted testing program, enhancement to the transference of nonlinear test results to linear acceptance criteria 

and the supplementary (cumulative) adjustment factors could be investigated. 

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 Beam-to-Column Connections 

Table 3-27 provides a summary of the performance of the FR beam-to-column connections (RBS) 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. Similar to the results from the linear 

procedures, the RSA-designed frames have difficulty satisfying the acceptance criteria when using the NDP 

for both the LS and CP BPL. Although the median response is biased less by a collapsed state of a given 

frame than the mean response, the results are not significantly improved, except for the 16-story SMF. The 

NDP consistently indicates poorer performance of the connections than that given by the NSP alone. The 

ELF-designed frames consistently satisfy the performance criteria for both the LS and CP BPL for both 

procedures, except for the 8-story frame under the BSE-2 EHL using the NDP, which has a special situation 

described subsequently. 

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The notable performance concerns of the beam-to-column connections is due to the cumulative penalty 

associated with strong panel zones and connection detailing per AISC 341 (i.e., continuity plate thickness 

in one-sided connections)—see LSP and LDP assessment results discussions. Further, the span-to-depth 

ratio requirements change between linear and nonlinear procedures. In many cases, the span-to-depth ratio 

triggered a reduction to the linear criteria but not similarly to the nonlinear criteria. Moreover, base hinges 

in the exterior columns in the 8-story frames directly influenced the rapid progression toward a collapsed 

state and, in turn, the poor performance of the beam-to-column connections. 

Table 3-27. Performance Summary of FR Connections (BC) per Frame, Nonlinear Procedures 

Archetype Design 

LS

NSP 

CP 

NDP 

(based on mean response of record set) 

LS CP 

ELF All BC Pass All BC Pass All Pass All Pass 

4-Story 

RSA All BC Pass 

Ext. BC Fail (2) 

Int. BC Pass 

8% 

Ext. BC Fail (2) 

Int. BC Pass 

8% 

Ext. BC Fail (8) 

Int. BC Fail (16) 

100% 

8-Story 

ELF 

RSA 

All BC Pass 

All BC Pass 

All BC Pass 

All BC Pass 

All BC Pass 

Ext. BC Fail (8) 

Int BC Fail (16) 

50% 

Ext. BC Fail (6) 

Int BC Fail (12) 

38% 

Ext. BC Fail (10) 

Int BC Fail (20) 

63% 

ELF All BC Pass All BC Pass All BC Pass All BC Pass 

16-Story 

RSA All BC Pass All BC Pass All BC Pass 

Ext. BC Fail (30) 

Int. BC Fail (56) 

90% 

3.2.3.2.2 Panel Zones 

Table 3-28 summarizes the performance of the panel zones for each nonlinear assessment procedure for the 

CP BPL. Similar to the results from the linear procedures, panel zones consistently satisfy the performance 

criteria for the LS and CP BPL for both procedures. 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. The DCRN values all remained 

small compared to unity (see LSP and LDP assessment results discussions). The panel zones consistently 

do not achieve four times the yield shear strain at BSE-2 EHL—the deformation associated with the panel 

zone strength given in AISC 360 §J. This strain level is associated with panel zone design given in AISC 

360 §J at 2/3×MCER (taken here to be BSE-1 EHL) using Mpr. The third floor of the 8-story RSA-designed 

SMF is the only frame that shows a potential issue with panel zones. As discussed previously, this is a 

corollary of beam-to-column connection performance and base column hinging and not a panel zone 

performance concern. It is not yet fully understood whether good performance of panel zones is strictly due 

to increased strengths resulting from drift criteria, conservative design approaches (for the panel zones), or 

industry practice of increasing column size. 

3-123
 
 

 

 

Table 3-28. Performance Summary of Panel Zones (PZ) per Frame, Nonlinear Procedures 

Archetype Design 

LS

NSP 

CP 

NDP 

(based on mean response of record set) 

LS CP 

ELF --­ All PZ Pass --­ All PZ Pass 

4-Story 

RSA --­ All PZ Pass --­ All PZ Pass 

ELF --­ All PZ Pass --­ All PZ Pass 

8-Story 

RSA --­ All PZ Pass ---

Ext. PZ Pass 

Int. PZ Fail (2) 

6% 

ELF --­ All PZ Pass --­ All PZ Pass 

16-Story 

RSA --­ All PZ Pass --­ All PZ Pass 

3.2.3.2.3 Member Cross-section Strength (flexural hinge) and Global Strength (member stability) 

Table 3-29 provides a summary of the performance of the column hinges for each nonlinear assessment 

procedure for the CP BPL Hinges in beam members that are part of the beam-to-column connection are 

discussed above and not addressed in this section. 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 addition to assessment results, the 

strong-column weak-beam (SCWB) philosophy prescribed in AISC 341 was verified to confirm locations 

of expected hinges at the BSE-2 EHL (CP BPL). 

Base column hinges at the exterior of the 8-story frames consistently fail the performance criteria. These 

failures are a corollary of the modeling parameters for P-M hinges in ASCE 41 (see linear discussion). 

These columns are force-controlled for flexure in the 8-story ELF-designed frame and the 16-Story RSAdesigned frame (shaded in the table) 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, which is the case in the exterior base 

columns in the 8-story frames (see calculations below). These column base hinges reach the CP deformation 

limit prior to the adjacent beam-to-column connections. The maximum axial force from the NDP in this 

column (and hinge component) is 992 kips, which provides an axial load ratio, P / PCL, of 0.6 (which would 

3-124
 
 

 

 

require force-controlled action). The axial load ratio based on the section axial strength using expected 

material properties, P / Pye, is 0.35 (which would require deformation-controlled action). 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. Further, it is theoretically inconsistent to model the component strengths within the same 

column as a function of both Pye and PCL. As is evident in the 8-story frame response, base column failures 

can initiate a rapid progression towards a collapsed state, analytically speaking. 

W18×175 (8-Story ELF-designed SMF Exterior Base Column):
 

Pgravity = Dead + Superimposed Dead + 0.25×Unreduced Live Floor = 457 kips 

PCL = Pn,y = 1639 kips (1724 kips using Fye) 

Pye = 2822 kips 

Pgravity / PCL = 0.28 > 0.2 (Pgravity / PCLe = 0.27) 

Pgravity / Pye = 0.16 

Table 3-29. Performance Summary of Column Hinges (CH) per Frame, Nonlinear Procedures 

Archetype Design 

LS

NSP 

CP 

NDP 

(based on mean response of record set) 

LS CP 

ELF --­ All CH Pass 

SCWB ok --­ All CH Pass SCWB ok 

4-Story 

RSA --­ All CH Pass 

SCWB ok --­ All CH Pass SCWB ok 

8-Story 

ELF

RSA 

--­

---

Ext. CH Fail (2) 

Int. CH Pass 

3% 

SCWB ok 

Ext. CH Fail (2) 

Int. CH Pass 

3% 

SCWB ok 

---

Ext. CH Fail (4) 

Int. CH Pass 

6% 

SCWB Not ok 

---

Ext. CH Fail (4) 

Int. CH Pass 

6% 

SCWB Not ok 

ELF --­ All CH Pass 

SCWB ok --­ All CH Pass SCWB ok 

16-Story 

RSA --­ All CH Pass 

SCWB ok ---

Ext. CH Fail (22) 

Int. CH Fail (12) 

27% 

SCWB ok 

Table 3-30 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 

3-125
 
 

 

 

(i.e., hinge uses Pye and member uses PCL). Except for the 8-story ELF- and RSA–designed frames, which 

indicate column hinges form in the upper stories using the NDP, analytical results of the member stability 

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 deep wide-flanged steel beam-columns has illustrated that the weakaxis buckling strength of a wide-flange is not affected by plastic hinges from in-plane flexure. 

Table 3-30. Performance Summary of Column Members (CM) per Frame, Nonlinear Procedures 

Archetype Design 

LS

NSP 

CP 

NDP 

(based on mean response of record set) 

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 

3.2.3.2.4 Summary 

Table 3-31 summarizes the performance of the archetype buildings in reference to the BSO for both 

nonlinear procedures. Column hinge performance, primarily in the base columns, from both assessment 

procedures controls the overall assessment of the frames. Base column failure is more detrimental to the 

overall structural performance than beam-to-column connection performance. As noted above, additional 

research is needed on assessment criteria for beam-to-column connections and columns. In the end, only 

the 4- and 16-story ELF-designed frames satisfy the seismic performance objective using either nonlinear 

procedure (recall from Chapter 2 that the ELF procedure is not permitted for design of the 16-story SMF). 

The shaded area in the table indicates which frames do not satisfy the NSP criteria due to supplemental 

verification using the LDP (see linear discussion above). The qualitative ratings are assigned primarily 

based on the performance of the column members and, for a few cases, the performance of the columns 

coupled with the performance of the beam-to-column connections. 

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

Archetype Design 

BC 

NSP 

CH PZ 

Design 

NDP 

(based on mean response of record set) 

BC CH PZ 

4-Story ELF 

RSA

Pass 

Fail 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA

Pass Pass Pass 

Fail Pass Pass 

8-Story ELF 

RSA 

Pass 

Pass 

Fail 

Fail 

Pass 

Pass 

ELF 

RSA

Fail Fail Pass 

Fail Fail Fail 

16-Story ELF 

RSA 

Pass 

Pass 

Pass 

Pass 

Pass 

Pass 

ELF 

RSA

Pass Pass Pass 

Fail Fail Pass 

The assessment results from the NSP and NDP illustrate that on average the ELF-designed SMF performs 

better than the RSA-designed SMF for all archetype buildings. This can be attributed to the increased 

3-126
 
strength and stiffness provided to the ELF-designed frames (see Table 2-4 and Table 2-5) by differences in 

the ELF and RSA procedures, including associated scaling provisions, in ASCE 7. 

