Quantifi cation of Building

Seismic Performance

Factors: Component 

Equivalency Methodology 

FEMA P-795 / June 2011

FEMA

FEMA P-795/ June 2011 

Quantification of Building Seismic 

Performance Factors: 

Component Equivalency Methodology

Prepared by 

APPLIED TECHNOLOGY COUNCIL

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

www.ATCouncil.org

Prepared for

FEDERAL EMERGENCY MANAGEMENT AGENCY

Michael Mahoney, Project Officer

Robert D. Hanson, Technical Monitor 

Washington, D.C. 

ATC MANAGEMENT AND OVERSIGHT

Christopher Rojahn (Project Executive)

William T. Holmes (Project Technical Monitor)

Jon A. Heintz (Project Quality Control Monitor) 

Ayse Hortacsu (Project Manager)

PROJECT MANAGEMENT COMMITTEE

Charles Kircher (Project Technical Director) 

Gregory Deierlein

Andre Filiatrault 

James R. Harris

John Hooper 

Helmut Krawinkler 

Kurt Stochlia 

WORKING GROUPS 

Curt Haselton 

Abbie Liel 

Seyed Hamid Shivaee 

Jackie Steiner

PROJECT REVIEW PANEL

S.K. Ghosh 

Mark Gilligan 

Ramon Gilsanz* 

Ronald O. Hamburger 

Richard E. Klingner

Philip Line 

Bonnie E. Manley

Rawn Nelson 

Andrei M. Reinhorn 

Rafael Sabelli

*ATC Board Representative
Notice

Any opinions, findings, conclusions, or recommendations expressed in this publication do not necessarily 

reflect the views of the Applied Technology Council (ATC), the Department of Homeland Security 

(DHS), or the Federal Emergency Management Agency (FEMA). Additionally, neither ATC, DHS,

FEMA, nor any of their employees, makes any warranty, expressed or implied, nor assumes any legal 

liability or responsibility for the accuracy, completeness, or usefulness of any information, product, or 

process included in this publication. Users of information from this publication assume all liability 

arising from such use.
FEMA P-795 Foreword iii

Foreword

The Federal Emergency Management Agency (FEMA) has the goal of 

reducing the ever-increasing cost that disasters inflict on our country. 

Preventing losses before they happen by designing and building to withstand 

anticipated forces from these hazards is one of the key components of 

mitigation, and is the only truly effective way of reducing the cost of 

disasters. 

As part of its responsibilities under the National Earthquake Hazards 

Reduction Program (NEHRP), and in accordance with the National 

Earthquake Hazards Reduction Act of 1977 (PL 94-125) as amended, FEMA 

is charged with supporting activities necessary to improve technical quality 

in the field of earthquake engineering. The primary method of addressing 

this charge has been supporting the investigation of seismic and related 

multi-hazard technical issues as they are identified by FEMA, the 

development and publication of technical design and construction guidance 

products, the dissemination of these products, and support of training and 

related outreach efforts. These voluntary resource guidance products present 

criteria for the design, construction, upgrade, and function of buildings 

subject to earthquake ground motions in order to minimize the hazard to life 

in all buildings and increase the expected performance of critical and higher 

occupancy structures.

This publication builds upon an earlier FEMA publication, FEMA P-695 

Quantification of Building Seismic Performance Factors (FEMA, 2009b). 

FEMA P-695 presents a procedural methodology for reliably quantifying 

seismic performance factors, including the response modification 

coefficient, R, the system overstrength factor, ΩO, and the deflection 

amplification factor, Cd, used to characterize the global seismic response of a 

system. 

While the methodology contained in FEMA P-695 provides a means to 

evaluate complete seismic-force-resisting systems proposed for adoption into 

building codes, a component-based methodology was needed to reliably 

evaluate structural elements, connections, or subassemblies proposed as 

substitutes for equivalent components in established seismic-force-resisting 

systems. The Component Equivalency Methodology presented in this 

document fills this need by maintaining consistency with the probabilistic, 
iv Foreword FEMA P-795

system-based collapse assessment concepts of FEMA P-695 while providing 

simple procedures for comparing the tested performance of different 

components. It is intended to be of assistance to organizations, such as the 

International Code Council Evaluation Service, who need to compare the 

seismic performance of alternate components to those contained in 

established seismic force resisting system.

FEMA wishes to express its sincere gratitude to Charlie Kircher, Project 

Technical Director, and to the members of the Project Team for their efforts 

in the development of this publication, including the Project Management 

Committee consisting of Greg Deierlein, Andre Filiatrault, Jim Harris, John 

Hooper, Helmut Krawinkler, and Kurt Stochlia; the Project Working Groups

consisting of Curt Haselton, Abbie Liel, Jackie Steiner, and Seyed Hamid 

Shivaee; and the Project Review Panel consisting of S.K. Ghosh, Mark 

Gilligan, Ramon Gilsanz, Ron Hamburger, Rich Klingner, Phil Line, Bonnie 

Manley, Rawn Nelson, Andrei Reinhorn, and Rafael Sabelli. Without their 

dedication and hard work, this project would not have been possible. 

Federal Emergency Management Agency
FEMA P-795 Preface v

Preface

In 2008, the Applied Technology Council (ATC) was awarded a “Seismic 

and Technical Guidance Development and Support” contract (HSFEHQ-08-

D-0726) by the Federal Emergency Management Agency (FEMA) to 

conduct a variety of tasks, including one entitled “Quantification of Building 

System Performance and Response Parameters.” Designated the ATC-63-1

Project, this work was the continuation of the ATC-63 Project, funded under 

an earlier FEMA contract, which resulted in the publication of the FEMA 

P-695 report, Quantification of Building Seismic Performance Factors

(FEMA, 2009b). This report outlined a procedural methodology for reliably 

quantifying seismic performance factors, including the response 

modification coefficient, R factor, the system overstrength factor, Ω0, and 

the deflection amplification factor, Cd, used to characterize the global 

seismic response of a system. 

While the FEMA P-695 Methodology provided a means to evaluate 

complete seismic-force-resisting systems proposed for adoption into building 

codes, a component-based methodology was still needed that could reliably 

evaluate structural elements, connections, or subassemblies proposed as 

substitutes for equivalent components in current code-approved seismicforce-resisting systems. The purpose of the ATC-63-1 Project was to 

develop such a methodology.

The recommended Component Equivalency Methodology described in this 

report balances the competing objectives of: (1) maintaining consistency 

with the probabilistic, analytical, system-based collapse assessment concepts 

of the FEMA P-695 Methodology; and (2) providing simple procedures for 

comparing the tested performance of different components. It was 

developed based on probabilistic concepts using results from collapse 

sensitivity studies on key performance parameters.

ATC is indebted to the leadership of Charlie Kircher, Project Technical 

Director, and to the members of the ATC-63-1 Project Team for their efforts 

in the development of the recommended methodology. The Project 

Management Committee, consisting of Greg Deierlein, Andre Filiatrault, Jim

Harris, John Hooper, Helmut Krawinkler, and Kurt Stochlia monitored and 

guided the technical development efforts. The Project Working Groups,

which included Curt Haselton, Abbie Liel, Seyed Hamid Shivaee, and Jackie 
vi Preface FEMA P-795

Steiner, deserve special recognition for their contributions in developing, 

investigating, and testing the methodology, and in preparing this report. The 

Project Review Panel, consisting of S.K. Ghosh, Mark Gilligan, Ramon 

Gilsanz, Ronald Hamburger, Richard Klingner, Philip Line, Bonnie Manley, 

Rawn Nelson, Andrei Reinhorn, and Rafael Sabelli provided technical 

review, advice, and consultation at key stages of the work. Ayse Hortacsu 

served as ATC project manager for this work. The names and affiliations of 

all who contributed to this report are provided in the list of Project 

Participants.

ATC also gratefully acknowledges Michael Mahoney (FEMA Project 

Officer), Robert Hanson (FEMA Technical Monitor), and William Holmes 

(ATC Project Technical Monitor) for their input and guidance in the 

preparation of this report, Peter N. Mork for ATC report production services, 

and Ramon Gilsanz as ATC Board Contact.

Jon A. Heintz Christopher Rojahn

ATC Director of Projects ATC Executive Director
FEMA P-795 Table of Contents vii

Table of Contents

Foreword....................................................................................................... iii

Preface.............................................................................................................v

List of Figures...............................................................................................xv

List of Tables............................................................................................ xxiii

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

1.1 Background and Purpose ............................................................. 1-1

1.2 Objectives and Scope................................................................... 1-3

1.3 Assumptions and Limitations...................................................... 1-4

1.3.1 Equivalency Approach........................................................1.4

1.3.2 Suitability of Proposed Components ................................. 1-4

1.3.3 Suitability of the Reference Seismic-Force-Resisting 

System................................................................................ 1-5

1.3.4 Limitations on Test Data and Design Requirements ......... 1-6

1.4 Anticipated Use and Implementation .......................................... 1-7

1.5 Technical Approach..................................................................... 1-7

1.5.1 Identification of Key Component Performance

Parameters.......................................................................... 1-8

1.5.2 Development of Component Testing Requirements.......... 1-8

1.5.3 Development of Probabilistic Acceptance Criteria............ 1-9

1.6 Content and Organization.......................................................... 1-10

2. Component Equivalency Methodology.............................................. 2-1

2.1 Introduction ................................................................................. 2-1

2.1.1 Scope.................................................................................. 2-1

2.1.2 General Approach.............................................................. 2-2

2.1.3 Description of Process....................................................... 2-2

2.1.4 Terminology....................................................................... 2-4

2.1.5 Notation ............................................................................. 2-6

2.1.6 Statistical Notation............................................................. 2-7

2.2 Component Testing Requirements .............................................. 2-8

2.2.1 General Requirements for Component Testing ................. 2-9

2.2.2 Cyclic-Load Testing ........................................................ 2-10

2.2.3 Monotonic-Load Testing ................................................. 2-13

2.3 Applicability Criteria................................................................. 2-15

2.3.1 Required Information and Data ....................................... 2-16

2.3.2 Reference Seismic-Force-Resisting-System: Collapse 

Performance Criteria........................................................ 2-16

2.3.3 Quality Rating Criteria..................................................... 2-16

2.3.4 General Criteria................................................................ 2-16

2.4 Reference Component Test Data Requirements........................ 2-17

2.4.1 Define Reference Component Design Space................... 2-17

2.4.2 Compile or Generate Reference Component Test Data... 2-18
viii Table of Contents FEMA P

-795

2.4.3 Interpret Reference Component Test Results...................2-18

2.4.4 Define Reference Component Performance Groups........2-18

2.4.5 Compute Summary Statistics........................................... 2.19

2.5 Proposed Component Design Requirements..............................2-19

2.5.1 Component Design Strength and Stiffness.......................2-19

2.5.2 Component Detailing Requirements................................2-20

2.5.3 Component Connection Requirements.............................2-20

2.5.4 Limitations on Component Applicability and Use...........2-20

2.5.5 Component Construction, Inspection, and Maintenance 

Requirements....................................................................2-20

2.6 Proposed Component Test Data Requirements..........................2-21

2.6.1 Define Proposed Component Design Space.....................2-21

2.6.2 Select Proposed Component Configurations for Testing.2-21

2.6.3 Perform Cyclic-Load and Monotonic-Load Tests............2-21

2.6.4 Interpret Proposed Component Test Results....................2-21

2.6.5 Define Proposed Component Performance Groups .........2-22

2.6.6 Compute Summary Statistics...........................................2-22

2.7 Quality Rating Criteria...............................................................2-22

2.7.1 Quality Rating of Test Data .............................................2-22

2.7.2 Quality Rating of Design Requirements ..........................2-24

2.8 Component Equivalency Acceptance Criteria ...........................2-25

2.8.1 Overall Approach to Establishing Equivalency ...............2-25

2.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation Capacity..................2-25

2.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness..................................................2-27

2.8.4 Requirements Based on Cyclic-Load Test Data: Effective 

Ductility Capacity ............................................................2-28

2.8.5 Requirements Based on Monotonic-Load test Data:

Ultimate Deformation ......................................................2-28

2.9 Documentation and Peer Review Requirements........................2-29

2.9.1 Documentation .................................................................2-29

2.9.2 Documentation of Test Data ............................................2-29

2.9.3 Peer Review Panel Requirements ....................................2-30

2.9.4 Peer Review Panel Selection............................................2-30

2.9.5 Peer Review Panel Responsibilities.................................2-31

3. Commentary on the Component Equivalency Methodology...........3-1

3.1 Introduction..................................................................................3-1

3.2 Component Testing Requirements...............................................3-2

3.2.1 General Requirements for Component Testing..................3-3

3.2.2 Cyclic-Load Testing...........................................................3-4

3.2.3 Monotonic-Load Testing..................................................3-12

3.3 Applicability Criteria .................................................................3-12

3.3.1 Required Information and Data........................................3-12

3.3.2 Reference Seismic-Force-Resisting System: Collapse

Performance Criteria ........................................................3-13

3.3.3 Quality Rating Criteria.....................................................3-13

3.3.4 General Criteria................................................................3-13

3.4 Reference Component Test Data Requirements........................3-20

3.4.1 Define Reference Component Design Space ...................3-21
FEMA P

-795 Table of Contents ix

3.4.2 Compile or Generate Reference Component Test Data...3-22

3.4.3 Interpret Reference Component Test Results..................3-22

3.4.4 Define Reference Component Performance Groups........3-22

3.4.5 Compute Summary Statistics...........................................3-25

3.5 Proposed Component Design Requirements.............................3-25

3.5.1 Component Design Strength and Stiffness......................3-26

3.5.2 Component Detailing Requirements................................3-26

3.5.3 Component Connection Requirements............................3-26

3.5.4 Limitations on Component Applicability and Use ..........3-27

3.5.5 Component Construction, Inspection, and 

Maintenance Requirements..............................................3-27

3.6 Proposed Component Test Data Requirements.........................3-27

3.6.1 Define Proposed Component Design Space ....................3-27

3.6.2 Select Proposed Component Configurations for Testing.3-28

3.6.3 Perform Cyclic-Load and Monotonic-Load Tests...........3-28

3.6.4 Interpret Proposed Component Test Results....................3-28

3.6.5 Define Proposed Component Performance Groups ........3-28

3.6.6 Compute Summary Statistics...........................................3-29

3.7 Quality Rating Criteria ..............................................................3-29

3.7.1 Quality Rating of Test Data .............................................3-29

3.7.2 Quality Rating of Design Requirements..........................3-31

3.8 Component Equivalency Acceptance Criteria...........................3-33

3.8.1 Overall Approach to Establishing Equivalency...............3-33

3.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation.................................3-34

3.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness.................................................3-36

3.8.4 Requirements Based on Monotonic-Load Test Data: 

Ductility Capacity............................................................3-37

3.8.5 Requirements based on Monotonic-Load Test Data:

Ultimate Deformation......................................................3-37

3.9 Documentation and Peer Review Requirements .......................3-38

4. Example Application...........................................................................4-1

4.1 Introduction .................................................................................4-1

4.2 Component Testing Requirements ..............................................4-1

4.3 Evaluation of Applicability Criteria ............................................4-2

4.4Reference Component Test Data.................................................4-2

4.4.1 Define Reference Component Design Space.....................4-2

4.4.2 Compile or Generate Reference Component Test Data.....4-2

4.4.3 Interpret the Reference Component Test Results ..............4-3

4.4.4 Define Reference Component Performance Groups..........4-9

4.4.5 Compute Summary Statistics.............................................4-9

4.5 Proposed Component Design Requirements.............................4-10

4.5.1 Component Design Strength and Stiffness......................4-10

4.5.2 Component Detailing Requirements................................4-11

4.5.3 Component Connection Requirements............................4-12

4.5.4 Limitations on Component Applicability and Use ..........4-13

4.5.5 Component Construction, Inspection, and 

Maintenance Requirements..............................................4-13

4.6Proposed Component Test Data ................................................4-13
x Table of Contents FEMA P-795

4.6.1 Define Proposed Component Design Space.....................4-13

4.6.2 Select Proposed Component Configurations for Testing .4-14

4.6.3 Perform Cyclic-Load and Monotonic-Load Tests ...........4-15

4.6.4 Interpret Proposed Component Test Results....................4-16

4.6.5 Define Proposed Component Performance Groups .........4-17

4.6.6 Compute Summary Statistics...........................................4-18

4.7 Evaluate Quality Ratings ...........................................................4-18

4.7.1 Quality Rating of Test Data .............................................4-18

4.7.2 Quality Rating of Design Requirements ..........................4-19

4.8 Evaluate Component Equivalency.............................................4-20

4.8.1 Overview..........................................................................4-20

4.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation .................................4-20

4.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness..................................................4-22

4.8.4 Requirements Based on Cyclic-Load Test Data: 

Effective Ductility Capacity.............................................4-23

4.8.5 Requirements Based on Monotonic-Load Test Data:

Ultimate Deformation ......................................................4-23

4.9 Summary of Example Component Equivalency Evaluation......4-24

5. Conclusions and Recommendations...................................................5-1

5.1 Introduction..................................................................................5-1

5.2 Findings from Supporting Studies ...............................................5-1

5.2.1 Key Performance Parameters.............................................5-1

5.2.2 Cyclic-Load and Monotonic-Load Test Data 

Requirements......................................................................5-4

5.2.3 Probabilistic Acceptance Criteria.......................................5-5

5.3 Findings of Test Applications......................................................5-6

5.3.1 General Findings................................................................5-6

5.3.2 Specific Findings: Stapled-Wood Shear Wall

Components........................................................................5-8

5.3.3 Specific Findings: Buckling Restrained Brace 

Components........................................................................5-8

5.3.4 Specific Findings: Pre-Frabricated Wall Components....... 5.9

5.3.5 Specific Findings: Nailed Wood Shear Wall Reference 

Component Data Set ..........................................................5-9

5.4 Recommendations for Further Study .........................................5-10

5.4.1 Compilation of Available Reference System 

Benchmark Data...............................................................5-10

5.4.2 Development of Additional Reference System 

Benchmark Data...............................................................5-10

5.4.3 Development of Standard Cyclic-Load Testing 

Methods............................................................................5-11

5.4.4 Implications for Design Requirements Related to 

Overstrength.....................................................................5-11

Appendix A: Identification of Component Parameters Important 

for Equivalency...................................................................A-1

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

A.2 Representative Component Behavior..........................................A-1
FEMA P-795 Table of Contents xi

A.3 Literature Review ....................................................................... A-4

A.3.1 Collapse Studies.............................................................. A-4

A.3.2 Non-Collapse Studies...................................................... A-6

A.4 Wood Light-Frame Building Collapse Sensitivity Studies......... A-9

A.4.1 Building Models and Baseline Component Parameter 

Values.............................................................................. A-9

A.4.2 Sensitivity Study Results for Three-Story Building: 

Full Replacement .......................................................... A-12

A.4.3 Sensitivity Study Results for Three-Story Planar Model:

Mixing-and-Matching Over the Height of Building ..... A-15

A.4.4 Sensitivity Study Results for Three-Story ThreeDimensional Model: Mixing-and-Matching of Walls 

in Plan and over Height................................................. A-21

A.4.5 Summary of Parameter Importance for Wood LightFrame Buildings............................................................ A-24

A.5 Reinforced Concrete Special Moment Frame Collapse 

Sensitivity Study....................................................................... A-26

A.6 Summary of Key Component Parameters ................................ A-29

Appendix B: Development of Requirements for Cyclic-Load and 

Monotonic-Load Testing ....................................................B-1

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

B.2 Cyclic-Load Test Data Considerations........................................B-1

B.2.1 Importance of Cyclic Loading History.............................B-2

B.2.2 Overview of Commonly Used Loading Protocols...........B-3

B.2.3 Selection of Acceptable Loading Histories and 

Protocols...........................................................................B-5

B.2.4 Special Case: Same Loading Protocol Used to 

Generate Proposed and Reference Component Data .....B-10

B.2.5 Illustration: Comparison of Loading Histories...............B-10

B.2.6 Additional Considerations for Cyclic-Load Testing ......B-13

B.3 Monotonic-Load Test Data Considerations...............................B-13

B.3.1 Importance of Monotonic-Load Test Data in 

Component Methodology...............................................B-14

B.3.2 Illustration: Limitations of Using Only Cyclic-Load 

Test Data for Component Equivalency ..........................B-16

B.3.3 Monotonic-Load Test Data Requirements.....................B-19

Appendix C: Development of Probabilistic Acceptance Criteria......... C-1

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

C.2 Collapse Capacity Fragilities and the Effects of 

Uncertainty ..................................................................................C-1

C.3 Effect of Changes in Deformation Capacity on the Collapse 

Fragility .......................................................................................C-4

C.4 Effect of Changes in Strength on the Collapse Fragility .............C-7

C.5 Probabilistic Acceptance Criterion Used in Component 

Equivalency Methodology.........................................................C-10

C.5.1 Overall Approach...........................................................C-10

C.5.2 Development of the Penalty Factor for Differences in 

Uncertainty.....................................................................C-10
xii Table of Contents FEMA P-795

C.5.3 Development of the Penalty Factor for Differences in 

Strength.......................................................................... C-12

Appendix D: Test Application: Stapled Wood Shear Wall

Components ........................................................................D-1

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

D.2 Description of Stapled wood Shear Walls ..................................D-1

D.3 Evaluation of Applicability Criteria............................................D-3

D.4 Reference Component Test Data ................................................D-4

D.4.1 Define the Reference Component Design Space.............D-4

D.4.2 Compile or Generate Reference Component Test Data...D-4

D.4.3 Interpret Reference Component Test Results..................D-5

D.4.4 Define Reference Component Performance Groups .......D-9

D.4.5 Compute Summary Statistics...........................................D-9

D.5 Proposed Component Design Requirements...............................D-9

D.5.1 Component Design Strength and Stiffness......................D-9

D.5.2 Component Detailing Requirements .............................D-10

D.5.3 Component Connection Requirements..........................D-12

D.5.4 Limitations on Component Applicability and Use ........D-12

D.5.5 Component Construction, Inspection, and 

Maintenance Requirements...........................................D-12

D.6 Proposed Component Test Data................................................D-13

D.6.1 Define Proposed Component Design Space..................D-13

D.6.2 Select Component Configurations for Testing ..............D-13

D.6.3 Perform Cyclic-Load and Monotonic-Load Tests.........D-13

D.6.4 Interpret Proposed Component Test Results.................D-14

D.6.5 Define Proposed Component Performance Groups 

and Compute Summary Statistics..................................D-15

D.7 Evaluate Quality Ratings ..........................................................D-16

D.7.1 Quality Rating of Test Data...........................................D-16

D.7.2 Quality Rating of Design Requirements........................D-16

D.8 Evaluate Component Equivalency............................................D-17

D.8.1 Overview .......................................................................D-17

D.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation ..............................D-17

D.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness...............................................D-19

D.8.4 Requirements Based on Cyclic-Load Test Data: 

Effective Ductility Capacity ..........................................D-20

D.8.5 Requirements Based on Monotonic-Load Test Data: 

Ultimate Deformation....................................................D-20

D.8.6 Summary of Component Equivalency Evaluation ........D-20

D.9 Iteration: Evaluate Component Equivalency with 

Modifications............................................................................D-20

D.10 Summary of Component Equivalency Evaluation of Stapled 

Wood Shear Walls ....................................................................D-21

Appendix E: Test Application: Buckling-Restrained Brace 

Components ........................................................................E-1

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

E.2 Description of Buckling-Restrained Braces................................ E-2
FEMA P

-795 Table of Contents xiii

E.3 Evaluation of Applicability Criteria ............................................E-3

E.4 Reference Component Test Data.................................................E-5

E.4.1 Define Reference Component Design Space ...................E-5

E.4.2 Define of Reference Component Performance Groups....E-6

E.4.3 Compile or Generate Reference Component Test Data ...E-6

E.4.4 Interpret Reference Component Test Results...................E-9

E.4.5 Compute Summary Statistics.........................................E-13

E.5 Proposed Component Design Requirements.............................E-14

E.5.1 Component Design Strength and Stiffness.....................E-15

E.5.2 Component Detailing Requirements..............................E-16

E.5.3 Component Connection Requirements...........................E-16

E.5.4 Limitations on Component Applicability and Use.........E-16

E.5.5 Component Construction, Inspection, and 

Maintenance Requirements............................................E-16

E.6 Proposed Component Test Data ................................................E-17

E.6.1 Define Proposed Component Design Space...................E-19

E.6.2 Select Component Configurations for Testing...............E-19

E.6.3 Perform Cyclic-Load and Monotonic-Load Tests..........E-20

E.6.4 Interpret Proposed Component Test Results..................E-21

E.6.5 Compute Summary Statistics.........................................E-23

E.7 Evaluate Quality Ratings...........................................................E-23

E.7.1 Quality Rating of Test Data ...........................................E-23

E.7.2 Quality Rating of Design Requirements ........................E-24

E.8 Evaluate Component Equivalency.............................................E-25

E.8.1 Overview........................................................................E-25

E.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation ...............................E-25

E.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness................................................E-26

E.8.4 Requirements Based on Cyclic-Load Test Data: 

Effective Ductility Capacity...........................................E-26

E.8.5 Requirements Based on Monotonic-Load Test Data:

Ultimate Deformation ....................................................E-27

E.8.6 Summary of Component Equivalency Evaluation .........E-27

E.9 Loading Protocol Suitability......................................................E-28

E.10 Summary of Component Equivalency Evaluation of 

Buckling-Restrained Braces ......................................................E-30

E.11 Limitations of Test Application ................................................E-30

E.11.1 Reference Component Test Data Do Not Fully 

Represent the Design Space ...........................................E-30

E.11.2 The Equivalency Evaluation May Not Adequately 

Account for System Differences....................................E-30

E.11.3 Component Parameters are Approximate ......................E-31

Appendix F: Test Application: Pre-Fabricated Wall Components ......F-1

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

F.2 Description of Pre-Fabricated Wall Component .........................F-1

F.3 Evaluation of Applicability Criteria ............................................F-2

F.4 Reference Component Test Data.................................................F-3

F.5 Proposed Component Design Requirements...............................F-3

F.6 Proposed Component Test Data ..................................................F-4
xiv Table of Contents FEMA P-795

F.7 Evaluate Quality Ratings .............................................................F-6

F.7.1 Quality Rating of Test Data..............................................F-6

F.7.2 Quality Rating of Design Requirements...........................F-7

F.8 Evaluate Component Equivalency...............................................F-7

F.8.1 Overview ..........................................................................F-7

F.8.2 Requirements Based on Cyclic-Load Test Data:

Strength and Ultimate Deformation ................................F-8

F.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness..................................................F-9

F.8.4 Requirements Based on Cyclic Test Data: 

Effective Ductility Capacity .............................................F-9

F.8.5 Requirements Based on Monotonic Load Test Data: 

Ultimate Deformation.....................................................F-10

F.9 Summary of Component Equivalency Evaluation for PreFabricated Wall Components.....................................................F-11

References...................................................................................................G-1

Project Participants......................................................................................H-1
FEMA P-795 List of Figures xv

List of Figures

Figure 1-1 Conceptual boundaries defined by the Component 

Methodology applicability criteria of Section 2.3............. 1-5

Figure 2-1 Process for establishing and documenting component 

equivalency........................................................................ 2-3

Figure 2-2 Illustration of cyclic-load test data, envelope curve and 

maximum load, QM, effective yield deformation, ∆Y,eff,

ultimate deformation, ∆U, and initial stiffness, KI, 

parameters, for a component test specimen..................... 2-12

Figure 2-3 Illustration of a monotonic curve and determination of 

maximum load, QMM, and ultimate deformation, ∆UM, 

parameters for a component test specimen...................... 2-15

Figure 3-1 Monotonic and cyclic responses of identical steel 

specimens, and cyclic envelope curve fit to cyclic 

response.. ........................................................................... 3-2

Figure 3-2 Cyclic-load test data and cyclic envelope curve for 

a nailed wood light-frame shear wall specimen (data 

from Rosowsky et al., 2004).............................................. 3-8

Figure 3-3 Illustration of cyclic envelope curve and key component 

performance parameters obtained from positive and 

negative loading directions based on Figure 3-2 ............... 3-8

Figure 3-4 Cyclic-load test data and cyclic envelope curve for a 

nailed wood shear wall specimen (data from Rosowsky 

et al., 2004) ........................................................................ 3-9

Figure 3-5 Cyclic-load test data and cyclic envelope curve for a 

nailed wood shear wall specimen (data from Rosowsky 

et al., 2004) ........................................................................ 3-9

Figure 3-6 Cyclic-load test data and cyclic envelope curve for a 

nailed wood shear wall specimen (data from Rosowsky 

et al., 2004) ...................................................................... 3-10

Figure 3-7 Cyclic-load test data and cyclic envelope curve for a 

nailed wood shear wall specimen (data from Rosowsky 

et al., 2004) ...................................................................... 3-10
xvi List of Figures FEMA P-795

Figure 3-8 Cyclic-load test data and cyclic envelope curve for a 

nailed wood shear wall specimen (data from Rosowsky 

et al., 2004).......................................................................3-11

Figure 3-9 Cyclic response and cyclic envelope curve of a single HSSsection brace (data from Wakabayashi et al., 1979). In this

case the initial stiffness should be determined from the 

negative quadrant only.....................................................3-11

Figure 3-10 Cyclic response and cyclic envelope curve of an X-brace 

configuration (data from Wakabayashi et al., 1979). In this 

case the initial stiffness should be determined from the 

negative quadrant only.....................................................3-12

Figure 3-11 Illustration of proposed component and connection 

definitions for a steel concentrically braced seismicforce-resisting system.......................................................3-14

Figure 3-12 Illustration of two alternative definitions for the proposed 

component boundary for a steel concentrically braced

seismic-force-resisting system (Engelhardt, 2007)..........3-15

Figure 3-13 Illustration of the proposed component boundary for a 

buckling-restrained brace seismic-force-resisting

system (Engelhardt, 2007) ...............................................3-16

Figure 3-14 Illustration of proposed component boundaries for 

various wood light-frame shear walls, including 

(a) Simpson Strong-Tie (2009), (b) Simpson Steel 

Strong-Wall (Photo courtesy of Tools of the Trade 

Magazine, 2006), and (c) Hardy frame (Photo courtesy

of SBE Builders).............................................................3-17

Figure 3-15 Illustration of proposed component boundary for the 

fuse element in a steel eccentrically braced frame 

seismic-force-resisting system (Engelhardt, 2007)..........3-18

Figure 3-16 Illustration of a proposed component boundary for a steel 

plate shear wall in a seismic-force-resisting system 

(Sabelli, 2007)..................................................................3-19

Figure 3-17 Illustration of the difficulty in identifying an isolated 

component boundary in a multistory reinforced 

concrete shear wall seismic-force-resisting system .........3-19

Figure 3-18 Overview of test data used in the reference component 

data set..............................................................................3-20

Figure 4-1 Illustration of cyclic response of a nailed wood shear 

wall, data from Line et al. (2008) and Rosowsky et al. 

(2004).................................................................................4-4
FEMA P-795 List of Figures xvii

Figure 4-2 Illustration of cyclic response and envelope curve for 

a nailed wood shear wall, data from Line et al. (2008) 

and Rosowsky et al. (2004). .............................................. 4-4

Figure 4-3 Illustration of cyclic envelope curve and calculation of 

component response quantities for a nailed wood shear 

wall, data from Line et al. (2008) and Rosowsky et al. 

(2004)................................................................................. 4-5

Figure A-1 Representative monotonic component behavior............... A-2

Figure A-2 Illustration of the cyclic behavior of the component 

model. Test data from the PEER Structural Performance 

Database (Berry et al., 2004) for test index numbers 8, 

48, 154, and 212................................................................ A-3

Figure A-3 Example fitting of backbone curve to SAWS model, 

for the one-story high aspect ratio building No. 2.......... A-11

Figure A-4 Component parameters that are highly important for 

collapse response of three-story building ....................... A-13

Figure A-5 Component parameters that are moderately important 

for collapse response of three-story building ................. A-14

Figure A-6 Component parameters that are not important the 

collapse response of three-story building ....................... A-15

Figure A-7 Schematic diagram of the various mix-and-match cases 

considered for the building No. 10 sensitivity study. This 

considers possible mixing-and-matching over the height 

of the building................................................................. A-16

Figure A-8 Effects of strength on collapse capacity of building 

No. 10, for the mix-and-match case of only story one 

being replaced................................................................. A-17

Figure A-9 Effects of strength on collapse capacity of three-story 

building for the mix-and-match case of stories two and 

three being replaced........................................................ A-17

Figure A-10 Sensitivity study results for three-story building for 

the mix-and-match case with the bottom story walls 

replaced........................................................................... A-19

Figure A-11 Sensitivity study results for three-story building, for 

the mix-and-match case with the upper story 

(stories 2-3) walls replaced............................................. A-20

Figure A-12 Schematic diagram of the various mix-and-match cases 

considered in the sensitivity study. Mixing-and-
xviii List of Figures FEMA P-795

matching both in plan and over the height of the 

building are considered ...................................................A-21

Figure A-13 Sensitivity study results for mix-and-match case where 

walls are only replaced on the South and West sides 

of the building .................................................................A-22

Figure A-14 Sensitivity study results for mix-and-match case where 

walls are only replaced on the first story of the South 

and West sides of the building........................................A-23

Figure A-15 Sensitivity study results for mix-and-match case where 

walls are only replaced on the second and third stories

of the South and West sides of the building ..................A-24

Figure A-16 Sensitivity study results for the 4-story building 

ID1003, for the case of full replacement.........................A-28

Figure B-1 Identical steel specimens tested at the University of 

California at San Diego under different loading histories 

(Figure from PEER/ATC-72-1, data from Uang et al.,

2000) ................................................................................. B-2

Figure B-2 Comparison of cyclic envelope curves obtained for 

identical specimens under different loading protocols 

(from Gatto and Uang 2002), illustrating the effects of 

loading history choice on strength and deformation 

capacity ............................................................................. B-3

Figure B-3 Illustration of two cyclic-loading protocols for an 

example component test specimen: (a) CUREE; and 

(b) SPD.............................................................................. B-6

Figure B-4 Illustration of normalized cumulative deformation 

plot, showing (a) SAC loading protocol, (b) plot of

normalized cumulative deformation vs. normalized 

deformation amplitude .................................................... B-11

Figure B-5 Normalized cumulative deformation plots for an 

example reference component protocol (CUREE) and 

several candidate protocols. This plot is created 

based on specific assumptions about the proposed 

and reference component and is not generally 

applicable ........................................................................ B-13

Figure B-6 Cyclic behavior of an element experiencing (a) only 

cyclic strength deterioration, and (b) only in-cycle 

strength deterioration, figures from FEMA P-440A,

(FEMA, 2009)................................................................. B-15
FEMA P-795 List of Figures xix

Figure B-7 Hypothetical cyclic-load and monotonic-load test data for 

reference component (top) and proposed component

(bottom) illustrating the importance of considering both 

cyclic and monotonic behavior. Identical cyclic test 

parameters may obscure differences in monotonic behavior 

due to differences in cyclic and in-cycle strength 

deterioration. ..................................................................B-17

Figure B-8 Example time-history response of the proposed and 

reference component SDOF models subjected to a 

single ground motion scaled to Sa(1.0s) = 1.0g. ..............B-18

Figure B-9 Collapse fragility curves for the proposed and reference 

component SDOF models subjected to 20 ground 

motions ............................................................................B-18

Figure C-1 Illustration of two collapse capacity fragilities, with 

the same 10th percentile collapse capacity but different 

variability and medians......................................................C-2

Figure C-2 Relationship between component deformation capacity 

and system-level collapse capacity, for a three-story 

wood light frame building (from Figure A-4 of 

Appendix A). .....................................................................C-5

Figure C-3 Relationship between component strength and systemlevel collapse capacity, for a three-story wood lightframe building showing the results for: (a) full 

replacement; and (b) mixing-and-matching when only 

stories 2-3 are replaced with the stronger components......C-8

Figure D-1 Failure modes of stapled wood shear wall test specimens 

showing: (a) staple withdrawal for wall number 4-C; (b) 

staple and splitting of top plate for wall number 12-A; (c) 

anchor rod failure and splitting of sill plate for wall number 

8-C; and (d) staple shear and blocking failure for wall 

number 8-B (from Talbot et al., 2009) ............................. D-3

Figure D-2 Illustration of several stapled wood shear wall 

detailing requirements, including hold-down, studto-sill plate connector, and backup anchor bolt. Photo 

from Talbot et al. (2009)................................................. D-11

Figure D-3 Illustration of cyclic response of stapled wood shear 

wall specimen 8C (Talbot et al. 2009)............................ D-14

Figure E-1 Conventional (left) and buckling-restrained (right) braces 

under cyclic loading (from Kumar et al., 2007) ................E-2

Figure E-2 Features of a typical buckling-restrained brace (from 

Tsai and Hsiao, 2008)........................................................E-3
xx List of Figures FEMA P-795

Figure E-3 Illustration of reference component and definition 

of component boundary (Engelhardt, 2007) ..................... E-4

Figure E-4 Illustration of proposed component and definition of 

component boundary (Photo from Star Seismic).............. E-5

Figure E-5 Illustration of cyclic response of X-brace configuration 

tested by Clark (2009) for a two-story frame 

configuration. .................................................................... E-8

Figure E-6 Illustration of cyclic response of single HSS-section 

brace from Kotulka (2007) for a 1-story, 1-bay frame...... E-9

Figure E-7 Cyclic test data for X-brace specimen TCBF-HSS-R 

(Test Index 1) tested by Clark (2009) showing: (a) cyclic 

response and cyclic envelope curve; and (b) cyclic 

envelope curve and component response quantities, in 

terms of brace axial force and elongation. The frame 

height and width are 6660 mm........................................ E-10

Figure E-8 Plot of test data for specimen HSS-12 (Test Index 9) 

from Kotulka (2007) showing: (a) cyclic response and 

cyclic envelope curve; and (b) combination of response in 

the positive and negative direction for calculation of 

component parameters for single brace specimen, tested

in a 1-bay, 1-story frame with height and width of 

12 ft. ................................................................................ E-13

Figure E-9 Dimensions needed for computing the design stiffness 

for BRBs (Figure from Black et al., 2002) ..................... E-15

Figure E-10 Photo of steel core after fracture in buckling-restrained 

brace specimen (Merritt et al., 2003a) ............................ E-19

Figure E-11 Illustration of cyclic response of buckling-restrained 

brace Specimen 3 (Benzoni and Innamorato, 

2007) ............................................................................... E-20

Figure E-12 Illustration of cyclic response, cyclic envelope curve 

and calculation of component response quantities of 

BRB Specimen 1 (Benzoni and Innamorato, 2007)........ E-21

Figure F-1 Example residential building application of highaspect ratio pre-fabricated wall components......................F-2

Figure F-2 Example commercial building application of highaspect ratio, pre-fabricated wall components.....................F-2

Figure F-3 Illustration of cyclic-load testing data and cyclic 

envelope curve (from Figure 2-2) ......................................F-4
FEMA P-795 List of Figures xxi

Figure F-4 Cyclic response and envelope curve for pre-fabricated 

component test specimen No.1 ..........................................F-5

Figure F-5 Cyclic response and envelope curve for pre-fabricated 

component test specimen No.2 ..........................................F-5

Figure F-6 Cyclic response and envelope curve for pre-fabricated 

component test specimen No.3 ...................................... F-6

FEMA P-795 List of Tables xxiii

List of Tables

Table 2-1 Quality Rating of Test Data............................................. 2-23