The NSP (without supplemental verification) consistently results in lower DCRN values than the NDP for 

both the ELF- and RSA-designed frames for all archetype buildings, an indication that a more accurate 

distribution of seismic demands is not well captured in taller frames using the NSP (LDP results are 

consistently greater than NSP, albeit a direct comparison is problematic as discussed previously). Nonlinear 

results indicate that the NSP has a tendency to underestimate the demands in the upper stories. This occurs 

primarily because of the differences in the distribution of seismic demands and the lack of modal 

representation other than the fundamental mode in the NSP. This effect was also noticed in NIST GCR 10­

917-9: Applicability of Nonlinear Multi-Degree-of-Freedom Modeling for Design (NIST 2010c). 

The results from the NDP are sensitive to excitation input, analysis parameters, and component modeling. 

In this study, generalized component models were incorporated with degradation effects calibrated to an 

experimental test. Future research should critically examine the applicability of the generalized modeling 

parameters for steel components in ASCE 41. Experimental research has shown that subassembly tests can 

have large scatter in acceptable performance given the stochastic variations in the type of loading, that being 

cyclical, near-fault, random, etc. (e.g., SAC project). Future research should investigate the influence of the 

loading protocol adopted to establish the deterministic acceptance criteria for connections and member 

hinges. 

Analytical results based on component-level performances obtained from the NSP and NDP suggest that 

special moment frames designed in accordance with ASCE 7 and its referenced standards have difficulty 

achieving the selected seismic performance objective of an existing building intended to be equivalent to a 

new building. This notion is driven by the performance of the columns and beam-to-column connections. 

The results for the columns can be enhanced by more mechanistically consistent column provisions and 

analytical modeling parameters. Although the acceptance criteria for a connection are derived from a highly 

vetted testing program, enhancement to the (cumulative) adjustment factors to the criteria could be 

investigated. 

Comparison between Linear and Nonlinear Assessment Results 

Table 3-32 summarizes the performance of the archetype buildings for each analysis procedure. The results 

indicate that the linear procedures consistently provide DCRN values greater than that given by the nonlinear 

procedures, highlighting the conservatism in the linear assessment 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. Still, on average, the LSP and LDP are capable of identifying 

potential performance concerns within critical areas of the frame as compared to the results from the NSP 

and NDP. Consistency is evident in the global performance rating of the 8-story SMF as well as frames 

designed per the MRSA procedure among the various assessment procedures. However, not all component 

performance failures align between the procedures. The conservatism of the linear procedures is also 

apparent, as expected. 

3-127
 
 

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 components than identified using the nonlinear procedures. The results presented emphasize the inherent 

conservatism in the linear procedures. However, this conservatism is coupled with a reduction in required 

resources and analytical proficiency. 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 demands that cannot be captured efficiently in a 

linear analysis using a smooth generalized spectrum. Furthermore for the NSP, the force distribution is 

potentially inadequate for frames that exhibit increased higher mode participation, either elastically or 

triggered by nonlinearity. 

Table 3-32. BSO Performance Summary of Archetype Buildings 

NDP 

Archetype Design LSP LDP NSP (based on mean 

response of 

record set) 

4-Story ELF 

RSA 

Fail 

Fail 

Pass 

Fail 

Pass 

Fail 

Pass 

Fail 

8-Story ELF 

RSA 

Fail 

Fail 

Fail 

Fail 

Fail 

Fail 

Fail 

Fail 

16-Story ELF 

RSA 

Fail 

Fail 

Pass 

Fail 

Pass 

Fail 

Pass 

Fail 

In contrast to the nonlinear procedures, the linear analysis model and assessment is implied to be less 

rigorous and more conservative. As already discussed, the linear procedures yielded more conservative 

results for the deformation-controlled components. The linear procedures can also illustrate the trend in 

demands but may fail to highlight critical performance zones within a given frame. 

The columns that failed the linear criteria are typically force-controlled because of high axial loads, a result 

of using PUF / PCL in lieu of PUF / 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). 

3-128
 
 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 prescribed 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 the structural seismic performance assessment using ASCE 41 procedures 

and performance measures of buildings utilizing steel special moment frames (SMF) as the lateral forceresisting system (LFRS). 

A suite of archetype buildings that incorporate SMFs 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 Procedure and Modal Response Spectrum Analysis. Both analysis 

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

intensity region. As such, a LFRS may include significant overstrength to resist nonseismic loads or satisfy 

other design criteria. A design space of varied building parameters is used to investigate the effects of 

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

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

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

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

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

analysis procedures prescribed in ASCE 41: 

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 with 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 SMFs is designated as a primary component 

in accordance with ASCE 41. 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 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. 

As stated earlier, the goals of this research are as follows: 

 Assess new structural steel buildings utilizing SMFs 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 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
 
Special Moment Frames 

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

the assessment of the special moment frames. More details about the specific items are in the relevant 

sections of the assessment discussion in Chapter 3. 

	 Analytical results based on component-level performances indicate that new SMFs 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 columns and beam-to-column connections. 

	 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 SMFs. 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 beam-to-column connections with a reduced beam section 

(RBS) 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. 

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

41 acceptance criteria. These failures are in beam-columns classified by analysis as “forcecontrolled”, which can be particularly problematic when the columns are located at the base of a 

frame. The results for columns can be enhanced by more mechanistically consistent assessment 

provisions and analytical modeling parameters for columns. Refinement of the relevant interaction 

equations to evaluate specific failure mechanisms could assist by allowing what would be a forcecontrolled column to be classified as “deformation-controlled”. 

	 A significant number of RBS beam-to-column connections, primarily at the exteriors of the frames, 

did not satisfy the ASCE 41 acceptance criteria for the LSP and NDP. Although the nonlinear 

acceptance criteria and detailing recommendations in ASCE 41 were derived from experimental 

test data, the rationale for the quantitative development of the cumulative reduction factors on these 

criteria (i.e., 0.8 multipliers in ASCE 41 §5.4.2.4.3-4) is unclear. The analytical results indicate that 

step function-based cumulative reduction factors can have a significant impact on the performance 

of an SMF. Further, reduction factors for the span-to-depth ratio limitations for beam-to-column 

connections have potentially opposing effects that could impact the results between linear and 

nonlinear assessment procedures. 

	 Assessment results illustrate that panel zones designed per ASCE 7 and its referenced standards, 

including the common practice of upsizing columns to offset the need for doubler plates and/or 

continuity plates, consistently satisfied the ASCE 41 acceptance criteria by a large margin. 

Consequently, the panel zones are deemed stronger than required by ASCE 41. Specifically, 

upsizing columns can impact the strength of panel zones in reference to the balance yield approach 

adopted by ASCE 41 and in turn can influence the performance of the beam-to-column connections. 

	 Components of the special moment frames 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 

4-6
 
design routines (i.e., ELF and RSA). This makes it difficult to definitively suggest that using ASCE 

41 to design a new SMF 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 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). 

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 

RBS beam-to-column connections in the MC8 buildings. Even if secondary component criteria 

were implemented, the DCRN values still indicate unsatisfactory performance in the lower 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. 

Fully Restrained Moment Frames 

The following items are considerations for future studies to enhance ASCE 41 assessment provisions for 

FR moment frames: 

	 Case studies should examine the seismic performance and cost of SMFs with lighter column sizes 

that include doubler plates. This cost-benefit analysis will shed light on relating construction costs 

to seismic performance and post-earthquake repair costs for various regions of the country. 

	 Research should investigate the assessment of panel zones in relation to the design methodology 

using AISC 341, as well as a critical examination of the acceptance criteria in regard to 

experimental test results. This research can be linked with the above study on the use of double 

plates and lighter columns. 

	 Case studies should investigate the frame design using the Direct Analysis Method in AISC 360 

and the associated seismic assessment results. Some aspects of the Direct Analysis Method have 

been introduced in ASCE 41-13. 

	 Research is needed to develop acceptance criteria and modeling parameters for column-to-base 

connections, including embedded connections. 

	 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 

4-8
 
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 be considered. 

	 Research should critically examine the applicability of the generalized modeling parameters in 

ASCE 41 for plastic hinges in beams, beam-to-column connections, and columns for use in the 

nonlinear procedures. 

 Research should investigate the influence of the loading protocol adopted to establish the 

deterministic acceptance criteria for connections and member hinges. 

 Research is needed to justify the fixed reductions (i.e., 0.8 factor) to acceptance criteria of FR beamto-column connections based on connection detailing. 

 Research should investigate the correlation between acceptance criteria for the linear and nonlinear 

procedures. 

 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 Moment Frames 

The following items are considerations for future studies to enhance AISC 341 provisions of special 

moment frames: 

	 In general, the SCWB provision in AISC 341 adequately limits column hinges (other than at the 

column-to-base connection) at the MCER. However, assessment results suggest that this provision 

may need adjustment for taller frames with increased participation of higher modes. Strictly 

speaking, assessment results depend on the design methodology adopted for the beam-columns 

(i.e., adjusted K factor that is dependent on the deformed shape of the column at buckling, 

computation of the nominal flexural capacity of the column, and interaction formula). Furthermore, 

column hinges above the base may have been produced by other phenomenon and thus column 

hinging is a supplementary indicator of frame collapse. Similarly, the yield surface model for the 

4-9
 
section flexural strength of a wide-flange column adopted in the nonlinear analysis (as well as that 

prescribed in ASCE 41) is slightly different than that prescribed for the SCWB provision, which is 

a conservative yield surface to cover many different column types. Efforts could couple the two 

standards in terms of yield surfaces used to define the section flexural strength of a column. 

	 Analysis results indicate that the axial force demand prescribed in the SCBW provision (i.e., using 

o) is a reasonably conservative approximation compared to a full yield mechanism and results 

from the NDP. The conservatism increases as the aspect ratio of the frame increases. Research 

should investigate the applicability of a full yield mechanism for design. 

	 Design of the frame columns was based on two interaction equations in accordance with AISC 360 

§H1.3 using the Effective Length Method. On average, this method provided acceptable minimum 

sizes for column strength. In the upper stories of taller frames where drift control was not as 

significant, a few (slender) column sizes were governed by out-of-plane stability (AISC 360 

Equation H1-2) and also SCWB (i.e., Mnc < Mpc). However, research is needed to examine the 

effects of the Lateral-Torsional Buckling Modification Factor, Cb, including the influence of axial 

load and pre-curvature on Cb when computing the buckling strength of SMF columns. Similarly, 

research should investigate the influence of a plastic hinge on deep wide-flange column stability— 

see NIST GCR 11-917-13: Research Plan for the Study of Seismic Behavior and Design of Deep, 

Slender Wide-Flange Structural Steel Beam-Column Members (NIST 2011c). 

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 Moment Frame 

Table A-1 summarizes the 14 strong motion records used for the nonlinear dynamic procedure (NDP) for 

the E-W direction of MC4 special moment frame (SMF). 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 records completed for the BSE-1 and BSE-2 for the ELF design. 

All records completed for the BSE-1 for the RSA design. All analyses except those using records 1, 4, 7, 9, 

and 12 completed for the BSE-2 for the RSA design. 

Table A-1. Ground Motion Records for E-W Direction of MC4 

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 3.055 2.037 0.010 23 

2 12 Imperial Valley El Centro Array #11 2 30 4.115 2.744 0.005 40 

3 31 Superstition Hills El Centro Imp. Co. 1 31 2.839 1.893 0.005 40 

4 10 Imperial Valley Delta 2 32 2.433 1.622 0.010 100 

5 5 Duzce, Turkey Bolu 1 34 2.021 1.347 0.010 56 

6 28 Loma Prieta Gilroy Array #3 2 39 2.018 1.345 0.005 40 

7 17 Kocaeli, Turkey Duzce 1 41 2.562 1.708 0.005 28 

8 15 Kobe, Japan Shin-Osaka 1 41 3.028 2.019 0.010 41 

9 22 Landers Yermo Fire Station 2 45 4.479 2.986 0.020 44 

10 3 Northridge Canyon Country-WLC 1 46 2.094 1.396 0.010 20 

11 14 Kobe, Japan Nishi-Akashi 2 47 3.020 2.013 0.010 41 

12 41 San Fernando LA - Hollywood Stor 1 51 5.010 3.340 0.010 28 

13 29 Manjil, Iran Abbar 1 52 2.839 1.893 0.020 54 

14 7 Hector Mine Hector 1 52 4.617 3.078 0.010 46 

Notes: 

1. Component Number. See FEMA P-695 Appendix A for additional parameters associated to each component of an event. 

2. Single composite error value computed in Step 3. 

3. Scaling factor for the component for the BSE-2 or BSE-1 EHL (BSE-1 = 2⁄3×BSE-2). 

4. Time step in seconds. 

5. Total time of record in seconds. 

A-3 
3 7 

 Code Code

 121222 121222

 120622 6 120622

Original EQ 121211

 120612

Scaled EQ 121211

 120612

5

Spectral Acceleration (g) 

 120411

2 121022

 120811

 120721

 120912

 120121

 120712

 121511

1 121111

 120521

 Average 

Spectral Acceleration (g) 

 120411

 121022

 120811

4 120721

 120912

 120121

3 120712

 121511

 121111

2 120521

 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 

 Code

 Average

 0.2T1,avg

1 

 1.5T1,avg

T1,avg 

0 

01 2 3 4 5 6 

Period (sec)

Figure A-1. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for E-W Direction of MC4 

A-4 
3 6 3 

5 

EQ 1 EQ 2 EQ 3 

2 4 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) 

 Code

3 120622 Scaled

 120622 Unscaled 

2 

 Code

 121211 Scaled

 121211 Unscaled 

 Code

 121222 Scaled

 121222 Unscaled 

1 1 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 5 3 

EQ 4 4 EQ 5 EQ 6 

2 

1 

 Code

 120612 Scaled

 120612 Unscaled 

2 

1 

 Code

 121022 Scaled

 121022 Unscaled 

3 Code

 120411 Scaled

 120411 Unscaled 

2 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 3 3 

EQ 7 EQ 8 EQ 9 

2 

1 

 Code

 120811 Scaled

 120811 Unscaled 

2 

1 

 Code

 120721 Scaled

 120721 Unscaled 

2 

1 

 Code

 120912 Scaled

 120912 Unscaled 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

3 5 4.0 

3.5
 

EQ 10 4
 EQ 11 3.0 EQ 12 

3 

 Code

 120712 Scaled

 120712 Unscaled 

2 

1 

Spectral Acceleration (g) 2.5 

 Code

 121511 Scaled 2.0 121511 Unscaled 

1.5 

1.0 

2 

1 

 Code

 120121 Scaled

 120121 Unscaled 

0.5 

0 0 0.0 

01 234 56 01 234 56 01 234 56 

Period (sec) Period (sec) Period (sec)

6 4 

5 

EQ 13 3 EQ 14 

Spectral Acceleration (g) 4 

 Code

 121111 Scaled 3 121111 Unscaled 

2 

Spectral Acceleration (g) 

 Code

 120521 Scaled 2 120521 Unscaled 

1 

1 

0 0 

01 234 56 01 234 56 

Period (sec) Period (sec)

Figure A-2. Acceleration Response Spectra: Original and Scaled for Each Selected Record for E-W Direction of MC4 

A-5 
 

 

 

 

 

 

 

 

 

 

 

A.4 Eight-Story Archetype Building 

8-Story Special Moment Frame 

Table A-2 summarizes the 14 strong motion records used for the NDP for the E-W direction of MC8 (SMF). 

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 records completed for the 

BSE-1 for the ELF design. All analyses with records except 8, 10, and 13 completed for the BSE-2 for the 

ELF design. All analyses except those using records 8 and 14 completed for the BSE-1 for the RSA design. 

All analyses except those using records 1, 2, 3, 4, 7, 8, 10, 12, 13, and 14 completed for the BSE-2 for the 

RSA design. 

Table A-2. Ground Motion Records for E-W Direction of MC8 

I BSE-2 BSE-1 EQ No. Event Name Station Comp.1

 Error2 Step4 Time5 

D Scaling3 Scaling3 

1 12 Imperial Valley El Centro Array #11 2 29 3.862 2.575 0.005 40 

2 21 Landers Yermo Fire Station 1 56 2.842 1.894 0.020 44 

3 10 Imperial Valley Delta 2 58 2.371 1.581 0.010 100 

4 27 Loma Prieta Gilroy Array #3 1 59 5.483 3.656 0.005 40 

5 5 Duzce, Turkey Bolu 1 61 2.036 1.358 0.010 56 

6 34 Superstition Poe Road (temp) 2 62 3.132 2.088 0.010 23 

Hills 

7 29 Manjil, Iran Abbar 1 63 3.034 2.023 0.020 54 

8 39 Chi-Chi, Taiwan TCU045 1 63 4.768 3.179 0.005 90 

9 42 San Fernando LA - Hollywood Stor 2 66 6.846 4.564 0.010 28 

10 19 Kocaeli, Turkey Arcelik 1 67 8.760 5.840 0.005 30 

11 7 Hector Mine Hector 1 74 5.307 3.538 0.010 46 

12 31 Superstition El Centro Imp. Co. 1 74 2.844 1.896 0.005 40 

Hills 

13 44 Friuli, Italy Tolmezzo 2 80 9.476 6.318 0.005 37 

14 38 Chi-Chi, Taiwan CHY101 2 88 0.993 0.662 0.005 90 

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 12 

 Code Code 11 120622 120622

 120911 120911 10 120612 Scaled EQ 120612 Original EQ 121021 9 121021

Spectral Acceleration (g) 

 120411

Spectral Acceleration (g) 

 120411

2 121222 8 121222

 121111

 121421

 121512

 120821

 120912

 121211

 121111 7 121421

 121512 6 120821

5 120912

 121211

4 121712

 121412 3 Average 

1 121712

 121412

 Average 

2 

1 

0 0
 

0123456 0123456 
 

Period (sec) Period (sec)

4 

Scaled Average Spectrum 

3 Scaled to 100% of MCE r 

between 0.2 and 1.5T1,avg 

Spectral Acceleration (g) 2 

 Code

 Average

 0.2T1,avg

1 1.5T1,avg

T1,avg 

0 

01 2 3 4 5 6 

Period (sec)

Figure A-3. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for E-W Direction of MC8 