Table 2-2 Quality Rating of Design Requirements.......................... 2-24

Table 2-3 Penalty Factor to Account for Uncertainty...................... 2-26

Table 2-4 Penalty Factor to Account for Differences in Load 

(Strength)......................................................................... 2-27

Table 3-1 Sample Reference Component Data Set.......................... 3-25

Table 3-2 Sample Proposed Component Data Set ........................... 3-29

Table 4-1 Summary of Nailed Wood Shear Wall Configurations 

in the Reference Component Data Set............................... 4-6

Table 4-2 Summary of Important Component Parameters for 

the Reference Component Data Set................................... 4-8

Table 4-3 Summary Statistics for Reference Component 

Parameters........................................................................ 4-10

Table 4-4 Proposed Component Design Strengths for Hypothetical 

Combinations of Sheathing Type and Connector 

Spacing ............................................................................ 4-10

Table 4-5 Proposed Component Design Stiffness for Each 

Panel Geometry................................................................ 4-12

Table 4-6 Summary of Proposed Component Wall Configurations 

for Cyclic-Load Testing................................................... 4-14

Table 4-7 Summary of Proposed Component Wall Configurations 

for Monotonic-Load Testing............................................ 4-15

Table 4-8 Summary of Important Component Parameters from

the Proposed Component Cyclic-Load Data Set ............. 4-16

Table 4-9 Summary of Important Component Parameters from

the Proposed Component Monotonic-Load Data Set ...... 4-17

Table 4-10 Summary Statistics for Proposed Component 

Parameters from Cyclic-Load Test Data ......................... 4-18

Table 4-11 Penalty Factor to Account for Uncertainty (from 

Table 2-3)......................................................................... 4-20
xxiv List of Tables FEMA P-795

Table 4-12 Penalty Factor to Account for Difference in 

Component Strengths (from Table 2-4)...........................4-21

Table 4-13 Evaluation of Equivalency Acceptance Criteria ..............4-22

Table 4-14 Summary of Acceptance Criteria Evaluation for 

Proposed Component Shear Walls...................................4-24

Table 5-1 Relative Importance of Component Parameters ................5-2

Table A-1 Summary of Component Parameter Studies in 

Literature with Focus on Collapse Capacity.....................A-5

Table A-2 Summary of Component Parameter Studies in 

Literature with a Focus Different than Collapse 

Capacity ............................................................................A-7

Table A-3 Wood Light-Frame Structural Design Properties (after 

FEMA P-695 Table 9-20) ...............................................A-10

Table A-4 Baseline Strength and Stiffness Component Properties 

for Wood Light-Frame Building Models........................A-11

Table A-5 Values of Component Parameters for Wood LightFrame Building Models ..................................................A-12

Table A-6 Summary of the Level of Importance of Component 

Parameters for Eight Wood Light-Frame Buildings.......A-25

Table A-7 Reinforced Concrete Special Moment Frame Structural 

Design Properties............................................................A-26

Table A-8 Values of Component Parameters for the Reinforced 

Concrete Moment Frame Models ...................................A-27

Table A-9 Summary of the Level of Importance of Component 

Parameters for Six Reinforced Concrete Special 

Moment Frame Buildings ...............................................A-29

Table B-1 Key Features of Selected Loading Protocols.................... B-5

Table C-1 Relationship Between Component Ultimate Deformation 

and System-Level Collapse Capacity for Wood LightFrame Buildings................................................................ C-6

Table C-2 Relationship Between Component Ultimate Deformation 

and System-Level Collapse Capacity for Reinforced 

Concrete Special Moment Frame Buildings..................... C-6

Table C-3 Relationship Between Component Strength and SystemLevel Collapse Capacity for Wood Light-Frame 

Buildings........................................................................... C-9
FEMA P-795 List of Tables xxv

Table C-4 Penalty Factor to Account for Uncertainty......................C-11

Table C-5 Penalty Factor to Account for Differences in Strength ...C-13

Table D-1 Overview of Stapled Wood Shear Wall Configurations 

Tested (after Talbot et al. 2009) ....................................... D-2

Table D-2 Summary of Nailed Wood Shear Wall Configurations 

in the Reference Component Data Set.............................. D-6

Table D-3 Summary of Important Component Parameters for the 

Reference Component Data Set........................................ D-7

Table D-4 Summary Statistics for the Reference Component 

Parameters......................................................................... D-9

Table D-5 Summary of Important Component Parameters for

Proposed Component Data Set ....................................... D-15

Table D-6 Summary Statistics for Proposed Component 

Parameters....................................................................... D-16

Table D-7 Penalty Factor to Account for Uncertainty (from 

Table 2-3)........................................................................ D-18

Table D-8 Penalty Factor to Account for Difference in Component 

Strengths (from Table 2-4) ............................................. D-18

Table D-9 Evaluation of Equivalency Acceptance Criteria for 

Stapled Wood Shear Walls............................................. D-19

Table D-10 Summary of Acceptance Criteria Evaluation for 

Proposed Stapled Wood Shear Component.................... D-21

Table E-1 Summary of Conventional Brace Configurations in the 

Reference Component Data Set: X-Brace Tests................E-7

Table E-2 Summary of Conventional Brace Configurations in the 

Reference Component Data Set: Single Brace Tests........E-7

Table E-3 Summary of Important Component Parameters for the 

Reference Component Data Set.......................................E-14

Table E-4 Summary Statistics for the Reference Component..........E-14

Table E-5 Summary of Buckling-Restrained Brace Configurations

in the Proposed Component Data Set ..............................E-17

Table E-6 Summary of Important Component Parameters for the 

Proposed Component Data Set ........................................E-22

Table E-7 Summary Statistics for the Proposed Component ...........E-23
xxvi List of Tables FEMA P-795

Table E-8 Summary of Acceptance Criteria and Equivalency 

Evaluation ....................................................................... E-28

Table F-1 Summary Statistics for the Reference Component 

Parameters (from Table 4-3)..............................................F-3

Table F-2 Values of Strength, Stiffness, Ductility and Deformation 

Capacity Parameters and Summary Statistics for the 

Proposed Component .........................................................F-6

Table F-3 Summary of Acceptance Criteria Evaluation for 

Pre-Fabricated Wall Components....................................F-11
FEMA P-795 1: Introduction 1-1

Chapter 1

Introduction

This report describes a recommended methodology for evaluating the seismic 

performance equivalency of components, which are structural elements, 

connections, or subassemblies experiencing inelastic response that controls 

the collapse performance of a seismic-force-resisting system. The 

recommended Component Equivalency Methodology (referred to as the 

Component Methodology) is a statistically based procedure for developing, 

evaluating, and comparing test data for new components (proposed 

components) that are proposed as substitutes for selected components 

(reference components) in a current code-approved seismic-force-resisting 

system (reference SFRS). 

The Component Methodology is derived from the general methodology

contained in FEMA P-695 Quantification of Building Seismic Performance 

Factors (FEMA, 2009b). Like the general methodology in FEMA P-695, the 

intent of the Component Methodology is to ensure that code-designed 

buildings have adequate resistance to earthquake-induced collapse. In the 

case of component equivalency, this intent implies equivalent safety against 

collapse when proposed components are substituted for reference 

components in a reference SFRS.

Proposed components found to be equivalent using the Component 

Methodology can be substituted for components of the reference SFRS, 

subject to design requirements and seismic design category restrictions on 

the use of the reference SFRS. Reference systems include the seismic-forceresisting systems contained in ASCE/SEI 7-10 Minimum Design Loads for 

Buildings and Other Structures (ASCE, 2010). For clarity, it should be noted 

that the term “component” in ASCE/SEI 7-10 refers exclusively to 

nonstructural components, which is different from how the term is used in 

this report. In the Component Methodology, the term “component” refers to 

structural elements that are part of the seismic-force-resisting system.

1.1 Background and Purpose

The Applied Technology Council (ATC) was commissioned by the Federal 

Emergency Management Agency (FEMA) under the ATC-63 Project to 

develop a methodology for quantitatively determining the response 

modification coefficient, R, the system overstrength factor, ΩO, and the 
1-2 1: Introduction FEMA P-795

deflection amplification factor, Cd, used in prescriptive seismic design 

procedures found in modern building codes. Collectively referred to as 

seismic performance factors, these factors are fundamentally critical in the 

specification of seismic design loading. They are used to estimate strength 

and deformation demands on seismic-force-resisting systems that are 

designed using linear methods of analysis, but are responding in the 

nonlinear range. 

The resulting FEMA P-695 report outlines a procedural methodology for 

quantifying collapse behavior and establishing seismic performance factors 

for newly proposed structural systems. The FEMA P-695 Methodology

relies on collapse simulation through nonlinear response history analysis of 

structural systems. It accounts for potential uncertainties in ground motions, 

component design parameters, structural configuration, and behavioral 

characteristics of structural elements based on available laboratory test data. 

It is anticipated that this methodology will be used by the nation’s seismic 

code development committees to set minimum acceptable design criteria for 

code-approved systems, and to provide guidance in the selection of 

appropriate design criteria for other systems when linear design methods are 

utilized.

While complete systems have been proposed for adoption as new seismicforce-resisting systems, it is also common that new structural elements, 

connections, or subassemblies are proposed for use in current code-approved

seismic-force-resisting systems. Such components, as they are referred to in 

this report, have been typically evaluated on the basis that their substitution

for components in a reference system would result in equivalent (or better) 

seismic performance. 

Although the FEMA P-695 Methodology could be used to evaluate the 

seismic performance capability of new components, FEMA initiated the 

ATC-63-1 Project to simplify and adapt the general methodology contained 

in FEMA P-695 for use in evaluating the specific case of component 

equivalency. Whereas the FEMA P-695 Methodology is based on both 

experimental testing and nonlinear dynamic analyses of archetypical 

structural systems, a key difference is that the Component Equivalency 

Methodology is based primarily on experimental testing of components. 

The resulting Component Methodology described in this report is not 

intended to replace the FEMA P-695 Methodology for the evaluation of new 

systems. Instead, it is intended to provide an additional tool for evaluating 

the performance equivalency of components meeting the applicability criteria

described herein.
FEMA P-795 1: Introduction 1-3

1.2 Objectives and Scope 

The Component Methodology measures the equivalency of proposed 

components and reference components by comparing key performance 

parameters, such as strength, stiffness, effective ductility, and deformation 

capacity. Values of these key parameters are determined from statistical 

evaluation of test data. The Component Methodology is based on the 

following two basic performance objectives:

• Proposed components can replace reference components in the reference 

SFRS without changing the seismic performance of the reference SFRS.

• The collapse performance of the reference SFRS is comparable (or 

assumed to be comparable) to seismic-force-resisting systems that 

comply with the collapse performance objectives of the FEMA P-695 

Methodology.

The first objective is the basis of the quantitative acceptance criteria used in

the Component Methodology. The second objective recognizes that many 

seismic-force-resisting systems in ASCE/SEI 7-10 have not been 

comprehensively evaluated using the FEMA P-695 Methodology. 

Evaluation of selected seismic-force-resisting systems has shown that current 

code-approved systems generally comply with the collapse performance 

objectives of the FEMA P-695 Methodology (FEMA, 2009b and NIST,

2010). Therefore, provided that currently approved seismic-force-resisting

systems have well established design criteria and supporting test data, they 

are permitted to be used as a reference SFRS in the Component 

Methodology. 

The scope of the Component Methodology is limited to proposed 

components that meet certain applicability criteria. These criteria determine 

the suitability of the seismic-force-resisting system for which the component 

is proposed (the reference SFRS), define minimum quality requirements for 

design and test data, and establish limits on the use of the procedures in terms 

of performance-related attributes. The Component Methodology applies to 

components that have well-defined boundaries within the reference SFRS, 

and where the overall seismic behavior of the reference SFRS is not 

otherwise changed by the replacement of reference components with 

proposed components. While the scope of the Component Methodology is 

intended for broad application, it may not be applicable to all types of 

proposed components. Where the Component Methodology does not apply,

the more general procedures of the FEMA P-695 Methodology should be 

used to evaluate seismic performance equivalency.
1-4 1: Introduction FEMA P-795

The Component Methodology considers that proposed components might be 

used to replace some or all reference components within a reference SFRS. 

While partial replacement (i.e., “mixing”) of proposed and reference 

components within a system might be desirable for design versatility, it could 

inadvertently create a vertical or horizontal irregularity in the seismic-forceresisting system if the proposed and reference components do not have 

sufficiently similar strength and stiffness. For this reason, the Component 

Methodology limits the differences in strength and stiffness between 

proposed and reference components to allow for partial replacement. 

1.3 Assumptions and Limitations

Subject to the applicability criteria described in Chapter 2, the Component 

Methodology is intended to apply broadly to component types proposed for 

use in any of the currently approved seismic-force-resisting systems 

contained in ASCE/SEI 7-10. Practical application of the Component 

Methodology, however, will likely be limited to reference components for 

which there is available test data that is of sufficient quality and quantity for 

judging equivalency. This section summarizes key assumptions and 

potential limitations of the Component Methodology. 

1.3.1 Equivalency Approach

The Component Methodology is based on the concept of component 

equivalency as a practical means of achieving an acceptable level of collapse 

safety for the seismic-force-resisting system of interest. The equivalency 

approach necessarily assumes that the collapse safety of the reference SFRS

is adequate before proposed components are substituted for reference 

components. The acceptance criteria of the Component Methodology are 

intended to ensure that collapse safety will remain adequate when the 

proposed substitutions are made. Applicability criteria limit application of 

the Component Methodology to: (1) proposed component types that are 

considered suitable for evaluation using an equivalency approach; and (2)

currently approved seismic-force-resisting systems that are considered 

suitable for use as a reference SFRS. 

1.3.2 Suitability of Proposed Components

While the Component Methodology is intended to apply broadly to different 

types of components, equivalency concepts may not be applicable, or 

appropriate, in all cases. Figure 1-1 conceptually illustrates two fundamental 

issues regarding the applicability of the Component Methodology. The first 

is whether or not the proposed product is a new “system” or a new 

“component.” The second is whether or not the new component has 
FEMA P-795 1: Introduction 1-5 

characteristics (and data) suitable for evaluation using an equivalency 

approach. 

The boundaries shown in Figure 1-1 are defined by the applicability criteria 

in Section 2.3. It is possible that some new products will not meet these 

criteria. In such cases, the FEMA P-695 Methodology should be used for 

evaluation of new products that are deemed inappropriate for evaluation by 

equivalency. 

Figure 1-1 Conceptual boundaries defined by the Component 

Methodology applicability criteria of Section 2.3.

1.3.3 Suitability of the Reference Seismic-Force-Resisting System

In the FEMA P-695 Methodology, adequacy of collapse resistance is 

evaluated in an absolute sense using criteria that define an acceptable 

probability of collapse when subjected to Maximum Considered Earthquake 

ground motions. In the Component Methodology, adequacy of collapse 

resistance is evaluated in a relative sense using criteria that compare 

proposed and reference component performance, assuming that the reference 

SFRS complies with the collapse performance criteria of the FEMA P-695 

Methodology.

Ideally, only systems with adequate collapse safety would be used as a 

reference SFRS. The Component Methodology, however, permits any 

system in ASCE/SEI 7-10 to be used as a reference system without being 

FEMA P-695

Component 

Methodology

FEMA P-695

New 

System

New 

Component

Components 

Suitable for 

Equivalency 

Components not 

Suitable for 

Equivalency

Boundaries 

Defined by 

Applicability 

Criteria 

(Section 2.3)
1-6 1: Introduction FEMA P-795

shown to comply with the FEMA P-695 Methodology. This is done for two 

reasons. First, it would not be practical for the Component Methodology to 

require implementation of the FEMA P-695 Methodology to evaluate a 

reference SFRS before evaluating component equivalency. Second, 

evaluations of several systems have shown that, with certain exceptions, 

current code-approved systems generally comply with the criteria of the 

FEMA P-695 Methodology. 

One such exception includes short-period configurations of all types of 

seismic-force-resisting systems. This exception reflects a shortcoming in

current seismic design requirements in general, and not in any one seismicforce-resisting system in particular. Such a shortcoming, while unfortunate, 

is not considered sufficient by itself to render any single system in

ASCE/SEI 7-10 unsuitable for use as a reference SFRS. 

1.3.4 Limitations on Test Data and Design Requirements 

The Component Methodology requires a minimum quality (and quantity) of 

component test data and a minimum quality of component design 

information. Lack of availability of this information, in particular reference 

component test data, could limit use the Component Methodology for some 

reference systems. 

Proposed component test data are expected to be developed as part of 

product development. Although the Component Methodology requires 

somewhat more extensive cyclic-load (and monotonic-load) testing than is 

typically used to support product development and approval, such testing is 

within the control of the product developer. Reference component test data 

are expected to be obtained from existing sources (previous tests of 

components within the reference system of interest). Unfortunately, sources 

of reference component test data can also be limited. 

While results of laboratory tests of structural elements of different material 

types appear frequently and extensively in a number of technical 

publications, few research programs have comprehensively investigated any 

given system of ASCE/SEI 7-10. The vast majority of the systems in Table 

12.2-1 of ASCE/SEI 7-10 do not have sufficient quality (or quantity) of data 

required for equivalency evaluation. Of the relatively small number systems 

with requisite test data, only a few (such as light-frame wood structural 

panels) have readily useable databases of test results. 

While it would be possible for product developers to conduct the necessary 

reference component testing, it is recognized that such testing may not be 

desirable or practical. Lack of readily useable, quality reference component 
FEMA P-795 1: Introduction 1-7

“benchmark” data is likely the most significant limitation on the use of the 

Component Methodology.

1.4 Anticipated Use and Implementation

The Component Methodology described in this report is intended as a 

technical resource for use by seismic codes and standards development 

committees, product evaluation services, product manufacturers, suppliers,

and their consultants.

Although the Component Methodology is based on the FEMA P-695

Methodology, the two methodologies are fundamentally different in their 

application. The FEMA P-695 Methodology is intended for use in the 

development of seismic performance factors for new seismic-force-resisting 

systems for which seismic codes and standards committees are responsible

for adoption. The Component Methodology is intended for use in 

establishing the equivalency of a new component for which product 

evaluation services have traditionally been responsible for issuing evaluation 

reports.

While seismic codes and standards committees may choose to reference, or 

possibly adopt, applicable portions of this report, it is envisioned that product 

evaluation services are the most likely immediate users of this information. 

In this case, the Component Methodology provides a technically sound basis 

for establishing acceptance criteria to be used in product evaluation reports.

How this document will be implemented by interested organizations and 

potential users is ultimately the responsibility of others, and is not known at 

this time. As part of on-going work by the National Institute of Building 

Science’s Building Seismic Safety Council (BSSC) Provisions Update 

Committee (PUC) to develop the 2014 edition of the NEHRP Recommended 

Seismic Provisions for New Buildings and Other Structures, a special Issue 

Team has been formed to study implementation of the FEMA P-695 

Methodology and the Component Methodology described herein. This Issue 

Team will be responsible for deciding if, and in what manner, the PUC will

make use of these methodologies.

1.5 Technical Approach

Development of the Component Methodology necessarily balanced two 

competing objectives: (1) maintaining consistency with the probabilistic,

analytical, and system-based collapse assessment concepts of the FEMA 

P-695 Methodology; and (2) providing simple procedures for comparing the 

tested performance of different components. Work involved the following 
1-8 1: Introduction FEMA P-795

tasks designed to systematically investigate the trade-offs between these 

objectives:

• Identification of key component performance parameters 

• Development of component testing requirements

• Development of probabilistic acceptance criteria

1.5.1 Identification of Key Component Performance Parameters

Key component performance parameters were identified through literature 

review and numerical collapse sensitivity studies on two- and threedimensional models of wall and frame structures. Collapse sensitivity 

studies considered full replacement (i.e., proposed components being used 

throughout the reference SFRS), as well as partial replacement (i.e., the 

“mixing” of proposed components and reference components within the 

reference SFRS). The following parameters were identified as critical for 

establishing equivalency in seismic collapse resistance: 

• Deformation capacity (ultimate deformation)

• Strength (ratio of measured ultimate strength to design strength) 

• Initial stiffness (ratio of measured initial stiffness to design stiffness)

• Effective ductility (ratio of ultimate deformation to effective yield 

deformation)

Component deformation capacity and strength were found to be the most 

important parameters affecting the collapse safety of a seismic-forceresisting system. Initial stiffness, in general, had less of an effect on collapse 

safety, but was included as a key parameter because of its fundamental

relation to ASCE/SEI 7-10 design processes, including: (1) story drift limits;

(2) the second-order stability coefficient; (3) the distribution of force 

demands to components within a statically indeterminate structural system;

and (4) other seismic checks such as those related to horizontal and vertical 

stiffness irregularities. Like initial stiffness, effective ductility had less of an 

effect on collapse safety, but was still considered important for preventing

inconsistencies in the hysteretic behavior of components and potential 

stiffness and strength irregularities that can result when elastic code-based 

seismic design procedures are used.

1.5.2 Development of Component Testing Requirements

Component testing requirements were drawn from the requirements 

contained within the FEMA P-695 Methodology and ASTM E2126-09

Standard Test Method for Cyclic (Reversed) Load Test for Shear Resistance 
FEMA P-795 1: Introduction 1-9

of Vertical Elements of the Lateral Load Force Resisting System for 

Buildings (ASTM, 2009), tailored to meet the needs of the Component 

Methodology. Cyclic-load and monotonic-load testing requirements address 

the number of component configurations that need to be tested, the number 

of test specimens per configuration, and the selection of load histories for 

cyclic-load testing.

Cyclic-load test data are the primary basis for establishing equivalency of 

proposed and reference components. Since the measured component 

strength and deformation capacity may differ depending on the cyclic-load 

history applied, guidelines for the selection and comparison of loading 

histories are needed to ensure that performance parameters of the proposed 

and reference components are appropriately compared. Accordingly, the 

Component Methodology ensures that the loading history used to test the 

proposed component be at least as damaging (quantified in terms of 

accumulated deformation imposed on the specimen) as the loading history

used to test the reference component.

Monotonic-load test data are required in addition to cyclic-load test data to 

help distinguish between different characteristics of component strength 

deterioration, such as cyclic versus in-cycle degradation that can influence 

system collapse behavior. 

1.5.3 Development of Probabilistic Acceptance Criteria

Acceptance criteria were developed to ensure that a seismic-force-resisting

system containing full or partial replacement of proposed components would 

have equivalent (or better) resistance to seismic-induced collapse as the same 

system containing reference components alone. Specifically, these criteria 

require that the ground shaking intensity large enough to cause a 10% 

probability of collapse in the seismic-force-resisting system would be

equivalent in both cases. This requirement is consistent with the 

probabilistic concepts of the FEMA P-695 Methodology.

While based on probabilistic equations and results from numerical collapse 

sensitivity studies documented in Appendix C, the resulting criteria are 

deliberately simple. The principal acceptance criterion is that the factored 

median deformation capacity of the proposed component must be as large as,

or larger than, the median deformation capacity of the reference component. 

The required margin between the proposed and reference component median 

deformation capacities is defined by two factors that account for 

uncertainties associated with component test data and design requirements,
1-10 1: Introduction FEMA P-795

and differences in strength. The factors are unity when the uncertainties and 

differences in strength are relatively small.

Additional acceptance criteria are provided to ensure that the proposed and 

reference components have comparable values of initial stiffness when 

implemented in the reference SFRS, and that the effective ductility of the 

proposed component is at least 50 percent of the effective ductility of the 

reference component.

1.6 Content and Organization

This report is written and organized to facilitate use and potential adoption

(with some modification) by seismic codes and standards development 

committees and product evaluation services with an interest in evaluating 

component equivalency. 

Chapter 1 explains the background, objectives, and approach used in 

developing the recommended Component Methodology.

Chapter 2 presents the complete requirements of the Component 

Methodology. It defines the scope, terminology, and applicability, and 

provides step-by step requirements and acceptance criteria for evaluating 

component equivalency. The intent of Chapter 2 is to describe the 

Component Methodology in a stand-alone form that could readily be used as 

the basis for code, standard, or acceptance criteria requirements for 

component equivalency. The text, however, is not written in mandatory

language and would require modification before adoption into a code, 

standard, or acceptance criteria document.

Chapter 3 is closely related to Chapter 2, providing section-by-section 

commentary on the requirements of the Component Methodology. 

Chapter 4 provides an example application of the Component Methodology

applied to the proposed substitution of a hypothetical new product in place of

nailed wood structural panels in wood light-frame construction. 

Chapter 5 concludes the main body of the report, providing a summary of the 

work and recommendations for future related research.

The appendices provide background information on the technical 

development of the Component Methodology and summarize test 

applications on additional components and reference seismic-force-resisting 

systems. Appendix A documents the analytical studies used to identify the 

key performance parameters related to collapse resistance of a seismic-forceresisting system. 
FEMA P-795 1: Introduction 1-11

Appendix B provides supporting material related to requirements for cyclic 

and monotonic testing of proposed and reference components. 

Appendix C describes development of probabilistic-based acceptance criteria

that are consistent with the collapse performance objectives of the FEMA 

P-695 Methodology. 

Appendix D describes a test application of the Component Methodology for 

the substitution of stapled wood shear walls for nailed wood shear walls in a

wood light-framed seismic-force-resisting system. 

Appendix E describes a test application of the Component Methodology for 

the substitution of buckling-restrained braces for conventional braces in a

special steel concentrically braced frame system. 

Appendix F describes a test application of the Component Methodology for 

the substitution of a pre-fabricated wall product for nailed wood shear walls 

in a wood light-framed seismic-force-resisting system.

FEMA P-795 2: Component Equivalency Methodology 2-1

Chapter 2

Component Equivalency 

Methodology

2.1 Introduction

2.1.1 Scope

The Component Equivalency Methodology (referred to as the Component 

Methodology) is a statistically based procedure for evaluating and comparing 

test data to determine the seismic performance equivalency of new 

components (proposed components) that are proposed as substitutes for 

selected components (reference components) in a current code-approved 

seismic-force-resisting system (reference SFRS). The Component 

Methodology is intended for evaluation of proposed components whose 

inelastic deformation behavior is a central aspect to the performance of the 

reference SFRS. The Component Methodology is intended for evaluation of 

proposed components whose inelastic deformation behavior is a central 

aspect to the performance of the reference SFRS.

The Component Methodology is derived from the general methodology 

contained in FEMA P-695 Quantification of Building Seismic Performance 

Factors (FEMA, 2009b). Similar to the general methodology in FEMA 

P-695, the intent of the Component Methodology is to ensure that codedesigned buildings have adequate resistance to earthquake-induced collapse. 

In the case of component equivalency, this intent implies equivalent safety 

against collapse when proposed components are substituted for reference 

components in a reference SFRS.

Proposed components found to be equivalent by the Component 

Methodology can be substituted for components of the reference SFRS, 

subject to design requirements and seismic design category restrictions on 

the use of the reference SFRS. Reference seismic-force-resisting systems

include those systems contained in ASCE/SEI 7-10 Minimum Design Loads 

for Buildings and Other Structures (ASCE, 2010) and other building code 

standards.

The Component Methodology is applicable to proposed components that 

meet the criteria of Section 2.3. For components that do not meet the criteria 

of Section 2.3, the more general procedures of the FEMA P-695 
2-2 2: Component Equivalency Methodology FEMA P-795

Methodology should be used to demonstrate seismic performance 

equivalency.

2.1.2 General Approach

The Component Methodology evaluates equivalency between proposed 

components and reference components based on criteria that compare 

statistical values of key performance parameters determined through cyclicload and monotonic-load testing.

The primary criterion is based on deformation capacities determined from 

cyclic-load and monotonic-load testing. Additional parameters related to 

component strength, stiffness, and effective ductility are used to establish 

limits on acceptable differences between the properties of proposed and 

reference components.

Component test data are evaluated by comparing statistics of test data that 

are classified into component performance groups, comprised of component 

configurations that share common features. Multiple performance groups are 

required for components that have significantly different behavioral 

characteristics associated with distinctly different design features. For 

example, a component would require separate performance groups if

behavior changed significantly as a function of component geometry (e.g., 

wood panel performance as function of wood panel aspect ratio). For each 

performance group, equivalency between proposed and reference 

components is evaluated by comparing median values of performance 

parameters for components in that group.

Each performance group contains a set of component configurations, which

are defined by the component geometry, design strength, and other defining 

attributes. A large number of component configurations are required to 

statistically evaluate performance for the range of intended application of the 

proposed component. At least two component test specimens are required for 

each proposed component configuration. In addition to a basic check on the 

median deformation capacity of the entire performance group, the 

deformation capacity of each proposed component configuration is checked 

to ensure that no configuration has a deformation capacity that is 

substantially lower than the range of values within the performance group.

2.1.3 Description of Process

Figure 2-1 provides a flowchart illustrating the steps of the Component 

Methodology. The process is based on test data developed for the proposed 

and reference components in accordance with Section 2.2. It includes an

evaluation of the applicability of the Component Methodology to the 
FEMA P-795 2: Component Equivalency Methodology 2-3

proposed component and the reference SFRS of interest (Section 2.3). 

Criteria for evaluating the applicability of the Component Methodology are 

based (in part) on the quality ratings of the test data and component design 

requirements defined in Section 2.7. Application of the Component 

Methodology is limited to reference SFRSs with test data and design 

requirements of reasonable quality. In cases where the Component 

Methodology is not applicable, the FEMA P-695 Methodology should be 

used to evaluate seismic performance equivalency.

Figure 2-1 Process for establishing and documenting component 

equivalency.

Reference component test data and design requirements for the reference 

SFRS must be assembled (Section 2.4). Component performance groups are 

identified and test data are collected for different component configurations

in each performance group. Statistical values of performance parameters are 

Assemble Reference 

Component Data

Document 

Results

Section 2.3: Applicability Criteria 

Conduct Peer Review

Section 2.4: Reference Component 

Test Data Requirements

Section 2.5: Proposed Component 

Design Requirements

Section 2.6: Proposed Component 

Test Data Requirements

Section 2.7: Quality Rating Criteria

Section 2.8: Component Equivalency 

Acceptance Criteria

Section 2.9: Documentation and Peer 

Review Requirements

Evaluate Component 

Equivalency

FEMA P-695

Yes

No

Applicable?

Yes

No

Equivalent?

Cyclic and Monotonic 

Testing Criteria

Section 2.2: Component Testing 

Requirements

Evaluate Methodology 

Applicability

Assess Quality Ratings 

for Design and Test Data

Develop Proposed 

Component Test Data

Develop Proposed 

Component Design Data
2-4 2: Component Equivalency Methodology FEMA P-795

calculated from test data of the reference component. Although it is expected 

that reference component test data will be collected from available sources of 

information, some testing of reference components may be necessary for 

adequate comparison with proposed component test data.

Design requirements and test data are developed for the proposed component 

(Section 2.5 and Section 2.6, respectively). Where significant reference 

component data already exist, testing plans for the proposed component can 

be tailored to coincide with data and meet the needs of the Component 

Methodology. Component performance groups and component 

configurations for proposed and reference components should be compatible, 

and should represent the full range of the intended application of the 

proposed component. Statistical measures of performance parameters are 

developed from cyclic-load and monotonic-load test data. Although

monotonic-load test data are optional for reference components, they are 

required for proposed components.

Quality of test data and design requirements are assessed using the criteria in

Section 2.7. Quality ratings for the reference component are used to ensure 

that the seismic-force-resisting system of interest is suitable for use as a 

reference SFRS. Quality ratings for the proposed component are used to 

establish the acceptance criteria for equivalency. More stringent criteria are 

imposed for proposed components with lower quality test data and design 

requirements.

Component equivalency is evaluated by comparing statistical values of the

reference and proposed component performance parameters in accordance 

with Section 2.8. Proposed components that meet the equivalency criteria 

can be used to replace components in the reference SFRS, subject to other 

design criteria and restrictions on use. For proposed components that do not 

meet the equivalency criteria, design requirements could be revised (e.g., use 

could be restricted to those configurations with acceptable performance), or 

test data could be augmented to improve the quality rating, and the proposed 

component could be re-evaluated with revised data.

Finally, use of the Component Methodology to determine equivalency should 

be fully documented and peer reviewed (Section 2.9). 

2.1.4 Terminology

Component: A structural element, connection, or subassembly of the 

seismic-force-resisting system, or combination thereof, within the component 

boundary.
FEMA P-795 2: Component Equivalency Methodology 2-5

Component Boundary: Defined boundary between the component and the 

balance of the reference SFRS.

Component Configuration: Specific combination of component properties 

including component geometry, detailing, and the manner in which the 

component connects to the rest of the seismic-force-resisting system.

Component Design Space: Range of possible configurations in which the 

structural component can be used. 

Component Performance Group: A subset of the component design space 

containing a group of component configurations that share a common set of 

features or behavioral characteristics. 

Component Test Specimen: Fabricated structural element, connection, or 

subassembly representing a component configuration.

Cyclic-Load Testing: Physical testing that is based on complete reversals in 

the direction of loading. Example requirements related to cyclic-load testing 

can be found in ASTM E2126-09 Standard Test Method for Cyclic 

(Reversed) Load Test for Shear Resistance of Vertical Elements of the 

Lateral Load Force Resisting System for Buildings (ASTM, 2009).

Cyclic Envelope Curve: Envelope of cyclic-load test data for a particular 

component, used to evaluate maximum load, QM, initial stiffness, KI,

effective yield deformation, ∆Y,eff, and ultimate deformation, ∆U, parameters, 

as illustrated in Figure 2-2.

Load History: The amplitude and sequence of deformations applied to the 

test specimen during cyclic-load testing.

Loading Protocol: The procedures governing cyclic-load and monotonicload testing of components.

Monotonic-Load Testing: Physical testing that is based on loading the test 

specimen in a single direction, with no reversals in the direction of loading.

Monotonic Curve: Plot of monotonic-load test data used to evaluate the 

monotonic maximum load, QMM, and ultimate deformation, ∆UM, parameters, 

as illustrated in Figure 2-3.

Proposed Component: Structural component proposed for substitution in 

the designated reference SFRS.

Quality Rating: Judgment-based measure of the quality of component test 

data and design requirements, based on criteria provided in Section 2.7.
2-6 2: Component Equivalency Methodology FEMA P-795

Reference Component: Structural component of the reference SFRS used 

to evaluate equivalency of the proposed component.

Reference SFRS: Seismic-force-resisting system in which proposed 

components would be substituted for reference components.

2.1.5 Notation

KD = Design stiffness of proposed or reference component

configuration, as derived from, or specified in, design 

requirements documentation.

KI = Effective value of initial stiffness of the component test 

specimen through the secant at 0.4QM, based on positive and 

negative cycles of loading, as shown in Figure 2-2.

PQ = Penalty factor due to the difference in the maximum load 

(strength) ratios of proposed and reference components, as 

defined in Table 2-4.

PU = Penalty factor due to the collective uncertainty associated with 

proposed component design requirements, βDR, and test data, 

βTD, as defined in Table 2-3.

Q = Generic load (i.e., force, moment) on proposed or reference 

component test specimen, or load specified for design.

QD = Load corresponding to the specified design strength of a 

component configuration, as derived from, or specified in, 

design requirements documentation.

QM = Maximum load applied to a component during cyclic-load 

testing, based on positive and negative cycles of loading, as 

shown in Figure 2-2.

QMM = Maximum load applied to a component during monotonic 

testing, as shown in Figure 2-3.

RK = Ratio of initial stiffness, KI, to design stiffness, KD, for a 

component test specimen.

RQ = Ratio of the maximum cyclic load, QM, to the design load, QD, of 

a component test specimen.

βDR = Uncertainty associated with the design requirements of the 

proposed or reference component, as specified in Section 2.7.2.

βTD = Uncertainty associated with the test data of the proposed or 

reference component, as specified in Section 2.7.1.

∆ = Generic deformation (e.g., displacement, rotation) of a proposed 

or reference component test specimen.

∆U = Ultimate deformation of a component test specimen at 0.8QM

based on positive and negative cycles of loading during cyclicload testing, as shown in Figure 2-2.
FEMA P-795 2: Component Equivalency Methodology 2-7

∆UM = Ultimate deformation of a component test specimen at 0.8QMM

based on monotonic-load testing, as shown in Figure 2-3.

∆Y,eff = Effective yield deformation of a component test specimen during 

cyclic-load testing based on positive and negative cycles of 

loading, defined by the ratio, QM /KI, as shown in Figure 2-2.

μeff = Effective ductility capacity of a component test specimen, 

defined as the ultimate deformation, ∆U, divided by the effective 

yield deformation, ∆Y, eff.

2.1.6 Statistical Notation

Note: The following median and lognormal standard deviation parameters 

are calculated from the associated data set assuming that the variable of 

interest has a lognormal probability distribution.

DC  = Median cumulative damage factor based on the cyclic-load 

testing protocol, as defined in Section 2.8.5.

R K PC ,  = Median value of the initial stiffness ratio, RK, for a proposed 

component (PC) performance group.

R K RC ,  = Median value of the initial stiffness ratio, RK, for a reference 

component (RC) performance group.

RQ PC ,  = Median value of the maximum load (strength) ratio, RQ, for a

proposed component (PC) performance group.

RQ RC ,  = Median value of the maximum load (strength) ratio, RQ, for a

reference component (RC) performance group.

∆ U PC ,  = Median value of ultimate deformation based on cyclic-load 

testing for a proposed component (PC) performance group.

∆ Uj PC ,  = Median value of ultimate deformation based on cyclic-load 

testing for a proposed component (PC) of configuration j.

∆ UM PC ,  = Median value of ultimate deformation based on monotonic-load 

testing for a proposed component (PC) performance group.

∆ U RC ,  = Median value of ultimate deformation based on cyclic-load 

testing for a reference component (RC) performance group.

∆ UM RC ,  = Median value of ultimate deformation based on monotonic-load 

testing for a reference component (RC) performance group.

∆Y eff PC , ,  = Median value of the effective yield deformation for a proposed 

component (PC) performance group.

∆Y eff RC , ,  = Median value of the effective yield deformation for a reference 

component (RC) performance group.
2-8 2: Component Equivalency Methodology FEMA P-795

μ eff PC ,  = Median value of effective ductility capacity for a proposed 

component (PC) performance group. 

μ eff RC ,  = Median value of effective ductility capacity for a reference

component (RC) performance group.

σRK,PC = Lognormal standard deviation (variability) of the initial stiffness 

ratio, RK, of a proposed component (PC) performance group.

σRK,RC = Lognormal standard deviation (variability) of the initial stiffness 

ratio, RK, of a reference component (PC) performance group.

σRQ,PC = Lognormal standard deviation (variability) of the maximum load

(strength) ratio, RQ, of a proposed component (PC) performance 

group.

σRQ,RC = Lognormal standard deviation (variability) of the maximum load

(strength) ratio, RQ, of a reference component (PC) performance 

group.

σ∆U,PC = Lognormal standard deviation (variability) of the ultimate cyclicload testing deformation for a proposed component (PC) 

performance group.

σ∆U,RC = Lognormal standard deviation (variability) of the ultimate cyclicload testing deformation for a reference component (RC) 

performance group.

σ∆Ι,PC = Lognormal standard deviation (variability) of the initial stiffness 

deformation, ∆I, for a proposed component (PC) performance 

group.