A-7 
6 2 3 

5 

EQ 1 EQ 2 EQ 3 

4 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

 120612 Scaled

 120612 Unscaled 

 Code 3 1 120911 Scaled 120622 Scaled 120911 Unscaled 120622 Unscaled 

2 1 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

12 5 4 

11 

10 

9 EQ 4 4 EQ 5 3 EQ 6 

8 

3 7 Code Code Code 120411 Scaled

 120411 Unscaled 

 121021 Scaled 6 2 121222 Scaled 121021 Unscaled 121222 Unscaled 

5 

4 

3 

2 

1 

1 

2 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

6 7 5 

6
 

EQ 7
 

5 

EQ 8 4 EQ 9 

5 

 Code 4 121421 Scaled

 121421 Unscaled 

3 

2 

4 

 Code

3 121111 Scaled

 121111 Unscaled 

2 

3 

2 

 Code

 121512 Scaled

 121512 Unscaled 

1 1 1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

7 3 3 

6 

EQ 10 EQ 11 EQ 12 

5 

2 

1 

 Code

 120912 Scaled

 120912 Unscaled 

2 

1 

 Code

 121211 Scaled

 121211 Unscaled 

 Code

4 120821 Scaled

 120821 Unscaled 

3 

2 

1 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

10 2 

9 

8 EQ 13 EQ 14 

Spectral Acceleration (g) Spectral Acceleration (g) 

 Code

 121412 Scaled 1 121412 Unscaled 

7 

6 Code

 121712 Scaled 5 121712 Unscaled 

4 

3 

2 

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 E-W Direction of MC8 

A-8 
 

 

 

 

 

 

 

 

 

 

A.5 Sixteen-Story Archetype Building 

16-Story Special Moment Frame 

Table A-3 summarizes the 14 strong motion records used for the NDP for the E-W direction of MC16 

(SMF). Figure A-5 illustrates the set of acceleration response spectra, original and scaled, and the scaled 

average spectrum. Figure A-6 illustrates the acceleration response spectra, original and scaled, for each 

select record. For comparison, the ASCE 41 code spectrum is shown in the figures. All analyses completed 

for the BSE-1 and BSE-2 for the ELF design. All records completed for the BSE-1 for the RSA design. All 

analyses except those using records 1, 2, 5, and 10 completed for the BSE-2 for the RSA design. 

Table A-3. Ground Motion Records for E-W Direction of MC16 

Comp. BSE-2 BSE-1 ID EQ No. Event Name Station 1 Error2 Step4

 Time5 

Scaling3 Scaling3 

1 12 Imperial Valley El Centro Array #11 2 66 3.664 2.443 0.005 40 

2 29 Manjil, Iran Abbar 1 74 3.295 2.197 0.020 54 

3 19 Kocaeli, Turkey Arcelik 1 83 8.383 5.589 0.005 30 

4 7 Hector Mine Hector 1 88 4.992 3.328 0.010 46 

5 9 Imperial Valley Delta 1 93 3.061 2.041 0.010 100 

6 22 Landers Yermo Fire Station 2 94 3.089 2.059 0.020 44 

7 5 Duzce, Turkey Bolu 1 97 2.724 1.816 0.010 56 

8 42 San Fernando LA - Hollywood Stor 2 97 7.119 4.746 0.010 28 

9 17 Kocaeli, Turkey Duzce 1 103 1.673 1.115 0.005 28 

10 32 Superstition Hills El Centro Imp. Co. 2 105 2.940 1.960 0.005 40 

11 14 Kobe, Japan Nishi-Akashi 2 106 4.286 2.857 0.010 41 

12 27 Loma Prieta Gilroy Array #3 1 108 6.015 4.010 0.005 40 

13 16 Kobe, Japan Shin-Osaka 2 118 7.346 4.897 0.010 41 

14 37 Chi-Chi, Taiwan CHY101 1 121 1.241 0.827 0.005 90 

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 13 

 Code Code 12 120622 120622

 121111 11 121111

 120821 Scaled EQ 120821 Original EQ 120521 10 120521

Spectral Acceleration (g) 

 120611

2 120912

 121512

 120411

 120811

 121212

 120712

 121021

1 120722

 121411

 Average 

Spectral Acceleration (g) 

 120611 9 120912

8 121512

 120411 7 120811

6 121212

 120712

5 121021

 120722 4 121411

3 Average 

2 

1 

0 0
 

0123456 0123456 
 

Period (sec) Period (sec)

4 

Scaled Average Spectrum 

3 Scaled to 100% of MCE r 

between 0.2 and 1.5T1,avg 

Spectral Acceleration (g) 2 

 Code

 Average

 0.2T1,avg

1 1.5T1,avg

T1,avg 

0 

01 2 3 4 5 6 

Period (sec)

Figure A-5. Acceleration Response Spectra: Original, Scaled, and Scaled Average Spectrum for E-W Direction of MC16 

A-10 
6 6 6 

5 5 5 

EQ 1 EQ 2 EQ 3 

4 4 4 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) 

 Code Code

3 120821 Scaled

 120821 Unscaled 

2 

 Code 3 3 121111 Scaled 120622 Scaled 121111 Unscaled 120622 Unscaled 

2 2 

1 1 1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

4 3 2 

EQ 4 EQ 5 EQ 6 3 

2 

 Code Code

 120521 Scaled Code 120611 Scaled

 120611 Unscaled 2 1 120912 Scaled 120521 Unscaled 120912 Unscaled 

1 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

7 5 2 

6 

EQ 7 4 EQ 8 EQ 9 

5 

4 

3 

3 Code

 120411 Scaled

 120411 Unscaled 

 Code

 121512 Scaled

 121512 Unscaled 

 Code

1 120811 Scaled

 120811 Unscaled 

2 

1 

2 

1 

0 0 0 

0123456 0123456 0123456 

Period (sec) Period (sec) Period (sec)

2 7 13 

12 

6 11
 

EQ 10
 EQ 11 10 EQ 12 

5 

4 Code

 120712 Scaled

 120712 Unscaled 3 

2 

9 

 Code 8 121212 Scaled

 121212 Unscaled 

 Code 7 121021 Scaled 1 121021 Unscaled 6 

5 

4 

3 

2 1 

1 

0 0 0 

012 3456 012 3456 012 3456 

Period (sec) Period (sec) Period (sec)

6 2 

5 

EQ 13 EQ 14 

Spectral Acceleration (g) 4 

 Code

 120722 Scaled 3 120722 Unscaled 

2 

1 

Spectral Acceleration (g) 

 Code

 121411 Scaled 1 121411 Unscaled 

0 0 

012 3456 012 3456 

Period (sec) Period (sec)

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

 SMF beam and RBS beam-to-column connection 

 SMF column 

 SMF panel zone 

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 

76 89 Roof 15 Roof 

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 x

 (kips)

(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 

          C 

I 

d 

i x x 1 x e ( x 1) e (B-2) e 

PI P   x    x xe ( 1)  e  2i  x ie  (B-3) Vh C Vh i sx d i sx 

 2i 1i  (B-4) 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 
 

 

 

 

 

 

 

 

3 

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 Figure 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 

Lateral Force, F x

 RSA

 ELF

 Wind (700-Year) 

Floor 

8 

7 

6 

5 

4 

3 

2 

Floor Base Base 

 (kips) Story Shear, V x

 (kips)

(a) Lateral Forces (b) Story Shears 

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

B-7 

2 
 

 

 

 

 

2 

3 

4 

5 

6 

7 

8 

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

Floor 

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 

Roof 

Base 

18 6671 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 

RSA

 ELF

 Wind (10-Year) 

Floor 

0 50 100 150 200 250 300 

93 

112 

131 

146 

159 

174 

192 

192 

139 

190 

226 

250 

264 

271 

273 

273 

37 

55 

73 

89 

105 

121 

136 

136 

RSA

 ELF

8 Wind (10-Year)

7 

6 

5 

4 

3 

2 

Base 

0 20 40 60 80 

Lateral Force, F x (kips) Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

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

B-8 
 

 

 

 

 

 

 

 

0.0110 0.0134 Roof Roof 

8 8 

7 

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 

7 

6 

Floor 

5 

4 

3 

2 

Base 

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 

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 (kips)

x

(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. Lastly, 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 

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 

2 
 

 

 

 

 

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, x / h sx Expected Floor Displacement, x

 (inch)

(a) Story Drift ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-12. Story Drift Ratios and Deflected Shape 

Table B-21 and Table B-22 provide the tabulated data for verifying the allowable story drifts and the seismic 

stability coefficient per ASCE 7 §12.8.6 and ASCE §12.8.7 for each archetype building design. 

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

the N-S direction only. Lastly, the equivalent story forces for the RSA design are backed out from the story 

B-15 
 

 

 

 

 

 

 

 

 

 

 

 

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 

8 

Roof 27 168 Roof 161 

8
 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) 

7
 

6
 

5
 

4
 

3
 

2
 

6
 

Floor 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-14. Drift Design Lateral Forces and Story Shears 

Roof 0.0090 0.0121 Roof 

0 4 8 12 16 

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 

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 

8
 

7
 

6
 

5
 

4
 

3
 

2
 

Base 

7
 

6
 

5
 

Base 

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-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. Lastly, 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 (kips) x

(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) 

4 

3 

2 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base Base 

Lateral Force, F (kips)

x Story Shear, V x

 (kips)

(a) Lateral forces (b) Story Shears 

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

Roof 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

0.0060 0.0091 

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, a / h sx 

Floor Roof 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

Base 

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 

0.000	 0.005 0.010 0.015 0.020 0 4 8 12 16 20 

Expected Story Drift Ratio,  / h Expected Floor Displacement, x

 (inch) x sx

(a) Story Drift ratios at Center of Mass (b) Floor Displacements at Center of Mass 

Figure B-18. Story Drift Ratios and Deflected Shape 

B-20 

24 

24.4 
 

 

 

 

 

 

 

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. 

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 

a max / avg 

MC4 MC8 MC16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof MC16 - - - - 1.015 1.012 

16 - - - - 1.011 1.009 

15 - - - - 1.012 1.008 

14 - - - - 1.011 1.007 

13 - - - - 1.010 1.008 

12 - - - - 1.010 1.007 

11 - - - - 1.009 1.007 

10 - - - - 1.009 1.007 

9 (Roof MC8) - - 1.016 1.011 1.008 1.007 

8 - - 1.013 1.009 1.009 1.007 

7 - - 1.012 1.008 1.008 1.006 

6 - - 1.011 1.007 1.008 1.007 

5 (Roof MC4) 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 

a. Values include accidental torsion with Ax = 1.0. 

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

a ( / hsx) x / ( / hsx) x+1 

 MC4 MC8 MC16 

Floor (x) ELF RSA ELF RSA ELF RSA 

Roof MC16 - - - - - -

16 - - - - 1.22 1.27 

15 - - - - 1.07 1.13 

14 - - - - 1.09 0.97 

13 - - - - 1.04 0.89 

12 - - - - 1.07 1.02 

11 - - - - 1.04 1.02 

10 - - - - 0.97 0.98 

9 (Roof MC8) - - - - 0.93 0.95 

8 - - 1.26 1.20 0.99 1.00 

7 - - 0.99 1.07 0.99 0.98 

6 - - 1.07 1.02 0.98 0.93 

5 (Roof MC4) - - 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 

a.  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 MC16 - - - - - -

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 (Roof MC8) ­ ­ ­ ­ 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 (Roof MC4) ­ ­ 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      hsx 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 
 

W18×175

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): 

 SMF beam and beam-to-column connection, MC8 RSA 

 SMF column , MC8 RSA 

 SMF panel zone, MC8 RSA 

Example calculations for components of the SCBF can be found in Volume 2 (Harris and Speicher 2015). 

Special Moment Frame Example 

Member Selection 

After several design and analysis iterations, the final member sizes are shown in Figure B-19. 

Figure B-19. SMF Member Sizes, 8-story RSA 

W18×106

W18×192 W18×192 W18×143 W18×119 

W18×71 W18×55 

B-29 
SMF Beam and RBS Beam-to-Column Connection 

The second floor frame beam (No. 1) along grid line 1 between grid lines B and C is selected for this 

example (see circled element in Figure B-19): 

 W24×84 with reduced beam sections 

 L = 30 ft. (centerline) 

 A992 Steel: Fy = 50 ksi, Ry = 1.1, E = 29000 ksi, G = 11200 ksi 

B.4.1.2.1 Flexural Demand 

The flexural demand from the controlling load combination from ASCE 7 at the center of the RBS is: 

M u  5696 kip-in. = 475 kip-ft. 

B.4.1.2.2 Flexural Strength 

The controlling beam strength is at the center of the RBS (a = 4.75 in., b = 16 in., and c = 2.25 in.—see 

AISC 358). Composite action is neglected in the design for positive moment strength. The effective plastic 

modulus at the center of the RBS is: 

Z Z 2ct d  t   224  2 2.25 0.77 24.1  0.770 143.16 e x f   in.3   f 

The nominal beam capacity at the reduced section is: 

 M   F Z   143.16 b n b y e 0.9 50   6442 kip-in. = 536 kip-ft. 

b M n  Mu (ratio = 1.12) 

The beam is braced along its length per AISC 360 and AISC 341. 

E E L L  1.76 r  40.4 r  0.086 r  45.3 r (note that AISC 360 is more strict) b p y y y y F ye Fye 

M  Z F  224 50   11200 kip-in = 933 kip-ft. p x y 

b n u M  M

B-30 
B.4.1.2.3 Fully Restrained Connection 

The moment capacity at the face of the column needs to be verified (the expected moment capacity at the 

face of the column needs to be greater than the probable maximum moment at the center of the fully yielded 

and strain hardened RBS projected to the face of the column). 

The expected moment capacity at the column face is: 

M  Z R F    50 pe b y y 224 1.1   12320 kip-in. (AISC 358 Equation 5.8-7) 

The probable moment at the RBS is: 

pr e M 1.15 1.1 50  kip-in. (AISC 358 Equation 5.8-5) pr  C R F Z y y     143.16   9055 

The moment at the column face resulting from the Mpr at the RBS is: 

wSh   2 0.0829 12.75 2 

M M  V S   9057 70.7 12.75      9962 kip-in. f pr RBS h 2 2 

2M pr wL  2 9057   0.0829 314.3   VRBS      70.7 kips L 2 314.3 2 

where VRBS is the probable shear force at the center of the RBS. 

b M pe   12320  M f 1.0 12320  9962 

The shear strength is computed as: 

h 29000  42.5  2.24  53.9C 1.0 v tw 50
 

V  0.6 F A C  0.6   50 1.0 15.56    = 467 kips n y w v 

 V 1.0 467    467 V  70.7 vn RBS 

SMF Column 

The first story column (No. 1) at the intersection of grid lines 1 and B is selected for this example (see 

circled element in Figure B-19): 

 W18×175
 

 hsx = 18 ft.(Lb of the column is conservatively taken as hsx) 

B-31 
 

 

 

 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 

163 -123.90 -123.90 672.20 168.81 Pu,min 

117 -757.01 -753.18 -689.41 -137.83 Pu,max 

134 -212.09 -209.62 685.32 -140.51 Mu,A,min 

66 -676.27 -672.98 -702.53 171.49 Mu,A,max 

107 -449.00 -445.17 666.02 179.93 Mu,B,min 

173 -433.82 -431.90 -683.23 -148.95 Mu,B,max 

Pr = 757 kips and Mr,x = 690 kip-ft.—from the load combination selected for this example (#117 in Table 

B-48). 

SMF column design is also governed by the capacity design requirements specified in AISC 341 §D1.4a 

(2), which permits flexural forces resulting from seismic drift of the frame to be neglected in this case. 

Pu,	 1065 kips o 

B.4.1.3.2 Axial Strength 

The axial compression strength of the column is calculated per AISC 360 §E3.
 

P n  A Fg cr 	 

Flexural Buckling about the y-axis (out-of-plane): 

KL y y	 F y 1.0 216   50   3.25  4.71 

ry	 E 2.76 29000
 

2 E 2 29000 F    46.7 ksi e y, 2 2

 K L 	  1.0 216     yy     r	  2.76  y	   

	 FF 

 y e y,   Fcr  0.658 Fy  32.0 ksi  

 P	 

,  0.9 51.3  32.0   0.9 1639   1475
 kips → governs c ny

B-32 
 

 

Flexural Buckling about the x-axis (in-plane): 

K2x = 2.59 → computed using the story buckling method in AISC 360 (assuming only vertical loads 

triggers story buckling—independently of the stories above and below). 

KL x x 	 F y 2.59 216   50   2.83  4.71 

rx	 E 8.20 29000
 

2 E 2 29000  F    61.5 ksi e x, 2 2

 xx   2.59 216 
    
 KL  

r 8.20  x   

FF y e x,  Fcr  0.658  Fy  35.6 ksi  

c nx P ,	  0.9 51.3  	 35.6   0.9 1825    1643 kips → see c ny P,

B.4.1.3.3 Flexural Strength 

The flexural capacity of the column is: 

M  CM  M  0.7FS L  L  /  L  L  n b p p y x b p r p p    M  
 

  0.7 50  344  15.7  9.7 

M 1.99 1658	 1.99 1548 n   1658        3080  M p 1658 kip-ft. 	  12   46.8  9.7 

bMn  bM p  0.9 1658   kip-ft. = 17900 kip-in. 

B.4.1.3.4 Strength Check 

The interaction equation check is done using AISC 360 §H1.3.
 

(a) In-plane stability (AISC 360 Equation H1-1a) using LC #117—see Table B-48 

Pr 757   0.46
 Pnx 1643
 , 

For Pr / Pn,x ≥ 0.2, the interaction equation in AISC 360 §H1.1 is:
 

Pu 8  M ,  757 8  8273    ux     0.46  0.41  0.87 1.0      P , 9 b M , 1643 9 17900  c nx  nx 

B-33 
 

 

 

(b) Out-of-plane stability (AISC 360 Equation H1-2) using LC #117—see Table B-48 

P r P 757  u   0.51

 Pn y P 1475 cy c , 

u  P   M , 

2 

8273 

2 

P u ux  1.5  0.5      0.51 1.5   0.5 0.51   

 P  n y 

  

 

1.99(0.9) 18576 



 c n y,  c P ,  Cbb Mn,LTB, x   

 0.63  0.062  0.69 1.0 

(c) Amplified seismic load with system overstrength factor from ASCE 7 

Pr, 1065 o   0.72 1.0

 P 1475 c ny ,

SMF Panel Zone 

The panel zone at the top of the first story column located at the intersection of grid lines 1 and B is selected 

for this example (see circled element in Figure B-19): 

 Column = W18×175 (No. 1) 

 Beam = W24×84 (No. 1)
 

 A992 Steel: Fy = 50 ksi, Ry = 1.1, E = 29000 ksi, G = 11200 ksi
 

B.4.1.4.1 Shear Demand 

The panel zone demand is determined using the projected probable moment strength at the center of the 

RBS (AISC 341 E3.6e (1) states expected moments; however, most design examples use the probable 

moment because of prequalification testing). 