σ∆Ι,RC = Lognormal standard deviation (variability) of the initial stiffness 

deformation, ∆I, for a reference component (RC) performance 

group.

2.2 Component Testing Requirements

This section includes general requirements for component testing. It

describes test procedures and test data specific to cyclic-load testing and 

monotonic-load testing of components. These requirements are general in 

nature and apply to testing of both reference components and proposed 

components. Guidance on selecting specific component configurations for 

testing is provided in Section 2.4 (reference components) and Section 2.6

(proposed components). Criteria for rating the quality of test data are given 

in Section 2.7. Test data are used directly or with other specified data, in 

order to calculate statistical values of performance parameters required for 

component equivalency evaluation.

When interpreting test data, the generalized load, Q, and the generalized 

deformation, ∆, can be expressed in different ways, depending on the 

properties of the component. The choice of the appropriate load quantity 
FEMA P-795 2: Component Equivalency Methodology 2-9

(e.g., shear, moment) and the appropriate deformation quantity (e.g., 

displacement, drift, rotation) will depend on the component under 

consideration, but the quantities should be consistent between the proposed 

and reference component performance groups.

2.2.1 General Requirements for Component Testing

The following criteria should be considered when developing a program for 

component testing (e.g., testing of proposed component specimens), or when 

evaluating the quality of existing data from a previous testing program (e.g., 

assembling reference component test data).

• Size effects. Tests should be performed on full-size components unless 

it can be shown by theory or experimentation that testing of reducedscale specimens will not significantly affect behavior.

• Boundary conditions. The boundary conditions of component tests 

should be: (1) representative of constraints that a component would 

experience in a typical structural system; and (2) sufficiently general so 

that the results can be applied to boundary conditions that might be 

experienced in other system configurations (within the bounds of those 

considered in Section 2.6.1). Boundary conditions should not impose

beneficial effects on seismic behavior that would not exist in common 

system configurations.

• Load application. Loads should be applied to test specimens in a 

manner that replicates the transfer of load to the component as it would 

occur in common system configurations, and tests should generally be 

conducted using displacement control unless the component under 

investigation requires load-control testing (e.g., anchorage devices in a 

wood light-frame system).

For components that resist vertical loads (gravity and overturning loads), 

test loading should include these loads, unless it can be shown that they 

do not significantly influence component performance.

Exception. Reference component test data without applied vertical loads 

can be utilized, provided that the inclusion of vertical loads would not 

increase the reference component ultimate deformation (∆U,RC and 

∆UM,RC).

• Test specimen construction. Specimens should be constructed in a 

setting that simulates commonly encountered field conditions. For 

example, if field conditions necessitate a particular construction 

technique (e.g., overhead welding) then the same techniques should be 

used in the construction of the test specimen.
2-10 2: Component Equivalency Methodology FEMA P-795

• Quality of test specimen construction. The component should be of a 

construction quality that is equivalent to what will be commonly 

implemented in the field. Special construction techniques or quality 

control measures should not be employed, unless they are a required part 

of the design requirements for the component (see Section 2.5).

• Testing of materials. Material testing should be conducted when such 

data are needed to develop properties for component design 

requirements.

• Laboratory accreditation. Testing laboratories used to conduct an

experimental investigation program should generally comply with 

national or international accreditation criteria, such as the ISO/IEC 

17025 General Requirements for the Competence of Testing and 

Calibration Laboratories (ISO, 2005). 

Exception. Testing laboratories that are not accredited may be used for 

the experimental investigation program provided that the same 

information required by ISO/IEC 17025 is provided to the peer review 

panel, and the panel verifies acceptability of the laboratory.

• Instrumentation. Instrumentation should be installed to permit reliable 

measurement of all required strength, stiffness, and deformation 

quantities. Where necessary, deformation measurements should be 

corrected to remove rigid body displacement effects, inertial effects, or 

deformations due to the flexibility of the test apparatus.

2.2.2 Cyclic-Load Testing

Procedures used for cyclic-load testing of reference and proposed 

components should, as a minimum, comply with the requirements of this 

section.

Cyclic-Load Testing Protocol 

Cyclic-load testing should be performed in accordance with the following 

protocol:

• Proposed components and reference components should be tested with 

load histories that are equivalently damaging, quantified in terms of 

accumulated deformation imposed on the test specimen.

• The number of cycles should be sufficient to measure possible 

degradation of strength, stiffness, or energy dissipation capacity of the 

component under repeated cycles of loading.

• The deformation history should be described in terms of a well-defined 

quantity (e.g., displacement, story drift, rotation) and should consist of 
FEMA P-795 2: Component Equivalency Methodology 2-11

essentially symmetric deformation cycles of step-wise increasing 

amplitude. Cycles of smaller amplitudes between cycles of increasing 

amplitudes (trailing cycles) should only be included in the deformation 

history if they affect the cyclic response of the component.

• Proposed and reference component specimens should be tested to 

deformations large enough to achieve a 20% reduction in applied load, 

and therefore reach the ultimate deformation, ∆U, in at least one direction 

of loading.

Exception. Proposed component specimens need only be tested to 

deformations large enough to ensure compliance with the minimum 

equivalency criteria.

Number of Cyclic Test Specimens 

Cyclic test specimens for all component configurations in each performance 

group should meet the following minimum requirements:

• The number of component configurations should be sufficiently large in 

number to characterize the range of design parameters and component 

behavior for the performance group (with the actual number requiring

approval by the peer review). As a minimum, four component 

configurations should be included in each performance group.

Exception. The number of component configurations in a given 

performance group need not exceed the number of possible 

configurations of the proposed component, provided that the 

performance group includes at least eight component test specimens.

• A minimum of two component test specimens should be included for

each component configuration. A minimum of three tests should be 

included if any of the following occur: (1) if rapid and unpredicted 

deterioration occurs (such as that caused by brittle fracture); (2) if the 

strength, QM, varies by more than 15% between the two tests; or (3) if the

ultimate deformation capacity, ∆U, varies by more than 20% between the 

two tests.

Exception. For the reference component data set only one specimen per 

configuration is permitted, provided that a minimum of 8 test specimens 

are included in the performance group, rapid and unpredictable 

deterioration is not observed, and the ultimate deformation capacity, ∆U,

does not vary by more than 20% as compared to specimens of similar 

configuration.
2-12 2: Component Equivalency Methodology FEMA P-795

Cyclic-Load Test Data

• The following parameters should be determined using the cyclic 

envelope curve from the cyclic-load test data of each component test 

specimen:

o Ultimate load, QM

o Ultimate deformation, ∆U (deformation at 0.8QM)

o Initial stiffness, KI (based on force and deformation at 0.4QM)

o Effective yield deformation, ∆Y,eff (∆Y,eff = QM / KI )

o Effective ductility capacity, μeff (μeff = ∆U / ∆Y,eff)

• Values of each parameter should be measured from both positive and 

negative portions of the envelope curve, as illustrated in Figure 2-2.

Figure 2-2 Illustration of cyclic-load test data, envelope curve, and 

maximum load, QM, effective yield deformation, ∆Y,eff,

ultimate deformation, ∆U, and initial stiffness, KI

, parameters

for a component test specimen.

• The value of the ultimate deformation, ∆U, is taken as the deformation 

corresponding to 80 percent of the maximum load, QM.

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Q )

Cyclic-Load Data

Envelope Curve

∆Y,eff+ ∆U

+

QM+

0.8QM+

0.4QM+

KI

+

KI

-

QM0.8QM0.4QM-

∆Y,eff ∆ - U

-

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Envelope Curve

∆Y,eff+ ∆U

+

QM+

0.8QM+

0.4QM+

KI

+

KI

-

QM0.8QM0.4QM-

∆Y,eff ∆ - U

-
FEMA P-795 2: Component Equivalency Methodology 2-13

Exception. If the vertical load-carrying capacity of the component is 

compromised at a deformation less than that corresponding to 0.8QM, 

then the ultimate deformation capacity, ∆U, should be calculated as the 

deformation corresponding to loss of vertical-load carrying capacity.

• For components with reasonably symmetric behavior, values of ultimate 

deformation, ∆U, initial stiffness, KI, effective yield deformation, ∆Y,eff, 

and the effective ductility, μeff , should be calculated as the average of 

their respective values determined from the positive and negative 

portions of the envelope curve. 

• For components with significant asymmetric behavior, positive and 

negative values of ultimate deformation, ∆U, initial stiffness, KI, effective 

yield deformation, ∆Y,eff, and effective ductility capacity, μeff , should be 

calculated and evaluated separately for each loading direction.

Construction of the Cyclic Envelope Curve

The cyclic envelope curve should be constructed in accordance with the 

following requirements:

• The curve for should be constructed separately for positive and negative 

directions of loading. 

• At each level of deformation, up to the peak load experienced in the test, 

the load value of the cyclic envelope curve should be taken as the greater 

of: (1) the maximum value of load for all cycles at that level of

deformation; or (2) the value of load described by a series of straight 

lines that connect points of peak load at subsequent deformation 

amplitudes. 

• After the peak load has been reached, the envelope curve should be 

defined using only (1) above for the following two cases:

o If there is more than 20% difference in peak loads at subsequent 

deformation amplitudes.

o If the cyclic response curve has a negative stiffness (i.e., strength is 

lost in a single cycle of loading).

• The value of the cyclic envelope curve should drop to zero load at the 

maximum deformation executed in the test.

2.2.3 Monotonic-Load Testing

Procedures used for monotonic-load testing of reference and proposed 

components should, as a minimum, comply with the requirements of this 

section.
2-14 2: Component Equivalency Methodology FEMA P-795

Monotonic-Load Testing Protocol

Monotonic-load testing should be performed in accordance with the 

following protocol:

• Component test specimens should be tested in both directions for 

components that have significant asymmetric behavior.

• Component test specimens should be tested to deformations large enough 

to achieve a 20% reduction in applied load, and therefore reach the 

ultimate deformation, ∆UM.

Exception. Proposed component specimens need only be tested to 

deformations large enough to ensure compliance with the minimum 

equivalency criteria.

Number of Monotonic-Load Test Specimens

Monotonic-load test specimens should meet the following minimum 

requirements:

• For each performance group, the set of component configurations used 

for monotonic-load testing should be representative of the larger set of 

configurations used for cyclic-load testing.

• A minimum of two component configurations should be included for 

each component performance group.

• A minimum of two component test specimens should be included for 

each selected component configuration. A minimum of three tests 

should be included if any of the following occur: (1) rapid and 

unpredicted deterioration (such as that caused by brittle fracture); (2) the 

strength, QMM, varies by more than 15% between the two tests; or (3) the

ultimate deformation capacity, ∆UM, varies by more than 30% between 

the two tests.

Exception. Monotonic-load test data are not required for reference 

components, provided that the ultimate deformation capacity of the 

proposed component is shown to comply with Equation 2-6.

Monotonic-Load Test Data

The following parameters should be determined from the monotonic-load test 

data of each component test specimen:

• Ultimate load, QMM

• Ultimate deformation, ∆UM (deformation at 0.8 QMM)
FEMA P-795 2: Component Equivalency Methodology 2-15

Values of these parameters should be measured from the monotonic curve, as 

illustrated in Figure 2-3:

Figure 2-3 Illustration of a monotonic curve and determination of 

maximum load, QMM, and ultimate deformation, ∆UM, 

parameters for a component test specimen.

The value of the ultimate deformation, ∆UM, is taken as the deformation 

corresponding to 80 percent of the maximum load, QMM.

Exception. If the vertical load-carrying capacity of the component is 

compromised at a deformation less than that corresponding to 0.8QMM, then 

the ultimate deformation capacity, ∆UM, should be calculated as the 

deformation corresponding to loss of vertical-load carrying capacity.

For components whose cyclic response is essentially symmetric, the value of 

the ultimate deformation, ∆UM, may be calculated for a single direction of 

monotonic-load testing. For components with asymmetric behavior, separate 

test specimens are required for testing in each direction of deformation, and 

values of the maximum load, QMM, and the ultimate deformation, ∆UM, should 

be calculated separately for each direction (i.e., both positive and negative 

values are required for component equivalency evaluation).

2.3 Applicability Criteria

The Component Methodology may be used to evaluate a proposed 

component that complies with the criteria of this section. Applicability 

criteria address the suitability of the reference SFRS, the adequacy of 

reference component design criteria and test data, the adequacy of proposed 

0

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Monotonic-Load Testing Curve

∆UM

QMM

0.8QMM
2-16 2: Component Equivalency Methodology FEMA P-795

component design criteria and test data, and the characteristics of a proposed 

component that would permit the use of the Component Methodology.

2.3.1 Required Information and Data

Design requirement information and test data should be collected or 

developed for proposed and reference components in order to:

• Determine applicability of the Component Methodology

• Determine values of all parameters required by the Component 

Methodology 

2.3.2 Reference Seismic-Force-Resisting System: Collapse 

Performance Criteria

The reference SFRS should comply with the collapse performance criteria

contained in the FEMA P-695 Methodology. For purposes of the 

Component Methodology, it is assumed that currently approved seismicforce-resisting systems contained within ASCE/SEI 7-10 comply with these 

criteria.

2.3.3 Quality Rating Criteria

Quality of test data and design requirements of the reference and proposed 

components should be rated in accordance with the requirements of Sections

2.7.1 and 2.7.2, respectively, and should comply with the following criteria:

• For reference components, the quality rating of design requirements and 

test data should be Good or Superior.

• For proposed components, the quality rating of design requirements and 

test data should be Fair, Good, or Superior.

2.3.4 General Criteria

The proposed component, reference component, and reference SFRS should 

comply with the following general criteria:

• Component boundary. The boundary between the components and the 

balance of the reference SFRS should be defined, such that:

o Component test specimens and their connections to the reference 

SFRS are clearly defined.

o Testing boundary conditions are clearly established and realistically 

represent the interaction between the component and the reference 

SFRS.

o The component boundary is the same for the proposed and reference 

components and the transfer of forces across the component 
FEMA P-795 2: Component Equivalency Methodology 2-17

boundary is essentially the same for proposed and reference 

components.

Exception. When proposed and reference component configurations 

are substantially different and necessitate different component 

boundaries, then different component boundaries are permitted 

provided that the transfer of forces across the proposed component 

boundary does not adversely affect the vertical-load carrying 

capacity of the proposed component and performance of the balance 

of the structure.

• Balance of structure. The balance of the reference SFRS and the 

distribution of forces and deformations beyond the component boundary 

are essentially unchanged by replacement of reference components with

proposed components.

• Component properties. Load-deformation properties of proposed and 

reference components are substantially independent of the rate of loading 

(e.g., components are not velocity dependent).

• Component testing. Nonlinear (inelastic) response of components can 

be reliably measured by cyclic-load and monotonic-load testing.

• Component similarity. Proposed and reference components have a 

comparable range of seismic load resistance and capacity to support 

vertical loads (for components that support vertical loads).

• Vertical-load carrying capacity. For components that support vertical 

loads, the vertical-load carrying capacity of the proposed component is 

sufficient to resist vertical loads in combination with earthquake-induced 

deformations up to the ultimate deformation, ∆U.

• Seismic isolators and dampers. Proposed and reference components 

are not intended for use as either an isolator unit, as defined by Chapter 

17 of ASCE/SEI 7-10, or a damping device, as defined by Chapter 18 of 

ASCE/SEI 7-10.

2.4 Reference Component Test Data Requirements

2.4.1 Define Reference Component Design Space

The reference component design space should be established based on 

component configurations derived from established practice for the reference 

SFRS and the intended substitution with proposed components. The 

reference component design space should be developed in parallel with the 

proposed component design space (Section 2.6.1), and there should be 

consistency between the two.
2-18 2: Component Equivalency Methodology FEMA P-795

The range of component configurations should include variations in system 

geometry, component section and material properties, and detailing 

requirements that are used in practice. Configurations should reflect any

fundamental differences in how the reference component is used or in how it

performs for different permissible configurations.

2.4.2 Compile or Generate Reference Component Test Data 

The reference component test data should be compiled for component 

configurations and performance groups that reflect current use of the 

reference component. Data should be compiled from published sources or 

obtained from tests that are conducted specifically for the equivalency

evaluations. Cyclic-load and monotonic-load test data should comply with 

the minimum requirements of Section 2.2.

2.4.3 Interpret Reference Component Test Results

Performance parameters should be determined from results of cyclic-load 

and monotonic-load testing for each test specimen, in accordance with 

Section 2.2. In addition to the measured quantities, QM, KI, ∆U, ∆Y,eff, μeff, 

QMM, and ∆UM, the following quantities should be computed using the design 

strength and stiffness values, QD and KD, as determined by the reference 

component design requirements:

• Ratio of measured maximum strength to design strength (RQ = QM / QD)

• Ratio of measured initial stiffness to design stiffness (RK = KI / KD) 

2.4.4 Define Reference Component Performance Groups

The reference component data set should be placed into a single performance 

group unless there are fundamental differences in behavior among reference 

component data.

If there are fundamental differences in behavior among reference component 

data, the reference component data set should be separated into two or more

performance groups that reflect major divisions, or changes in behavior, 

within the set of data that can be associated with different component 

geometries, detailing requirements, or loading conditions. Separation of 

reference component test data into performance groups should be based on 

the following considerations:

• A fundamental change in component design requirements

• A systematic difference in failure mode among different configurations
FEMA P-795 2: Component Equivalency Methodology 2-19

• A fundamental geometric difference that tangibly affects the ratio of the 

inelastic deformation capacity to the effective yield deformation of the 

component (e.g., a short versus long cantilever column) 

• A substantial difference between loading histories used in testing

• A difference in the load or deformation quantity used to quantify 

component performance

• Any other difference that causes a clear change in the behavior or 

performance of the component

When separation into performance groups is necessary, reference component 

performance groups should be established in parallel with proposed 

component performance groups (Section 2.6.5), and there should be 

consistency in the manner in which the data are organized for both reference 

components and proposed components. 

2.4.5 Compute Summary Statistics

Reference component summary statistics (i.e., median and lognormal 

standard deviation values) should be computed for each of the component 

parameters listed in Sections 2.2 and 2.4.3. Median and lognormal standard 

deviation values should be computed separately for each parameter in each 

component performance group, assuming that the component parameters 

have a lognormal probability distribution.

2.5 Proposed Component Design Requirements

A comprehensive set of design requirements should be developed for the

proposed component.

2.5.1 Component Design Strength and Stiffness

Design requirements should include methods to predict both the design 

strength and design stiffness (effective stiffness at the design strength, QD) of 

the component. Methods for computing design strength and stiffness should 

identify the adopted design procedure (e.g., Load and Resistance Factor 

Design (LRFD) or Allowable Stress Design (ASD)). Where applicable, 

design requirements should include parameters to determine the expected 

strength of components that might be necessary for design of other elements

in the reference SFRS (e.g., Ry factors for steel structures).

Certain acceptance criteria in Section 2.8 are related to restrictions on 

proposed components that are imposed within the design requirements. 

Proposed component design requirements should, therefore, be developed 

consistent with these restrictions. In addition, design strength requirements 
2-20 2: Component Equivalency Methodology FEMA P-795

should be appropriate for other non-seismic concerns, such as elastic 

serviceability checks, design for gravity and wind loading, and fire 

resistance.

2.5.2 Component Detailing Requirements

Design requirements should include comprehensive provisions for seismic 

detailing of proposed components. Detailing requirements should cover the 

range of allowable configurations defined in Section 2.6.1.

2.5.3 Component Connection Requirements

Design requirements should include provisions for attachment of the 

proposed component to the balance of the reference SFRS. These 

requirements should ensure that the connection is strong enough to develop 

the full ultimate strength of the component, such that inelastic behavior 

occurs in the element, connection, or subassembly that is defined as the

proposed component, and not at the boundary between the proposed 

component and the balance of the reference SFRS.

2.5.4 Limitations on Component Applicability and Use

Design requirements should include provisions that reasonably restrict the 

proposed component usage to the range of allowable configurations defined 

in Section 2.6.1. They should consider the vertical-load carrying capacity of 

the proposed component (for components that support vertical load) and 

ensure that the vertical-load carrying capacity of the proposed component is 

equal to, or greater than, that of the reference component.

For components tested without vertical loads, design provisions should

restrict usage to ensure that the component cannot be substituted in a system 

where the level of vertical loads would tangibly affect the strength,

deformation capacity, or stability of the component. 

2.5.5 Component Construction, Inspection, and 

Maintenance Requirements

Design and quality assurance requirements should include provisions to

ensure that the proposed component and the connection between the 

proposed component and the balance of the reference SFRS are properly 

constructed. These requirements should ensure that the as-built performance 

of the component will be consistent with the laboratory test data used as the 

basis for demonstrating equivalency.

Design and quality assurance requirements should include provisions related 

to inspection and maintenance that are necessary to ensure that the seismic 
FEMA P-795 2: Component Equivalency Methodology 2-21

performance of the proposed component and connection to the balance of the 

seismic-force-resisting system do not measurably deteriorate over the 

intended life of the structure.

2.6 Proposed Component Test Data Requirements

2.6.1 Define Proposed Component Design Space

The range of allowable configurations of the proposed component should be 

defined and documented. These configurations comprise the proposed 

component design space, and allowable configurations should adhere to the 

same requirements as described in Section 2.4.1 for reference components. 

The proposed component design space should be established in parallel with 

the reference component design space (Section 2.4.1), and there should be 

consistency between the two. 

Exception. The proposed component design space may be more restrictive 

than the reference component design space, provided the design requirements 

similarly restrict the applicability and use of the proposed component.

2.6.2 Select Proposed Component Configurations for Testing

Proposed component configurations should be selected for testing based on 

the proposed component design space, which encompasses the envisioned 

use of the proposed component. The selected set of configurations should be 

sufficiently broad to capture the full range of the component design space. 

Selected configurations should represent all failure modes that are possible 

within the component design space. In addition, this selection process should

consider those configurations expected to be most frequently used in 

practice. 

2.6.3 Perform Cyclic-Load and Monotonic-Load Tests

The selected set of proposed component configurations should be tested in 

accordance with the requirements of Section 2.2.

2.6.4 Interpret Proposed Component Test Results

Performance parameters should be determined from results of cyclic-load 

and monotonic-load testing for each test specimen, in accordance with the 

requirements of Section 2.2. In addition to the measured quantities, QM, KI,

∆U, ∆Y,eff, QMM, μeff, and ∆UM, the following quantities should be computed 

using the design strength and stiffness values, QD and KD, as determined by 

the proposed component design requirements:

• Ratio of measured maximum strength to design strength (RQ = QM / QD)
2-22 2: Component Equivalency Methodology FEMA P-795

• Ratio of measured initial stiffness to design stiffness (RK = KI / KD) 

2.6.5 Define Proposed Component Performance Groups

The proposed component data set should be placed into a single performance 

group unless there are fundamental differences in behavior among proposed 

component data. If there are fundamental differences in behavior among the 

proposed component data, the data should be separated into two or more

performance groups following the same requirements specified for reference 

components in Section 2.4.4. 

When two or more performance groups are necessary, proposed component 

performance groups should be established in parallel with the reference 

component performance groups (Section 2.4.4). There should be consistency 

in the manner in which the data are organized into performance groups, to 

the extent that the divisions used for the reference component are also 

applicable to the proposed component. Each proposed component 

performance group should be clearly associated with a reference component 

performance group in which the proposed components are intended to be 

substituted for reference components.

2.6.6 Compute Summary Statistics

Proposed component summary statistics (i.e., median and lognormal standard 

deviation values) should be computed for each of the component parameters 

listed in Sections 2.2 and 2.6.4. Median and lognormal standard deviation 

values should be computed separately for each parameter in each component 

performance group, assuming that the component parameters have a 

lognormal probability distribution.

2.7 Quality Rating Criteria

2.7.1 Quality Rating of Test Data 

Test data for the reference component and the proposed component should be 

rated in accordance with the criteria in Table 2-1. The quality rating of test 

data should be based on the completeness and robustness of the overall 

testing program, and confidence in the test results. Minimum quality ratings 

for applicability of the Component Methodology are defined in Section 2.3.3. 

Completeness and Robustness of Tests

Evaluation of the completeness and robustness of the testing program should 

be based on the following considerations:
FEMA P-795 2: Component Equivalency Methodology 2-23

• The degree to which relevant testing issues have been considered in the 

development of the testing program.

• The extent to which the testing program and other documented 

experimental evidence quantify the necessary material, component, and 

connection properties (connection between the component and the rest of 

the structural system) and important behavior and failure modes. 

Table 2-1 Quality Rating of Test Data 

Completeness and Robustness of 

Tests

Confidence in Test Results

High Medium Low

High. Material, component, and 

connection behavior well understood 

and accounted for. All, or nearly all, 

important testing issues addressed.

Superior Good Fair

Medium. Material, component, 

and connection behavior generally 

understood and accounted for. 

Most important testing issues 

addressed.

Good Fair Not 

Permitted

Low. Material, component, and 

connection behavior fairly 

understood and accounted for. 

Several important testing issues not 

addressed.

Fair Not 

Permitted

Not 

Permitted

Confidence in Test Results

Confidence in test results is related to the reliability and repeatability of the 

results obtained from the testing program, corroboration with available 

results from other relevant testing programs, and the extent to which the 

chosen (or generated) test data is representative of the typical usage of 

reference components in practice and the future usage of proposed 

components. Evaluation of the confidence in test results should be based on 

the following considerations:

• Consideration as to whether or not the experimental test data exhibit 

consistent behavior, performance, and failure modes.

• The number of tests completed.

• The number of independent labs and researchers that have completed the 

tests (i.e., independent investigators obtaining similar results leads to 

increased confidence).

• The extent to which the test results are supported by numerical or 

analytical modeling based on the basic principles of mechanics.

• The extent to which the data set represents the range of possible 

component configurations allowed within the component design space.
2-24 2: Component Equivalency Methodology FEMA P-795

• The computed standard deviations of key component parameters from 

proposed component test data as compared with the same quantities in 

the reference component data set. If the standard deviation values are 

significantly larger in the proposed component data set, indicating the 

parameters of the proposed component are more uncertain, the quality 

rating should reflect a lower confidence in proposed component test

results. This consideration only applies to the quality rating of the 

proposed component data set.

2.7.2 Quality Rating of Design Requirements

Design requirements for the reference component should be rated in 

accordance with the criteria in Table 2-2. The quality rating of design 

requirements should be based on the completeness and robustness of the 

requirements and on the confidence in the underlying methods and design 

data. Minimum quality ratings for applicability of the Component 

Methodology are defined in Section 2.3.3.

Table 2-2 Quality Rating of Design Requirements

Completeness and Robustness of 

Design Requirements

Confidence in Basis of Design 

Requirements

High Medium Low

High. Extensive safeguards against 

unanticipated failure modes. All 

important design and quality assurance 

issues are addressed.

Superior Good Fair

Medium. Reasonable safeguards 

against unanticipated failure modes. 

Most of the important design and 

quality assurance issues are 

addressed.

Good Fair Not 

Allowed

Low. Questionable safeguards 

against unanticipated failure modes. 

Many important design and quality 

assurance issues are not addressed.

Fair Not 

Allowed

Not 

Allowed

Completeness and Robustness of Design Requirements

Completeness and robustness should be evaluated based on how well the 

design requirements address issues that could potentially lead to 

unanticipated failure modes, as well as quality assurance measures to ensure 

proper implementation of design through fabrication, erection, and final 

construction. Additionally, the rating should be based on how the design 

requirements also address important behavioral issues, such that the use of 

the design requirements results in highly reliable component behavior. 
FEMA P-795 2: Component Equivalency Methodology 2-25

Confidence in Design Requirements

Confidence should be evaluated based on the degree to which the prescribed 

material properties, strength criteria, stiffness parameters, and design 

equations are representative of actual behavior, and that the component will 

perform as intended. High confidence requires evidence to substantiate that 

the design requirements reflect actual behavior (e.g., experimental data,

supporting analytical studies, history of use, observations from previous 

seismic events, or demonstrated similarity with other components).

2.8 Component Equivalency Acceptance Criteria

2.8.1 Overall Approach to Establishing Equivalency

Acceptance criteria evaluate component equivalency using summary 

statistics of proposed and reference component performance parameters in

each component performance group. Summary statistics of each proposed 

component performance group are compared with those of the associated 

reference component performance group. Proposed components are deemed 

equivalent to reference components when comparisons of summary statistics

comply with the acceptance criteria of this section across all performance

groups.

For cyclic-load testing parameters, summary statistics on proposed and 

reference component data sets of all component configurations in the 

respective performance groups are compared to evaluate equivalency. 

Separately, potential outliers are checked by comparing data for each 

individual proposed component configuration with the summary statistics of 

the associated reference component performance group. 

For monotonic-load testing, summary statistics on subsets of proposed and 

reference component configurations in the respective performance group are 

compared to evaluate equivalency. The ultimate deformation capacity of the 

reference component determined from cyclic-load testing (factored to 

account for differences in the test protocol) may be used in lieu of the 

ultimate deformation capacity of the reference component determined from 

monotonic-load testing.

2.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation Capacity

Requirements for Component Performance Groups

For each proposed component performance group, the median value of 

ultimate deformation, ∆ U PC ,  , should be compared with the median value of 
2-26 2: Component Equivalency Methodology FEMA P-795

ultimate deformation capacity for the associated reference component 

performance group, ∆ U RC ,  , using Equation 2-1:

∆ ∆  

U PC U RC U Q , , ≥ P P (2-1)

The uncertainty penalty factor, PU, is obtained from Table 2-3, using the 

quality rating of the proposed component test data and the relative quality 

ratings of the proposed and reference component design requirements. 

Combinations of quality ratings that fall outside of those given in Table 2-3 

are not permitted.

Table 2-3 Penalty Factor to Account for Uncertainty

Penalty Factor for Uncertainty (PU)

Quality Rating of Proposed 

Component Test Data1

Quality Rating of Proposed Component Design 

Requirements Relative to Reference Component 

Design Requirements1

Higher2 Same3 Lower4

Superior 0.95 1.00 1.15

Good 1.00 1.05 1.25

Fair 1.15 1.25 1.40

1. Quality ratings are computed in accordance with Sections 2.7.1 and 2.7.2.

2. Higher: Quality ratings of proposed component design requirements are higher than 

reference component design requirements (e.g., Superior versus Good).

3. Same: Quality ratings of proposed and reference component design requirements 

are the same.

4. Lower: Quality ratings of proposed component design requirements are lower than 

reference component design requirements (e.g., Good versus Superior, or Fair versus

Good).

The load penalty factor, PQ, is obtained from Table 2-4 using the strength 

ratio R R Q PC Q RC , ,   . Values of R R Q PC Q RC , ,   less than 0.5, or greater than 1.2,

are not permitted.

Exception. Values of R R Q PC Q RC , ,   greater than 1.2, but not greater than 2.0 

are permitted, provided that the force-controlled and capacity-designed 

elements of the reference SFRS are designed for the expected strength of the 

component (i.e., proposed component design strength scaled up by a factor of

RQ PC ,  ).

The value of the load penalty factor, PQ, may be taken as equal to 1.2, for 

values of R R Q PC Q RC , ,   greater than 1.2, provided that: (1) the design 

requirements of the proposed components require full replacement of all 

reference components with proposed components (i.e., prohibit mixing of 

reference and proposed components in a building); and (2) the force-
FEMA P-795 2: Component Equivalency Methodology 2-27

controlled and capacity-designed components of the reference SFRS are 

designed for the expected strength of the component (i.e., the component 

design strength scaled up by a factor of RQ PC ,  ).

Table 2-4 Penalty Factor to Account for Differences in Load (Strength)

Penalty Factor for Differences in Strength (PQ)

1

PQ PQ

0.50 1.88 1.10 1.00

0.60 1.55 1.20 1.00

0.70 1.31 1.30 1.04

0.80 1.14 1.40 1.09

0.90 1.00 1.50 1.13

1.00 1.00 1.80 1.24

1.10 1.00 2.00 1.32

1. Linear interpolation is permissible between tabulated values.

Requirements for Individual Component Configurations

For each configuration j of the proposed component, the median value of the 

ultimate deformation, ∆ Uj PC ,  , should be compared with the median value of 

ultimate deformation capacity for the associated reference component 

performance group, ∆ U RC ,  , using Equation 2-2:

, (1 1.5 , , )( ) ∆ σ∆  

Uj PC ≥ − ∆U RC U RC U Q P P (2-2)

If the value of σ ∆U ,RC exceeds 0.3, then 0.3 should be used in Equation 2-2.

2.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness

The median value of the proposed component initial stiffness ratio, R K PC ,  ,

should be within the range specified in Equation 2-3:

,

,

0.75 1.33 K PC

K RC

R

R

≤ ≤



 (2-3)

Exception. Proposed components need not comply with Equation 2-3, 

provided that at each floor level, proposed components do not resist more 

than 25% of the design seismic force on a given line of framing in the 

direction of interest.

R R Q PC Q RC , ,   R R Q PC Q RC , ,  
2-28 2: Component Equivalency Methodology FEMA P-795

2.8.4 Requirements Based on Cyclic-Load Test Data: 

Effective Ductility Capacity

The median value of the effective ductility capacity of the proposed 

component should not be less than 50% of the median value of the effective 

ductility capacity of the reference component, in accordance with Equation 

2-4.

, , 0.5 μ μ eff PC ≥ eff RC   (2-4)

Exception. Proposed components need not comply with Equation 2-4, 

provided that at each floor level, proposed components do not resist more 

than 25% of the design seismic force on a given line of framing in the 

direction of interest.

2.8.5 Requirements Based on Monotonic-Load Test Data: 

Ultimate Deformation 

For each component performance group, the median value of the proposed 

component ultimate deformation, ∆ UM PC ,  , should meet the requirements of 

either Equation 2-5 or Equation 2-6:

∆ ∆  

UM PC UM RC U Q , , ≥ P P (2-5)

, , 1.2 ∆ ∆ UM PC ≥ D PP C U RC U Q    (2-6)

In Equation 2-6, the cyclic-load ultimate deformation, ∆ U PC ,  , may be used in 

lieu of the monotonic-load ultimate deformation, ∆ UM PC ,  .

In Equation 2-6, the value of the median cumulative damage factor, DC

 , 

should be computed for the reference component performance group of 

interest and should be based on the median number of inelastic deformation 

cycles that occur prior to reaching the ultimate deformation, ∆U, of the 

reference component. An inelastic deformation cycle is defined as a cycle in 

which the deformation exceeds the effective yield deformation, ∆Y, eff. The 

DC

 value should be taken as 1.0 for reference component cyclic-load testing 

protocols that have not more than 10 cumulative cycles of such inelastic 

deformation, and 1.5 for cyclic-load testing protocols that have 30 or more 

such cumulative cycles of inelastic deformation. Linear interpolation should 

be used to determine the value of the damage factor, DC

 , for cyclic-load 

testing protocols that have between 10 and 30 such cumulative cycles of 

inelastic deformation.
FEMA P-795 2: Component Equivalency Methodology 2-29

2.9 Documentation and Peer Review Requirements

2.9.1 Documentation

The results of the Component Methodology should be thoroughly 

documented at each step of the process for review and approval by both the 

peer review panel and the authority having jurisdiction over its eventual use.

Documentation of component equivalency should include, as a minimum, the 

following information:

• Clear and complete description of the proposed component design 

requirements, including but not limited to methods and criteria for 

determining proposed component design stiffness and design strength.

• Proposed component detailing requirements.

• Description of limitations on proposed component usage within the

reference SFRS.

• Description of component configurations and component performance 

groups for both the proposed and reference component data.

• Summary of experimental test data for cyclic-load and monotonic-load 

testing of reference and proposed components.

• Summary statistics of key component parameters for monotonic-load and 

cyclic-load testing data of each proposed and reference component 

performance group.

• Summary of the comparisons completed based on the acceptance criteria 

of Section 2.8, including all summary statistics of proposed component 

and reference component data sets, as well as quality ratings, penalty 

factors, and results for each acceptance criterion.

2.9.2 Documentation of Test Data

The documentation of each proposed component experiment should be 

comprehensive. For reference component test data, all available 

experimental information should be collected, but complete information may 

not always be available. Documentation of test data should include the 

following:

• Date of the test, test sponsor or agency, test facility name and location, 

and specimen identification number.

• Geometry and configuration of each test specimen.

• Important details of each test specimen, including construction process 

and fabrication details.
2-30 2: Component Equivalency Methodology FEMA P-795

• Details of the test setup, including description of the connections to the 

proposed component test specimen. 

• Type, location, and calibration of instruments used for measurement of 

important response parameters. 

• Pertinent material test data for the construction material used in the test 

specimen. 

• A record of all important events prior to and during the test, including 

documentation of the ability of the specimen to maintain any applied 

vertical loads.

• Important visual observations.

• A set of digital experimental data generated for component performance 

evaluation.

• Plots of load versus deformation data from all tests, including the cyclic

envelope curves of cyclic-load testing.

• Values of the key component parameters, including the values for each 

direction of loading, as well as any computed average values.

2.9.3 Peer Review Panel Requirements

It is recommended that a peer review panel consisting of knowledgeable 

experts be retained for this purpose. The peer review panel should be 

familiar with the procedures of this Component Methodology, should have 

sufficient knowledge to render an informed opinion on the developmental 

process, and should include expertise in the following areas:

• Component testing 

• Engineering design and construction

Members of the peer review panel must be qualified to critically evaluate the 

development of proposed and reference component test data.

2.9.4 Peer Review Panel Selection

It is envisioned that the cost of the peer review panel will be borne by the 

proposed component sponsor. As such, it is expected that members of the 

peer review panel will be selected by the proposed component sponsor. It is 

intended, however, that the peer review panel be an independent set of 

reviewers who will advise and guide the development team at each step in 

the process. It is recommended that other stakeholders, including authorities 

with jurisdiction over the eventual use of the proposed component in design 

and construction, be consulted in the selection of peer review panel members. 
FEMA P-795 2: Component Equivalency Methodology 2-31

2.9.5 Peer Review Panel Responsibilities

The peer review panel is responsible for reviewing and commenting on the 

following:

• Test data for compliance with the component testing requirements of 

Section 2.2, including verification that the deformation history used for 

cyclic-load testing of the proposed component is equivalently damaging

(or more damaging) as the deformation history used for cyclic-load 

testing of the reference component.

• Applicability of the Component Methodology for equivalency evaluation 

of the proposed component (Section 2.3).

• Values of monotonic-load and cyclic-load testing data obtained from 

individual test specimens of reference and proposed components,

including envelope curves of cyclic-load testing (Sections 2.4 and 2.6).

• Adequacy of the design requirements for the proposed component, i.e., 

design methods and criteria related to component design stiffness and 

design strength (Section 2.5), and documentation of these requirements 

for use in design of proposed components for use in the reference SFRS.

• Quality ratings assigned to reference component design requirements and 

test data, and quality ratings assigned to proposed component design 

requirements and test data (Section 2.7).

• Statistical values of performance parameters (Sections 2.4 and 2.6), and 

their use in the component equivalency evaluation (Section 2.8).

• Documentation of the Component Methodology process (Section 2.9).

FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-1

Chapter 3

Commentary on the Component 

Equivalency Methodology

3.1 Introduction

The Component Equivalency Methodology (Component Methodology) is an 

adaptation of the FEMA P-695 Methodology, which is a procedural 

methodology for quantifying collapse behavior and establishing seismic 

performance factors for newly proposed structural systems. Application of 

the FEMA P-695 Methodology requires significant effort, involving testing 

of materials, components, and connections, design of a large set of prototype 

buildings, creation of nonlinear models for each building, and running of 

nonlinear dynamic analyses. It evaluates an absolute level of collapse safety 

based on the response of the entire seismic-force-resisting system. 

In contrast, the Component Methodology evaluates the seismic performance 

equivalency of structural components that are proposed as substitutes for 

selected components in an established seismic-force-resisting system. It

evaluates a relative level of safety based on comparisons between the tested 

behavior of proposed and reference components. The Component 

Methodology is less comprehensive in scope and requires less effort to 

implement in the specific case of judging component equivalency.

The Component Methodology is intended for use on deformation-controlled

elements in a structural system. In such elements, the behavior and 

controlling limit states in the overall system can be related to the inelastic 

deformation and energy dissipation characteristics of the elements. The 

Component Methodology relies on statistical comparisons of data from 

cyclic-load and monotonic-load tests on proposed and reference components. 

Statistical comparisons are based on probabilistic assessments of collapse 

risk, but the final acceptance criteria are deliberately simple. 

The Component Methodology builds on previous methodologies that have 

been developed to establish seismic equivalency, such as AC322 Acceptance 

Criteria for Prefabricated, Cold-Formed, Steel Lateral-Force-Resisting 

Vertical Assemblies (ICC-ES, 2007). AC322 evaluates the equivalency of

possible replacement components for the specific case of nailed wood shear 
3-2 3: Commentary on the Component Equivalency Methodology FEMA P-795

walls in light-frame construction. The Component Methodology is similar, 

but is intended to apply to a wider range of components and reference 

seismic-force-resisting systems. It is supported by rigorous analytical 

studies conducted within a probabilistic framework. 

3.2 Component Testing Requirements

A comprehensive experimental program is necessary to quantify the 

performance of reference and proposed components. Test results from 

previous research can be used to supplement an experimental investigation 

program, but such data should come from reliable sources and be well 

documented.

The Component Methodology requires both cyclic-load and monotonic-load 

testing. The data are interpreted using the following two curves, as 

illustrated in Figure 3-1. These curves are defined as follows:

• Cyclic Envelope Curve: The force-displacement curve formed by 

enveloping the cyclic-load test data of a specimen. The rules for 

constructing the cyclic envelope curve are defined in Section 2.2.2.

• Monotonic Curve: The force-displacement curve obtained from a 

monotonic-load test of a specimen.

Figure 3-1 Monotonic and cyclic responses of identical steel specimens, 

and cyclic envelope curve fit to cyclic response. Data from 

Tremblay et al. (1997), figure from PEER/ATC-72-1 (2010).
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-3

Practical considerations limit the scope of an experimental testing program, 

but the number and quality of the component experimental tests will affect 

how well the collapse resistance of the seismic-force-resisting system can be 

characterized. Accordingly, the quality of test data, rated as described in 

Section 2.7.1, is a key aspect of the Component Methodology.

In applying the Component Methodology, the load and deformation 

quantities used to assess the proposed and reference component data sets 

must be comparable, and the relationship between component loaddeformation properties and the system-level response must be well

understood. It is expected that load-deformation quantities will often be the 

component shear force (load quantity) versus story drift (deformation 

quantity), but other load and deformation quantities might be appropriate for 

some components.

Where story drift is not the primary deformation quantity of interest, the 

relationship between component deformation and story drift in the seismicforce-resisting system must be similar for the proposed and reference 

components. Provided that the forces and deformations in the balance of the 

seismic-force-resisting system are comparable, slight differences between 

story drift and component deformation relations can be accommodated 

through kinematic adjustment factors in the deformation quantities for the 

proposed and reference components. 

3.2.1 General Requirements for Component Testing

The experimental program is expected to focus on component testing, 

including testing of the proposed component, compiling existing test data for 

the reference component, and testing of the reference component (as needed

to fill in gaps in existing data). In addition to the guidance provided in 

Section 2.2.1, other suggested sources for information on testing include

ACI T1.1-01 Acceptance Criteria for Moment Frames Based on Structural 

Testing and Commentary (ACI, 2001), ANSI/AISC 341-10 Seismic 

Provisions for Structural Steel Buildings (AISC, 2011), ASTM E2126-09 

Standard Test Method for Cyclic (Reversed) Load Test for Shear Resistance 

of Vertical Elements of the Lateral Load Force Resisting System for 

Buildings (ASTM, 2009), ATC-24 Guidelines for Cyclic Seismic Testing of 

Components of Steel Structures (ATC, 1992), Clark et al. (1997), FEMA 461 

Interim Testing Protocols for Determining the Seismic Performance 

Characteristics of Structural and Nonstructural Components (FEMA, 2007), 

as well as AC322.
3-4 3: Commentary on the Component Equivalency Methodology FEMA P-795

Load Application (Vertical Loads)

For components that resist vertical loads (gravity load and overturning 

effects) in the seismic-force-resisting system, test loading should include 

these loads unless they do not significantly affect component performance. 

For components tested without vertical loads, it must be shown by analysis 

or experimentation that vertical loads expected to be present in buildings 

would not cause an appreciable change in the parameters used to establish 

equivalency.

Testing of Materials

Material testing will often be an important part of the experimental program 

for a proposed component, because new design requirements are often based 

on material properties. The need for materials testing will depend on the 

composition of the proposed component, so specific material testing 

requirements are not included in the Component Methodology. A proposed 

component constructed from a new type of material, for example, will likely 

require more materials testing than one constructed from an established 

material with behavior that is well understood. The extent of the materials 

testing program should be considered when determining the quality rating of 

the test data (Section 2.7.1).

Testing of the Connection between the Proposed Component

and the Balance of the Seismic-Force-Resisting System

Properties of the connection between the proposed component and the rest of 

the seismic-force-resisting system are an important part of the proposed 

component design requirements (Section 2.5.3). It should be shown by 

analysis or experimental evidence that these connections remain essentially 

elastic when the proposed component is tested up to the ultimate 

deformation, ∆U. If the connection does not remain essentially elastic, then 

the connection must be included as part of the tested component 

configuration. 

3.2.2 Cyclic-Load Testing 

Cyclic-Load Testing Protocol

Equivalently Damaging Load Histories. Section 2.2.2 requires that the 

cyclic-load history used for the proposed component is at least as damaging 

as that used for the reference component. Quantitative methods to fulfill this 

requirement should be approved by the peer review panel. One such method 

is provided in Section B.2.3 of Appendix B.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-5

The method in Appendix B suggests that loading histories for the proposed 

and reference components are acceptable if the median normalized 

cumulative deformation imposed by the proposed component loading history 

at ∆U is at least 0.75 the of comparable value for the reference component 

loading history (Equation B-3). This check is to be completed for each of 

the associated pairs of proposed and reference component performance 

groups. Per Section B.2.4, the method assumes that the requirements of 

Section 2.2.2 are automatically satisfied under the following conditions: (1) 

the same loading protocol is used for all reference and proposed 

components; and (2) the control variable used in the loading protocol is 

based on a measure of ultimate or maximum displacement. Additionally, 

Equations B-1 and B-2 provide requirements to ensure reasonable similarity 

between the normalized cumulative deformations of the loading histories of 

the various test specimens in each performance group.

Number of Cycles. Section 2.2.2 requires that the loading history have a 

sufficient minimum number of cycles to measure degradation of the 

component under repeated cycles of loading. The method of Appendix B

states that all loading histories should have a normalized cumulative 

deformation equal to or greater than 6.0. Alternate quantitative methods are 

also allowable, but all methods should be approved by the peer review panel.

Appendix B also considers the possibility of specifying an upper limit on the

number of cycles in the cyclic load protocol (or, more quantitatively, an 

upper limit on the normalized cumulative deformation of the protocol). The 

rationale for such an upper limit would be to avoid the use of an overly 

energetic cyclic load protocol that is not compatible with expected 

earthquake-induced motions, resulting in unrealistic failure modes and 

masking the true expected failure modes of the component. However, such 

an upper limit was not imposed on the Component Methodology because 

monotonic-load data are also used as an integral part of the acceptance 

criteria. It is expected that the acceptance criteria based on monotonic-load 

data will catch most problems introduced by the use of an overly energetic 

cyclic-load protocol. It is desirable that the loading protocol produce damage 

and failure mechanisms that are consistent with what is expected (or has 

been observed) in earthquakes. 

Description of Deformation History. It is envisioned that loading histories 

will be displacement-controlled because structural components are expected 

to yield and lose strength throughout the loading history, and these effects 

cannot be captured using load-controlled loading histories. 
3-6 3: Commentary on the Component Equivalency Methodology FEMA P-795

Reduction in Applied Load. Section 2.2.2 requires that cyclic-load testing 

continue to deformations large enough to achieve at least 20% reduction in 

applied load for reference component data. A similar requirement is 

included in Section 2.2.3 for monotonic-load testing. This is necessary to 

prevent ∆U from being underestimated for the reference component data set. 

If the reference component ultimate deformation is underestimated, the 

Component Methodology acceptance criteria would be non-conservative

(i.e., easier for the proposed component to pass). 

To provide more flexibility in the Component Methodology, this

requirement need only be met in one direction of loading (for cyclic-load 

testing). This is done to permit the use of a greater proportion of the 

reference component data that might be available in the literature. If a 20% 

reduction in applied load is achieved in one direction only, the ultimate 

deformation should be averaged with the maximum deformation in the 

opposite direction. Based on test application data in Appendix D, this 

approximation was found to provide a reasonable representation of the 

ultimate deformation.

Number of Cyclic Test Specimens

The number of component configurations to be tested depends on the range 

of configurations that are allowed in the proposed component design space. 

The use of at least four component configurations per performance group

(and two or three specimens per configuration) is intended to ensure that a 

sufficiently large number of tests are obtained to reliably estimate the 

median of the component performance parameters. 

Two exceptions are allowed regarding the minimum number of 

configurations and the minimum number of test specimens for each 

configuration. First, if fewer than four configurations are possible for the 

proposed component (e.g., if there is no possible way to use the proposed 

component in four different configurations), then it is permissible to test 

fewer than four configurations. Second, when creating the reference 

component data set, it is permissible (within some constraints) to ignore the 

requirement of having multiple test specimens for each component 

configuration. This second exception was created to provide more flexibility 

when using existing test data to create the reference component data set.

The minimum requirements of Section 2.2.2 acknowledge that the costs of 

testing a large number of specimens for many performance groups may be 

prohibitive for some types of proposed components. These minimum 

requirements are generally comparable with requirements of other recent 

codes and standards such as ASTM E2126-09 and Section 1.3.1.3.2 of 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-7

ASCE/SEI 7-10 Minimum Design Loads for Buildings and Other Structures

(ASCE, 2010).

Beyond these minimum requirements, it is expected that four component 

configurations will often be insufficient to span the range of design 

parameters and component behavior for the performance group. A larger 

number of tests should be conducted for performance groups when

warranted by a large range of possible configurations or large variability in 

response.

The values of 15% and 20% difference that trigger the need for a third 

component test for a given configuration were informed by similar criteria in 

ASTM E2126-09 and ASCE/SEI 7-10 Section 1.3.1.3.2.

Cyclic-Load Test Data

The cyclic-load data are interpreted through the use of a cyclic envelope 

curve. Key component performance parameters are then measured from the 

cyclic envelope curve and used in the later acceptance criteria. The short list 

of key component performance parameters was determined primarily from 

the sensitivity studies in Appendix A.

Construction of the Cyclic Envelope Curve

Section 2.2.2 contains the rules for constructing the cyclic envelope curve, 

which are based on the response in the first loading cycle under increasing 

deformation amplitudes, consistent with ASTM E2126-09 and 

PEER/ATC-72-1 Modeling and Acceptance Criteria for Seismic Design and 

Analysis of Tall Buildings (PEER/ATC, 2010). The first loading cycle is 

used because it de-emphasizes the effects of cyclic strength deterioration

(i.e., the loss of strength between each subsequent cycle of loading at a given 

level of deformation). Cyclic strength deterioration is intentionally deemphasized due to the findings of Appendix A.

Figures 3-2 and 3-3 illustrate the fitting of an envelope curve to cyclic-load 

test data along with identification of the resulting component properties. 

Figure 3-3 indicates values for positive and negative loading directions as 

“+” and “–,” respectively. Since this particular component is a symmetric 

shear panel, the final values would be the average of these values for each 

direction of loading.

Figures 3-4 through 3-8 provide additional examples of cyclic-load test data 

and the associated envelope curves for nailed wood light-frame shear wall 

data. These figures are meant to illustrate how to construct the envelope 

curves under various circumstances. For example, Figure 3-4 shows a case 
3-8 3: Commentary on the Component Equivalency Methodology FEMA P-795

where there are two subsequent cycles with negative stiffness. Figure 3-6 

and Figure 3-8 show cases with negative stiffness in both directions of 

loading.

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

Figure 3-2 Cyclic-load test data and cyclic envelope curve for a nailed 

wood light-frame shear wall specimen (data from Rosowsky et 

al., 2004).

Figure 3-3 Illustration of cyclic envelope curve and key component 

performance parameters obtained from positive and negative 

loading directions based on Figure 3-2.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-9

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

Figure 3-4 Cyclic-load test data and cyclic envelope curve for a nailed 

wood shear wall specimen (data from Rosowsky et al., 2004). 

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

Figure 3-5 Cyclic-load test data and cyclic envelope curve for a nailed 

wood shear wall specimen (data from Rosowsky et al., 2004). 
3-10 3: Commentary on the Component Equivalency Methodology FEMA P-795

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

Figure 3-6 Cyclic-load test data and cyclic envelope curve for a nailed 

wood shear wall specimen (data from Rosowsky et al., 2004). 

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

Figure 3-7 Cyclic-load test data and cyclic envelope curve for a nailed 

wood shear wall specimen (data from Rosowsky et al., 2004). 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-11

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

Figure 3-8 Cyclic-load test data and cyclic envelope curve for a nailed 

wood shear wall specimen (data from Rosowsky et al., 2004). 

Figures 3-9 and 3-10 provide additional examples for steel brace 

components. These figures illustrate the fitting of cyclic envelope curves for 

behaviors that are drastically different from wood light-frame shear wall 

examples. Additionally, these figures show cases in which the initial 

stiffness estimate would be based on a single direction of loading.

Figure 3-9 Cyclic response and cyclic envelope curve of a single HSSsection brace (data from Wakabayashi et al., 1979). In this case 

the initial stiffness should be determined from the negative 

quadrant only.
3-12 3: Commentary on the Component Equivalency Methodology FEMA P-795

Figure 3-10 Cyclic response and cyclic envelope curve of an X-brace 

configuration (data from Wakabayashi et al., 1979). In this case 

the initial stiffness should be determined from the negative 

quadrant only.

The value of ultimate deformation, ∆U, is typically computed from the cyclic 

envelope curve as the deformation at 0.8QM. However, Section 2.2.2 

provides guidance regarding how the value of ultimate deformation, ∆U, 

should not be based on the cyclic envelope curve when the vertical-load 

carrying ability of the component is compromised before 0.8QM is reached

(note that this modification is not illustrated in Figure 3-3 through Figure 

3-10). The approach taken in Section 2.2.2 for dealing with vertical-load 

carrying ability is similar to the approach taken in AC322.

3.2.3 Monotonic-Load Testing 

Monotonic-load test data are required because cyclic-load test data alone are 

not sufficient for establishing equivalency in seismic collapse resistance 

(more detail is provided in Appendix B). 

Monotonic-load test data are required for the proposed component and are 

desirable for the reference component. When monotonic-load data are not 

available for the reference component, the ultimate deformation capacities 

(i.e., ∆U and ∆UM) of the proposed component must satisfy Equation 2-6. The

rationale behind this check is discussed in more detail in Section 3.8.5.

3.3 Applicability Criteria

3.3.1 Required Information and Data

No commentary for this section.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-13

3.3.2 Reference Seismic-Force-Resisting System: Collapse 

Performance Criteria

Seismic-force-resisting systems used as a reference system in the Component 

Methodology should comply with collapse performance criteria contained in 

the FEMA P-695 Methodology. This requirement is intended to ensure that 

equivalency is judged against a system with an appropriate minimum 

absolute level of safety, and that a seismic-force-resisting system consisting 

of proposed components will have adequate collapse safety. 

Several seismic-force-resisting systems identified in ASCE/SEI 7 have been 

evaluated using the FEMA P-695 Methodology (FEMA, 2009b and NIST,

2010). These evaluations have shown that current code-approved systems, 

in general, appear to meet these criteria. Therefore, as a practical matter,

and for consistency with current building code requirements, the Component 

Methodology allows the use of any currently approved system in ASCE/SEI

7-10 as a reference seismic-force-resisting system. 

3.3.3 Quality Rating Criteria

Minimum quality ratings for reference and proposed component test data and

design requirements are intended to ensure that available information is

robust enough for application of the Component Methodology. The 

requirement of a Good quality rating for reference component test data 

reflects the concept that the Component Methodology should not be used for 

equivalency comparisons unless the reference component behavior is well 

understood. Proposed component test data are allowed to be rated as low as 

Fair, provided that the component is still able to pass the acceptance criteria 

of Sections 2.8.2 and 2.8.5 with the associated increase in the penalty factor, 

PU.

3.3.4 General Criteria

Proposed and reference components must be unambiguously defined with a 

clear definition of the component boundary, or the Component Methodology 

is not applicable. Proposed and reference components can consist of a single

element, a connection, or a sub-assemblage. In the Component 

Methodology, “connection” refers to whatever connects the proposed or 

reference component to the balance of the seismic-force-resisting system. It 

is possible that the proposed component could include elements that are 

typically thought of as a “connection.” 

To illustrate the definitions for proposed component, component boundary, 

and connection, several examples are discussed below. Figure 3-11 shows 

an example for a steel concentric brace. In this example, the proposed 
3-14 3: Commentary on the Component Equivalency Methodology FEMA P-795

component includes the brace and the gusset plate, because the gusset plate 

will likely also experience inelastic deformation when the brace buckles 

under compressive loading. The connection consists of bolts and welds that 

connect the gusset plate to the adjacent beams and columns. Section 2.5.3 

requires that these connections be strong enough to develop the full ultimate 

strength of the component, such that the inelastic deformation occurs in the 

component and not in the connection region.

Figure 3-11 Illustration of proposed component and connection definitions 

for a steel concentrically braced seismic-force-resisting system. 

The intent is that the primary failure mechanism, which drives the level of

collapse safety of the building, is contained within the component boundary. 

When this is the case, components being tested using the Component 

Methodology determine the performance of the system. This is difficult in 

some cases because there can be multiple components in a building that 

contribute to seismic behavior and collapse safety. Because of this, there are

no requirements prohibiting inelastic behavior in the seismic-force-resisting 

system outside of the component boundary. To provide some control, 

Section 2.3.4 requires the balance of the reference SFRS to be essentially 

unchanged by replacement of reference components with proposed 

components. This is to ensure consistency in the portion of the seismicforce-resisting system that is outside of the component boundary. 

Figure 3-12 shows another example of a steel concentrically braced frame

system. Here, the geometry of the brace-to-gusset plate connection is 

different, so when the brace buckles, it is possible that fracture or tearing 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-15

could occur in the weld region between the gusset plate and the beams and 

columns. Accordingly, these welded connections should be included within 

the component boundary in this case.

Figure 3-12 Illustration of two alternative definitions for the proposed 

component boundary in a steel concentrically braced seismicforce-resisting system (Engelhardt, 2007). 

Two possible definitions of the component boundary are shown in Figure 

3-12. A single brace could be defined as the proposed component, provided 

that strong interaction between adjacent braces does not occur. 

Alternatively, an assembly of two braces could also be defined as the 

proposed component. In this case, the pair of braces would need to be tested 

together in the assembly shown, and the proposed component design 
3-16 3: Commentary on the Component Equivalency Methodology FEMA P-795

requirements would need to require that pairs of braces always be used in the 

configuration shown.

Figure 3-13 shows an example component boundary for a bucklingrestrained brace element. Assuming that the gusset plates and connections 

are designed to remain elastic, ensuring that yielding only occurs in the 

braces themselves, the proposed component can consist of the brace alone. 

Figure 3-13 Illustration of the proposed component boundary for a bucklingrestrained brace seismic-force-resisting system (Engelhardt,

2007). 

Similar examples are provided in Figure 3-14 to illustrate the definition of 

proposed component and component boundary for various types of 

proprietary wood light-frame shear walls, showing that these elements can 

be successfully isolated from the balance of the seismic-force-resisting

system.

Figure 3-15 shows an example for a steel eccentrically braced frame, where 

the fuse is the proposed component. Consistent with the intended behavior 

of steel eccentrically braced frames, this definition assumes that a capacity 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-17

design philosophy has been used to ensure that all of the inelastic behavior 

occurs in the fuse element and not in the beams or braces.

(a) (b)

(c)

Figure 3-14 Illustration of proposed component boundaries for various wood 

light-frame shear walls, including (a) Simpson Strong-Tie (2009), 

(b) Simpson Steel Strong-Wall (Photo courtesy of Tools of the 

Trade Magazine, 2006), and (c) Hardy frame (Photo courtesy of 

SBE Builders).

(a)
3-18 3: Commentary on the Component Equivalency Methodology FEMA P-795

Figure 3-15 Illustration of proposed component boundary for the fuse element in a 

steel eccentrically braced frame seismic-force-resisting system 

(Engelhardt, 2007). 

Another example component boundary is illustrated in Figure 3-16, for a 

steel plate shear wall. This boundary assumes that the connections between 

the shear panel and the adjacent columns are capacity designed, such that all 

of the inelastic behavior occurs in the steel panel.

There are some cases where it might not be possible to clearly separate the 

component from the balance of the seismic-force-resisting system. One such 

example is a multistory reinforced concrete shear wall shown in Figure 3-17. 

In this case, the Component Methodology is not applicable, and the full 

FEMA P-695 Methodology should be used to assess the seismic 

performance equivalency of the proposed system.

Section 2.3.4 requires that the component boundary be the same for the 

proposed and reference components, unless their configurations are 

fundamentally different. One such example is the substitution of a 2’x 8’ 

prefabricated wall component in place of an 8’x 8’ site-built wood shear wall

component. In this case, the component boundaries are not identical (i.e., 

one boundary is 2’x 8’ and the other is 8’x 8’). Differences like this are 

permitted if the loads are transferred across the proposed component 

boundary in an acceptably similar manner. In this specific case, possible 

differences in load effects (such as overturning) should be directly 

investigated in the testing program or shown to be accommodated without 

detrimental effects on the proposed component or the balance of the 

reference SFRS up to the ultimate deformation, ∆U.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-19

Figure 3-16 Illustration of a proposed component boundary for a steel plate 

shear wall in a seismic-force-resisting system (Sabelli, 2007). 

Figure 3-17 Illustration of the difficulty in identifying an isolated component 

boundary in a multistory reinforced concrete shear wall seismicforce-resisting system.

Courtesy of Nippon Steel
3-20 3: Commentary on the Component Equivalency Methodology FEMA P-795

Section 2.3.4 requires that the vertical-load carrying capacity of components 

that support vertical loads must be maintained up to the ultimate 

deformation, ∆U. However, if the vertical-load carrying capacity is 

compromised before ∆U is reached, it is permissible to define a reduced ∆U

value corresponding to the deformation at which the vertical-load carrying 

capacity of the component was compromised.

3.4 Reference Component Test Data Requirements

Section 2.4 describes the data required for the reference component, and the 

approach taken in the Component Methodology when assembling this data 

set. The first step is to define the reference component design space (i.e., the 

range of possible component configurations for the reference component), 

and establish how often each configuration would be used in design practice. 

The data set should then be assembled to represent the design space, as 

illustrated in Figure 3-18. 

Figure 3-18 Overview of test data used in the reference component data set.

Within the design space, reference component configurations are typically 

placed into a single performance group. In some cases, they are divided into 

multiple performance groups (two groups in this example), that reflect 

significant differences in component failure modes or physical 

characteristics. Multiple component configurations populate each 

performance group. 

The data set will typically include both cyclic-load and monotonic-load test 

data. At a minimum, two test specimens are needed for each configuration. 

Most reference component data are expected to be assembled from previous 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-21

research and published information, but may need to be supplemented with 

additional testing. 

Reference component data serve as the basis against which the proposed 

component data are compared, so compiling the reference component data 

set is a critical aspect of the Component Methodology. The process of 

compiling the reference component data, including the definition of the 

design space, identification of representative component configurations and 

selection of test results, requires judgment and experience and should be 

subject to close peer review. 

3.4.1 Define Reference Component Design Space

The reference component design space should be established in parallel with 

the proposed component design space, in order to ensure consistency 

between the two. The definition of the reference component design space 

should consider typical component configurations and characteristics of the 

reference component, including: 

• Component geometry (e.g., global aspect ratio, local geometries such as 

flange thicknesses for steel)

• Component composition (e.g., connector sizes for wood, sheathing type 

for wood, rebar diameters in reinforced concrete)

• Detailing (e.g., connector spacing for wood, stirrup spacing for 

reinforced concrete, connection details)

• Expected axial loading (based on expected building height, expected 

location of component within the full building system)

• System geometry (e.g., relation of component to overall structural 

system)

The relative importance of these characteristics, and others not listed here,

depend on the nature of the reference component. When identifying the 

representative configurations for the reference component, care should be 

taken to identify any fundamental differences in how the component is used, 

or how the component performs for the various possible configurations. For 

example, in the case of wood light-frame construction, the aspect ratio of the 

wall component triggers a change in the required design strength. In other 

cases, some reference component configurations can result in a brittle failure 

while others result in ductile failure. Such differences in design 

requirements and failure modes should be clearly identified when compiling 

the reference component data set. 
3-22 3: Commentary on the Component Equivalency Methodology FEMA P-795

3.4.2 Compile or Generate Reference Component Test Data 

Section 2.4.2 provides general guidance for compiling reference component 

test data, recognizing the diversity of these data and their sources. When 

there is a choice of reference component (e.g., where more than one 

reference component is allowed within the reference SFRS) or associated 

sources of test data, the user is expected to choose the reference component 

and associated data that best represent current use of the reference SFRS.

When there is a choice of data sets, the user is expected to use all applicable 

data, or to select a data set that represents better performance of the 

reference component. As a possible exception, the user may select the data 

set corresponding to the “original benchmark” of the reference SFRS.

For many components, it is expected that much of the reference component 

data will be obtained from previous testing programs and available published

literature. Even so, supplementary testing of the reference component may

be necessary to complete the reference component data set, especially when 

monotonic-load data are needed. The data set should be compiled to include 

the representative configurations and the relative frequency with which these 

configurations are expected to be used in practice.

Many different cyclic-load histories are permitted in the test data that 

comprise the reference component data set. It is important to keep in mind, 

however, that the cyclic-load histories used in the reference component data 

set dictate the cyclic-load histories that are permitted in creating the 

proposed component data set.

It is expected that the sources of monotonic-load data from previous testing 

programs will be more limited than cyclic-loading data. For this reason, 

fewer monotonic-load data are required. When no suitable monotonic-load

data are available for the reference component, and the proposed component 

data can be shown to comply with Equation 2-6, it is not necessary to 

generate monotonic-load test data for the reference component. 

3.4.3 Interpret Reference Component Test Results

No commentary for this section.

3.4.4 Define Reference Component Performance Groups 

The default approach to defining performance groups is to place all of the 

reference component data into a single performance group. Data are only 

separated into multiple performance groups if there are fundamental 

differences in behavior between various test specimens that make it 

inappropriate to average the results of the various tests. When multiple 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-23

performance groups are created, the acceptance criteria of Section 2.8 are

applied separately for each associated pair of proposed and reference 

component performance groups. 

If some component configurations have significantly different design 

requirements, geometry, failure modes, or behavior (as described in Section 

2.4.4), then they should be separated into multiple performance groups. In 

such cases, separate performance groups are needed to ensure that the 

statistical assessment (averaging) does not mask a potential problem with the 

performance of certain component configurations. For example, consider a 

set of 15 reference component tests that have distinct component geometries, 

such that 13 of them clearly and predictably fail in flexure, while two clearly 

and predictably fail in shear. Averaging these 15 test results (as required to 

compute ∆ U,RC

 ) would mask the potentially inferior performance of the 

shear-critical configurations. 

Configurations should be separated into different performance groups based 

on fundamental changes related to component design requirements. For 

example, if component design requirements include a trigger that requires

additional detailing for components subject to high levels of axial load, then 

two performance groups should be defined: one populated with component 

configurations that include the additional detailing and the other populated 

with component configurations that do not include this detailing.

Configurations should be separated into different performance groups based 

on systematic differences in failure mode. This is intended to ensure that:

(1) dissimilar data are not grouped together; and (2) failure modes are 

closely scrutinized in the equivalency process. For example, in a steel 

eccentrically braced frame system, link beam fuses differ significantly in 

height or length such that some configurations fail in shear (web yielding) 

while some configurations fail in bending (flange yielding). If a new fuse 

component is proposed for steel eccentrically braced frame systems, the 

configurations should be separated into different performance groups based 

on failure mode. 

Random differences in failure modes for tests with very similar component 

configurations, however, do not warrant separation into different 

performance groups. For example, in the case of wood light-frame shear 

walls, most tests exhibit fastener failures, but some tests experience sill-plate 

splitting failures. Since these different failures occurred randomly, rather 

than systematically, it would not be considered necessary to separate these 

data into performance groups by failure mode. 
3-24 3: Commentary on the Component Equivalency Methodology FEMA P-795

Configurations should be separated into different performance groups based

on fundamental differences in geometry that tangibly affect the ratio of the 

inelastic deformation to the elastic (pseudo-yield) deformation of the 

component. Since the acceptance criteria of Section 2.8 are computed from 

ultimate deformation of the component, including both elastic and inelastic

deformations, it is undesirable to group configurations together which have 

fundamental differences in the ratio of the inelastic to elastic deformations. 

Of course, all tests are expected to have slight differences in inelastic and 

elastic deformations, so separation of data into different performance groups 

is only warranted when fundamental differences are observed in the 

component behaviors.

Configurations should be separated into different performance groups based 

on substantial differences in loading histories used in testing. The 

recommended method for establishing the equivalence of loading histories is 

described in Section B.2.3 (Equations B-1 and B-2). Alternative quantitative 

methods are permitted provided they meet the intent of Section 2.4.4 and are 

approved by the peer review panel.

Reference component performance groups should be established in parallel 

with the proposed component performance groups, and there should be 

consistency in how the data are organized into performance groups. Each 

proposed component performance group must then be clearly associated 

with a reference component performance group (Section 2.6.5). 

Determining such associations can be complicated. For example, consider a 

well-behaved proposed component that fails in flexure and cannot fail in 

shear. Comparing such a component to reference component configurations 

that only fail in flexure would overlook the potential benefits of the 

improved resistance to shear failure. In this case, the proposed component 

(which cannot fail in shear) should be compared to a reference component 

performance group that includes the full range of configurations for which it 

is a suitable replacement (which would include configurations that exhibit 

both shear and flexural failures).

Table 3-1 illustrates a sample reference component data set in tabular form, 

showing the separation of data into performance groups and the required 

number of cyclic-load and monotonic-load tests for each component 

performance group and component configuration.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-25

Table 3-1 Sample Reference Component Data Set

Reference 

Component (RC)

Performance 

Group

Component 

Configuration

Number of 

Cyclic-Load Tests

Number of 

Monotonic-Load 

Tests

RC-A

Config. A-1 ≥ 21

≥ 0

Config. A-2 ≥ 21

Config. A-3 ≥ 21

Config. A-4 ≥ 21

..... ≥ 21

RC-B

Config. B-1 ≥ 21

≥ 0

Config. B-2 ≥ 21

Config. B-3 ≥ 21

Config. B-4 ≥ 21

..... ≥ 21

1. Minimum of three cyclic load tests are required if any of the following occur: (1) 

rapid deterioration; (2) if the strength varies more than 15%; or (3) if the ultimate 

deformation capacity varies more than 20% between two tests.

3.4.5 Compute Summary Statistics

Summary statistics are computed for each performance group of the 

reference component data set, in accordance with the guidelines of Section 

2.4.5. 

From cyclic-load test data, the following statistics are required: 

• Median of each parameter for each performance group

( , , , and ∆∆ μ U,RC Y,eff,RC eff,RC R K,RC     )

• Lognormal standard deviation of each parameter for each performance 

group ( U σ ∆ ,RC , etc.)

From monotonic-load test data, the following statistics are required (if 

monotonic data are utilized for the reference component, per the 

requirements of Section 2.8.5):

• Median ultimate deformation for each performance group

(only ∆ UM,RC

 )

3.5 Proposed Component Design Requirements 

A comprehensive set of design and quality assurance requirements should be 

created for the proposed component. In many cases, this process will be 

iterative, such that the test data and the acceptance criteria of Section 2.8 

serve as mechanisms to inform necessary revisions to the design 

requirements. 
3-26 3: Commentary on the Component Equivalency Methodology FEMA P-795

3.5.1 Component Design Strength and Stiffness

Design requirements should include methods to predict both the design 

strength and design stiffness of the proposed component. Design strength is 

more precisely characterized as the ratio of ultimate load to design load.

Initial stiffness is a fundamental property used in the ASCE/SEI 7-10 design 

processes related to: (1) story drift limits; (2) stability coefficient limits; (3) 

the distribution of force demands to components within a statically 

indeterminate structural system; and (4) other checks such as horizontal and 

vertical stiffness irregularities.

Requirements are intended to ensure that the proposed component and 

reference component strength and stiffness are sufficiently similar to avoid 

potential problems due to overstrength or stiffness irregularities when 

proposed components are substituted for reference components in the 

seismic-force-resisting system. 

3.5.2 Component Detailing Requirements

When necessary, design requirements for the proposed component should 

include comprehensive provisions for the detailing of the component. 

3.5.3 Component Connection Requirements

In the Component Methodology, the “connection” is defined as the interface 

between the proposed component and the balance of the seismic-forceresisting system (see Figure 3-11 through Figure 3-15). Design requirements 

should include provisions related to connections. Specifically, they should 

ensure that inelastic behavior occurs in the component, connection, or 

subassembly that is defined as the proposed component, and not in the 

connection between the proposed component and the balance of the seismicforce-resisting system. 

It is expected that connection design requirements will be based on a 

capacity-design philosophy. It should be shown by analysis or experimental 

evidence that the connections remain essentially elastic when the proposed 

component is tested up to the ultimate deformation, ∆U. Some limited 

yielding of the connections may be permissible at the discretion of the peer 

review panel, provided that such yielding will not result in additional failure 

modes not observed in component testing.

The intent of this requirement is to ensure that the proposed component (as 

defined and tested) captures the critical failure modes governing the collapse 

performance of the seismic-force-resisting system. If the connection 

between the proposed component and the balance of the seismic-force-
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-27

resisting system is the critical weak link, then tests of the proposed 

component excluding the connection would provide insufficient information 

about the collapse resistance of the seismic-force-resisting system.

3.5.4 Limitations on Component Applicability and Use

Design requirements should include provisions that reasonably restrict use of 

the proposed component to the range of configurations that were considered 

in testing and in the development of the component design space. Clear 

limitations are needed to ensure that the proposed component is used, in 

practice, in a manner that is consistent with the configurations that were 

determined to be equivalent. 

For components tested without vertical loads, design provisions should 

restrict the allowable range of use (e.g., height limitations or other 

limitations that control vertical load demands) to ensure that the component 

cannot be used in a configuration where vertical loads might appreciably 

affect component performance. This limitation ensures that a proposed 

component tested without vertical loads cannot be constructed in a system 

where vertical loads can trigger a different failure mode or other important 

changes in performance or behavior that were not observed as part of the 

proposed component testing program. This issue is also discussed in Section 

3.2.1.

3.5.5 Component Construction, Inspection, and Maintenance 

Requirements

No commentary for this section.

3.6 Proposed Component Test Data Requirements

Section 2.6 describes the test data required for the proposed component, and 

the approach of the Component Methodology in creating this data set. The 

first step is to define the proposed component design space (i.e., the range of 

permissible configurations for the proposed component). Specific proposed 

component configurations, selected to represent the overall range of the 

permissible configurations, are then tested experimentally and separated into 

component performance groups of tests sharing common features and 

behavioral characteristics. Summary statistics are then computed for each 

performance group and compared with those of the reference component 

data in the equivalency process.

3.6.1 Define Proposed Component Design Space

No commentary for this section.
3-28 3: Commentary on the Component Equivalency Methodology FEMA P-795

3.6.2 Select Proposed Component Configurations for Testing

A subset of configurations should be selected for testing based on the 

proposed component design space. Selected configurations should represent 

all possible failure modes and should represent those configurations 

expected to be used most frequently in practice. The required number of 

configurations and test specimens are described in Sections 2.2.2 and 2.2.3. 

3.6.3 Perform Cyclic-Load and Monotonic-Load Tests

The selected set of proposed component configurations should be tested in 

accordance with the requirements of Section 2.2, with related commentary 

provided in Section 3.2. 

3.6.4 Interpret Proposed Component Test Results

Proposed component tests are used to determine cyclic-load test parameters 

for each test specimen. These parameters are related to component strength, 

stiffness, ultimate deformation, and effective ductility capacity, and are 

listed in Section 2.6.4. These parameters should be determined by 

constructing a cyclic envelope curve for each test, as described in Section 

2.2.2 (and illustrated in Section 3.2.2). 

From monotonic-load testing, the monotonic-load ultimate deformation,

∆ UM,PC , is to be determined for each test specimen. Monotonic data are used 

in the acceptance criteria of Section 2.8.5 to ensure that there is adequate 

monotonic deformation capacity of the proposed components. 

3.6.5 Define Proposed Component Performance Groups 

Consistent with the approach used in defining performance groups for

reference component test data (Section 3.4.4), the default approach for 

proposed components is to place all test data into a single performance 

group. Proposed component test data are only separated into multiple 

performance groups if there are fundamental differences in behavior between 

various test specimens.

When multiple performance groups are necessary, similar divisions should 

be used to separate proposed and reference component data (Section 2.4.4),

and each proposed component performance group should be clearly 

associated with a reference component performance group (Section 2.6.5). 

Table 3-2 illustrates a sample proposed component data set in tabular form, 

showing the separation of data into performance groups and the required 

number of cyclic-load and monotonic-load tests for each component 

performance group and component configuration.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-29

Table 3-2 Sample Proposed Component Data Set

Proposed 

Component (PC)

Performance 

Group

Component 

Configuration

Number of 

Cyclic-Load Tests

Number of 

Monotonic-Load Tests

PC-A

Config. A-1 ≥ 21

≥ 2 configurations 

(≥ 4 tests)

Config. A-2 ≥ 21

Config. A-3 ≥ 21

Config. A-4 ≥ 21

..... ≥ 21

PC-B

Config. B-1 ≥ 21

≥ 2 configurations 

 (≥ 4 tests)

Config. B-2 ≥ 21

Config. B-3 ≥ 21

Config. B-4 ≥ 21

..... ≥ 21

1. Minimum of three cyclic load tests are required if any of the following occur: (1) 

rapid deterioration; (2) if the strength varies more than 15%; or (3) if the ultimate 

deformation capacity varies more than 20% between two tests.