M pr pr y y RBS  C R F Z 1.15 1.1  50 143.16    9057 kip-in = 755 kip-ft. 

Projecting this demand to the face of the column: 

M f  M pr VRBS Sh  9057  70.7 12.75    9956 kip-in = 830 kip-ft.

The approximate panel zone demand is: 

1 , fL , V ,  M 



M fR 

u PZ Vc

d1  t f 1  d2  t f 2 
 

B-34 
M ,  M fL fR , 0  9956 V    51.9 (assumes inflection point at mid-height of columns) c hb ht     216  168           2 
 

9956
 

   2 2   2 

, V 0  51.9  375 kips u PZ   24.1  0.77

Mf,R is the moment from the right beam and Mf,L = 0 since the panel zone is part of a one-sided 

beam-to-column connection. 

Alternatively, the shear demand can be approximated with ASCE 41 §5.4.2.4.2. 

M f  L  h d  b  830 / 12  360 192  24.1  VPZ          382 kips db  L  dc  h  24.1  360  20  192 

B.4.1.4.2 Shear Strength 

The panel zone strength is calculated from AISC Equation J10-11: 

 3bt 2   3bt 2  cf cf cf cf V n  0.60F y c w d t 1  V y 1   ddt ddt     b cw   b c w 

V  0.60 F d t  0.60   50 20.0 0.89   534 kips y y c w 

 3 11.4   1.59 

2 

Vn Vy 1   534(1.2)  642 kips  24.1 20.0 0.89       

B.4.1.4.3 Strength Check 

The panel zone strength check is: 

Vr 375   0.58  1.0 (using probable moment) Vn 1.0 642  

Also, 

Vr 375   0.7 1.0 (using probable moment) Vy 534 

Therefore, the panel zone is not expected to yield at the probable moment. 

B-35 
SMF Strong-Column / Weak-Beam 

AISC 341 §E3.4a requires that the sum of the nominal flexural strengths of SMF columns at a joint— 

projected to the joint—be stronger than the expected flexural strengths of the beam-to-column connections 

at the joint—projected to the joint. 



M pc 

 1.0 (AISC 341 Equation (E3-1)) M pb 

AISC 341 §E3.4a permits the use of a straight line interaction equation to determine the column flexural 

strength, Mpc (which is a lower-bound nominal plastic section strength). This moment strength is projected 

to the beam centerline assuming that the shear in column, Vc, is in equilibrium with Mpc: 

   

  P r top ,  h   h t  P ,   r bot b

M pc 

 F  A  d x bot  F 

A  d  Zx top , y    Z , y   

 b g  b  g 

 ht  

   hb    2   2 

Because this is the base column, the assumption that the inflection point occurs at mid-height of the first 

story is likely invalid due to the fixity of the column-to-base connection. A more accurate estimate can be 

obtained by a nonlinear static analysis or by taking moments from the elastic analysis. Using Load 

Combination #117—see Table B-48, the point of inflection, z, from the base is approximately: 

 Mbot   689 

z    L  192 158 in.   

  M   M 689  138  bot top   

24.1 and h  216  158  46 in. b 2 

The inflection point at the second story is assumed to be at mid-height; therefore, 

 907  84   1065  46 

M 

  398 50   398 50   30790 kip-in. pc  

        51.3  84  24.1 2  51.3  46  24.1 2    

The sum of the projections of the expected flexural strengths of the beams is: 



M pb  M pr  Muv 

Mpr is the sum of the probable moments produced at each RBS centerline determined previously. Muv is 

the sum of the moments produced at the column centerline by the shear at the plastic hinges: 

B-36 
 2M wL  2 9057 0.0829 314.3     VRBS  pr     70.7 kips L 2 314.3 2
 

  b dc   16 20   M  V a    70.7 4.75    70.7 22.75 1608 kip-in. uv  RBS         2 2   2 2 

 M 

pb  9057 1608 10665 kip-in. = 889 kip ft. 

Therefore, 

M 

pc 30790   2.9 1.0 M 

pb 10665 

The previous calculations intend to protect the column against from hinging but does not also check the 

column against instability at the probable strength of the beam-to-column connection(s). The low ratio 

result suggests that column instability will not be a concern. 

Assuming adequate lateral bracing at the ends of the columns, using AISC 360 Equation H1-2 for out-ofplane buckling with in-plane moments: 

Pr,  P   M , 

2 

o 1.5  0.5 u    ux  1.0

P  P CM    n y,  n y,   b n, LTB, x 

P  P  r,o r,o 1065  1065  M  C M 1 1.5  0.5  1.99(18576) 1  1.5  0.5 pc x , b n, LTB, x  P P   n y n y, 1638  1638   , 

M pc x  36966 1  0.65 1.5  0.5(0.65) 18000 kip-in = 1500 kip-ft. ,  

Similarly, using AISC 360 Equation H1-1a for in-plane buckling with in-plane moments, 

P r, 8 M pc x , o  1.0 (Pn,x uses KxLx = Lx) P n x, 9 Mn x, 

9  Pr ,o  9  1065  M  M 1    (19900) 1   9323 kip-in. = 777 kip-ft. → governs pc x , , n x     8 Pnx 8  1825   , 

Both values for Mpc associated with the axis of buckling above must be less than Mpc computed from the 

chosen yield surface, which can be approximated using AISC 360 Equation H1-1a. 

B-37 
P r, 8 M pc x, o  1.0

Py 9 M p x ,

9  Pr,o 

 9  1065  M pc x,  M , 1   (19900) 1 13092 kip-in. = 1092 kip-ft. p x  8  Py  8  51.3(50)   

For the column above, Mpc,x = 12637 kip-in. Thus, 

 84   46 

 M 

pc 12637   9323  27380 kip-in.  

   84  24.1 2 46  24.1 2    
 

 M 

pb 10665 kip-in.
 

 M 

pc 27380    2.6 1.0  M pb 10665 

The above calculations assume that a plastic hinge formed at the column base does not influence the 

interaction curves and conservatively assumes Kx for in-plane buckling is invariant to that used for design 

(which conservatively encompasses all load combinations and load patterns). 

B-38 
 

 

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): 

 SMF beam and beam-to-column connection, MC8 RSA 

 SMF column, MC8 RSA 

 SMF panel zone, 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) 

SMF Frame Beam and RBS Beam-to-Column Connection 

The second floor frame beam (No. 1) along grid line 1 between grid lines B and C is selected for this 

example (see circled element in Figure B-19). 

 W24×84 with reduced beam sections 

 L = 30 ft. (centerline) 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi
 

Flexural Demand 

C.1.1.1.1 Frame Beam 

Flexural actions in the beam are deformation-controlled (assuming small axial loads); therefore, 

MUD  MG  M E (ASCE 41 §3.4.2.1.1) 

Based on the controlling load combination, the moment at the center of each RBS is: 

MUD,L = 2336 kip-ft. → left MUD,R = 2130 kip-ft. → right 

C-1 
 

 

C.1.1.1.2 FR Connection 

Flexural action in a FR connection is deformation-controlled, therefore: 

M  M  M (ASCE 41 §3.4.2.1.1) UD G E 

Based on the controlling load combination, the moment at the face of each column is: 

MUD,L = 2533 kip-ft. → left MUD,R = 2327 kip-ft. → right 

Flexural Strength 

C.1.1.2.1 Beam 

Per ASCE 41 §5.4.2.3.2.1, the flexural strength is determined from AISC 360 Chapter F. Because this is 

new construction designed in accordance with AISC 360 and AISC 341, the beam is braced sufficiently to 

develop its plastic moment strength. 

E E L L  1.76 r  40.4 r  0.086 r  45.3 r (note that AISC 360 is more strict) b p y y y y F ye Fye 

M  M  M  Z F  224 55 12320 kip-in = 1027 kip-ft. CE n p x ye  

The controlling beam strength is at the center of the RBS (a = 4.75 in., b = 16 in., and c = 2.25 in., see AISC 

358). The effective plastic modulus at the center of the RBS is: 

          in.3 Z Z 2ct d  t  224  2 2.25 0.77 24.1 0.770 143.2 e x f f 

The expected plastic moment at the center of the RBS is: 

M  M  Z F 143.2 55    7876 kip-in. = 656 kip-ft. CE pe e ye 

C.1.1.2.2 Fully Restrained Connection 

Per ASCE 41 §5.4.2.4-4, QCE shall be taken as the capacity of the critical connection component. The 

acceptance criteria in ASCE 41 for beam-to-column connections are applicable for demands at the face of 

the column. Thus, QCE is taken as the expected flexural strength of the RBS projected to the column face. 

The corresponding moment strength at the face of the column is: 

C-2 
        L 314 M clear 

CE  M f  M pe    7876   = 8512 kip-in. = 709 kip-ft.   b    16  L  2 a  314  2 4.75   clear        2    2 

where Lclear is the clear distance between column faces. 