3.6.6 Compute Summary Statistics

Summary statistics are computed for each performance group of the 

proposed component data set, in accordance with the guidelines of Section 

2.6.6. 

From cyclic-load test data, the following statistics are required: 

• Median of each parameter for each component performance group 

( ∆ U,PC

 , ∆Y eff PC , ,  , μ eff,PC  , RQ PC ,  , and R K PC ,  )

• Lognormal standard deviation of each parameter for each component 

performance group ( , σ ∆U PC , etc.)

• Median ultimate deformation for an individual configuration ( ∆ Uj PC ,  ). 

From monotonic load test data, the following statistics are required: 

• Median deformation for each component performance group ( ∆ UM PC ,  )

3.7 Quality Rating Criteria

3.7.1 Quality Rating of Test Data 

Quality ratings are assigned because uncertainty in the collapse capacity of a 

structural system is affected by the uncertainty (quality) of the test data on 

which the collapse prediction is based. The quality of the test data is rated in 

accordance with the requirements of Section 2.7.1. The data are rated as 

Superior, Good, or Fair, based on the completeness and robustness of the 

testing program and resulting data. The quality rating approach for test data 

was adopted from the FEMA P-695 Methodology, with some modification. 
3-30 3: Commentary on the Component Equivalency Methodology FEMA P-795

The quality rating should be completed separately for the reference 

component test data set and the proposed component test data set. Section 

2.3.3 requires that the rating should be a minimum of Good when applied to 

the reference component data set, and a minimum of Fair when applied to 

the proposed component data set. The quality of the proposed and reference 

component data affect the acceptance criteria of Section 2.8.

Completeness and Robustness of Tests

Completeness and robustness characteristics of test data are rated from high 

to low, based on the following information:

• High. All, or nearly all, important general testing issues of Section 2.2

are addressed comprehensively in the testing program and other 

supporting evidence. Experimental evidence is sufficient so that all, or 

nearly all, important behavior aspects at all levels (material, component, 

connections to rest of structure) are well understood, and the results can 

be used to quantify all important component parameters that affect the 

design requirements or that are used in the acceptance criteria. There is 

confidence that the manner of testing accurately reflects the demands 

that the component will experience as part of the full structural system. 

• Medium. Most of the important general testing issues of Section 2.2 are 

addressed adequately in the testing program and other supporting 

evidence. Experimental evidence is sufficient so that all, or nearly all, 

important behavior aspects at all levels are generally understood, and the 

results can be used to quantify or deduce the important component 

parameters that significantly affect the design requirements or that are 

used in the acceptance criteria. The behavior of the full structural 

system is acceptably well understood, and there is moderate confidence 

that the manner of testing accurately reflects the demands that the 

component will experience as part of the full structural system.

• Low. Several important general testing issues of Section 2.2 are not 

addressed adequately in the testing program and other supporting 

evidence. Experimental evidence is sufficient so that the most important 

behavior aspects at all levels are fairly well understood, but the results 

are not adequate to quantify or deduce, with high confidence, some of 

the important component parameters that significantly affect the design 

requirements or that are used in the acceptance criteria. The behavior of 

the full structural system is not well understood, such that there is 

questionable confidence that the manner of testing accurately reflects the 

demands that the component will experience as part of the full structural 

system.
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-31

Confidence in Test Results

The confidence in test results is rated from high to low based on the 

following information:

• High. Reliable experimental information is produced on all important 

parameters. Test results are fully supported by basic principles of 

mechanics. The data set includes all component configurations needed 

to fully represent the expected populations. 

For use only when rating the proposed component data: The standard 

deviations of the proposed component parameters are not appreciably 

larger than the standard deviations of associated parameters in the 

reference component data.

• Medium. Moderately reliable experimental information is produced on 

all important parameters. Test results are supported by basic principles 

of mechanics. The reference and proposed component data sets are 

reasonably robust and include nearly all component configurations 

needed to represent the expected populations. 

For use only when rating the proposed component data: Most of the 

standard deviations for the proposed component parameters are not 

appreciably larger than the standard deviations of associated parameters 

in the reference component data.

• Low. Experimental information produced on many of the important 

parameters is of limited reliability. Basic principles of mechanics do not 

support some of the results of the testing program. The robustness of the

data set is questionable; the set possibly still includes many component 

configurations, but the included component configurations do not 

adequately represent the expected populations.

3.7.2 Quality Rating of Design Requirements

The quality of the design requirements affects the uncertainty in the overall 

collapse performance of the structural system. The selection of a quality 

rating for design requirements considers the completeness and robustness of 

the requirements, and confidence in the basis for the design equations. The 

quality rating approach for design requirements was adopted from the FEMA 

P-695 Methodology, with some modification. 

The highest rating of Superior applies to a comprehensive set of design 

requirements that provides safeguards against unanticipated failure modes. 

For a Superior rating, there should be a high level of confidence that the 

design requirements produce the anticipated structural performance. 
3-32 3: Commentary on the Component Equivalency Methodology FEMA P-795

Existing code requirements for components of special concrete moment 

frames, for example, have been vetted with detailed experimental results and 

real-world earthquake performance. Design and detailing provisions include 

capacity design requirements to safeguard against unanticipated behaviors. 

Such a set of requirements would be rated Superior.

The lowest ratings (e.g., “Not Allowed” in Table 2-2) apply to design 

requirements that have minimal safeguards against unanticipated failure 

modes, do not ensure a hierarchy of yielding and failure, and would 

generally be associated with components that exhibit behavior that is 

difficult to predict.

The quality rating approach outlined in Section 2.7.2 should be applied 

separately for the reference component design requirements and the 

proposed component design requirements. Section 2.3.3 requires that the

rating should be a minimum of Good when applied to the reference 

component design requirements, and be at least Fair when applied to the 

proposed component design requirements. The quality of the proposed 

component design requirements affects the acceptance criteria of Section 

2.8.

Completeness and Robustness of Design Requirements

Completeness and robustness characteristics of design requirements are rated 

from high to low based on the following information:

• High. Design requirements are extensive, well-vetted and provide 

extensive safeguards against unanticipated failure modes. All important 

behavioral issues have been addressed, resulting in a high reliability in 

the behavior of the component. Through mature construction practices

and tightly specified quality assurance requirements, there is a high 

likelihood that the design provisions will be well executed through 

fabrication, erection, and final construction.

• Medium. Design requirements are reasonably extensive and provide 

reasonable safeguards against unanticipated failure modes, leaving some 

limited potential for the occurrence of such modes. While most 

important behavioral issues have been addressed, some have not, which 

somewhat reduces the reliability of the component. Quality assurance 

requirements are specified but may not fully address all the important 

aspects of fabrication, erection and final construction.

• Low. Design requirements provide questionable safeguards against 

unanticipated failure modes. Design requirements do not address all 

important behaviors, resulting in marginally reliable behavior of the 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-33

component. Quality assurance is lacking, written guidance is not 

provided, and construction practices are not well-developed for the type 

of system and materials.

Simplified, but conservative, design requirements by themselves are not a 

reason for a low Completeness and Robustness rating. However, if the 

conservatism is being used to compensate for the lack of safeguards against 

unanticipated failure modes, then a lower quality rating may be warranted.

Confidence in Design Requirements

Confidence in design requirements is rated from high to low based on the 

following information:

• High. There is substantiating evidence (experimental data, history of 

use, similarity with other components) that results in a high level of 

confidence that the properties, criteria, and equations provided in the 

design requirements will result in components that perform as intended. 

• Medium. There is some substantiating evidence that results in a 

moderate level of confidence that the properties, criteria, and equations 

provided in the design requirements will result in component designs 

that perform as intended. 

• Low. There is little substantiating evidence (little experimental data, no 

history of use, no similarity with other systems) that results in a low 

level of confidence that the properties, criteria, and equations provided 

in the design requirements will result in component designs that perform 

as intended.

3.8 Component Equivalency Acceptance Criteria

3.8.1 Overall Approach to Establishing Equivalency

Consistent with the FEMA P-695 Methodology, the intent of the Component 

Methodology is to ensure that code-designed buildings have adequate 

resistance to earthquake-induced collapse. Specifically, the Component 

Methodology ensures equivalent system-level collapse performance between 

seismic-force-resisting systems utilizing: (1) the reference component; (2) 

the proposed component; and (3) when permitted by the design provisions, 

any combination of the reference and proposed components.

The Component Methodology evaluates equivalency based on comparison of 

statistical values of performance parameters from proposed and reference 

components, calculated from results of both cyclic-load and monotonic-load 

tests. The primary component performance parameter is ultimate 
3-34 3: Commentary on the Component Equivalency Methodology FEMA P-795

deformation of component test specimens, obtained from monotonic-load or 

cyclic-load testing, i.e., ∆U or ∆UM. Additionally, other acceptance criteria 

are based upon the component strength, stiffness, and effective ductility 

capacity. 

This short-list of component parameters is necessarily and intentionally a 

simplification of the many parameters that could be extracted from the 

component test data, and could have an impact on collapse behavior. For 

example, an additional deformation parameter was considered at 50% 

strength loss (as compared with ∆U and ∆UM being defined at 20% strength 

loss), in order to capture the post-capping deformation capacity behavior, but 

it was decided that the added complication outweighed the potential benefit. 

Additionally, other parameters were also discussed, such as a specific 

measure of cyclic deterioration behavior and a measure of residual strength. 

These and other parameters were ultimately not included in the acceptance 

criteria of the Component Methodology for reasons of simplicity.

When component configurations are separated into groups with different 

behavioral characteristics, reference and proposed component test data are 

evaluated by performance group. The acceptance criteria to establish 

equivalency compares key performance parameters from each proposed 

component performance group to the associated reference component 

performance group. Each performance group should contain test data 

representing different component configurations. The number of different 

configurations should be sufficiently large to characterize behavior for the 

range of possible applications of the component of interest. 

The overall process of establishing equivalency will often be iterative. If the 

proposed component does not meet the acceptance criteria, the user may 

introduce additional test data, thereby improving the quality rating of the test 

data and changing the acceptance criteria requirements. If particular 

performance groups or individual component configurations do not meet the 

acceptance criteria, the proposed component design requirements may be 

altered to prohibit such configurations, thus allowing the improved proposed 

component to pass the equivalency criteria. 

3.8.2 Requirements Based on Cyclic-Load Test Data: Strength 

and Ultimate Deformation 

Requirements for Component Performance Groups

For each proposed component performance group, the median value of 

ultimate deformation, ∆ U,PC

 , should be compared with the median value of 

ultimate deformation for the associated reference component performance 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-35

group, ∆ U,RC

 , according to Equation 2-1. It is notable that this criterion is a 

median-to-median comparison and not a criterion based on a high level of 

statistical confidence. A high statistical confidence approach was attempted

and studied at length. It was determined that such an approach, by 

definition, would lead to acceptance criteria requiring proposed component 

parameters to greatly exceed reference component parameters (e.g., much 

larger ultimate deformation capacities). It was decided that such an 

approach would appear to unfairly penalize proposed components, so a

median-to-median approach was adopted as the philosophical basis for the 

criterion in Equation 2-1.

In Equation 2-1, the reference component deformation is increased by 

penalty factors that account for uncertainties associated with component test 

data and design requirements, and differences in strength between the 

proposed and reference components. The derivation of these factors is

described in Appendix C.

The penalty factor for strength, PQ, accounts for a reduction in structural 

collapse resistance associated with a decrease in strength of its constituent 

components. If the proposed components are stronger than the reference 

components, there may also be a detrimental impact on structural collapse 

resistance if proposed and reference components are used together, because 

the stronger proposed components may cause damage localization in the 

weaker reference component or other elements in the structure.

Consider for example, a wood light-frame shear wall seismic-force-resisting

system, in which the reference component is used in the first story and the 

stronger proposed component is used for upper stories (as shown in 

Appendix A). The strengthened upper stories may worsen the collapse 

performance, creating a weak first story in the structure. A penalty factor for 

strength, PQ, greater than 1.0 is therefore applied if the normalized strength 

of the proposed component, quantified by RQ,PC, is significantly greater or 

significantly smaller than the normalized strength of the reference 

component, quantified by RQ,RC. The value of PQ is obtained from Table 2-4

and depends on the ratio of RQ,PC to RQ,RC. 

PQ may be taken as 1.0 if: (a) the design requirements do not allow mixing of 

the proposed and reference components in the same structure; and (b) the 

proposed component is stronger than the reference component (subject to a 

maximum additional strength ratio of 1.2 in some cases, per Section 2.8.2). 

This exception is permitted because a stronger proposed component is not 

detrimental to collapse safety when the proposed component is used 

consistently throughout the seismic-force-resisting system.
3-36 3: Commentary on the Component Equivalency Methodology FEMA P-795

The value of R R Q PC Q RC , ,   is limited to 1.2. This requirement is intended to 

protect capacity-designed and force-controlled components from additional 

overstrength that was not initially expected during the creation of the 

reference component design provisions. An exception to this requirement 

permits values of R R Q PC Q RC , ,   greater than 1.2 to be used, provided that the 

design of such capacity-designed and force-controlled components is 

properly accounted for in the design provisions. If the typical ΩO approach 

is used for designing such capacity-designed and force-controlled 

components, R R Q PC Q RC , ,   values greater than 1.2 could be accounted for by 

increasing the seismic-force-resisting system design ΩO value by a factor of 

(R R Q PC , , ) (1.2 Q RC )   , to account for the additional overstrength from the 

proposed component. 

Requirements for Individual Component Configurations

Additional acceptance criteria related to individual component 

configurations (Equation 2-2) ensure that unsafe configurations are not 

approved because poor-performing configurations are averaged with betterperforming configurations. This criterion also discourages the use of 

proposed components that have a standard deviation of ∆U that is 

substantially larger than the reference component (i.e., more uncertain 

behavior). 

3.8.3 Requirements Based on Cyclic-Load Test Data: Effective 

Initial Stiffness

Requirements for initial stiffness of the proposed component in Section 2.8.3

ensure that the stiffness of the component, and by extension the seismicforce-resisting system, is acceptably similar when the proposed component is 

fully substituted or partially substituted for the reference component. These 

requirements lead to equivalently stiff seismic-force-resisting systems, 

regardless of whether the design is controlled by strength requirements or 

drift limits. 

In most cases, the collapse performance of a seismic-force-resisting system

is less dependent on component initial stiffness than parameters related to 

component deformation capacity and strength (see Appendix A). However, 

component stiffness is identified as a key parameter in the Component 

Methodology because it is fundamental to ASCE/SEI 7-10 design procedures

(see Section 3.5.1).

The requirement of Equation 2-3 specifies that R K PC ,  must be acceptably 

similar to R K RC ,  (recall that R KK K ID =   ). This equation ensures that the 

proposed component design requirements for predicting initial stiffness are
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-37

compatible with the related design requirements for the reference 

component. If design of the seismic-force-resisting system is controlled by 

drift, this requirement ensures that the stiffness of the overall structure is 

comparable using either proposed components, reference components, or a 

mixture of both.

In the unusual case that a reference component does not have a method to 

predict initial stiffness, the proposed component initial stiffness prediction 

should be calibrated such that R K PC ,  is approximately equal to unity.

To add flexibility to this requirement, Section 2.8.3 provides an exception 

that proposed components need not comply with Equation 2-3 if they resist

only a limited amount of lateral force along any framing line (i.e., less than 

or equal to 25% of the design force).

3.8.4 Requirements Based on Cyclic-Load Test Data: Effective 

Ductility Capacity

Section 2.8.4 (Equation 2-4) requires that the proposed component effective 

ductility capacity should be acceptably similar to that of the reference 

component. This requirement is enforced because studies in Appendix A 

showed that large changes in the energy dissipation capacity of a component 

can lead to important changes in the collapse capacity of a seismic-forceresisting system. Equation 2-4 is calibrated to catch possible extreme cases 

in the reduction of energy dissipation capacity, related to a large (more than 

50%) reduction in post-yield deformation capacity.

Section 2.8.4 provides an exception that proposed components need not 

comply with Equation 2-4 if they resist only a limited amount of lateral force 

along any framing line (i.e., less than or equal to 25% of the design force).

3.8.5 Requirements Based on Monotonic-Load Test Data: 

Ultimate Deformation 

For each performance group, the median value of proposed component

ultimate deformation from monotonic-load testing, ∆ UM,PC

 , should meet the 

requirements of either Equation 2-5 or Equation 2-6. Equation 2-5 is similar 

to the criterion for ultimate deformation from cyclic-load testing (Equation 

2-1). Equation 2-6 is different, and was specifically designed for the case 

where monotonic-load test data are not readily available for the reference 

component. In this case, it must be shown that the median ultimate 

deformation from monotonic-load testing of the proposed component,

∆ UM,PC

 , is acceptably larger than the median ultimate deformation of the 

reference component determined from cyclic-load testing, ∆ U,RC

 . The intent 

of Equation 2-6 is to identify and prohibit proposed components that have 
3-38 3: Commentary on the Component Equivalency Methodology FEMA P-795

only a small difference between the monotonic curve and the required cyclic 

envelope curve. This is necessary because the seismic-force-resisting system 

containing these components might have a smaller collapse resistance than 

would be expected based on cyclic-load test data alone (see Section B.3 of 

Appendix B). 

The ratio between the monotonic-load and cyclic-load ultimate 

deformations, ( ∆ ∆ UM U

  ), depends on the cyclic-load history used in testing. 

Past research listed below shows that there is significant variability in the 

ratio of (∆UM / ∆U). 

• ∆UM / ∆U = 1.0-2.0 for wood light frame shear walls subjected to a 

variety of cyclic-load histories (Gatto and Uang, 2002)

• ∆UM / ∆U = 1.7-1.8 for reinforced concrete columns (Panagiotakos and 

Fardis, 2001; Fardis and Biskini, 2003)

• ∆UM / ∆U = 1.5-1.6 based on data from both reinforced concrete and steel 

elements (PEER/ATC-72-1).

To differentiate between cyclic-load testing protocols that have either a 

small number or a large number of cycles, the 1.2 DC

 term is a reasonable 

representation of the ratio between the monotonic and cyclic values of 

ultimate deformation, (∆UM / ∆U). The median cumulative damage factor, 

DC

 , ranges from 1.0 to 1.5 and approximately accounts for the number of 

cycles in the cyclic-load testing protocol. This factor reflects the fact that 

there is naturally a larger difference between ∆UM and ∆U for cyclic-load 

testing protocols that have a larger number of cycles before reaching ∆U. 

The DC

 value of 1.0 (resulting in an approximate target of ∆UM / ∆U = 1.2) is 

based on observations for cyclic-load testing protocols that have a relatively 

small number of cycles (e.g., the CUREE protocol). The DC

 value of 1.5 

(resulting in an approximate target of ∆UM / ∆U = 1.8) is based on 

observations for cyclic-load testing protocols that have a relatively large 

number of cycles (but still with fewer cycles than protocols like SPD). As a 

point of comparison, the ratio of , , ( ) ∆ ∆ U CUREE U SPD

  is 0.035/0.0210 = 1.7, 

based on comparison of the wood light-frame shear wall data sets in Chapter 

4 and Appendix D. This would suggest a DC

 value of 1.7 for loading 

protocols with an extremely large number of cycles (like SPD), but the DC



value is capped at a maximum of 1.5 for simplicity. 

3.9 Documentation and Peer Review Requirements

Use of the Component Methodology to determine equivalency should be 

fully documented and peer reviewed. Peer review encompasses the entire 
FEMA P-795 3: Commentary on the Component Equivalency Methodology 3-39

process and is most effective when implemented at the outset. The 

Component Methodology was developed to be generally applicable to a 

broad base of component types, but the peer review process will likely be 

needed to interpret the intent of the requirements for special circumstances 

related to proposed components, reference components, or the reference 

seismic-force-resisting system.

FEMA P-795 4: Example Application 4-1

Chapter 4

Example Application

4.1 Introduction

This chapter illustrates the application of the Component Methodology to a 

possible substitution for nailed wood shear wall reference components in a

wood light-frame seismic-force-resisting system. The objective is to 

determine if a hypothetical proposed component is equivalent to line A.15 in 

Table 12.2-1of ASCE/SEI 7-10, Minimum Design Loads for Buildings and 

Other Structures (ASCE, 2010), which reads “Light-framed (wood) walls 

sheathed with wood structural panels rated for shear resistance or steel 

sheets.” An actual component with complete set of test data fulfilling all of 

the requirements of the Component Methodology was not readily available, 

so a hypothetical proposed component with fictitious data was utilized in 

order to provide a full illustration of the Component Methodology. 

In addition to illustrating the application of the Component Methodology, 

this example also presents the development of a robust and representative 

data set containing cyclic-load test results for nailed wood shear wall 

components available in the literature. The data set is based on Line et al. 

(2008), but has been modified to comply with the reference component 

design space used in this example. The data set consists of wall components 

with aspect ratios ranging from 2:1 to 1:1 that were tested using the CUREE 

loading protocol, which is a loading protocol that was developed as part of 

the CUREE-Caltech Woodframe Project (Krawinkler et al., 2000). 

The steps in this example follow directly from the requirements of the 

Component Methodology defined in Sections 2.2 through 2.8. 

4.2 Component Testing Requirements

The component testing requirements of Section 2.2 are fulfilled by the 

reference component data given in Section 4.4 and proposed component data 

created for the purpose of this example. Gravity loads were not included in 

either testing program, so a limitation on the building height was enforced for 

the proposed component (see Section 4.5.4). This was deemed acceptable 

because a moderate level of gravity load was not expected to have a 

substantial effect on the lateral load resistance of the shear wall components.
4-2 4: Example Application FEMA P-795

To fulfill the requirement of equivalency between cyclic loading protocols, 

both the reference component and proposed component data sets utilized data 

from tests that employed only the CUREE loading protocol. 

4.3 Evaluation of Applicability Criteria

Based on the criteria of Section 2.3, including minimum acceptable quality 

ratings of test data and design requirements, the Component Methodology 

was deemed applicable for evaluating equivalency between the proposed 

component (hypothetical shear walls) and the reference component (nailed 

wood shear walls). In this example, quality ratings for test data are 

developed in Section 4.7.1, and quality ratings for design requirements are 

developed in Section 4.7.2. Based on the reported quality ratings, both the 

reference and proposed components meet the minimum applicability criteria 

for test data and design requirements. Additionally, both the reference and 

proposed shear wall components can be isolated from the remainder of the 

seismic-force-resisting system by a clear component boundary.

4.4 Reference Component Test Data

4.4.1 Define Reference Component Design Space 

To clearly define the range of possible reference components, the reference 

component was defined as a nailed wood shear wall with the following 

representative configurations:

• Wall dimensions (height and length): 8’x4’ to 8’x8’

• Aspect ratio (height/length): 2:1 to 1:1 (aspect ratios above 2:1 are not 

included in the design space)

• Sheathing: OSB and STR, 3/8” to 19/32” thickness

• Nails: 6d to 10d common nails

• Nail spacing (on-center): Edge spacing: 2” to 6”; field spacing: 6” to 12”

• Openings: No openings are considered. While openings are likely to 

occur in any wood light-frame building, the proposed component design 

requirements will be based on a segmented shear wall design approach, 

such that only full height piers (without openings) will be considered as 

part of the seismic-force-resisting system. Accordingly, the compiled 

reference component test data do not consider openings.

4.4.2 Compile or Generate Reference Component Test Data 

The set of reference component test data were compiled based on the

requirements of Sections 2.4.1, 2.4.2, and 2.2. 
FEMA P-795 4: Example Application 4-3

Line et al. (2008) compiled CUREE cyclic-load data from a total of 80 test 

specimens. This data set includes results from 48 wall tests that were 

compiled as part of the International Code Council Evaluation Services 

Acceptance Criteria AC322 effort (ICC-ES, 2007), as well as results from 32 

additional tests. To create the reference component data set for nailed wood 

shear walls used in this example, data were removed for walls with openings, 

stapled walls, and walls with box nails, leaving a total of 65 tests in the final 

data set. This set is considered to be a robust and representative data set for 

nailed wood shear walls with aspect ratios ranging from 2:1 to 1:1, tested 

using the CUREE loading protocol. 

4.4.3 Interpret the Reference Component Test Results 

Test data were interpreted in accordance with the requirements of Section 

2.4.3. The force quantity was taken as the horizontal shear force in the wall, 

and the displacement quantity was taken as the lateral drift in the wall (lateral 

displacement divided by height). 

Figures 4-1 through 4-3 show the cyclic response and construction of the 

cyclic envelope curve for a nailed wood shear wall specimen from the above 

data set (Specimen E-A2, test index 17, which is an 8’x8’ wall with 7/16” 

OSB sheathing nailed with 8d common nails at 3” edge spacing and 12” field 

spacing). 

Figure 4-2 shows the cyclic response and the cyclic envelope curves 

superimposed for the same wall specimen. The cyclic envelope curve was

constructed using the requirements of Section 2.2.2, which differ slightly 

from the rules utilized by Line et al. (2008), so the values of ultimate 

deformation also differ slightly from those reported in Line et al. (2008).

Figure 4-3 shows the envelope curve with the parameters that are utilized in 

the acceptance criteria of the Component Methodology. The maximum 

strengths in the positive and negative directions are 11,330 lbs. and 9,892 

lbs., respectively, with an average VM = 10,611 lbs. Using the shear wall 

strength table, Table 2306.4.1, in the 2006 International Building Code (ICC, 

2006), the allowable stress design strength, VD, of this shear wall is 3,920 lbs.

(490 lb/ft), so VM / VD = 2.7. This value is denoted as RQ in the Component 

Methodology. 
4-4 4: Example Application FEMA P-795

Figure 4-1 Illustration of cyclic response of a nailed wood shear wall, data 

from Line et al. (2008) and Rosowsky et al. (2004).

Figure 4-2 Illustration of cyclic response and envelope curve for a nailed 

wood shear wall, data from Line et al. (2008) and Rosowsky et 

al. (2004).

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

-1

-0.5

0

0.5

1

x 104

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

(a)
FEMA P-795 4: Example Application 4-5

Figure 4-3 Illustration of cyclic envelope curve and calculation of

component response quantities for a nailed wood shear wall, 

data from Line et al. (2008) and Rosowsky et al. (2004).

The initial stiffness was computed as the secant stiffness at 40% of the peak 

strength. The average of the positive and negative loading directions is 

KI = 20,755 lb/in. Using the allowable stress design (ASD) load of 3,920 lbs.

and the displacement at the ASD design load (computed according to IBC 

Equation 23-2), the design initial stiffness is KD = 19,311 lb/in. Therefore, 

for this test specimen, KI / KD = 1.1. This value is denoted as RK in the 

Component Methodology.

Computing the effective ductility capacity, μeff, requires calculation of the

effective yield displacement, ∆Y,eff. The values of ∆Y, eff were computed 

separately in the positive and negative directions, and the average value was

∆Y,eff = 0.53% drift for this test specimen.

The ultimate deformation, ∆U, is 0.032 in/in. in the negative loading 

direction. In the positive loading direction, the specimen does not experience 

a 20% loss in the applied maximum load, so the deformation capacity was

limited to the maximum displacement reached in the positive direction, 

which corresponds to a drift of 0.048 in/in. The final average ultimate 

deformation is ∆U = 0.040 in/in. for this specimen. Per Section 2.2.2, the 

value of ∆U could be affected if the vertical load-carrying ability of the 

specimen were compromised. In this example, such a modification was not 

necessary. Using the final value of ∆U and the previously computed value of 

∆Y,eff, the effective ductility capacity was calculated to be μeff = 7.5. 
4-6 4: Example Application FEMA P-795

These calculations were completed for each of the 65 sets of data included in 

the reference component data set. Table 4-1 summarizes the configuration of 

each test specimen and the failure modes observed during testing.

Table 4-2 summarizes the values of important response quantities (e.g.,

strength, stiffness, ultimate deformation) for each specimen of the reference 

component data set. Per the requirements of Section 2.2.2, values of the 

ultimate deformation, ∆U, were not reported for test specimens in which the 

loading was not continued to 20% strength loss. 

Table 4-1 Summary of Nailed Wood Shear Wall Configurations in the 

Reference Component Data Set

Test

Index

Wall 

Dimensions 

(HxL)

OSB 

Sheathing Fastener

Fastener 

Spacing 

(edge/field)

Failure Mode

1 8.5' x 4.5' 15/32" Str. 1 10d com 2"/12" Not Reported

2 8.5' x 4.5' 15/32" Str. 1 10d com 2"/12" Not Reported

3 8' x 8' 7/16" 8d com 4"/6" Not Reported

4 8' x 8' 7/16" 8d com 4"/6" Not Reported

5 8' x 8' 7/16" 8d com 4"/6" Not Reported

6 8' x 8' 19/32" 10d com 2"/12" Not Reported

7 8' x 8' 19/32" 10d com 2"/12" End Post Tension

8 8' x 8' 19/32" 10d com 2"/12" Not Reported

9 8' x 8' 19/32" 10d com 2"/12" Not Reported

10 8' x 8' 7/16" 8d com 4"/6" Not Reported

11 8' x 8' 7/16" 8d com 4"/6" Not Reported

12 8' x 8' 7/16" 8d com 4"/6" Not Reported

13 8' x 8' 7/16" 8d com 4"/6" Not Reported

14 8' x 8' 7/16" 8d com 4"/6" Not Reported

15 8' x 8' 7/16" 8d com 4"/6" Not Reported

16 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

17 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

18 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

19 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

20 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

21 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

22 8' x 8' 7/16" 8d com 3"/12" Sill Plate Splitting

23 8' x 8' 7/16" 8d com 3"/12" Sill Plate Splitting

24 8' x 8' 7/16" 8d com 3"/12" Sill Plate Splitting

25 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

26 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

27 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

28 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

29 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

30 8' x 8' 7/16" 8d com 3"/12" Fastener Failure
FEMA P-795 4: Example Application 4-7

Table 4-1 Summary of Nailed Wood Shear Wall Configurations in the 

Reference Component Data Set (continued)

Test

Index

Wall 

Dimensions 

(HxL)

OSB 

Sheathing Fastener

Fastener 

Spacing 

(edge/field)

Failure Mode

31 8' x 8' 7/16" 8d com 3"/12" Sill Plate Splitting

32 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

33 8' x 8' 7/16" 8d com 3"/12" Fastener Failure

34 8' x 8' 3/8" Str.1 6d com 6"/6" Fastener Failure

35 8' x 8' 3/8" Str.1 6d com 6"/6" Fastener Failure

36 8' x 4' 3/8" Str.1 6d com 6"/6" Fastener Failure

37 8' x 4' 3/8" Str.1 6d com 6"/6" Fastener Failure

38 8' x 8' 3/8" Str.1 6d com 2"/6" Fastener Failure

39 8' x 8' 3/8" Str.1 6d com 2"/6" Fastener Failure

40 8' x 4' 3/8" Str.1 6d com 2"/6" Fastener Failure

41 8' x 4' 3/8" Str.1 6d com 2"/6" Fastener Failure

42 8' x 8' 7/16" 8d com 6"/6" Fastener Failure

43 8' x 8' 7/16" 8d com 6"/6" Fastener Failure

44 8' x 4' 7/16" 8d com 6"/6" Fastener Failure

45 8' x 4' 7/16" 8d com 6"/6" Fastener Failure

46 8' x 8' 7/16" 8d com 2"/6" Fastener Failure

47 8' x 8' 7/16" 8d com 2"/6" Fastener Failure

48 8' x 4' 7/16" 8d com 2"/6" End Post Failure

49 8' x 4' 7/16" 8d com 2"/6" Fastener Failure

50 8' x 8' 19/32" 10d com 6"/12" Fastener Failure

51 8' x 8' 19/32" 10d com 6"/12" Fastener Failure

52 8' x 4' 19/32" 10d com 6"/12" Fastener Failure

53 8' x 4' 19/32" 10d com 6"/12" Fastener Failure

54 8' x 8' 19/32" 10d com 2"/12" Fastener Failure

55 8' x 8' 19/32" 10d com 2"/12" Fastener Failure

56 8' x 4' 19/32" 10d com 2"/12" Fast./Post Failure

57 8' x 4' 19/32" 10d com 2"/12" Fastener Failure

58 8' x 8' 3/8" Str.1 8d com 6"/6" Fastener Failure

59 8' x 8' 3/8" Str.1 8d com 6"/6" Fastener Failure

60 8' x 4' 3/8" Str.1 8d com 6"/6" Fastener Failure

61 8' x 4' 3/8" Str.1 8d com 6"/6" Fastener Failure

62 8' x 8' 3/8" Str.1 8d com 2"/6" Fastener Failure

63 8' x 8' 3/8" Str.1 8d com 2"/6" Fastener Failure

64 8' x 4' 3/8" Str.1 8d com 2"/6" Fastener Failure

65 8' x 4' 3/8" Str.1 8d com 2"/6" Fastener Failure
4-8 4: Example Application FEMA P-795

Table 4-2 Summary of Important Component Parameters for the Reference 

Component Data Set

Test

Index

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD

(lb) RQ

KI

(lb/in)

KD

(lb/in) RK

ΔY,eff

(in/in) μeff ΔU (in/in)

1 10,239 3,915 2.6 7,594 14,961 0.5 0.013 n/a n/a

2 10,461 3,915 2.7 7,520 14,961 0.5 0.014 2.7 0.037

3 7,019 2,800 2.5 21,195 15,043 1.4 0.003 7.6 0.026

4 6,965 2,800 2.5 18,475 15,043 1.2 0.004 10.2 0.040

5 6,701 2,800 2.4 19,496 15,043 1.3 0.004 11.1 0.040

6 15,947 6,960 2.3 30,989 27,981 1.1 0.005 7.0 0.038

7 15,953 6,960 2.3 26,755 27,981 1.0 0.006 6.0 0.037

8 17,856 6,960 2.6 24,219 27,981 0.9 0.008 6.2 0.048

9 17,421 6,960 2.5 24,903 27,981 0.9 0.007 6.6 0.048

10 7,184 2,800 2.6 7,007 15,043 0.5 0.011 2.8 0.030

11 7,454 2,800 2.7 6,431 15,043 0.4 0.012 2.6 0.031

12 6,906 2,800 2.5 12,020 15,043 0.8 0.006 5.5 0.033

13 7,136 2,800 2.5 11,516 15,043 0.8 0.006 5.0 0.032

14 7,631 2,800 2.7 28,419 15,043 1.9 0.003 9.3 0.026

15 7,478 2,800 2.7 28,346 15,043 1.9 0.003 9.5 0.026

16 10,208 3,920 2.6 12,721 19,311 0.7 0.008 n/a n/a

17 10,611 3,920 2.7 20,755 19,311 1.1 0.005 7.5 0.040

18 11,151 3,920 2.8 15,990 19,311 0.8 0.007 5.7 0.042

19 10,877 3,920 2.8 18,639 19,311 1.0 0.006 5.8 0.035

20 11,554 3,920 2.9 22,241 19,311 1.2 0.005 7.9 0.043

21 11,396 3,920 2.9 21,876 19,311 1.1 0.005 7.7 0.042

22 10,952 3,920 2.8 11,337 19,311 0.6 0.010 3.5 0.036

23 10,574 3,920 2.7 15,910 19,311 0.8 0.007 6.0 0.041

24 11,156 3,920 2.8 14,604 19,311 0.8 0.008 4.8 0.038

25 10,863 3,920 2.8 20,521 19,311 1.1 0.006 n/a n/a

26 10,771 3,920 2.7 21,449 19,311 1.1 0.005 n/a n/a

27 10,265 3,920 2.6 13,381 19,311 0.7 0.008 n/a n/a

28 10,794 3,920 2.8 19,110 19,311 1.0 0.006 6.2 0.036

29 10,923 3,920 2.8 19,181 19,311 1.0 0.006 6.4 0.038

30 10,920 3,920 2.8 20,288 19,311 1.1 0.006 6.1 0.034

31 10,113 3,920 2.6 18,624 19,311 1.0 0.006 5.8 0.033

32 10,831 3,920 2.8 20,115 19,311 1.0 0.006 6.3 0.035

33 11,079 3,920 2.8 19,328 19,311 1.0 0.006 6.1 0.036

34 4,573 1,780 2.6 16,020 7,517 2.1 0.003 9.5 0.028

35 4,280 1,780 2.4 16,406 7,517 2.2 0.003 10.3 0.028

36 2,502 890 2.8 7,929 3,674 2.2 0.003 11.1 0.036

37 2,467 890 2.8 7,076 3,674 1.9 0.004 11.7 0.042

38 12,753 4,530 2.8 27,980 18,253 1.5 0.005 7.6 0.036

39 12,805 4,530 2.8 16,722 18,253 0.9 0.008 4.2 0.034

40 6,746 2,265 3.0 7,076 8,642 0.8 0.010 4.4 0.043

41 5,888 2,265 2.6 10,985 8,642 1.3 0.006 8.1 0.045

42 5,750 1,920 3.0 21,464 11,105 1.9 0.003 11.1 0.031

43 6,273 1,920 3.3 22,698 11,105 2.0 0.003 10.0 0.029

44 2,889 960 3.0 5,554 5,369 1.0 0.005 7.4 0.040

45 3,305 960 3.4 6,840 5,369 1.3 0.005 8.0 0.040
FEMA P-795 4: Example Application 4-9

Table 4-2 Summary of Important Component Parameters for the Reference Component 

Data Set (continued)

Test

Index

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD (lb) RQ

KI

(lb/in)

KD

(lb/in) RK

ΔY,eff

(in/in) μeff ΔU (in/in)

46 16,058 4,680 3.4 23,492 32,858 0.7 0.007 4.2 0.030

47 16,345 4,680 3.5 19,476 32,858 0.6 0.009 3.6 0.032

48 7,584 2,340 3.2 7,444 14,922 0.5 0.011 3.4 0.036

49 6,590 2,340 2.8 7,602 14,922 0.5 0.009 3.6 0.033

50 6,577 2,720 2.4 18,481 12,311 1.5 0.004 7.9 0.029

51 6,851 2,720 2.5 18,897 12,311 1.5 0.004 9.8 0.037

52 3,345 1,360 2.5 6,574 5,931 1.1 0.005 6.4 0.034

53 3,296 1,360 2.4 6,474 5,931 1.1 0.005 7.4 0.039

54 16,826 6,960 2.4 28,283 24,443 1.2 0.006 5.9 0.036

55 16,992 6,960 2.4 27,607 24,443 1.1 0.006 5.6 0.036

56 7,504 3,480 2.2 8,626 11,368 0.8 0.009 4.5 0.041

57 7,363 3,480 2.1 9,443 11,368 0.8 0.008 5.3 0.043

58 5,614 1,840 3.1 22,288 12,458 1.8 0.003 10.8 0.028

59 5,646 1,840 3.1 20,629 12,458 1.7 0.003 8.4 0.024

60 2,757 920 3.0 8,469 6,000 1.4 0.003 8.6 0.029

61 2,849 920 3.1 7,570 6,000 1.3 0.004 8.8 0.034

62 15,695 4,880 3.2 20,870 36,571 0.6 0.008 4.0 0.031

63 14,804 4,880 3.0 23,317 36,571 0.6 0.007 5.3 0.035

64 6,838 2,440 2.8 8,909 16,438 0.5 0.008 4.6 0.036

65 7,216 2,440 3.0 9,510 16,438 0.6 0.008 4.7 0.038

Median: 2.7 RQ =  1.00 R K =  6.3 μeff = 0.035 ∆ U = 

Variability: 0.11 σ RQ = 0.42 σ RK = , 0.38 σ μ eff = 0.16 σ ∆U =

4.4.4 Define Reference Component Performance Groups 

Based on the requirements of Section 2.4.4, the reference component data 

were placed into a single performance group. 

4.4.5 Compute Summary Statistics

The summary statistics for each component parameter were computed in 

accordance with Section 2.4.5, assuming an underlying lognormal 

distribution of the test data. Table 4-3 presents the summary statistics for the 

data set, which is information repeated from the bottom of Table 4-2. 

Example calculations for summary statistics are illustrated in Section 4.6.6 

using the proposed component test data.
4-10 4: Example Application FEMA P-795

Table 4-3 Summary Statistics for Reference Component 

Parameters

Summary 

Statistic

RQ

(=VM / VD)

RK

(=KI / KD) μeff ∆U (in/in)

Median 2.7 Q R =  1.00 K R =  6.3 μeff  = 0.035 U ∆ = 

Variability 0.11 σ RQ = 0.42 σ RK = , 0.38 σ μ eff = 0.16 σ ∆U =

4.5 Proposed Component Design Requirements

In accordance with Section 2.5, a comprehensive set of design requirements 

is needed for the proposed component. This section presents the hypothetical 

design requirements for the proposed component.

4.5.1 Component Design Strength and Stiffness

To meet the acceptance criteria of Section 2.8, the ASD strengths of the 

proposed component were roughly calibrated to the experimental test data. 

Table 4-4 provides the design strengths in the traditional format for each 

hypothetical combination of sheathing type and connector spacing. 

Table 4-4 Proposed Component Design Strengths for 

Hypothetical Combinations of Sheathing Type and 

Connector Spacing

Proposed Component Allowable Stress Design Strengths (lbs/ft)

Sheathing 

Type / Thickness 

Connector Spacing Pattern

1 2 3

1 225 450 540

2 250 500 600

3 280 570 680

Design requirements are also needed for the prediction of initial stiffness. 

Initial stiffness is an important aspect of design for various code 

requirements (e.g., checking design drift limits) as well as for proper 

modeling to distribute system-level forces to individual components. 

In some wood light-frame components, the design stiffness is included 

implicitly within the published design strength values. In this example, 

however, the initial stiffness values were considered separately. Various

approaches could be used for computing the design stiffness. For example, 

Equation 23-2 in the 2006 IBC could be used for computing the wall 

displacement at the design load, and this equation is repeated below.

Another viable option would be to consider the use of Equation 4.3-1 of 
FEMA P-795 4: Example Application 4-11

ANSI/AF&PA SDPWS-2008 Special Design Provisions for Wind and 

Seismic with Commentary (AF&PA, 2009). 

To compute these values, parameters in the equation, such as the connector 

deformation value, en, were calibrated based on available test data, with the 

goal of making the stiffness ratio, , , , R R K PC K RC

  approximately equal to 

unity. 

3 8 0.75 n a

vh vh h he d

Eab Gt b

∆ = ++ +

where:

a = area of boundary element (in2

)

b = wall width (feet)

da = vertical elongation of overturning anchorage at the design shear 

load (v) (inches)

E = elastic modulus of boundary element (pounds/inch/inch)

en = connector deformation (inches)

Gt = panel rigidity through the thickness (pounds/inch)

h = wall height (feet)

v = maximum shear due to design loads, applied at the top of the wall 

(pounds/foot)

The design stiffness values in this example were computed for each 

hypothetical combination of sheathing, connector, and panel geometry, and 

summarized in Table 4-5. It should be noted that the values in Table 4-5 do 

not include any effect of anchorage deflection. Anchorage deflection would 

need to be considered separately if determined to be important to the overall 

as-built component stiffness.

4.5.2 Component Detailing Requirements

A proposed component must have a complete set of design detailing 

requirements. It is not possible, however, to illustrate the development of 

these requirements in a meaningful way for a hypothetical proposed 

component. The specific test applications presented in the Appendices of 

this report provide additional illustration of this important step in the process.
4-12 4: Example Application FEMA P-795

Table 4-5 Proposed Component Design Stiffness for Each 

Panel Geometry

Proposed Component Design Stiffness (lb/in) - For 8'x4' Panels 

Sheathing 

Type / Thickness 

Connector Spacing Pattern

1 2 3

1 3,300 5,400 9,000

2 3,500 5,800 9,600

3 3,700 9,600 10,000

Proposed Component Design Stiffness (lb/in) - For 8'x8' Panels 

Sheathing 

Type / Thickness 

Connector Spacing Pattern

1 2 3

1 7,200 12,000 19,800

2 7,700 12,800 21,200

3 8,000 13,300 22,000

Proposed Component Design Stiffness (lb/in) - For 8'x12' Panels 

Sheathing 

Type / Thickness 

Connector Spacing Pattern

1 2 3

1 12,600 20,400 33,000

2 13,500 21,800 35,300

3 14,000 22,600 36,600

4.5.3 Component Connection Requirements

To meet the requirements of Section 2.5.3, connection requirements for the 

proposed component were developed to specify that, in addition to vertical

loads, the framing members of the proposed component shear wall must be

designed to resist induced seismic forces per the design methods listed in 

Section 2.1.2 of ANSI/AFPA SDPWS-2008. The connections between the 

wall and the rest of the structural system must also be designed to resist the 

induced seismic forces per the design methods listed in ANSI/AFPA 

SDPWS-2008, and the boundary elements of the proposed component shear 

wall (i.e., the end studs) must be designed to transfer the design tension and 

compression forces to the rest of the structural system.

Though not explicitly demonstrated in this example, it is assumed that these 

connection requirements ensure that the inelastic behavior occurs in the 
FEMA P-795 4: Example Application 4-13

proposed shear wall components and not in the connections between the wall 

and the balance of the seismic-force-resisting system.

4.5.4 Limitations on Component Applicability and Use

The Component Methodology requires that the use of the proposed 

component must be reasonably restricted to the range of possible 

configurations that were considered in the testing program (i.e., use must be 

restricted to the “component design space”). Accordingly, the hypothetical 

proposed component should only be used within the range of configurations

outlined in Section 4.6.1 (e.g., aspect ratios less than 2:1).

Additionally, since the tests were completed without applied vertical loads, 

the proposed component design provisions include a restriction to the use of 

the component to ensure that applied vertical loads would not tangibly affect 

the behavior and performance of the component. In this example, the current 

height limits in ASCE/SEI 7-10 (i.e., 65’ in high seismic regions) were 

deemed sufficient to meet the requirements of Section 2.5.4.

4.5.5 Component Construction, Inspection, and Maintenance 

Requirements

The proposed component was assumed to be a pre-fabricated component that 

would have quality control standards pertaining to the quality and 

consistency of the as-built pre-fabricated shear wall components. 

Additionally, it was assumed that the proposed component would also have 

requirements for on-site installation, inspection, and maintenance.

4.6 Proposed Component Test Data

4.6.1 Define Proposed Component Design Space

The proposed component design space includes wall components with the 

following representative configurations:

• Wall height and length: 8’x 4’ to 8’x12’

• Aspect ratio (height/length): 2:1 to 0.67:1. This range is broader than the 

reference component data set, but such differences are permitted when 

the transfer of forces across the component boundary is not significantly 

affected.

• Sheathing type/thickness: Hypothetical sheathing types 1, 2, and 3

identified in Table 4-4.

• Connectors: Hypothetical connectors with spacing patterns 1, 2, and 3 

identified in Table 4-4.
4-14 4: Example Application FEMA P-795

• Openings: No openings are included in the test specimens. Since 

openings are likely to occur in wood light-frame building applications, a 

segmented shear wall design approach will be used, such that only full 

height piers will be considered as part of the seismic-force-resisting 

system.

4.6.2 Select Proposed Component Configurations for Testing

Table 4-6 summarizes the proposed component configurations that were 

selected for cyclic-load testing in this example.

Table 4-6 Summary of Proposed Component Wall 

Configurations for Cyclic-Load Testing 

Test

Index

Wall 

Dimensions 

(HxL)

Sheathing 

Type/ 

Thickness 

Connector 

Spacing 

Pattern

Connector 

Type

1 8' x 4' 1 2 1

2 8' x 4' 1 2 1

3 8' x 4' 2 2 1

4 8' x 4' 2 2 1

5 8' x 4' 3 2 1

6 8' x 4' 3 2 1

7 8' x 4' 2 1 1

8 8' x 4' 2 1 1

9 8' x 4' 2 3 1

10 8' x 4' 2 3 1

11 8' x 8' 1 2 1

12 8' x 8' 1 2 1

13 8' x 8' 2 2 1

14 8' x 8' 2 2 1

15 8' x 8' 3 2 1

16 8' x 8' 3 2 1

17 8' x 8' 2 1 1

18 8' x 8' 2 1 1

19 8' x 8' 2 3 1

20 8' x 8' 2 3 1

21 8' x 12' 1 2 1

22 8' x 12' 1 2 1

23 8' x 12' 1 2 1

24 8' x 12' 3 2 1

25 8' x 12' 3 2 1

26 8' x 12' 2 1 1

27 8' x 12' 2 1 1
FEMA P-795 4: Example Application 4-15

Component configurations used for cyclic-load testing should span the 

component design space. The selected configurations fulfill the minimum 

test data requirements of four configurations per performance group with at 

least two specimens per configuration. These configurations do not cover all 

possible combinations of sheathing, connector spacing, and component 

geometry. Even so, it is assumed that the peer review panel would agree that 

this test matrix was sufficiently extensive because it spanned the design 

space in a reasonably complete manner, and no problematic trends were 

observed in the chosen configurations, so there is no expectation that the 

behavior would be systematically different in the configurations that were 

not tested.

Table 4-7 summarizes the proposed component configurations chosen for 

monotonic testing in this example. Configurations selected for monotonicload testing are more limited, but they fulfill the minimum test data 

requirements of Section 2.2.3, which specifies a minimum of two

configurations per performance group with at least two specimens per 

configuration. The selected configurations were chosen because they were 

considered the most representative of the configurations used in the full 

cyclic data set. 

Table 4-7 Summary of Proposed Component Wall 

Configurations for Monotonic-Load Testing 

Test

Index

Wall 

Dimensions 

(HxL)

Sheathing 

Type/ 

Thickness 

Connector 

Spacing 

Pattern

Connector 

Type

3 8' x 4' 2 2 1

4 8' x 4' 2 2 1

13 8' x 8' 2 2 1

14 8' x 8' 2 2 1

4.6.3 Perform Cyclic-Load and Monotonic-Load Tests

Cyclic-load testing would need to be completed for the component 

configurations listed in Table 4-6. Because the reference component data set

utilized the CUREE loading protocol, the proposed component specimens 

were tested with the CUREE loading protocol to satisfy requirements for 

equivalency of loading history. 

Similarly, monotonic-load testing would also need to be completed for the 

component configurations listed in Table 4-7. The hypothetical specimens 

were considered to have nominally symmetric behavior, and were therefore 

pushed monotonically in only one direction, in accordance with the 

requirements of Section 2.2.3. 
4-16 4: Example Application FEMA P-795

4.6.4 Interpret Proposed Component Test Results

Test data were compiled for each of the 27 proposed component shear wall 

cyclic-load tests and summarized in Table 4-8.

Table 4-8 Summary of Important Component Parameters from the Proposed Component CyclicLoad Data Set

Test

Index

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD (lb) RQ

KI

(lb/in) KD (lb/in) RK

ΔY,eff

(in/in) μeff ΔU (in/in)

1 5,645 1,800 3.1 3,897 5,400 0.7 0.015 3.4 0.052

0.051

2 5,786 1,800 3.2 4,125 5,400 0.8 0.015 3.4 0.050

3 5,485 2,000 2.7 4,456 5,800 0.8 0.013 3.3 0.042

0.044

4 6,125 2,000 3.1 4,658 5,800 0.8 0.014 3.4 0.046

5 6,030 2,280 2.6 7,035 9,600 0.7 0.009 6.5 0.058

0.057

6 5,895 2,280 2.6 7,212 9,600 0.8 0.009 6.6 0.056

7 2,889 1,000 2.9 3,325 3,500 1.0 0.009 4.0 0.036

0.038

8 3,158 1,000 3.2 4,100 3,500 1.2 0.008 5.0 0.040

9 7,056 2,400 2.9 4,987 9,600 0.5 0.015 3.3 0.048

0.050

10 6,590 2,400 2.7 5,123 9,600 0.5 0.013 3.9 0.052

11 10,564 3,600 2.9 10,245 12,000 0.9 0.011 4.5 0.048

0.046

12 10,250 3,600 2.8 12,560 12,000 1.0 0.009 5.3 0.045

13 11,890 4,000 3.0 9,594 12,800 0.7 0.013 3.3 0.043 0.042

14 12,236 4,000 3.1 11,256 12,800 0.9 0.011 3.6 0.041

15 14,592 4,560 3.2 10,589 13,300 0.8 0.014 3.6 0.051

0.050

16 15,624 4,560 3.4 11,305 13,300 0.9 0.014 3.4 0.049

17 5,750 2,000 2.9 13,251 7,700 1.7 0.005 8.0 0.036

0.035

18 6,273 2,000 3.1 9,856 7,700 1.3 0.007 5.3 0.035

19 16,058 4,800 3.3 14,095 21,200 0.7 0.012 3.8 0.045

0.046

20 15,987 4,800 3.3 11,686 21,200 0.6 0.014 3.4 0.048

21 18,956 5,400 3.5 21,897 20,400 1.1 0.009 4.7 0.042

22 21,560 6,000 3.6 22,589 21,800 1.0 0.010 2.8 0.028 0.035

23 19,258 5,400 3.6 20,156 20,400 1.0 0.010 3.8 0.038

24 22,561 6,840 3.3 27,895 22,600 1.2 0.008 5.3 0.045

0.042

25 23,520 6,840 3.4 28,945 22,600 1.3 0.008 4.7 0.040

26 10,678 3,000 3.6 10,057 13,500 0.7 0.011 3.4 0.038

0.037

27 10,253 3,000 3.4 9,762 13,500 0.7 0.011 3.3 0.036

Median: 3.1 RQ =  0.86 RK =  4.1 μeff = 0.043 ∆ U = 

Variability: 0.10 σ RQ = 0.28 σ RK = , 0.26 σ μ eff = 0.17 σ ∆U =
FEMA P-795 4: Example Application 4-17

The test data were also compiled for each of the four proposed component 

shear wall monotonic-load tests and summarized in Table 4-9.

Table 4-9 Summary of Important Component Parameters 

from the Proposed Component Monotonic-Load 

Data Set

Test Index VMM (lb) VD (lb) VMM / VD ΔUM (in/in)

3 5,645 2,000 2.8 0.070

4 5,786 2,000 2.9 0.064

13 5,485 4,000 1.4 0.056

14 6,125 4,000 1.5 0.061

Median: 2.0 0.062

4.6.5 Define Proposed Component Performance Groups

The proposed component data were placed in a single performance group, 

consistent with the requirements of Section 2.6.5, and also consistent with 

the approach taken for the reference component data set.

Although strength and stiffness values differ between various wall

configurations, these differences were considered to be minor so that the test 

data need not be separated into multiple performance groups. Additionally, 

there were no strong trends in component behavior (i.e., failure modes) that 

would necessitate breaking the data set into multiple performance groups.

For use in the acceptance criteria evaluation, the following statistical 

parameters were computed for the proposed component data set. Similar 

parameters are also needed for the reference component (unless otherwise 

noted below). 

Per for mance Par ameter s based on C yclic-L oad T esting:

• Median value of ultimate deformation, ∆ U PC , 

• Lognormal standard deviation of ultimate deformation, σ∆U,PC

• Individual configuration median ultimate deformation, ∆Uj PC ,  (not needed 

for the reference component)

• Median value of the stiffness ratio, R K PC , 

• Median value of the load (strength) ratio, RQ PC , 

• Median value of the effective ductility capacity, μeff,PC 
4-18 4: Example Application FEMA P-795

Perfor mance Par ameter s based on M onotonic-L oad T esting:

• Median value of ultimate deformation, ∆ UM,PC

 (only needed for the 

reference component if Equation 2-6 cannot be fulfilled by the proposed 

component monotonic data)

4.6.6 Compute Summary Statistics

In accordance with the requirements of Sections 2.4.5 and 2.6.6, summary 

statistics were computed using the assumption of a lognormal distribution of 

the data. Using ∆ U,PC

 as an example, summary statistics can be calculated

from the following steps (for a given performance group):

1. Compute the natural logarithm of ∆U,PC , i.e., LN[∆U,PC], for each test. 

2. Compute the average of the LN[∆U,PC] values.

3. Compute the exponent of the result from step (2), i.e., e Mean(LN[ΔU,PC]). 

This value is the fitted median value, ∆ U,PC

 .

4. Compute the standard deviation of the LN[∆U,PC] values. This is the 

fitted logarithmic standard deviation value, σ∆U,PC.

The above process (steps 1-3) can also be used to compute the median 

ultimate deformation value for each individual component configuration,

∆ Uj,PC

 , as well as other statistical parameters. Proposed component summary 

statistics for cyclic-load test data were presented at the bottom of Table 4-8 

and are summarized again in Table 4-10. 

Table 4-10 Summary Statistics for Proposed Component 

Parameters from Cyclic-Load Test Data

Summary 

Statistic

RQ

(=VM / VD)

RK

(=KI / KD) μeff ∆ U (in/in)

Median 3.1 QR =  0.86 K R =  4.1 μeff  = 0.043 U ∆ = 

Variability 0.10 σ RQ = 0.28 σ RK = , 0.26 σ μ eff = 0.17 σ ∆U =

For the monotonic-load test data, the same approach is used to compute 

summary statistics. The only monotonic-load test summary statistic used in 

the acceptance criteria is the median ultimate deformation capacity value,

∆ UM,PC

 , which was computed to be 0.062 in this example. 

4.7 Evaluate Quality Ratings 

4.7.1 Quality Rating of Test Data

The reference component test data were rated as Superior. This comes from

a high rating for completeness and robustness and a high rating for 
FEMA P-795 4: Example Application 4-19

confidence in the test results. The high rating for completeness and 

robustness was based on all of the important testing issues being addressed 

and the expectation that all important failure modes were uncovered in the 

testing. The high rating for confidence in the test results was based on the 

large number of test data, as well as multiple researchers and test laboratories 

being involved in completing the testing. 

The proposed component test data were rated as Good. This rating comes 

from a medium rating for completeness and robustness and a high rating for 

confidence in the test results. The medium rating for completeness and 

robustness was based on the hypothetical panel component being made of a 

new type of material for which the material testing was deemed to be 

questionable by the peer review panel. The high confidence rating was based 

on the coherent and acceptably complete set of tested component 

configurations, as well as the fact that multiple researchers and labs were 

involved in completing the tests. 

4.7.2 Quality Rating of Design Requirements

The reference component design requirements were rated as Good. This 

rating comes from a medium rating for completeness and robustness and a 

high rating for confidence in the design requirements. The medium rating for 

completeness and robustness was based on the fact that even though there is 

a great deal of experience with the design and construction of nailed wood 

shear panel components, they are still site-built, leaving more room for error 

that could result in unanticipated failure modes. The high confidence rating 

was based on the existence of a long history of use, and a good understanding 

of component behavior. 

The proposed component design requirements were rated as Good. This 

comes from a high rating for completeness and robustness and a medium 

rating for confidence. The high rating for completeness and robustness was

based on the proposed component being pre-fabricated in a controlled lab 

environment with careful quality control, having well-developed connection 

design requirements, and having clear construction requirements. The 

medium rating for confidence was based on substantial experience and 

mature construction practices for similar components, but also based on 

questionable testing practices presumed to exist for the new material used in 

the hypothetical proposed component. 
4-20 4: Example Application FEMA P-795

4.8 Evaluate Component Equivalency 

4.8.1 Overview 

This section evaluates the possible equivalency between the proposed and 

reference components. Summary data were provided in Table 4-3 for the 

reference component and Table 4-10 for the proposed component.

4.8.2 Requirements Based on Cyclic-Load Test Data: Strength 

and Ultimate Deformation 

The median ultimate deformation of each proposed component performance 

group must satisfy Equation 2-1: 

∆ ∆  

U,PC U,RC U Q ≥ P P

The median ultimate deformation from the reference component data set, 

∆U RC ,  , is 0.035. The penalty factor for strength is based on the median 

proposed and reference component strength ratios, which is:

,

,

3.1 1.15

2.7

Q PC

Q RC

R

R = =





 

Table 4-11 shows how the uncertainty penalty factor, PU = 1.05, is retrieved 

from Table 2-3, based on the quality ratings discussed in Section 4.7. 

Similarly, Table 4-12 shows how the strength penalty factor, PQ = 1.00, is 

retrieved from Table 2-4.

Table 4-11 Penalty Factor to Account for Uncertainty (from 

Table 2-3) 

Penalty Factor for Uncertainty (PU)

Quality Rating of 

Proposed Component 

Test Data

Quality Rating of Proposed Component Design 

Requirements Relative to Reference Component 

Design Requirements

Higher Same Lower

Superior 0.95 1.00 1.15

Good 1.00 1.05 1.25

Fair 1.15 1.25 1.40
FEMA P-795 4: Example Application 4-21

Table 4-12 Penalty Factor to Account for Difference in Component 

Strengths (from Table 2-4)

Penalty Factor for Differences in Strength (PQ)

PQ PQ

0.50 1.88 1.10 1.00

0.60 1.55 1.20 1.00

0.70 1.31 1.30 1.04

0.80 1.14 1.40 1.09

0.90 1.00 1.50 1.13

1.00 1.00 1.80 1.24

1.10 1.00 2.00 1.32

Incorporating these values leads to the following check, showing that the 

median ultimate deformation value of 0.043 meets the criterion of Equation 

2-1. 

0.043 0.035 1.05 1.00 0.037 ≥ = ( )( )( ) OK

Because R R Q,PC Q,RC

  is less than 1.2, the exception of Section 2.8.2 does not 

need to be invoked. 

In addition, the median ultimate deformation value of each geometric 

configuration, ∆Uj PC ,  , must also meet the requirement of Equation 2-2, as 

shown below. According to Table 4-3, the variability in ultimate 

deformation, σ ∆U RC , , is 0.16 for the reference component data.

∆ σ∆  

Uj PC , ≥ − (1 1.5 ∆U RC U RC U Q , , )( )⋅ ⋅ P P

∆ Uj,PC ≥ −  ⋅ 1 1.5 0.16 0.035 1.05 1.00 0.028 ( ) ( ) ( )( ) =   

Table 4-13 summarizes the above acceptance criteria checks as applied to the 

full performance group and to each individual geometric configuration. The 

proposed component shear walls pass the basic ultimate deformation

acceptance criterion for the full performance group (i.e., 0.043 versus 0.037), 

and also pass the individual configuration criteria for each of the panel 

configurations (i.e., the 0.028 criteria). 

R R Q PC Q RC , ,   R R Q PC Q RC , ,  
4-22 4: Example Application FEMA P-795

Table 4-13 Evaluation of Equivalency Acceptance Criteria 

Test 

Index

Deformation Capacity Acceptance Check

∆ U

Median ∆U

And ∆ Uj

 Acceptanc

e Criteria Pass/ Fail

Perf. Group I: 0.043 ∆

U = 0.037 Pass

1 0.058

0.051 0.028 Pass

2 0.056

3 0.042

0.044 0.028 Pass

4 0.046

5 0.061

0.057 0.028 Pass

6 0.058

7 0.037

0.038 0.028 Pass

8 0.040

9 0.048

0.050 0.028 Pass

10 0.052

11 0.048

0.046 0.028 Pass

12 0.045

13 0.047 0.042 0.028 Pass

14 0.043

15 0.051

0.050 0.028 Pass

16 0.049

17 0.036

0.035 0.028 Pass

18 0.035

19 0.045

0.046 0.028 Pass

20 0.048

21 0.042

22 0.028 0.035 0.028 Pass

23 0.040

24 0.045

0.042 0.028 Pass

25 0.041

26 0.038

0.037 0.028 Pass

27 0.036

4.8.3 Requirements Based on Cyclic-Load Test Data: Effective 

Initial Stiffness

To fulfill the requirements of Section 2.8.3 (Equation 2-3), design provisions 

for initial stiffness were roughly calibrated based on the observed stiffness

values of the proposed and reference components. In this example, this was 

done by adjusting the en value for connector deformation in the design 

displacement equation. The other parameters of the equation, such as panel 

shear rigidity values, could have also been further calibrated, but the 

calculation below shows that the resulting ratio of 0.86 already falls within 
FEMA P-795 4: Example Application 4-23

the range of 0.75 to 1.33 allowed by Equation 2-3. Therefore, the design 

stiffness provisions fulfill the Equation 2-3 acceptance criterion without need 

for further calibration.

0.86 0.75 1.33

1.00

≤ ≤ OK

4.8.4 Requirements Based on Cyclic-Load Test Data: Effective 

Ductility Capacity 

In order to fulfill the requirements of Section 2.8.4 (Equation 2-4) and to 

ensure approximate parity between the post-yield deformation capacities

(and energy dissipation capacities) of the proposed and reference 

components, the median ductility capacity of the proposed components,

μeff PC ,  , must be at least half as large as the median ductility capacity of the 

reference components, μ eff RC ,  . In this example, μeff PC ,  = 4.1 and μeff RC ,  = 

6.3, so this requirement is fulfilled. Note that this difference in ductility 

capacity stems from the fact that the proposed components are systematically 

more flexible than the reference components.

4.8.5 Requirements Based on Monotonic-Load Test Data: 

Ultimate Deformation

The results of monotonic-load testing presented in Table 4-9 showed that the 

median ultimate monotonic deformation capacity for the proposed 

component, ∆ UM PC ,  , is 0.062. The first step is to determine if the cyclic 

deformation capacities are large enough to use Equation 2-6 and avoid the 

need for monotonic-load testing of the proposed or reference components. 

Based on the number of cycles in the CUREE loading protocol, the DC

 value 

is 1.0 (see Section 2.8.5). The median ultimate cyclic deformation capacity 

for the reference component, ∆ U RC ,  , is 0.035 (from Table 4-3). The 

calculation below shows that that ∆ UM PC ,  must be greater than 0.044: 

1.2 (1.0) (0.035) (1.05) (1.00) 0.044 ∆

UM,PC ≥⋅ ⋅ ⋅ ⋅ =

Note that this requirement cannot be fulfilled by using the cyclic-load test

data for the proposed component as a proxy for monotonic data (i.e., ∆ U PC ,  is 

0.043, which is less than 0.044). This requirement, however, is fulfilled by 

the monotonic-load test results for the proposed component data , ∆ UM PC ,  = 

0.062, which is greater than 0.44, so monotonic-load testing of the reference 

components is not necessary. 
4-24 4: Example Application FEMA P-795

4.9 Summary of Example Component Equivalency

Evaluation

Possible equivalency between hypothetical proposed component shear walls 

and reference component nailed wood shear walls was evaluated based on 

the requirements of the Component Methodology. This example showed that 

the hypothetical proposed component passed all of the acceptance criteria, as 

summarized below in Table 4-14, and that the proposed shear wall

components would be considered equivalent to the reference nailed wood 

shear wall components according to the criteria of the Component 

Methodology.

Table 4-14 Summary of Acceptance Criteria Evaluation for Proposed Component Shear Walls

Acceptance Criteria Equation 

Reference

Pass/Fail

Requirements Based on Cyclic-Load Test Data

Ultimate Deformation Capacity 

(performance group) ∆ ∆  

U,PC U,RC U Q ≥ ⋅⋅ P P 2-1 Pass

Ultimate Deformation Capacity 

(individual configurations) , (1 1.5 , , )( ) ∆ σ∆  

Uj PC ≥ − ∆U RC U RC U Q P P 2-2 Pass All

Initial Stiffness Ratio 0.75 1.33 K,PC

K,RC

R

R

≤ ≤ 

 2-3 Pass

Effective Ductility Capacity , , 0.5 μ μ eff PC ≥ eff RC   2-4 Pass

Requirements Based on Monotonic-Load Test Data

Ultimate Deformation Capacity

(Option 1) ∆ ∆  

UM PC UM RC U Q , , ≥ P P 2-5 Not Used

Ultimate Deformation Capacity

(Option 2) , , 1.2 ∆ ∆ UM PC ≥ D PP C U RC U Q    2-6 Pass
FEMA P-795 5: Conclusions and Recommendations 5-1

Chapter 5

Conclusions and 

Recommendations

5.1 Introduction

The recommended Component Equivalency Methodology (Component 

Methodology) provides a rational basis for evaluating the seismic 

performance equivalency of new components that are proposed as substitutes 

for selected components in a currently approved seismic-force-resisting 

system. Proposed components found to be equivalent using the Component 

Methodology can be substituted for components of a reference seismic-forceresisting system (reference SFRS), but are subject to design requirements and 

seismic design category restrictions on the use of the reference system.

This chapter summarizes findings from supporting studies that provided the 

technical basis for the development of the Component Methodology, 

observations from test applications, and recommendations for possible 

further study.

5.2 Findings from Supporting Studies

In the development of the Component Methodology, key performance 

parameters were identified (Appendix A), cyclic-load and monotonic-load 

testing requirements were investigated (Appendix B), and probabilistic 

acceptance criteria were developed (Appendix C). This section summarizes 

major findings from the supporting studies conducted on these topics.

5.2.1 Key Performance Parameters

Studies identifying key component parameters that are important to system 

collapse performance are presented in Appendix A. Also included are the 

results of a literature search for related studies, which was used to identify an 

initial list of potential parameters. This list was systematically evaluated 

using two- and three-dimensional analytical models of archetype buildings. 

Importance was based on relative changes to the system-level probability of 

collapse related to changes in the value of the component parameters. 

System-level probability of collapse was evaluated using the analysis 

methods of FEMA-P-695. The resulting component parameters and their 

relative importance to system collapse behavior are summarized in Table 5-1.
5-2 5: Conclusions and Recommendations FEMA P-795

Table 5-1 Relative Importance of Component Parameters

Importance Parameter

Consistently of High Importance • Inelastic deformation capacity

• Yield strength (maximum load)

Consistently of Moderate Importance

• Cyclic deterioration capacity 

(which controls cyclic strength 

degradation)

• Post-capping (post-maximum 

load) deformation capacity

• Post-yield strength gain

• Residual strength

Periodically of Moderate Importance • Initial stiffness

Consistently of Low Importance

• Details of the initial stiffness 

branch

• Hysteretic behavior (low, 

moderate, and high levels of 

pinching)

Based on these results, the Component Methodology included deformation 

capacity and strength as explicit measures for equivalency comparisons. 

Parameters identified to be consistently of moderate importance or 

periodically of high importance were considered indirectly, as discussed 

below.

Deformation Capacity 

The primary acceptance criterion of the Component Methodology is the 

ultimate deformation capacity of the component, as determined by cyclicload testing. This criterion is based on total deformation rather than inelastic 

deformation. However, since the elastic component of deformation is similar 

for the proposed and reference components (due to initial stiffness similarity 

requirements), the total deformations are fairly representative of the inelastic 

deformations. The total deformation is used to avoid having to define a yield 

deformation, because there is no clear yield deformation for many types of 

components.

Ultimate deformation capacity is defined as the deformation at which the 

component loses 20% of its strength. As such, the ultimate deformation 

metric reflects some degree of “post-capping” behavior (i.e., degradation 

after the peak strength has been achieved). While the effects of post-capping 

deformation are not fully accounted for at 20% strength loss, additional 

deformation levels (e.g., 50% strength loss) were not considered to be 

essential for equivalency evaluation, and were not included in the resulting 

Component Methodology to avoid unnecessary complexity.

Ultimate deformation capacity is based on cyclic-load testing for a required 

minimum number of cycles, and addresses, to some degree, cyclic
FEMA P-795 5: Conclusions and Recommendations 5-3

deterioration capacity (strength degradation). That is, the ultimate 

deformation capacity decreases with cyclic loss of strength, which is roughly 

associated with the energy dissipated per cycle. While the effects of cyclic 

deterioration capacity are not fully accounted for by the ultimate 

deformation, studies indicate that additional comparisons of energy-related 

parameters would not appreciably change the results.

In addition, the Component Methodology also included acceptance criteria 

based on monotonic-load test data. Criteria based on monotonic-load testing 

were necessary because the ultimate deformation under cyclic-load testing 

mixes the effects of component deformation capacity and cyclic strength 

deterioration behavior. In contrast, monotonic-load test data show a 

component deformation capacity that is independent of cyclic loading 

history. It was decided that this measure of deformation capacity should be 

quantified as part of the equivalency comparisons.

Strength

The Component Methodology effectively requires the ratios of tested

maximum strength and design maximum strength to be similar for proposed 

and reference components, and the acceptance criteria impose a penalty 

factor when the strength ratios differ. Maximum strength combines yield 

strength and post-yield strength gain parameters. Maximum strength was

used rather than yield strength for simplicity because yield strength is 

ambiguous for many types of components. This avoided the need to provide 

a definition for the calculation of yield strength.

Although found to be of lesser importance to collapse, the Component 

Methodology included initial stiffness and effective ductility capacity in 

equivalency comparisons. Similarity of these parameters was considered 

necessary to avoid potential design issues related to: (1) drift-based design;

(2) distribution of force demand based on relative component stiffness; and 

(3) potential horizontal and vertical stiffness irregularities. The requirement 

for similarity of initial stiffness also helps to ensure some parity between 

total and inelastic deformation so that it is not necessary to explicitly check 

both.

Absent from the list of equivalency parameters is an explicit check of 

hysteretic loop equivalency. Consistent with past findings in the literature, 

parametric studies found that pinching of the hysteresis loop (due to repeated 

cycles of load) was of little importance to collapse performance, unless 

pinching was extreme. This finding reflects the benefits of systems that 

stiffen (strengthen) at large amplitudes of cyclic deformation. These systems 

might exhibit different response characteristics and damage at lower 
5-4 5: Conclusions and Recommendations FEMA P-795

amplitudes of cyclic deformation, but in general, have no significantly 

greater likelihood of reaching deformation demands associated with collapse.

An explicit check of hysteretic loop equivalency was not included in the 

Component Methodology for the following reasons. First, consistent with 

the FEMA P-695 Methodology, the Component Methodology evaluates 

equivalency solely in terms of collapse performance. Second, equivalency of 

other parameters, namely ultimate deformation capacity, initial stiffness and 

effective ductility capacity, is believed to preclude radical differences in 

component damage (i.e., at other levels of deformation). Finally, the 

Component Methodology is not intended for use in evaluating equivalency of 

components whose performance depends directly on hysteretic behavior. 

The applicability criteria specifically exclude the use of the Component 

Methodology for evaluating equivalency of isolator units or dampers whose 

design properties are based directly on hysteretic energy dissipation.

5.2.2 Cyclic-Load and Monotonic-Load Test Data Requirements

Requirements for cyclic-load and monotonic-load testing of components are 

described in Appendix B. Also included are background information on 

various types of cyclic-load testing protocols, a recommended method a for 

judging the equivalency of load histories, and a discussion of the importance 

of monotonic-load testing. 

Component properties are highly dependent on the deformation history used 

to conduct cyclic-load tests. Deformation history affects the measurement of 

component ultimate deformation capacity, strength, and failure mode, so 

experimental investigations of proposed and reference components are 

required to be the same, or similar in terms of the normalized cumulative 

deformation (i.e., effective number of cycles to ultimate deformation 

capacity). The importance of the deformation history should not be 

underestimated, since the value of the ultimate deformation capacity can vary 

by a factor of two (or more) for cyclic-load testing with different deformation

histories.

Monotonic-load test data are required in addition to cyclic-load test data

because monotonic-load testing (single direction of push) provides collapse

displacement patterns that are more representative of actual earthquake 

collapse response. This is in contrast to a symmetric-cyclic deformation

history containing many cycles. When subjected to an earthquake large 

enough to cause collapse, story drift and component responses depend on 

failure mode, frequency characteristics, and duration of strong motion in the

seismic input. Component responses might be close to symmetric-cyclic 
FEMA P-795 5: Conclusions and Recommendations 5-5

until severe deterioration occurs, at which point they can become one-sided 

and closer to monotonic than symmetric-cyclic.

In general, ultimate deformation measured from monotonic-load testing will 

be larger than that measured from cyclic-load testing. In some cases it can be 

as much as 1.5 to 2.0 times as large. Systems with components that do not 

exhibit this behavior are more prone to sidesway collapse. Thus, components 

with the same value of cyclic-load ultimate deformation may not always be 

equivalent in terms of collapse performance, so a comparison of reference 

and proposed component ultimate deformations from monotonic-load testing 

was included as part of equivalency comparisons.

5.2.3 Probabilistic Acceptance Criteria

Development of probabilistic-based acceptance criteria for evaluating 

component equivalency is described in Appendix C. The probabilistic 

underpinnings of the criteria are based on the collapse safety goals contained 

within the FEMA P-695 Methodology, explicitly considering related sources 

of uncertainty. 

Median values of ultimate deformation are calculated using simple statistics 

for each performance group, where each performance group is assumed to 

represent a statistically homogeneous set of component configurations. 

Proposed components are deemed equivalent when the median value of 

ultimate deformation of the proposed component is equal to, or greater than, 

the factored median value of the reference component for the performance 

group of interest. In this sense, equivalency implies equal or better collapse 

performance. 

Median values of the reference component are adjusted by penalty factors

that account for uncertainties associated with design and data uncertainty, 

and potential differences in proposed and reference component strength

characteristics. Penalty factors are set equal to 1.0 (i.e., no penalty) for 

proposed components with high quality data and strength characteristics 

similar to those of the reference component.

In cases where proposed and reference component medians are equal, 

acceptance criteria for components with high quality data and similar 

strength characteristics essentially provide 50% confidence that the median 

value of the ultimate deformation capacity of the proposed component is 

equal to, or greater than, that of the reference component. Subject to the 

assumptions in variability implied by the quality ratings, the penalty factors 

maintain this 50% confidence where the medians differ.
5-6 5: Conclusions and Recommendations FEMA P-795

Although effectively more conservative than the acceptance criteria of other 

equivalency methods, such as AC322 Acceptance Criteria for Prefabricated, 

Cold-Formed, Steel Lateral-Force-Resisting Vertical Assemblies (ICC-ES, 

2007), the statistical approach underlying the Component Methodology was 

considered to be an appropriate and rational approach for evaluating

component equivalency that explicitly evaluates the probabilistic distribution 

and potential uncertainty of tested parameters. Penalty factors were included 

to encourage the use of high quality data and comparisons between 

components with similar strength characteristics. Use of lower quality data 

and components with appreciably different strength characteristics, however, 

is also permitted, and can result in equivalence for proposed components 

with median properties that are significantly better than the reference 

component of interest.

5.3 Findings of Test Applications

The Component Methodology was tested in applications evaluating

equivalency for substitution of: (1) stapled wood shear wall components for 

nailed wood shear wall components; (2) buckling-restrained braces for 

special steel concentric braces; and (3) pre-fabricated shear wall products for 

use in wood light-frame construction. This section discusses the findings 

from each of these test applications.

5.3.1 General Findings

The Component Methodology was found to provide a practical and rational 

process for evaluating component equivalency. 