Acceptance Criteria 

C.1.1.3.1 Beam 

The m-factor for the RBS defined as a beam (primary) is taken from ASCE 41 Table 5-5. 

bf 52  5.86  =7.01
 2t f Fye
 

h 418  45.9   56.4 

t w Fye 

  m 8

C.1.1.3.2 Fully Restrained Connection 

The initial m-factor for the RBS beam-to-column connection (primary) is taken from ASCE 41 Table 5-5. 

mi   6.2 0.032 d  6.2 0.032 24.1     5.43 

Per ASCE 41 Table 5-4, the RBS is considered a fully restrained (FR) connection and thus the acceptance 

criteria is subject to the following acceptance criteria modifications in ASCE 41 §5.4.2.4.3 (each modifier 

is taken as  here). 

Continuity Plate Modifier (ASCE 41 §5.4.2.4.2-4.1) 

tcf 1.59 in. and tcp  0.5 in. at both connections, bbf  9.02 in. and tbf  0.77 in. 

b b bf bf tbf  t  and continuity plates with t 
 7 cf 5.2 2
 

1.29  t 1.73 and t  0.39 cf cp 

 CP 1.0 for both connections 

C-3 
 

 

 

Panel Zone Strength Modifier (ASCE 41 §5.4.2.4.2-4.2) 

The shear demand in the panel zone is: 

L  
 V PZ     M y beam ,  h db 

d L  d h  c  

where My,beam is the moment at the face of the column, projected from the flexural yield strength of the 

critical connection component (i.e, S×Fye). 

The reduced moment of inertia, I’x, and the elastic section modulus, S’x, at the center of the RBS are: 

 2 2 in.4 I I 1   ct 4 3 t  6dt  d  1427 x x f f f 3 

Sx 

  2I x  d 118 in.3 

M  F S 1.1 50 118  6512 kip-in. = 543 kip-ft. y RBS , ye x   

The moment at the column face is—neglecting small gravity load contributions: 

 L 

M clear  M  M  7040 kip-in. = 587 kip-ft. f y beam , y RBS , 

  L  2a  b 2  clear 

The average story height of the columns is: 

168  216 h   192 in. 

2 

Therefore, the panel zone demands (left and rights) are: 

7040  360 192  24.1  V   271 kips PZ L,    24.1  360  20  192 

7040  7040 360 192  24.1 V   541 kips PZ R,    24.1  360  20  192 

The panel zone strengths (left and right) are: 

V  0.55F t d  538 kips Vy R  0.55F t dc  592 kips y L, ye cw c , ye cw 

The panel zone strength ratios (left and right) are: 

C-4 
 

 

 

VPZ Vy   0.50  0.6 VPZ Vy   0.91  0.9 L R 

  0.80 for both connections since the ratios are outside the range of 0.6 V Vy  0.9 . PZ PZ 

Clear Span-to-Depth Modifier (ASCE 41 §5.4.2.4.2-4.3) 

L 340 c   14.1 10 

d 24.1 

Lc  340   LD 1.4  0.04 1.4  0.04   0.836  d  24 

(The clear span-to-depth ratio is used differently for nonlinear analysis procedures.) 

Beam Web and Flange Slenderness Modifier (ASCE 41 §5.4.2.4.2-4.4) 

ASCE 41 is not clear if these compactness requirements are applicable at the column face or at the critical 

connection component (i.e., center of RBS). It is assumed here that the measurements are applicable at the 

face of the column because such an applicability provides the largest element slenderness values. 

b f 52  5.86   7.01 

2t f Fye 

h 418  45.9   56.4 

tw Fye 

 SL 1.0 

Therefore, the adjusted m-factors for the left and right beam-to-column connection are: 

m m   5.43 1.0 0.80 0.836 1.0          3.63 i CP PZ LD SL 

Acceptance Criteria Check 

C.1.1.4.1 Beam 

The acceptance criteria check for the beam (done at the center of the RBS) is: 

DCR MUD 2336 DCR NL     0.45 1.0 , m mMCE 8 656  

C-5 
DCR M 2130 DCR NR   UD   0.41 1.0 , m mMCE 8 656  

The left and right beam hinges satisfy the CP BPL acceptance criteria at the BSE-2 EHL. 

C.1.1.4.2 Fully Restrained Connection 

The acceptance criteria check for the beam-to-column connection (done at the face of the column) is: 

DCR M 2533 DCR   UD   0.98 1.0 NL m MCE  1.08  , m 3.63 656 

DCR MUD 2326 DCR     0.90 1.0 NR , m mMCE 3.63 709  

To check force-controlled action at the face of the column: 

QCLc  QCEb (ASCE 41 Eq. 5-14) 

 50  QCLc  M p 1027    934 kip-ft.  55 

QCEb  830 kip-ft. (= Mf — see previous beam-to-column connection calculation) 

Q CLc CEb  Q OK

In general, the deformation-control check at the center of the RBS (or converted to the face 

of the column as illustrated above) will control over the force-control check because of the 

strength requirements in AISC 358 at the face of the column. ASCE 41 should clarify this 

provision. For example, should the material strength change when the same member is 

used for the beam and connection calculations. 

The left and right beam-to-column connections satisfy the CP BPL acceptance criteria at the BSE-2 EHL. 

 SMF Column 

The first story column (No. 1) at the intersection of grid lines 1 and B is selected for this example (see 

circled element in Figure B-19): 

 W18×175
 

 hsx = 18 ft.(Lb of the column is conservatively taken as hsx) 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi
 

C-6 
 

Axial Demand 

The axial force in the column is force-controlled by default per ASCE 41: 

PE P  P  (ASCE 41 § 3.4.2.1.2) UF G C C J 12 

where 

C1 = 1.0 (T > 1.0 sec.) per ASCE 41 §3.3.1.3.1 

C2 = 1.0 (T > 0.7 sec.) per ASCE 41 §3.3.1.3.1 

min DCR  J  max   2.05 (min(DCR) roof beam = 0.83×2.47 = 2.05) (ASCE 41 §3.4.2.1.2) 

 2.0 

where DCR is the demand-to-capacity ratio of any component in the load path delivering force to the 

column. For the column in this example, this is interpreted to be all beam-to-column connection DCRs on 

the column line at and above the second floor. The minimum value of 2.0 allowed in ASCE 41 was selected 

because the building is considered to be in a zone with a high level of seismicity. 

Based on the controlling load combination, the demand on the column is: 

PG 1.1 P D  0.25 P L S  P  1.1 400   0.25 217    0  499 kips 

PE  1.0 Ex  0.3 Ey  869 kips 

869

PUF  499   926 kips 1.0 1.0 

Axial Strength 

In accordance with ASCE 41 §5.4.2.4.2, the lower-bound compression strength is determined as Pn from 

AISC 360 §E3 using c = 1 and Fy = Fy,LB = 50 ksi. Flexural buckling about the minor axis (y-axis) governs. 

P  P  A F 

  2.05 

CL n y , g cr y ,

KL y y Fy LB , 1.0 216   50   3.25  4.71 

ry E 2.76 29000 

C-7 
 

 

2 E 2 29000 F    46.7 ksi e y, 2 2
 

yy  KL  1.0 216   
 
      ry   2.76   

  FF y e   Fcr , y  0.658 Fy  32.0 ksi  

P    1639 kips CL 51.3 32.0 

PUF 926   0.56  0.50 → column is force-controlled for flexure 

PCL 1639 

PUF G , 499 P   0.30  UF  0.20 → m is reduced for P-M interaction

PCL 1639 PCL 

P UF 926   0.33 → column would be deformation-controlled for flexure per Pye 1.1(50)51.3
 

FEMA 273 

Flexural Demand 

The force-controlled flexure in the column is: 

M MUF  MG  E (ASCE 41 §3.4.2.1.2) C C J 12 

Based on the controlling load combination, the moment at the bottom of the column is: 

47052 MUF 10   23087 kip-in. = 1924 kip-ft. 1.0 1.0  2.05 

Flexural Strength 

Per ASCE 4 Section 5.4.6.4.3.2.2, the lower-bound flexural strength, MCL, is determined as Mn from AISC 

360 §F1 and §F2 using b = 1.0 and Fy = Fy,LB = 50 ksi. 

M  M  C 



M  M  0.7F S  L  L  /  L  L 

 CL n b p p y LB x b p r p ,  M p

  0.7 50 344     15.7  9.7 

M CL 1.44 1658   1658    1.44 1548    2229 kip-ft   12    46.8  9.7

C-8 
MCL  M p 1658 kip-ft. 

Acceptance Criteria Check 

The column acceptance criteria check is: 

P M 926 1924 DCR  UF  UF    0.56 1.16 1.72 1.0 (ASCE 41 §5.4.2.4) N P M 1639 1658 CL CL 

Therefore, the column fails to satisfy the CP BPL acceptance criteria at the BSE-2 EHL. However, it is 

uncertain what physical phenomenon is represented by this result—does a plastic hinge form in the column 

or does the column buckle out-of-plane. 

SMF Panel Zone 

The panel zone at the top of the first story column at the intersection of grid lines 1 and B is selected for 

this example (see circled elements in Figure B-19): 

 Column = W18×175 (No. 1) 

 Beam = W24×84 (No. 1) 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi 

Shear Demand 

The panel zone demand is obtained from summing the beam moments framing into the panel zone and then 

subtracting out the associated column shear—gravity loads are ignored for simplicity: 

M1 M2 29835 VUD  dt 



 t Vc 

  0 180 1099 kips    d   24.1  0.77  1 f 1 2 f 2 

M1 is the moment from the right beam and M2 = 0 because this panel zone is part of a one-sided beam-tocolumn connection. 