Performance Groups

As a default, proposed and reference component data are lumped into a 

single performance group. Sorting of proposed and reference components 

into separate performance groups and associated test data sets is required, 

when necessary, to properly consider behavior associated with difference 

component configurations and failure modes. While grouping is somewhat 

subjective and, therefore, poses a challenge, it also permits proponents to 

separate test data into sets that provide a more appropriate basis for 

comparing proposed component data with reference component data.

Some flexibility is permitted in choosing how to group reference and 

proposed component data. In the case of proposed components, the trade off 

is between using a larger number of performance groups with inherently less 

scatter in the data, and the alternative of using fewer performance groups,

which would presumably require less component testing. 
FEMA P-795 5: Conclusions and Recommendations 5-7

Simple statistical calculations of median (and lognormal standard deviation) 

values are used as a practical approach for summarizing test data for 

proposed and reference components. From a statistical perspective, some 

data sets will have too few data points to properly compute medians and 

lognormal standard deviations with high levels of confidence, but this was 

considered an acceptable compromise considering the large expense involved 

in generating large statistically robust sets of test data for each performance 

group.

Available Test Data

Test data of reasonable quality are required for reference components and 

proposed components. It is expected that reference component data will be 

compiled mostly from past research and existing sources of published 

literature. In the case of wood light-frame shear wall components, 

substantial data was found to be available. These data were considered 

suitable for use with the Component Methodology, but similar data for other

seismic-force-resisting systems listed in ASCE/SEI 7-10 Minimum Design 

Loads for Buildings and Other Structures (ASCE, 2010) may not be as 

readily available.

Proposed component data are expected to be generated by the developer, 

who will have control over what data are produced. Much of these data will 

likely be produced during product development or through preliminary 

research studies. If not specifically developed for use in the Component 

Methodology, however, it is likely that such data will not meet the necessary 

requirements, and that supplementary testing will be necessary for the 

purpose of evaluating equivalency. One such example is monotonic-load 

testing, which is often not routinely performed, but is a requirement of the 

Component Methodology. Additional cyclic-load testing may also be needed 

to complete component performance groups.

Cyclic-Load Testing Protocol

The cyclic-load testing protocol was found to significantly affect component 

parameters determined from cyclic-load testing. This had a direct effect on 

equivalency comparisons. In general, the same cyclic-load testing protocol 

should be used in generating the proposed component and reference 

component test data to avoid biasing results.

Iterative Process for Component Equivalency

The use of the Component Methodology was found to be iterative. Possible 

iterative approaches included improving the number and quality of test data, 

refining design requirements, and restricting use of the proposed component 
5-8 5: Conclusions and Recommendations FEMA P-795

to configurations that met the acceptance criteria. In many cases, such 

iterations served as a mechanism for improving the relative performance 

characteristics of the proposed component. 

5.3.2 Specific Findings: Stapled-Wood Shear Wall Components

Overall, based on the limited set of stapled wood shear wall data used in the 

test application, it was found that stapled wood shear walls have higher 

component overstrength and slightly lower median deformation capacity than

nailed wood shear walls. Application of the Component Methodology to 

these data sets did not find stapled wood shear walls to be equivalent to 

nailed wood shear walls. 

In order for stapled wood shear walls to be found equivalent, changes would 

need to be made to the design requirements, or additional test data would 

need to be generated. Possible changes included improvements to the 

detailing requirements to increase the deformation capacity, modifications to 

the strength design requirements to make the normalized strength ratios 

similar between the stapled and nailed wood shear walls, or generation of 

more stapled wood shear wall data to improve the quality rating of the test 

data.

5.3.3 Specific Findings: Buckling-Restrained Brace Components

Overall, the test application comparing buckling-restrained braces to special 

steel concentric braces found that buckling-restrained braces have a larger 

median deformation capacity and easily satisfied the criteria of the

Component Methodology. Although buckling-restrained braces have higher 

overstrength than conventional braces, connections are designed using a

capacity design philosophy that satisfied Component Methodology 

requirements for strength. Requirements based on stiffness and effective 

ductility capacity were also satisfied. As a result, application of the 

Component Methodology found that buckling-restrained braces are 

equivalent to special steel concentric braces. 

It should be noted, however, that available data for buckling-restrained 

braces and conventional braces lack monotonic-load test data, and did not 

include two component test specimens per brace configuration. This test 

application was based on the best data available at the time of this 

comparison and may not reflect the true variation in section and connection 

properties for steel braces. However, based on observed trends in available 

test results, it is expected that data from additional test specimens and 

monotonic-load testing would further confirm the above conclusions. 
FEMA P-795 5: Conclusions and Recommendations 5-9

5.3.4 Specific Findings: Pre-Fabricated Wall Components

In this case, pre-fabricated wall products are relatively strong, short (slender) 

wall products intended for substitution in wood light-frame systems, 

representative of similar proprietary products from a number of 

manufacturers. The test application on pre-fabricated wall products, 

although limited to the evaluation of just three cyclic-load test specimens of a 

single configuration, provided useful information regarding the relative 

stiffness of proposed and reference components (specifically, the case in 

which the proposed component is inherently more flexible than the reference 

component). 

Overall, the test application found that pre-fabricated wall components are

equivalent to nailed wood shear wall components, subject to restrictions on 

indiscriminate substitution of the product within a system, due to significant 

differences in the relative stiffness of proposed and reference components. 

This finding is consistent with findings of the International Code Council

Evaluation Services (ICC ES) for similar products using the acceptance 

criteria of AC322.

5.3.5 Specific Findings: Nailed Wood Shear Wall Reference 

Component Data Set

A robust and representative data set containing cyclic-load test results for 

nailed wood shear wall components was developed from information 

available in the literature. Line et al. (2008) compiled CUREE cyclic-load 

data from a total of 80 test specimens. This data set included results from 48 

wall tests that were compiled as part of the International Code Council 

Evaluation Services Acceptance Criteria AC322 effort (ICC-ES, 2007), as 

well as results from 32 additional tests. To create the reference component 

data set for nailed wood shear walls, data were removed for walls with 

openings, stapled walls, and walls with box nails, leaving a total of 65 tests in 

the final data set. 

The resulting reference component data set is considered to be a robust and 

representative data set for nailed wood shear wall configurations with aspect 

ratios ranging from 2:1 to 1:1, and tested using the CUREE loading protocol. 

Such a set is considered suitable for equivalency comparisons with 

appropriately similar components in applications of the Component 

Methodology.
5-10 5: Conclusions and Recommendations FEMA P-795

5.4 Recommendations for Further Study

The following recommendations are provided for possible future studies that 

would help to further improve and refine equivalency methods or to broaden 

the potential applications of the Component Methodology.

5.4.1 Compilation of Available Reference System Benchmark

Data

A potential hindrance to the use of the Component Methodology is a lack of 

sufficient quality test data for reference components (i.e., “benchmark” test 

data on components in current code-approved systems). A very real need 

exists to identify and compile component test data for as many systems in

ASCE/SEI 7-10 as possible. This effort would need to address configuration 

issues, failure modes, and other characteristics, as necessary to develop 

appropriate performance groups and associated statistics. 

The product of this effort would be median values of ultimate deformation 

and other parameters required for equivalency comparison using the 

Component Methodology. While this effort would likely generate 

benchmark test data for only a limited number of reference components, the 

contribution would still be very useful. Product developers would have 

access to reference component test data that they would otherwise be

required to compile and process, and regulatory agencies would have 

confidence that these data were developed in an appropriate and unbiased 

manner.

5.4.2 Development of Additional Reference System Benchmark

Data

It may be possible to expand the applicability of available test data 

(discussed above) to other systems recognizing possible trends in the 

relationship between the system R factor (and other related performance 

parameters) and the ultimate deformation capacity of reference components. 

Systems with larger values of R, in general, should have larger values of 

ultimate deformation capacity. Supplemented with appropriate FEMA P-695 

analytical studies, the compiled sets of reference component test data could 

be used to develop a complete set of benchmark data for use as surrogate 

reference component test data.

As envisioned, this surrogate benchmark test data would define, for example, 

the required minimum value of ultimate deformation capacity of proposed 

components (which would necessarily be based on an assumption regarding 

the cyclic-deformation history used in testing) as a function of the R factor of 

the reference system of interest, and possibly the initial (elastic) stiffness of 
FEMA P-795 5: Conclusions and Recommendations 5-11

the component of interest. This could be done for a large number of current 

code-approved seismic-force-resisting systems, and would remove the need 

for a proponent to develop a set of reference component data when using the 

Component Methodology. This concept is similar to existing AISC seismic 

provisions for steel moment frame systems that specify testing requirements 

for beam-column connections and acceptable values of deformation capacity 

(e.g., 4% story drift). While ambitious, this project, if successful, would be a 

major contribution to the development and approval of new component 

products.

5.4.3 Development of Standard Cyclic-Load Testing Methods

There is very clear need for standard test methods, similar to ASTM E2126-

09 (ASTM, 2009), for cyclic-load testing of components. A broader range of 

component applications and greater consideration of the testing protocol and 

its relationship to earthquake ground motions and component performance 

(e.g., collapse resistance) in terms of the appropriate number of damaging 

cycles of load are needed. Appendix B provides a starting point for such an 

effort.

5.4.4 Implications for Design Requirements Related to 

Overstrength

Development of the Component Methodology highlights areas where design 

standards could be improved to facilitate the safe adoption of alternative 

components. One such area is related to the issue of overstrength. Whereas 

typical building code provisions often rely on a single system overstrength 

factor, ΩΟ, for the design of force-controlled components, this single factor is 

a crude measure of the forces that can be developed in force-controlled 

components. 

In the development of the FEMA P-695 Methodology, system overstrength 

was shown to vary considerably for a given seismic-force-resisting system, 

depending on the configuration and proportions of the systems. 

Development of the Component Methodology has further highlighted 

situations where it may be necessary to revise design requirements for 

component connections, wall anchors, and other force-controlled 

components, where deformation-controlled replacement components have 

higher overstrength than the selected reference components. 

The Component Methodology addresses this by placing an upper-limit on the 

relative overstrength in replacement and reference components, but this

assumes that overstrength is accurately accounted for in the existing design 

provisions for the reference seismic-force-resisting system. It may still be 
5-12 5: Conclusions and Recommendations FEMA P-795

possible in certain cases to have “mismatches” within the system design. 

Moreover, unintentional overstrength may occur and not be detected by 

existing design requirements for the reference component system of interest.
FEMA P-795 A: Identification of Component Parameters A-1

Important for Equivalency

Appendix A

Identification of Component 

Parameters Important for 

Equivalency

A.1 Introduction

This appendix identifies key component parameters that are important 

contributors to system-level collapse performance and are therefore

considered in the component equivalency evaluation. 

To identify which component parameters tangibly affect system-level 

collapse performance, a representative component model was first 

developed. Related available research considering collapse behavior and 

non-collapse response was collected and reviewed to identify an initial list of 

potential parameters. 

To build on the findings of previous research, and further identify which 

component parameters were most important to system-level collapse 

performance, a collapse sensitivity study was performed utilizing multipledegree-of-freedom models of two-dimensional and three-dimensional wood 

light-frame buildings, and two-dimensional reinforced concrete moment 

frame structures. 

A.2 Representative Component Behavior

This section presents the representative component model considered in the 

literature review discussion and sensitivity studies. This model is capable of 

capturing monotonic and cyclic behaviors of most types of common 

structural components.

Figure A-1 illustrates the monotonic behavior of the component model which 

is consistent with recent research, such as Vamvatsikos and Cornell (2002),

Ibarra et al. (2005), Zareian (2006), Haselton et al. (2008), and with the 

model used in the FEMA P-440A report, Effects of Strength and Stiffness 

Degradation on Seismic Response (FEMA, 2009a). The primary difference 

between this model and similar models commonly used is the inclusion of

bilinear initial stiffness, which allows better representation of wood shear 
A-2 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

wall behavior, and also allows testing the importance of these initial stiffness 

assumptions in the sensitivity study.

Figure A-1 Representative monotonic component behavior. 

The following parameters are illustrated in Figure A-1 and studied in this 

appendix:

K1 = initial stiffness of component a low levels of load

K2 = reduced pre-yield stiffness of component a higher levels of load (due 

to cracking or other nonlinearities before primary yielding)

Vc = shear force at capping (maximum shear capacity of the component)

Vkink = shear at the transition between the initial stiffness (K1) and the 

reduced pre-yield stiffness (K2)

Vres = residual shear force capacity of component

Vy = yield shear force of component

∆cap = deformation of component at capping (at maximum force level)

∆cap,pl = deformation of component between yielding and capping

∆fail = deformation of component at failure (defined by zero strength)

∆kink = deformation of component and Vkink

∆ult = ultimate deformation of the component

K2

Δ

Vc

V

Vy

Vkink

Δkink Δy Δcap Δult Δfail

Δcap,pl Δpc

Vress

K1
FEMA P-795 A: Identification of Component Parameters A-3

Important for Equivalency

∆y = deformation of component at yielding

∆pc = post-capping deformation of component

In addition to the above illustrated monotonic component behavior, the 

component model is also able to capture important cyclic behaviors such as 

strength deterioration and various cyclic unloading and reloading behaviors. 

This component model was developed by Ibarra (2003) and Ibarra et al. 

(2005). The specific component model option used in this sensitivity study is 

based on a peak-oriented reloading behavior, has cyclic strength deterioration 

that is based on the energy dissipated throughout the loading history as a 

ratio to the energy dissipation capacity of the component (Ibarra et al., 2005), 

and has a pinching response where the degree of pinching can be varied by 

the user. The level of strength deterioration, which is based on the energy 

dissipation capacity of the component, and the level of pinching are 

parameters that are varied in the later sensitivity study. Figure A-2 illustrates 

cyclic behaviors of the component model, for a few various components and 

loading histories. While all four figures illustrate cyclic strength 

deterioration, Figure A-2a illustrates a clear negative stiffness and strength 

loss within a single cycle of loading, and Figure A-2d illustrates pinching 

behavior. 

Figure A-2 Illustration of the cyclic behavior of the component model. Test 

data from the PEER Structural Performance Database (Berry et 

al., 2004) for test index numbers 8, 48, 154, and 212.

-0.05 0 0.05 -400

-300

-200

-100

0

100

200

300

400

Load

Deformation

-0.05 0 0.05 -100

-50

0

50

100

Load

Deformation

-0.05 0 0.05 -400

-300

-200

-100

0

100

200

300

400

Load

Deformation

-0.1 -0.05 0 0.05 0.1 -400

-300

-200

-100

0

100

200

300

400

Load

Deformation

(a) (b)

(c) (d)
A-4 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

A.3 Literature Review

The expressed goal of “equivalency” is equal performance with respect to 

system-level collapse safety. The purpose of this section is to identify 

component-level parameters that tangibly affect the system-level collapse 

performance. Accordingly, this literature review is primarily based on 

analytical studies that are focused on collapse prediction; this is included in 

Section A.3.1. However, the number of such collapse sensitivity studies is 

limited, and there have been many other efforts that have been focused on 

displacement or ductility demands in structures rather than focusing 

specifically on collapse. Therefore, some of these non-collapse studies are 

also reviewed in Section A.3.2 for comparison to the findings of the collapse 

studies. 

A.3.1 Collapse Studies

Table A-1 summarizes the results of the literature review for recent analytical 

studies that focused on collapse capacity prediction. The remainder of this 

section discusses the results of each study in more detail. Note that the 

number of such studies is limited because most research efforts are focused 

on prediction of other structural responses (such as displacement or ductility 

demands) rather than collapse response.

Table A-1 first outlines the nature of the study by identifying the materials 

considered in the study and the types of analytical models considered (singledegree-of-freedom, (SDOF) or multiple-degree-of-freedom (MDOF)). The 

remainder of the table ranks each component parameter with respect to the 

impact that each parameter has on the collapse prediction. The parameters 

are ranked as H for high importance (e.g., strength and inelastic deformation 

capacity), M for medium importance, or L for low importance. A blank field 

indicates that the component parameter was not considered in the study 

described by that row in the table. 

Note that the ranking of importance as high, medium, or low is not always 

simple because some parameters are important in some cases and not in 

important in other cases (e.g., changes to the rate of cyclic deterioration are 

very important for rapid deterioration, but not important for slow 

deterioration). Even so, such qualitative rankings are important to help 

identify the importance of each parameter in a relatively simple manner that 

is tractable. To be more specific about the definitions of the importance 

levels, H is used when the parameter is important in most cases, M is used to 

describe two different situations (consistently of moderate importance, or 

sometimes highly important and sometime of low importance), and L is used 

for cases where the parameter is not important in most cases. 
FEMA P-795 A: Identification of Component Parameters A-5

Important for Equivalency

Table A-1 Summary of Component Parameter Studies in Literature with Focus on Collapse 

Capacity

Study Info. Component Parameters

Study

Material(s)

SDOF or MDOF

∆y

Vy

Vc/Vy

∆cap,pl

∆pc / ∆cap,pl

Vres/Vy or 

dfail

Hysteretic Model 

(B, P, or PO)

Cyclic Strength 

Deterioration

Cyclic Stiffness 

Deterioration

Level of P-Δ

Vamvatsikos and 

Cornell (2002) Gen SDOF H H H H H

Ibarra et al. (2005): 

SDOF Gen SDOF H H M L MH L-M H

Ibarra et al. (2005): 

MDOF Gen MDOF H H M L M L-M H

Zareian (2006) Gen MDOF H H L L L

Haselton and Deierlein 

(2007) RC-F MDOF L H L H L M H

FEMA P-440A (2009a) Gen SDOF H H H H L-M

Summary: L H L-H H L-M H L M L-M H

Hysteretic Model: B = bilinear, P = pinched, and PO = peak-oriented.

Importance: H is high importance, M is medium importance (or H/L), L = low importance, blank = not 

considered.

Materials: Gen = general, RC = concrete (-F = flexure).

The research by Ibarra, Medina, and Krawinkler is the most complete and 

rigorous study available that is specifically aimed at investigating the 

relationship between component parameters and system-level collapse 

performance. The study includes investigation of SDOF systems with 

periods from 0.1 to 4.0 seconds, as well as single bay MDOF frame systems 

from one to eighteen stories in height which have fundamental periods from 

0.3 to 3.6 seconds.

The findings of their research that are most relevant to the Component 

Methodology are summarized as follows (note that the terminology and 

notation is adapted to be consistent with this current report):

• The component deformation capacity, ∆cap,pl, has a significant effect on 

the collapse capacity for both SDOF systems and MDOF frame systems.

• The slope of the post-capping branch, (∆pc / ∆cap,pl), has a significant 

effect on the collapse capacity when ∆pc is small, but has a small effect 

when ∆pc is large. This effect is reduced when P-delta effects are 

included, especially for ductile systems.
A-6 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

• The strength of the system is important to collapse capacity. This point is 

not explicitly addressed in the Ibarra et al. study, but rather is an implicit 

conclusion by how the collapse capacity was defined in his study.

• The effects of cyclic deterioration (specifically strength deterioration) 

have an important, but not dominant, effect on collapse capacity.

• The type of hysteretic model used (bilinear, peak-oriented, or pinched) 

has small impact on collapse capacity.

• P-delta effects have a large effect on collapse capacity, especially for 

flexible long-period systems that are ductile. 

A.3.2 Non-Collapse Studies

To supplement the findings of the previous section, this section summarizes 

previous research that examines the effects of component modeling 

parameters on structural responses other than collapse, such as displacement 

response and ductility demands. 

The FEMA P-440A report contains a comprehensive literature review on this 

topic, covering the past 40 years of research. This includes: Clough and 

Johnston (1966), Iwan (1973, 1977, 1978), Riddell and Newmark (1979a and 

1979b), Mahin and Bertero (1981), Otani (1981), Bernal (1992, 1998), 

Rahnama and Krawinkler (1993), Foutch and Shi (1998), Gupta and 

Krawinkler (1998, 1999), Pincheira, Dotiwala and D’Souza (1999), Song 

and Pincheira (2000), Vian and Bruneau (2002, 2003), Miranda and Akkar 

(2003), Lee et al. (1999), Dolsek and Fajfar (2004), Medina and Krawinkler 

(2004), and Ruiz-Garcia and Miranda (2005). 

Table A-2 summarizes the focus of each study listed in the above report. 

Similarly to Table A-1, this table outlines the nature of each study, such as 

materials, model type, and the focus of the study. These studies focus on 

strength demands (such as required R factor), displacement demands, or 

dynamic instability (which is included in one study, along with discussion of 

strength demands). The remainder of the table ranks each component 

parameter with respect to the impact that each parameter has on the collapse 

prediction. 
FEMA P-795 A: Identification of Component Parameters A-7

Important for Equivalency

Table A-2 Summary of Component Parameter Studies in Literature with a Focus Different than Collapse 

Capacity

Study Information Component Parameters

Study

Material(s)

SDOF or MDOF

Response Parameter 

∆y

Vy

Vc/Vy

∆cap,pl and/or 

∆pc

Vres/Vy or 

dfail

Hysteretic Model 

(B, P, or PO)

Cyclic Strength 

Deterioration

Cyclic Stiffness 

Deterioration

Level of P-Δ

Lee et al. (1999) Gen SDOF S L L L

Ruiz-Garcia and Miranda 

(2005) Gen SDOF D L-M L-M L-M

Foutch and Shi (1998) Gen SDOF/MDOF D M L

Dolsek and Fajfar (2004) RC SDOF S M-H

Pincheira, Dotiwala, 

D'Souza (1999) RC SDOF D H H

Song, Pincheira (2000) Gen SDOF D H M M

Bernal (1992, 1998) Gen SDOF/MDOF S H

Miranda and Akkar 

(2003) Gen SDOF S/C M H

Vian and Bruneau (2002, 

2003) Gen SDOF C H

Clough and Johnston 

(1966) Gen SDOF D L L

Otani (1981) Gen SDOF D L

Iwan (1973, 1977, 1978) Gen SDOF S L L L

Riddell and Newmark 

(1979a and 1979b) Gen SDOF S L

Mahin and Bertero 

(1981) Gen SDOF D L-M

Rahnama and Krawinkler 

(1993) Gen SDOF S L L

Gupta and Krawinkler 

(1998, 1999) Gen SDOF D H M

Medina and Krawinkler 

(2004) Gen MDOF D M-H

Summary: M -- M M-H -- L M M H

Hysteretic Model: B = bilinear, P = pinched, and PO = peak-oriented.

Materials: Gen = general, RC = concrete.

Response parameter of interest: S = lateral strength demand, D = displacement, C = lateral strength associated with dynamic 

instability.

Importance: H = high importance in most cases, M = medium importance (or H/L), L= low importance, blank = not 

considered.
A-8 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

The parameters are ranked as H for high importance, M for medium 

importance, or L for low importance. A blank field indicates that the 

component parameter was not considered in the study described by that row 

in the table. 

In addition to the rough descriptions of importance that are summarized in 

Table A-2, several general conclusions from the above research are 

summarized as follows: 

• The hysteretic model is not highly important, meaning that the final 

structural response parameters are not sensitive to the exact features of 

the load-deformation path, as shown in Lee et al. (1999), Foutch and Shi 

(1998), Clough and Johnston (1966), Otani (1981), Iwan (1973, 1977, 

1978), Riddell and Newmark (1979a and 1979b), and Mahin and Bertero 

(1981). 

• To be more specific regarding the hysteretic model, pinching 

characteristics do not have a large influence on global response, as 

shown in Gupta and Krawinkler (1998 and 1999) and Lee et al. (1999).

• The rules for cyclic deterioration of strength and stiffness are not highly

important in all cases. However, in certain specific cases, cyclic 

deterioration of strength and stiffness are important. For example, they 

are important for short-period structures, for structures on soft soils and 

for relatively weak structures, as shown in Ruiz-Garcia and Miranda 

(2005), Foutch and Shi (1998), Song and Pincheira (2000), and Mahin 

and Bertero (1981). Medina and Krawinkler (2004) suggest that stiffness 

degradation may also be somewhat more important for MDOF structures.

• In general, response is not sensitive to post-yield hardening stiffness

(Vc/Vy), though short-period structures are more sensitive to this 

parameter than long period structures. Even so, within a reasonable 

range of post-yield stiffness, it is still only moderately important for 

short-period structures, as shown in Ruiz-Garcia and Miranda (2005).

• There is general agreement that capping behavior and the post-capping 

slope can have a significant influence on structural response. Postcapping slope seems to be more significant if the residual strength of the 

system is low, as shown in Dolsek and Fajfar (2004), Miranda and Akkar

(2003), Rahnama and Krawinkler (1993) and Gupta and Krawinkler 

(1998, 1999).
FEMA P-795 A: Identification of Component Parameters A-9

Important for Equivalency

A.4 Wood Light-Frame Building Collapse Sensitivity 

Studies

This section presents a sensitivity study that employs eight wood light-frame 

buildings, ranging from one to five stories in height. The purpose of this 

sensitivity study is threefold:

• Supplement past research by considering component parameters that 

have not been thoroughly investigated (e.g., K1 / K2 and Vc / Vy in Figure 

A-1).

• Supplement past research by considering the possibility of mixing-andmatching proposed components with reference components. 

Accordingly, this sensitivity study looks both at full replacement (where 

all parameters of all components are varied simultaneously) and mixingand-matching (where parameters of some components are varied, while 

parameters of other components are held at their baseline values).

• Create a set of sensitivity data that will be utilized later when developing 

quantitative Component Methodology acceptance criteria (see Appendix 

C).

First, the eight wood light-frame buildings used for sensitivity analyses are 

described, and the component parameter values that are assumed as the 

baseline of the sensitivity study are documented. Then the results of the fullreplacement sensitivity study are presented, followed by the two-dimensional 

mixing-and-matching sensitivity study, and the three-dimensional mixingand-matching sensitivity study. Results from all wood light-frame sensitivity 

studies are summarized.

A.4.1 Building Models and Baseline Component Parameter 

Values

This sensitivity study is based on eight of the wood light-frame buildings that 

were utilized in the FEMA P-695 project1

 1 For this study, preliminary models were used. Models used in the final FEMA 

P-695 report differ slightly.

(FEMA, 2009b). All eight 

buildings were designed for a high seismic site (SDC Dmax), ranging from 

one to five stories in height, with story heights of 10 feet for all buildings and 

evaluated using the Far-Field record set provided in FEMA P-695. Table A3 summarizes the designs showing properties such as height, fundamental 

period, design base shear, (V / W), and maximum considered earthquake 

(MCE) spectral acceleration demand for the site used for design, SMT. The 

first subset of buildings range in height from one to three stories, and utilize 
A-10 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

low aspect ratio walls. The second subset of buildings range in height from 

one to five stories, and utilize high aspect ratio walls. 

Table A-3 Wood Light-Frame Structural Design Properties (after FEMA 

P-695 Table 9-20) 

Model 

No.

No. of 

Stories

Building 

Configuration

Wall Aspect 

Ratio

Period T 

(sec) V/W SMT (g)

SDC Dmax – Low Aspect Ratio Walls

1 1 Commercial Low 0.25 0.167 1.50

5 2 Commercial Low 0.25 0.167 1.50

9 3 Commercial Low 0.36 0.167 1.50

SDC Dmax – High Aspect Ratio Walls

2 1 1&2 Family High 0.25 0.167 1.50

6 2 1&2 Family High 0.26 0.167 1.50

10 3 Multi-Family High 0.36 0.167 1.50

13 4 Multi-Family High 0.45 0.167 1.50

15 5 Multi-Family High 0.53 0.167 1.50

In the original FEMA P-695 study, the wood light-frame models were 

created using the SAWS software program (Seismic Analysis of Woodframe 

Structures) developed within the CUREE-Caltech Woodframe Project (Folz

and Filiatrault, 2004a, 2004b). For the purposes of this current sensitivity 

study, the general quadralinear model described in Section A.2.2 is calibrated 

to the SAWS model, an example of which is shown in Figure A-3. Using 

such a fit for each story, the OpenSees computer platform (OpenSees, 2009) 

is then used to create the MDOF model of the building. The structural model 

is then simplified slightly for purposes of the sensitivity study. The 

differences in strength and yield displacement are maintained between the 

different stories of the building, but all other parameters, such as story 

deformation capacity, are made uniform over the height of the building.

The MDOF OpenSees model consists of a single shear spring per story 

(describing the shear force versus interstory displacement behavior), masses 

and weights lumped at each floor level, and a leaning column element to 

account for P-delta effects. Information regarding building masses and 

loading can be found in Appendix C of FEMA P-695. 
FEMA P-795 A: Identification of Component Parameters A-11

Important for Equivalency

Figure A-3 Example fitting of backbone curve to SAWS model, for the onestory high aspect ratio building No. 2.

Table A-4 documents the baseline calibrated values of Vy and ∆y for each of 

the eight wood light-frame buildings. Table A-5 documents baseline and 

ranges of values used in the sensitivity study. Note that when the Vy and ∆y

values are varied in the sensitivity study, a multiplication factor is applied to 

all elements in the building (except for the mix-and-match cases, where only 

a portion of the building is modified). 

Table A-4 Baseline Component Strength and Stiffness Properties for Wood Light-Frame Building Models

Model 

No.

No. of 

Stories

Building 

Configuration

Baseline Strength and Stiffness Component Properties

Story 1 Story 2 Story 3 Story 4 Story 5

Vy [k] Δy/120" Vy [k] Δy/120" Vy [k] Δy/120" Vy [k] Δy/120" Vy [k] Δy/120"

Low Aspect Ratio Walls

1 1 Commercial 7.4 0.0086 -- -- -- -- -- -- -- --

5 2 Commercial 30.2 0.0093 14.5 0.0086 -- -- -- -- -- --

9 3 Commercial 53.5 0.0090 50.0 0.0098 18.0 0.0078 -- -- -- --

High Aspect Ratio Walls

2 1 1&2 Family 7.5 0.0088 -- -- -- -- -- -- -- --

6 2 1&2 Family 17.5 0.0095 9.3 0.0086 -- -- -- -- -- --

10 3 Multi-Family 31.8 0.0096 29.9 0.0108 11.2 0.0086 -- -- -- --

13 4 Multi-Family 36.0 0.0096 36.0 0.0096 34.0 0.0108 12.0 0.0083 -- --

15 5 Multi-Family 40.0 0.0089 40.0 0.0089 38.2 0.0102 26.5 0.0096 13.6 0.0081

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Displacement [inches]

Force [kips]

SAWS Model

Fit for OpenSees
A-12 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

Table A-5 Values of Component Parameters for Wood Light-Frame 

Building Models

Component Parameter Baseline Parameter 

Value

Range of Values 

Considered in 

Sensitivity Study

Vy / Vy,baseline 1.00 0.3 - 3.0

∆y / ∆y,baseline 1.00 0.3 - 3.0

K1/K2 2.50 1.0 - 5.0

Vkink /Vc 0.40 0.2 - 0.8

Vc / Vy 1.25 1.01 - 1.50

∆cap,pl / story height 0.025 0.005 - 0.10

∆pc / ∆cap,pl 4.00 1.0 - 10.0

Vres / Vy 0.001 0.001 - 0.50

∆fail Infinite n/a

Cyclic Deterioration Capacity (λ’) Infinite 5.0 - 100.0

Level of Pinching Moderate(2) None(1) - High(3) 

A.4.2 Sensitivity Study Results for Three-Story Building: Full 

Replacement 

This section presents the results of a sensitivity study looking at fully 

replacing all of the structural components in a three-story structural model

(building No. 10 in FEMA P-695). Figure A-4 shows the results for the two 

parameters shown to be highly important to collapse response, namely 

strength, Vy, and plastic deformation capacity, ∆cap,pl. Consistent with use of 

the FEMA P-695 Methodology, these figures present the collapse margin 

ratio (CMR), which is the ratio of the median collapse capacity and the MCE 

demand, as well as the adjusted collapse margin ratio (ACMR) which also 

accounts for the effects of spectral shape. The ACMR value is computed 

using the requirements of the FEMA P-695 Methodology, with the exception 

that β1 is computed directly from regression analyses of the collapse results 

rather than using Equation B-3 of FEMA P-695. This is done to avoid 

completing a pushover analysis at every step of the sensitivity study. This 

simplification can cause the ACMR line to be slightly more “bumpy” in 

some cases. Note that the ACMR value is used when assessing collapse 

performance. 

The changes in strength, Vy, are shown to be consistently important for all 

levels of strength. The changes to plastic deformation capacity, ∆cap,pl, are 

also shown to be important for all values, but are shown to be especially 

important for low levels of deformation capacity (for ∆cap,pl / story height <
FEMA P-795 A: Identification of Component Parameters A-13

Important for Equivalency

0.03). These findings are consistent with previous research (Ibarra and 

Krawinkler 2005, Haselton and Deierlein 2007).

Figure A-4 Component parameters that are important for collapse response of three-story building.

Figure A-5 shows the results for four parameters shown to be moderately 

important to collapse response, namely post-capping deformation capacity,

(∆pc / ∆cap,pl), the cyclic deterioration capacity, λ’, the level of pinching, and 

the post-yield strength gain, (Vc / Vy). The post-capping deformation capacity

is moderately important for all parameter values. In contrast, changes to λ’

are unimportant when λ’ is large (and does not dominate collapse response) 

but are highly important when λ’ is small (and the cyclic deterioration 

behavior dominates the collapse response). This observation is consistent 

with findings of previous work (FEMA P-440A, Haselton and Deierlein, 

2007, and Ibarra, 2003). The level of pinching only becomes important when 

the response is highly pinched (pinching level #3), but this level of pinching 

is a relatively extreme case. This unimportance of pinching, when predicting 

collapse capacity, is consistent with the observations from the literature 

review (Ibarra et al., 2005). The level of post-yield strength gain is only 

slightly important when the ratio of (Vc / Vy) is near unity.

Figure A-6 shows the results for the remaining four parameters that are not 

important to the collapse response of this building. These unimportant 

parameters are the initial stiffness, ∆Y, the related details of the initial 

stiffness branch (Vkink / Vc and K1 / K2), and the residual strength. 

The unimportance of residual strength seemingly disagrees with the previous 

findings of FEMA P-440A and work by Vamvatsikos and Cornell (2002), 

but this is not the case entirely. This wood light-frame building (and the 

other seven used in this sensitivity study) is relatively ductile, with (∆cap,pl / 

story height) = 0.025, and (∆pc / ∆cap,pl) = 4.0. This results in a case where the 

P-delta effect (even though small) is likely large enough to cause collapse 

before the residual strength is reached. 

0 1 2 3 4 0

1

2

3

4

5

V

y

/Vy,baseline

Collapse Margin Ratios

CMR

ACMR

0 0.02 0.04 0.06 0.08 0.1 0

1

2

3

4

5

∆cap,pl/story height

Collapse Margin Ratios

CMR

ACMR
A-14 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

Figure A-5 Component parameters that are moderately important for collapse response of 

three-story building.

0 2 4 6 8 10 0

1

2

3

4

5

∆

pc

/∆cap,pl

Collapse Margin Ratios

CMR

ACMR

0 50 100 150 200 0

1

2

3

4

5

λ′

Collapse Margin Ratios

CMR

ACMR

0 1 2 3 4 0

1

2

3

4

5

Level of Pinching

Collapse Margin Ratios

CMR

ACMR

0 0.5 1 1.5 2 2.5 3 0

1

2

3

4

5

Vc

/V

y

Collapse Margin Ratios

CMR

ACMR
FEMA P-795 A: Identification of Component Parameters A-15

Important for Equivalency

Figure A-6 Component parameters that are not important the collapse response of three-story building.

In summary, the following component properties were found to be highly 

important to the collapse response of the three-story building studied: (1) 

yield strength, Vy; and (2) inelastic deformation capacity, ∆cap,pl. In addition, 

the following parameters were found to be only moderately important: (1) 

post-capping deformation capacity, (∆pc / ∆cap,pl); (2) cyclic deterioration 

capacity, λ’; (3) hysteretic behavior (low, moderate, and high levels of 

pinching); and (4) post-yield strength gain, (Vc / Vy). The following 

parameters were not important to the collapse response: (1) initial stiffness,

∆y; (2) details of the initial stiffness branch (Vkink / Vc and K1 / K2); and (3) 

residual strength (Vres / Vy).

A.4.3 Sensitivity Study Results for Three-Story Planar Model: 

Mixing-and-Matching Over the Height of Building

This section investigates the effects of the same component parameters, but 

looks at the case of mixing-and-matching where some structural components 

are modified and some components are left to have their baseline properties. 

This section uses a two-dimensional structural model to investigate the 

effects of mixing-and-matching over the height of the building. 

0 1 2 3 4 0

1

2

3

4

5

∆

y

/∆y,baseline

Collapse Margin Ratios

CMR

ACMR

0 0.2 0.4 0.6 0.8 0

1

2

3

4

5

Vkink/Vc

Collapse Margin Ratios

CMR

ACMR

0 1 2 3 4 5 0

1

2

3

4

5

K1

/K2

Collapse Margin Ratios

CMR

ACMR

0 0.1 0.2 0.3 0.4 0.5 0.6 0

1

2

3

4

5

Vres/V

y

Collapse Margin Ratios

CMR

ACMR
A-16 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

This mixing-and-matching sensitivity study is important because some 

seemingly “good” changes to component properties may in fact cause 

detrimental changes in system-level collapse safety. For example, increased

strength is typically thought of as beneficial, but if the strengths of only the 

upper stories are increased, the damage will localize more in the first story 

causing a reduction in the system-level deformation capacity and a reduction 

in the resulting collapse capacity. In the development of the Component 

Methodology, this concept is important because it will likely lead to an upper 

bound on the expected strength of the proposed component.

Figure A-7 shows a schematic of the various cases that are considered for the

three-story building mixing-and-matching sensitivity study. The figure on 

the left represents the situation previously investigated in Section A.4.2, and

the remaining figures represent the two situations considered in this section. 

For the three-story building, the largest difference between mixing-andmatching and full replacement comes with changes to component strength. 

This observation is expected, because strength discontinuities over height can 

result in more damage localization, and can alter the collapse mechanism. 

Figure A-8 shows the results of modifying component strength for the mixand-match case of replacing only the first story walls. This shows that 

decreasing the first-story strength decreases collapse capacity, which is 

expected. These results also show that increasing the strength by 50% causes 

a 15% decrease in the collapse capacity, due to the damage localizing more 

over the height of the building.

 

Figure A-7 Schematic diagram of various cases considered for the sensitivity 

study. Possible mixing-and-matching over the height of the 

building was considered.
FEMA P-795 A: Identification of Component Parameters A-17

Important for Equivalency

Figure A-8 Effects of strength on collapse capacity for the mix-and-match 

case of only story one being replaced.

Figure A-9 shows the results for replacing the upper stories of the building. 

Similarly to Figure A-8, this shows that both increases and decreases in 

upper story strength result in a decreased collapse capacity. This occurs 

because an increase in upper story strength exacerbates the damage 

concentration in the first story, and causes the building to have a lower 

system-level deformation capacity. Alternatively, a decrease in upper-story 

strength changes the collapse mechanism from the first story to the weakened 

upper-stories, thereby also decreasing the collapse capacity.

Figure A-9 Effects of strength on collapse capacity of three-story building

for the mix-and-match case of stories two and three being 

replaced.

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

V

y

/Vy,baseline

Collapse Margin Ratios

CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

V

y

/Vy,baseline

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CMR

ACMR
A-18 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

For more complete documentation, Figure A-10 provides the sensitivity 

study results for the case where the first story walls are replaced. Similarly, 

Figure A-11 provides the sensitivity study results for the case where the 

upper story walls (stories 2-3) are replaced.