Shear Strength 

The panel zone strength is calculated from ASCE 41 Equation 5-5: 

V Vye  0.55F t d  538 CE ye cw kips (recall that no doubler plates are used in this study) c 

Acceptance Criteria 

The m-factor is taken from ASCE 41 Table 5-5: 

C-9 
m = 11 

Acceptance Criteria Check 

The panel zone acceptance criteria check is: 

DCR V 1099 DCR N   UD   0.19  1.0 

mV m CE 11 538  

Therefore, the panel zone satisfies the CP BPL acceptance criteria at the BSE-2 EHL. 

C.2 Nonlinear Assessment Examples 

The following example provides guidance to how the nonlinear assessment calculations were conducted 

in this study. Nonlinear assessment of the selected components is performed for the following criteria: 

 Nonlinear Dynamic Procedure (NDP) or Nonlinear Static Procedure (NSP) 

 Median value of the record set is used for the NDP 

 Collapse Prevention Building Performance Level for the BSE-2 EHL 

 SMF Beam 

The second floor beam along grid line 1 between grid lines B and C is selected for this example (see circled 

element in Figure B-19). 

 W24×84 with reduced beam sections 

 L = 30 ft. (centerline) 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi 

The demands for the SMF beam are taken from the median value of the record set from the NDP. 

Deformation Demand 

Total curvature demand (plastic plus elastic) in the beam-to-column connection (measured at the center of 

the RBS) is obtained directly from the moment-curvature response of the beam hinge in the PERFORM3D model. The total curvature demand for the left connections is: 

UD L,  0.02842 in./in. 

Additionally, the moment demand is: 

MUD L ,  9056 kip-in. 

C-10 
Acceptance Criteria 

The acceptance criteria in terms of plastic rotation are given in ASCE 41, Table 5-6. To compare against 

the moment-curvature results coming from PERFORM-3D, the plastic rotation is converted to total 

curvature: 

plastic    elastic  p AC , total AC ,   y pe  lp 

 M pe  y   EI 
  RBS
 

 M UD pe  M   pe    EI  RBS 

where lp is the plastic hinge length (taken as the length of the RBS),  is the total FR connection modifier 

considering the items described below, and  is the modifier that shifts the acceptance criteria from the face 

of the column to the centerline of the RBS. Per ASCE 41 Table 5-6, the initial plastic rotation acceptance 

criterion for a primary member with a RBS connection is: 

 ,  0.05  0.00030 d  0.05  0.00030(24.1)  0.0428 rad. p AC 

Per ASCE 41 Table 5-4, the RBS is considered an FR connection and thus the acceptance criteria is subject 

to the following acceptance criteria modifications in ASCE 41 §5.4.2.4.3 (each modifier is taken as  here). 

Continuity Plate Modifier (ASCE 41 § 5.4.2.4.3-4.1)
 

Refer to the linear analysis calculations above. 

 CP  1.0 for both connections 

Panel Zone Strength Modifier (ASCE 41 § 5.4.2.4.3-4.2) 

Refer to the linear analysis calculations above. 

 PZ  0.80 for both connections since the ratio is outside the range of 0.6  VPZ Vy  0.9 . 

Clear Span-to-Depth Modifier (ASCE 41 § 5.4.2.4.2-4.3) 

Lc 340   14.1  8

d 24.1 

C-11 
 LD 1.0 

Beam Web and Flange Slenderness Modifier (ASCE 41 § 5.4.2.4-4.4) 

Refer to the linear analysis calculations above. 

 SL 1.0 

Therefore, the adjusted m-factors for the left and right beam-to-column connections are: 

      1.0 0.80 1.0    1.0  0.8 CP PZ LD SL

Additionally,  is: 

Lclear 28.32     1.081 

L 26.19 

where L is the distance between RBS centerlines. This can be determined by using a simple cantilever 

model to convert rotation to the RBS to keep the same tip displacement. 

Therefore, the acceptance criterion is: 



 0.0428   0.8 1.081 p      0.002313 in/in.  16 

M  ZF  7874 kip-in. pe ye 

 y  7874  0.000194 in/in.

29000 1397  

9056  7874  pe   0.0000292 in/in.

29000 1397  

 ,  0.002313  0.000194  0.0000292  0.002535 in/in. total AC

Acceptance Criteria Check 

The beam-to-column connection acceptance criteria check is (based on the median of the record set): 

 plastic elastic 0.02842 DCR NL   11.1 1.0 ,   y pe   p AC  1.0 0.002535   , 

C-12 
The left beam-to-column connection does not satisfy the CP BPL acceptance criteria at the BSE-2 EHL. 

 SMF Column 

The first story column (No. 1) at the intersection of grid lines 1 and B is selected for this example (see 

circled element in Figure B-19): 

 W18×175 

 hsx = 18 ft.(Lb of the column is conservatively taken as hsx) 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi 

Given that the axial-moment demand changes for each earthquake record when doing the NDP, the 

demands for this example are taken from the NSP at the target displacement. 

Axial Demand 

The compressive axial load in the column at the target displacement is: 

P  780.1 kips 

Axial Strength 

In accordance with ASCE 41 §5.4.2.4.2, the lower-bound compression strength is determined as Pn from 

AISC 360 §E3 using c = 1 and Fy = Fy,LB = 50 ksi. Flexural buckling about the minor axis (y-axis) governs. 

PCL  P ,  51.3(32.0) 1639 kips → refer to the linear analysis calculations above n y 

P 780.1   0.48  0.50 → column is considered deformation-controlled for flexure 

PCL 1639 

Deformation Demand 

Total curvature demand (plastic plus elastic) in the column hinge is obtained directly from the momentcurvature response of the column hinge in the PERFORM-3D model. The total curvature demand is: 

UD  0.00123 in./in. 

Acceptance Criteria 

The acceptance criteria in terms of plastic rotation are given in ASCE 41 Table 5-6. To compare against 

the moment-curvature results coming from PERFORM-3D, the plastic rotation is converted to total 

curvature: 

C-13 
 

P  0.48  0.2

PCL 

bf 52  3.58  =7.01

2t f Fye 

h 260 18.0   35.1 

t w Fye 

 5 P 

 p,AC 11 1    y  2.27  y

 3 PCL 

From ASCE 41 Equation 5-2: 

P  F A  55 51.3    2822 kips ye ye 



 y P @ 0

ZF l ye c  P   780.1    1  0.00788 1   0.00570 rad. y 

    6EI c P  2822   ye 

However, to be consistent with the P-M interaction curve used to model the plastic hinge response, y, is 

taken as: 

 P 



1.1 1.5  y  y@ P0 

 1    0.00788 1 0.276  0.00683 rad. (a 20% increase from ASCE 41)  P   ye 

Therefore: 

  2.27 0.00683  0.0155 rad. p AC ,  

Therefore, the acceptance criterion is: 

plastic 

  elastic  p AC , 
 total AC ,    y   pe l p 

M pe 21890  y @ P0    0.000219 in./in.

EI 29000 3450  

C-14 
 

M 1.18 1   M    0.276   P 1.18 1 21890  18701 kip-in (ASCE 41 Eq 5-4) CE  pe  P  ye 

However, ASCE 41 Equation 5-4 is impossible to implement in PERFORM-3D. Thus to be consistent with 

the P-M interaction curve used to model the plastic hinge response, the following is used: 

 



P 1.1 1.5 MCE  M pe   1 

  21890  1 0.276 18984 kip-in. (see PERFORM-3D)  P ye 

M 18984  y  CE   0.000190 in./in.

EI 29000 3450  

M  M 20205 18984  pe  t CE   0.0000122 in./in.

EI 29000 3450  

Therefore, 



plastic 

0.0155  elastic 

   0.000190  0.0000122  0.0009783 in./in. total AC , 20.0 

Acceptance Criteria Check 

The column hinge acceptance criteria check is: 

 plastic elastic 0.00123 DCR N   1.26 1.0

  y pe   p AC  1.0 0.000978   , 

Therefore, the column fails to satisfy CP BPL acceptance criteria at the BSE-2 EHL—for the NSP. 

SMF Panel Zone 

The panel zone at the top of the first story column at the intersection of grid lines 1 and B is selected for 

this example (see circled element in Figure B-19). 

 Column = W18×175 (No. 1) 

 Beam = W24×84 (No. 1) 

 A992 Steel: Fy,LB = Fy = 50 ksi, Fye = 55 ksi, E = 29000 ksi, G = 11154 ksi 

The demands for the panel zone are taken from the NSP at the target displacement. 

C-15 
 

Deformation Demand 

The panel zone demand taken as the total shear deformation (plastic plus elastic) is obtained directly from 

the shear-shear strain response of the shear hinge in the PERFORM-3D model. The total shear strain 

demand is: 

 UD  0.00187 rad. 

Acceptance Criteria 

The acceptance criteria in terms of plastic shear angle are given in ASCE 41 Table 5-6. To compare against 

the strain results coming from PERFORM-3D, the plastic shear angle is converted to total shear angle: 

 p AC , 11 y rad. 

where y is the angular shear deformation of the panel zone. 

 y 0.55 F ye 0.55 55    y   y     0.00271 rad. 

G G 11154 

 p AC , 11 0.00271 0.0298   

  0.00271  0.0298  0.0325 total AC ,

Acceptance Criteria Check 

The panel zone acceptance criteria check is: 

 UD 0.00187 DCR N    0.057 1.0 

  AC 0.0325 

Therefore, the panel zone satisfies the CP BPL acceptance criteria at the BSE-2 EHL—for the NSP. 

C-16 
 

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