These figures show the effects of plastic deformation capacity, ∆cap,pl. Trends 

are similar between the case of full replacement and the mix-and-match cases 

where only the first story is modified. In the case where the plastic 

deformation capacity of upper stories is modified, this only affects the 

response when a decreased deformation capacity causes the collapse 

mechanism to more fully involve the upper stories.

The effect of post-capping deformation capacity, (∆pc / ∆cap,pl), is generally 

consistent for the full replacement case as well as both of the mix-and-match 

cases. The one exception is that an increased post-capping deformation 

capacity in the upper stories does not affect the collapse response.

The remainder of the results shown in Figure A-10 and Figure A-11 are 

relatively consistent between the full replacement and the two mixing-andmatching cases.
FEMA P-795 A: Identification of Component Parameters A-19

Important for Equivalency

Figure A-10 Sensitivity study results for three-story building for the mix-and-match case with the bottom story 

walls replaced.

0 1 2 3 4 0

1

2

3

4

V

y

/Vy,baseline

Collapse Margin Ratios

CMR

ACMR

0 0.02 0.04 0.06 0.08 0.1 0

1

2

3

4

∆cap,pl/story height

Collapse Margin Ratios

CMR

ACMR

0 2 4 6 8 10 0

1

2

3

4

∆

pc

/∆cap,pl

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CMR

ACMR

0 50 100 150 200 0

1

2

3

4

λ′

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CMR

ACMR

0 1 2 3 4 0

1

2

3

4

Level of Pinching

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CMR

ACMR

0 0.5 1 1.5 2 2.5 3 0

1

2

3

4

Vc/V

y

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CMR

ACMR

0 1 2 3 4 0

1

2

3

4

∆

y

/∆y,baseline

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CMR

ACMR
A-20 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

Figure A-11 Sensitivity study results for three-story building, for the mix-and-match case with the upper story 

(stories 2-3) walls replaced.

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

V

y

/Vy,baseline

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CMR

ACMR

0 0.02 0.04 0.06 0.08 0.1 0

1

2

3

∆cap,pl/story height

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CMR

ACMR

0 2 4 6 8 10 0

1

2

3

∆

pc

/∆cap,pl

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CMR

ACMR

0 50 100 150 200 0

0.5

1

1.5

2

2.5

3

λ′

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CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Level of Pinching

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CMR

ACMR

0 0.5 1 1.5 2 2.5 3 0

0.5

1

1.5

2

2.5

3

Vc/V

y

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CMR

ACMR

0 1 2 3 4 0

1

2

3

∆

y

/∆y,baseline

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CMR

ACMR
FEMA P-795 A: Identification of Component Parameters A-21

Important for Equivalency

A.4.4 Sensitivity Study Results for Three-Story Three-Dimensional

Model: Mixing-and-Matching of Walls in Plan and Over 

Height

In order to investigate possible mixing-and-matching cases that may occur in 

a building in more depth, this section utilizes a three-dimensional structural 

model to investigate other mixing-and-matching configurations. Figure A-12 

shows three additional mixing-and-matching cases considered for the threestory building. There are three variations where walls are replaced (marked 

with “R”) on the South and East sides of the building. The North and West 

walls are left with their original properties. The replacement is done either: 

(1) over the full height of the building; (2) only for the first story of the 

building; or (3) only for the upper stories (stories 2-3) of the building.

Figure A-12 Schematic diagram of the various mix-and-match cases 

considered in the sensitivity study. Mixing-and-matching both 

in plan and over the height of the building are considered.

Figure A-13 shows the sensitivity study results for the case where walls are 

replaced over the full height, Figure A-14 shows the results for the case 

where the walls are replaced only in the first story, and Figure A-15 shows 

the results for the case where the walls are replaced in only the upper stories. 

These results are similar to the results of the last section, which were based 

on mixing-and-matching only over the building height. 

The primary additional finding of this section is that the mixing-andmatching within a single story of the building (i.e., in the plan view) is 

suggested to be less detrimental to collapse safety as compared with mixingand-matching over the building height. This is based on the observation 

from Figure A-13 which shows that an increased strength is beneficial to the 

collapse capacity even though the proposed and reference components were 

mixed-and-matched. For the cases of mixing-and-matching over the building 

height (Section A.4.3), there was no case where increased strength led to 

increased collapse capacity. However, this is an observation based on only a 

N
A-22 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

single building, and additional study would be needed to confirm this for 

additional cases, in order to generalize this observation.

Figure A-13 Sensitivity study results for mix-and-match case where walls are 

only replaced on the South and West sides of the building.

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Vy

/Vy,baseline

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CMR

ACMR

0 0.02 0.04 0.06 0.08 0.1 0

1

2

3

∆cap,pl/story height

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CMR

ACMR

0 2 4 6 8 10 0

1

2

3

∆

pc

/∆cap,pl

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CMR

ACMR

0 50 100 150 200 0

0.5

1

1.5

2

2.5

3

λ′

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CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Level of Pinching

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CMR

ACMR

0 0.5 1 1.5 2 2.5 3 0

0.5

1

1.5

2

2.5

3

Vc/Vy

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CMR

ACMR

0 1 2 3 4 0

1

2

3

∆

y

/∆y,baseline

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CMR

ACMR
FEMA P-795 A: Identification of Component Parameters A-23

Important for Equivalency

 

 

Figure A-14 Sensitivity study results for mix-and-match case where walls are 

only replaced on the first story of the South and West sides of 

the building.

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Vy/Vy,baseline

Collapse Margin Ratios

CMR

ACMR

0 0.02 0.04 0.06 0.08 0.1 0

0.5

1

1.5

2

2.5

3

∆

cap,pl/story height

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CMR

ACMR

0 2 4 6 8 10 0

0.5

1

1.5

2

2.5

3

∆

pc

/∆cap,pl

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CMR

ACMR

0 50 100 150 200 0

0.5

1

1.5

2

2.5

3

λ′

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CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Level of Pinching

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CMR

ACMR

0 0.5 1 1.5 2 2.5 3 0

0.5

1

1.5

2

2.5

3

Vc/Vy

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CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

∆

y

/∆y,baseline

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CMR

ACMR
A-24 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

Figure A-15 Sensitivity study results for mix-and-match case where walls are 

only replaced on the second and third stories of the South and 

West sides of the building.

A.4.5 Summary of Parameter Importance for Wood Light-Frame 

Buildings

Table A-6 summarizes the importance of component properties as observed 

in the results of the sensitivity studies. These results for the full set of eight 

0 1 2 3 4 0

0.5

1

1.5

2

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3

Vy

/Vy,baseline

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CMR

ACMR

0 50 100 150 200 0

0.5

1

1.5

2

2.5

3

λ′

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CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Level of Pinching

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CMR

ACMR

0 0.5 1 1.5 2 2.5 3 0

0.5

1

1.5

2

2.5

3

Vc/Vy

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CMR

ACMR
FEMA P-795 A: Identification of Component Parameters A-25

Important for Equivalency

buildings confirm earlier observations made based on the study of one 

building.

Table A-6 Summary of the Level of Importance of Component Parameters for Eight Wood Light-Frame 

Buildings

Component Parameters

Wood Light-Frame Building 

Model

Walls Modified In 

Sensitivity Study Vy

dy 

K1/K2

Vkink/Vc

Vc/Vy

∆cap,pl

∆pc / ∆cap,pl

Vres/Vy

Cyclic Deterioration 

Capacity (l')

Level of Pinching

Full Replacement Sensitivity 

Study

1-story, low aspect ratio (No. 1) All L-M L L L L H H L-M M L

2-story, low aspect ratio (No. 5) All H L-M L L L H M L M L-M

3-story, low aspect ratio (No. 9) All H L-M L L L-M H M L M L-M

1-story, high aspect ratio (No. 2) All H L L L L-M H H M M L-M

2-story, high aspect ratio (No. 6) All H L L L L-M H H L M L-M

3-story, high aspect ratio (No. 10) All H L L L M H M L M L-M

4-story, high aspect ratio (No. 13) All H L-M L L L H M L M L-M

5-story, high aspect ratio (No. 15) All H M L L M H M L M L

Mix-and-Match Sensitivity Study: 3-Story No. 10

3-story, high aspect ratio (No. 10) All stories, all sides H L L L M H M L M L-M

3-story, high aspect ratio (No. 10) Story 1, all sides MH L L L L-M H M L M M

3-story, high aspect ratio (No. 10) Stories 2-3, all sides M L L L L-M M M L M L-M

3-story, high aspect ratio (No. 10) All stories, two sides H L L L L H M L M L-M

3-story, high aspect ratio (No. 10) Story 1, two sides M L L L L-M M L-M L L-M L

3-story, high aspect ratio (No. 10) Stories 2-3, two sides M L L L L M L-M L M L

Mix-and-Match Sensitivity Study: 5-Story No. 15

5-story, high aspect ratio (No. 15) All stories, all sides H M L L M H M L M L

5-story, high aspect ratio (No. 15) Story 1, all sides MH L L L M H M L M L-M

5-story, high aspect ratio (No. 15) Stories 1-2, all sides MH L-M L L M H M L M L

5-story, high aspect ratio (No. 15) Stories 2-5, all sides L-M M L L L-M MH L L L-M L

5-story, high aspect ratio (No. 15) Stories 3-5, all sides M L-M L L L M L L M L

Overall Summary

Summary for all Buildings -- H L L L L-M H M L M L-M

Legend: H means highly important in most cases, M is medium importance (or H is some cases and L in some cases), L is low importance in most 

cases.
A-26 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

As summarized in Table A-6, the wood light-frame sensitivity study 

identified the following parameters to be consistently of high importance to 

collapse response: (1) inelastic deformation capacity, ∆cap,pl; and (2) yield 

strength, Vy. In addition, the following parameters were found to be 

consistently of moderate importance, or periodically of high importance: (1) 

cyclic deterioration capacity, λ’; (2) post-capping deformation capacity, (∆pc

/ ∆cap,pl); and (3) post-yield strength gain (Vc / Vy).

A.5 Reinforced Concrete Special Moment Frame 

Collapse Sensitivity Study 

In order to generalize previous findings, this section presents a sensitivity 

study for a reinforced concrete special moment frame system. Table A-7 

summarizes the design properties for the six special moment frame buildings 

used in this sensitivity study. This table shows that the selected set of 

buildings includes heights ranging from two to twenty stories, fundamental 

periods from 0.45 to 3.36 seconds, and includes both space- and perimeterframes. The table also includes the design base shear coefficient (V / W) and 

the maximum considered earthquake (MCE) spectral acceleration demand 

for the site (SMT). These building designs and models were developed as a 

part of the development of the FEMA P-695 Methodology and were 

evaluated using the Far-Field record set provided in FEMA P-695. All six 

buildings were designed for a high seismic site (SDC Dmax of FEMA P-695). 

Table A-7 Reinforced Concrete Special Moment Frame Structural Design 

Properties

Model 

No. 

No. of 

Stories

Building 

Configuration

Bay 

Width

Period 

T (sec) V/W SMT (g)

2064 2 Perimeter 20' 0.45 0.125 1.50

1003 4 Perimeter 20' 0.81 0.092 1.11

1010 4 Space 30' 1.03 0.092 1.03

5013 12 Perimeter 20' 2.13 0.035 0.42

2009 12 Space 20' 2.13 0.035 0.42

5020 20 Perimeter 20' 3.36 0.022 0.27

Table A-8 shows the component parameters and parameter value ranges 

typically used in the sensitivity study, though some of the buildings were 

tested for more extreme parameter values beyond these ranges (as will be 

shown in Figure A-16). The differences between the moment frame and 

wood light-frame shear wall sensitivity studies are as follows:

• The moment frame study focuses solely on the full replacement case (no 

mixing-and-matching considered).
FEMA P-795 A: Identification of Component Parameters A-27

Important for Equivalency

• The force and deformation parameters are moment and element rotation,

rather than shear force and lateral drift, where

θcap,pl = deformation of component, defined in terms of rotation, between 

yielding and capping

θpc = post-capping deformation of component, defined in terms 

rotation

• The moment frame study does not investigate the details of the 

component behavior prior to yielding, because the wood light-frame 

study showed them to be clearly unimportant.

• The cyclic deterioration (energy dissipation) capacity, λ, is defined 

slightly differently, as defined by λ = λ' × θcap,pl / θy. 

• The initial stiffness term is defined as a stiffness parameter, K1, in terms 

of moment and rotation, rather than being defined as a yield deformation.

Table A-8 Values of Component Parameters for the 

Reinforced Concrete Moment Frame Models

Component Parameter Baseline 

Parameter Value

Range of Values 

Considered in 

Sensitivity Study

Vy / Vy,baseline 1.00 1.0 - 4.0 

K1 / K1,baseline 1.00 0.5 - 2.0

K1 / K2 1.00 --

Vkink/Vc -- --

Mc / My 1.20 1.01 - 1.50

θcap,pl 0.050 0.015 - 0.10

θpc / θcap,pl 1.50 0.5 - 5.0

Vres/Vy 0.00 --

∆fail Infinite --

λ 90.0 20 - Infinite

Level of Pinching None --

Figure A-16 provides sample sensitivity study results for the four-story 

building (ID1003), and Table A-9 summarizes the results for all moment 

frame buildings considered in this study. These findings are similar to those 

of the wood light-frame study, with the following differences:

• Both studies identify the strength and deformation capacity as the two 

most important parameters. However, changes to strength have greater 

impact for moment frame buildings and changes to deformation capacity 

have greater impact for shear wall buildings. This is discussed more 

quantitatively in Appendix C.
A-28 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

• The post-capping deformation capacity is less important for moment 

frame buildings.

• The cyclic deterioration capacity is more important for moment frame 

buildings.

Part of the reason that changes to deformation capacity have less impact for 

moment frame buildings is that when the deformation capacities are large, 

the P-delta effects drive the collapse response. This causes the benefits of 

increased deformation capacity to saturate. This saturation effect can even 

be seen for the four-story building results shown in Figure A-16. 

Additionally, this saturation effect becomes more predominant for taller 

buildings, causing increased deformation capacity to have less benefit to the 

collapse capacity; this is shown in the results of Table A-9. 

Figure A-16 Sensitivity study results for the 4-story building ID1003, for the 

case of full replacement.

0 1 2 3 4 5 0

1

2

3

4

Vy

/Vy,baseline

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CMR

ACMR

0 0.02 0.04 0.06 0.08 0.1 0

1

2

3

4

θ

cap,pl/storyheight

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CMR

ACMR

0 1 2 3 4 5 0

1

2

3

4

θ

pc/θ

cap,pl

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CMR

ACMR

0 100 200 300 400 500 0

1

2

3

4

λ

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CMR

ACMR

0.75 1 1.25 1.5 1.75 0

1

2

3

4

Mc

/My

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CMR

ACMR

0 0.5 1 1.5 2 2.5 0

1

2

3

4

K1/K1,baseline

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CMR

ACMR
FEMA P-795 A: Identification of Component Parameters A-29

Important for Equivalency

A.6 Summary of Key Component Parameters 

Based on the observations from the literature review, and the analytical 

collapse sensitivity studies, the following parameters are classified as highly 

important: (1) inelastic deformation capacity, ∆cap,pl and θcap,pl; and (2) yield 

strength, Vy. In addition, the following parameters were found to be 

consistently of moderate importance or periodically of high importance: (1) 

cyclic deterioration capacity, λ’; (2) post-capping deformation capacity, (∆pc

/ ∆cap,pl) and (θpc / θcap,pl); (3) post-yield strength gain, (Vc / Vy); (4) residual 

strength, (Vres / Vy). Initial stiffness, ∆y, was periodically of moderate 

importance. The following parameters were consistently of low or no 

importance: (1) details of the initial stiffness branch, (Vkink / Vc and K1 / K2); 

and (2) hysteretic behavior (low, moderate, and high levels of pinching).

Table A-9 Summary of the Level of Importance of Component Parameters for Six Reinforced 

Concrete Special Moment Frame Buildings 

Component Parameters

Reinforced Concrete 

Moment-Frame Building 

Model

Elements 

Modified In 

Sensitivity 

Study

Vy

Initial Stiffness (K1)

K1 / K2

Vkink/Vc

Mc/My

θcap,pl 

θpc / θcap,pl 

Vres/Vy

Cyclic Deterioration 

Capacity (l)

Level of Pinching

Full Replacement Sensitivity Study

2-story, perimeter frame All H L -- -- L-M H M -- H --

4-story, space frame All M L -- -- L-M H M -- H --

4-story, perimeter frame All H L -- -- L-M H L-M -- H --

12-story, space frame All H L -- -- L-M H L-M -- H --

12-story, perimeter frame All H L -- -- L-M M L -- M --

20-story, perimeter frame All H L-M -- -- L-M L-M L -- MH --

Overall Summary

Summary for all Buildings -- H L -- -- L-M MH L-M -- MH --

Legend: H means highly important in most cases, M is medium importance (or H is some cases and L in some 

cases), L is low importance in most cases.

The component parameters in the first two categories (highly or moderately 

important) are those that should be considered for inclusion in the 

Component Methodology. The following list summarizes the final 

acceptance criteria checks of the Component Methodology, and how the

criteria are designed to target these important component parameters:
A-30 A: Identification of Component Parameters FEMA P-795

Important for Equivalency

• Deformation Capacity. The primary acceptance criterion of the 

Component Methodology (Equation 2-1) is based on the ultimate 

deformation capacity of the component from cyclic-load testing. This 

ultimate deformation capacity is defined as the deformation at which the 

component loses 20% strength. This criterion is based on total 

deformation rather than inelastic deformation, but the elastic component 

of deformation should be similar for the proposed and reference 

components (based on the Equation 2-4 criterion), so these two 

approaches are judged to be roughly equivalent. The total deformation is 

used to avoid trying to define a yield deformation, because there is no 

clear yield deformation for many types of components.

The post-capping deformation capacity is not accounted for in the 

Component Methodology. The use of additional deformation levels were 

considered (such as the deformation at 50% strength loss), but were 

intentionally excluded from the final acceptance criteria of the 

Component Methodology, in order to reduce the complexity of the 

Methodology. The fact that the primary acceptance criterion (Equation 

2-1) is based on the deformation at 20% strength loss, means that the 

post-capping deformation capacity is somewhat, but far from fully, 

accounted for.

In addition to the primary acceptance criterion based on cyclic-load test 

data (Equation 2-1), Section 2.8.4 also includes acceptance criteria based 

on monotonic-load test data. This is done because the ultimate 

deformation under cyclic-load testing mixes the effects of the component 

deformation capacity and the cyclic strength deterioration behavior. In 

contrast, the monotonic-load test data clearly show the component 

deformation capacity, without mixing in any effects of cyclic strength 

deterioration; the monotonic-load ultimate deformation is a clearer 

measure of the deformation capacity that should be quantified for 

purposes of demonstrating collapse equivalency. This is more fully 

discussed in Appendix B.

• Strength. The primary acceptance criterion of the Component 

Methodology (Equation 2-1) includes a strength penalty factor, PQ,

which is based on the maximum strength from cyclic-load testing (called 

QM in Chapter 2 and called VC or MC in this Appendix). This approach is 

based on the maximum strength alone, rather than also trying to quantify 

some measure of a yielding strength. This was done intentionally, for 

purposes of simplicity and to avoid trying to define the yield strength in a 

generic manner, because there is no clear yield force for many types of 

components. The weakness of this approach is that it does not 
FEMA P-795 A: Identification of Component Parameters A-31

Important for Equivalency

differentiate between components with low yield strength and large postyield strength gain, versus high yield strength and small post-yield 

strength gain. Even so, it is judged that the simplicity of using the 

maximum strength alone outweighs this potential weakness. 

• Cyclic Deterioration Capacity. The acceptance criteria of the 

Component Methodology include ultimate deformation criteria under 

cyclic-load testing (Equation 2-1); this approach partially accounts for 

the cyclic deterioration capacity, λ’ or λ, of the component because a 

component with low cyclic deterioration capacity will have smaller 

ultimate deformation when subjected to cyclic loading. To supplement 

this, the Component Methodology also imposes a requirement on the 

effective ductility capacity of the component (Equation 2-4). The

sensitivity studies showed that small or moderate changes in the energy 

dissipation capacity of a component were often not critical, but that large 

changes could lead to meaningful reductions in the collapse capacity of 

the seismic-force-resisting system. Accordingly, the Equation 2-4 

criterion is liberal and is set up to catch only these possibly extreme 

cases in the reduction of energy dissipation capacity, related to a large 

(more than 50%) reduction in post-yield deformation capacity.

• Initial Stiffness. The initial stiffness is also included in the acceptance 

criteria of the Component Methodology (Equation 2-3) but this was done 

for reasons separate from the discussion of this Appendix. This is 

discussed in detail in Section 3.8.3.

• Residual Strength. The residual strength is not considered in the 

Component Methodology, primarily because the residual strength is 

difficult to reliably quantify from test data.

FEMA P-795 B: Development of Requirements for Cyclic-Load and B-1

Monotonic-Load Testing

Appendix B

Development of Requirements for 

Cyclic-Load and MonotonicLoad Testing

B.1 Introduction

This appendix describes the requirements for cyclic-load and monotonic-load 

testing of components for use in the Component Methodology. Since 

estimates of component strength and deformation capacity are highly 

dependent on the loading history used to conduct the tests, it is required that 

loading histories used in the experimental investigations for the proposed and 

reference components be similar. This appendix provides a method that may 

be used to show quantitatively that the cyclic-loading histories chosen meet 

the requirements of Section 2.2.2. 

This appendix also describes why monotonic-load test results are also 

required for acceptance criteria. Requirements for monotonic-load testing 

ensure that the proposed and reference components are compared with a set 

of experimental results that are not dependent on the loading history. In 

addition, monotonic-load testing provides a lower bound on the number of 

cycles the building may experience as it nears sidesway collapse, which may 

be more representative for some cases than testing with many cycles.

B.2 Cyclic-Load Test Data Considerations

This section provides guidelines for the selection and comparison of cyclicloading histories for use in testing proposed and reference component 

specimens. The guidelines ensure that the loading history used to test the 

proposed component is as damaging as that used in the reference component

tests, such that component parameters can be directly compared in 

acceptance criteria. 

It is anticipated that the proposed component loading protocols will be 

selected after reference component data have been assembled. In many 

cases, most or all reference component data will be obtained from past tests 

and the loading histories used in generating reference component parameters 

are known. These loading histories will vary and may or may not be based 

on an established loading protocol. Proposed and reference component tests 

performed as part of the equivalency evaluation should employ loading 
B-2 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

protocols in accordance with the criteria set forth in this appendix. The 

choice of loading protocols utilizes information about the past reference 

component tests and, if needed, preliminary tests of the proposed component. 

Procedures in this section show how to determine what loading histories may 

be used for experimental investigations of the proposed and reference 

components to satisfy the requirements of Section 2.2.2. Section B.2.4

considers the case where all proposed and reference component tests are 

conducted using the same loading history and certain other conditions are 

met; in this case, loading history requirements may be assumed to be 

automatically satisfied. Section B.2.5 illustrates an evaluation of 

acceptability for different cyclic-loading histories.

Any alternative method used to demonstrate that cyclic-loading histories 

fulfill the requirements of Section 2.2.2 should be quantitative and approved 

by the peer review panel. 

B.2.1 Importance of Cyclic-Loading History

It is well documented that the cyclic-loading history applied in a structural 

component test can impact the results and conclusions of experimental 

investigations. Specifically, the applied loading history has been shown to 

influence estimates of the following component parameters:

Component Deformation Capacity. In general, the larger the number of 

inelastic cycles, the smaller the deformation capacity that will be measured

during the experiment. This observation has been confirmed for a variety of 

different materials and subassemblage systems in PEER/ATC-72-1, 

(PEER/ATC, 2010), Krawinkler (2009) and Gatto and Uang (2002). The 

concept is illustrated in Figure B-1 and Figure B-2.

 

Figure B-1 Identical steel specimens tested at the University of California at 

San Diego under different loading histories (Figure from 

PEER/ATC-72-1, data from Uang et al., 2000).

Component Strength. Component strength measured may differ by as 

much as 20 to 30% under different loading histories, as shown in Krawinkler 

-0.1 -0.05 0 0.05 0.1 -2

-1.5

-1

-0.5

0

0.5

1

1.5

2 x 104

Chord Rotation (rad)

Moment (k-in)

Uang-SSR-00-LS-1-MomentRotation

-0.1 -0.05 0 0.05 0.1 -2

-1.5

-1

-0.5

0

0.5

1

1.5

2 x 104

Chord Rotation (rad)

Moment (k-in)

Uang-SSR-00-LS-2-MomentRotation
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-3

Monotonic-Load Testing

(2009) and Gatto and Uang (2002), with components subjected to a larger 

number of inelastic cycles exhibiting smaller strength. Cyclic-loading

histories generally lead to estimates of component strength that are less than 

or equal to those observed from monotonic-load tests of identical specimens. 

Figure B-2 Comparison of cyclic envelope curves obtained for identical 

specimens under different loading protocols (from Gatto and 

Uang 2002), illustrating the effects of loading history choice on 

strength and deformation capacity.

Failure Mode. The executed loading history may have a significant effect 

on the failure mode observed for the component and/or system. Loading 

histories with very large number of cycles may produce failure modes that 

are not representative of those expected in an earthquake (Krawinkler, 2009; 

Gatto and Uang, 2002). The applied loading history has not been shown to 

have an important influence on estimates of initial stiffness (Gatto and Uang,

2002).

Loading protocols and histories with different characteristics, therefore, may 

lead to substantially different estimates of key component performance 

parameters. The number and relative amplitude of cycles in a loading 

history, particularly the number of inelastic cycles before failure, is critical. 

The protocol control reference value used to define the loading history may 

also be important because it affects the number of cycles before the ultimate 

deformation, ∆U, is reached. 

B.2.2 Overview of Commonly Used Loading Protocols

Loading protocols are defined by a number of different characteristics, which 

have been shown to affect observed values of component deformation 

capacity and strength. These include:
B-4 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

• Number and relative amplitudes of cycles, particularly the number of 

inelastic cycles when close to failure. 

• Test control parameter which is a physical quantity used to control the 

loading applied to the test specimen. Specific reference values of the test 

control parameter are used to define the number and amplitudes of cycles 

applied to the specimen. Some reference values, such as the yield 

deformation, may be difficult to define, so that even with the same 

loading protocol two identical specimens may give different results 

depending on the definition of the reference value (Krawinkler et al.,

2000). 

• It is generally observed that specimens loaded more rapidly have higher 

strength (Uang et al., 2000).

A variety of different loading protocols have been used in past experimental 

studies and some of these are summarized in Table B-1. The Component 

Methodology does not limit the application of loading protocols (histories) to 

those shown here. However, the cyclic-loading history must meet the 

requirements of Section 2.2.2, and it is desirable that testing follow an 

established protocol. These protocols apply to quasi-static cyclic (reverse) 

testing of elements of the seismic force resisting system. All are deformation 

(rather than load) controlled in inelastic cycles. 

Table B-1 reports important characteristics of various loading protocols,

including the component type it was developed for and the test control 

reference values, denoted here as ∆control. This reference value is commonly 

related to some measure of the “yield” or “maximum” (“ultimate”) 

deformation. As Table B-1 shows, the ISO, CEN-long, CUREE and FEMA 

461 protocols are based on control reference values related to various 

definitions of ultimate/maximum deformation. The New Zealand, ATC-24, 

FCC, and SPD loading histories are based on control reference values related 

to an estimate of yield deformation. The SAC protocol implicitly assumes a 

yield story-drift ratio of 0.01, which provides the control reference value. 

Definitions of loading protocol and history are included in the references 

listed in the table and in Filiatrault et al. (2008), Krawinkler (2009) and Gatto 

and Uang (2002).
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-5

Monotonic-Load Testing

Table B-1 Key Features of Selected Loading Protocols

Loading 

Protocol/History

Component 

of Interest Test Control Reference Value

FEMA 461

(FEMA, 2007)

Primarily for 

nonstructural 

components

Test control defined by Δo (smallest 

deformation amplitude of interest), Δm (target 

maximum deformation amplitude), n (number 

of steps in loading history). 

ISO 

(ISO, 2003)

Wood 

connections/ 

walls

∆control = ∆max defined as the deformation at 

maximum load (obtained from an initial 

monotonic-load test)

CUREE (Krawinkler et 

al., 2000) Wood

∆control = ∆ defined as the maximum 

deformation the test specimen is expected to 

sustain before it triggers a prescribed failure 

criterion (e.g., 20% strength loss)

FCC

(Karacabeyli, 1998) Wood ∆control = ∆y (yield deformation)

SAC/AISC

(Clark et al., 1997) Steel ∆control = Interstory drift of 0.01

CEN – short

CEN – long

(CEN, 1995)

Wood

connections

∆control = ∆y multiplied by an assumed ductility 

(CEN – short)

∆control = ∆max defined as the deformation at 

maximum load (obtained from an initial 

monotonic-load test) (CEN- long)

ATC-24

(ATC,1992) Steel ∆control = ∆y (yield deformation) estimated from 

initial load control cycles

New Zealand 

(Cheung et al., 1991) Concrete

∆control = ∆y (yield deformation) estimated by a 

theoretical estimate of component strength 

and extrapolation of displacement of 

specimen during early, load-controlled cycles. 

SPD

(Porter, 1987)

Masonry 

(Wood)

∆control = deformation at FME (first major 

event; usually taken as event causing 

“yielding”)

Two commonly used loading histories are shown in Figure B-3, to illustrate 

key terms and features. Figure B-3a shows the CUREE protocol, assuming

∆control = 0.035, where 0.035 is the deformation at 20% strength loss, i.e., ∆u. 

Figure B-3b shows SPD protocol, executed to the same maximum drift of 

0.035. The control reference value is the deformation (drift) at the first major 

event, usually taken as the yield displacement. In this example, first major 

event (FME) is defined as a drift of 0.01 (though in practice this value may 

be much smaller). Tests may be continued beyond the deformation 

amplitude to obtain all necessary component response parameters for the 

Component Methodology. 

B.2.3 Selection of Acceptable Loading Histories and Protocols

This section suggests a method for showing that loading histories and 

protocols are acceptable according to Section 2.2.2. Requirements for 

acceptable cyclic-loading histories for the proposed and reference component
B-6 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

data sets are described below. In each case, general guidelines are provided, 

followed by a specific criterion. 

(a)

(b)

Figure B-3 Illustration of two cyclic-loading protocols for an example 

component test specimen: (a) CUREE; and (b) SPD. 

In the criteria that follow, normalized cumulative deformation demand is 

employed as a measure of how damaging the loading history is to the 

component of interest. The normalized cumulative deformation parameter is 

used to define criteria for identifying acceptable loading histories for testing.

More damaging protocols impose higher normalized cumulative deformation 

demands. Cumulative deformation is defined here as the sum of the 

deformation amplitudes of all relevant excursions (a cycle consists of two 

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 10 20 30

Drift

Cycle No.

Δcontrol = 0.035 (assumed for selected component)

Δ = 0.05Δcontrol

Δ= 0.00175

etc. for subsequent 

cycles

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 10 20 30 40 50 60

Drift

Cycle No.

Δcontrol = FME = Δy

Δcontrol = 0.01 (assumed for selected component)

Δ = 0.25Δcontrol

Δ = 0.0025

etc. for subsequent 

cycles
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-7

Monotonic-Load Testing

excursions, one in the positive direction and one in the positive direction).

The measured deformation at 20% strength loss from the cyclic envelope 

curve, ∆U, is employed to normalize the cumulative deformation demand. 

Examples showing how to compute the normalized cumulative deformation 

demand for a given loading history and component are given in Section 

B.2.5.

For the purpose of comparing specimens and loading histories, the 

cumulative deformation demand imposed during a specific test i before 

reaching the deformation amplitude of ∆U, normalized by ∆U, is denoted

normalized cumulative deformation demand, NCDi. The value of the 

normalized cumulative deformation demand depends on the loading history 

applied and the deformation capacity of the particular specimen. To show 

loading history acceptability, NCDi must be computed for every proposed 

and reference component test. 

Loading histories applied to proposed and reference components should be 

shown to satisfy the following guidelines, in order to meet the requirements 

of Section 2.2.2 and 2.4.4.

Experimental tests should be conducted using a cyclic symmetric 

deformation history of step-wise increasing amplitude. Loading histories 

should be deformation controlled in inelastic cycles, rather than load 

controlled. The features of the loading history, including the number of 

cycles per step and the amplitude of individual cycles in a step, may vary, as, 

for instance, in the CUREE protocol and the SPD protocol, as illustrated in 

Figure B-3.

The normalized cumulative deformation demand of each test (NCDi) is used 

to ensure that components tested with similarly damaging loading histories 

are grouped together in performance groups. 

Limits of Normalized Cumulative Deformation Demand

The normalized cumulative deformation demand from each test, NCDi,

should fall within the range defined by Equations B-1 or B-2, such that

, 0.5 2 NCD NCD NCD RC ≤ ≤ RC i RC   (B-1)

and

, 0.5 2 N D NCD D C PC ≤ ≤ PC i NC PC   (B-2)

where NCDRC  and NCDPC  are the median normalized cumulative 

deformation for each performance group for reference and proposed 

components, respectively. 
B-8 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

This comparison between the median and each individual test should be 

carried out for each performance group, ensuring that data for a given 

component performance group is sufficiently similar to be combined in 

generating statistics on key component parameters. If the component is 

grouped into several performance groups, multiple values of the median 

value will be computed. Tests falling outside this range are deemed 

substantially different and should be separated into a different performance 

group. The range defined in Equations B-1 and B-2 is based on judgment 

and review of experimental data. 

No tests with NCDi < 6.0 are permitted. Tests with NCDi < 6.0 were 

executed with a loading history that is not damaging enough to be used in the 

Component Methodology. The lower bound NCD of 6.0 is based on 

examination of data in Figure B-5 and falls significantly below the values of 

normalized cumulative deformation calculated for commonly used protocols. 

This lower bound is intended to ensure that most of the available protocols 

can be used with a variety of different types of components even those with 

characteristics different from what was assumed in Figure B-5. Under only 

an isolated number of cases, therefore, a test may have to be discarded for 

imposing too small a normalized cumulative deformation. 

The proposed component shall be tested under a loading protocol(s) that 

imposes approximately the same, or more, normalized cumulative 

deformation on the component, compared to the loading histories used to 

establish the reference component data set. Proposed components may not

be tested using protocols that impose significantly less normalized 

cumulative deformation, because these protocols are less damaging and will 

lead to overestimates of component strength and deformation capacity

relative to the reference component.

Selection Criteria for Proposed Component Loading History 

Loading histories for proposed component tests are considered to be 

acceptable provided that the median normalized cumulative deformation at 

the deformation amplitude of ∆U for the proposed component, NCDPC  is at 

least 75% of the median normalized cumulative deformation for the 

reference component, NCDRC  . Thus,

0.75 NCD NCD PC ≥ RC   (B-3)

This requirement should be met by comparing the NCDPC  for each proposed 

component performance group to the NCDRC  of the associated reference 

component performance group. 
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-9

Monotonic-Load Testing

There is no strict upper limit placed on NCDPC  , compared to NCDRC 

However, it is recommended that the proposed component not be tested 

using protocols that impose significantly more normalized cumulative 

deformation than is measured in the reference component tests. In this case, 

the proposed component protocol may have too many cycles to permit a 

realistic comparison between proposed and reference component parameters

for strength and deformation. In addition, a large number of cycles may lead 

to an underestimation of the component strength ratio. Estimations of 

strength are generally conservative, but not in the case where proposed and 

reference components will be used together in a structural system, such that 

disparities in component strength may lead to damage localization. The use 

of a proposed component protocol that has a normalized cumulative 

deformation demand significantly greater than the measured reference 

component demand is therefore discouraged.

Both the proposed and reference components should be tested under loading 

histories or protocols that are appropriate for the component under 

consideration, and it is desirable that the loading protocol produce damage 

and failure mechanisms that are consistent with what is expected (or has been 

observed) in earthquakes. Some of the loading protocols have built-in 

assumptions about behavior, according to the application for which the 

protocol was developed. For example, for moment frames designed for high 

seismic regions, the SAC protocol assumes a typical value of yield story drift 

of 0.01, which is appropriate for steel beam-column subassemblies but not 

necessarily other configurations. ASTM E2126 Standard describes several 

standard test methods and their applicability (ASTM, 2009).

When a generally accepted industry loading protocol exists for the material 

or component of interest, every effort should be made to use data obtained 

using this protocol to establish equivalency. 

Note that, in general, a loading protocol for the proposed component needs to 

be selected before the proposed component tests are conducted. To make 

this selection, a reasonable approximation of NCDPC  is needed for the 

different candidate protocols. If some information about proposed component

performance is already available, NCDPC  may be initially estimated from 

available data and the loading protocol of interest. If not, it may be 

necessary to test one or more proposed components with the loading 

protocols under consideration to determine if the selected protocol is likely to 

meet the requirements. However, the final assessment of loading history 

equivalency should be based on data obtained directly from proposed and 

reference component tests.
B-10 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

B.2.4 Special Case: Same Loading Protocol Used to Generate 

Proposed and Reference Component Data

Loading history requirements can be assumed to be automatically satisfied if 

the following conditions are met: (1) the same loading protocol is used for all 

proposed and reference component tests; and (2) the test control parameter 

and associated reference value are based on a measure of ultimate or 

maximum deformation.

If both of the above conditions are satisfied, the selected loading protocol is 

approximately equivalently damaging to the proposed and reference 

components in the Component Methodology, satisfying the requirements of 

Section 2.2.2. This special case takes advantage of Component Methodology 

requirements in Chapter 2, which ensure that ∆U,PC is approximately equal to 

∆U,RC. Given that the ultimate deformation is known to be similar for the 

proposed and reference components, a loading protocol will impose similar 

deformations to the proposed and reference component specimens, provided 

that the test control parameter is a similar measure of ultimate deformation. 

If these conditions are not satisfied, NCDi should be calculated for each test 

and loading histories must be shown to meet the requirement of Section 

B.2.3. The same loading protocol, when applied to components with 

different properties, may be more or less damaging, providing, the rationale 

for the rules in this appendix.

B.2.5 Illustration: Comparison of Loading Histories 

Computation of Normalized Cumulative Deformation 

In this illustration, the story drift, ∆U, is assumed as 0.035 for the 

hypothetical component under consideration. The SAC loading protocol, 

defined in terms of story drift, is shown in Figure B-4a. The first set of six 

cycles has a deformation (drift) amplitude of 0.00375, the second set of six 

cycles have a deformation amplitude of 0.005, and so on. The x-axis of the 

normalized cumulative deformation plot in Figure B-4b represents the 

maximum deformation amplitude the specimen has experienced. After the 

first set of positive and negative excursions to a deformation of 0.005 (one 

full cycle, point A), the maximum drift amplitude is 0.005. The deformation 

amplitude is normalized by ∆U, therefore 0.005/0.035 = 0.14, which 

corresponds to the x-value of the first point shown in Figure B-4b. The 

normalized cumulative deformation, shown on the y-axis of Figure B-4b, 

accounts for the total deformation experienced by the specimen. Before 

reaching the deformation amplitude of 0.005, the SAC protocol (Figure B4a) has pushed the specimen through 6 cycles +/- 0.00375 and one cycle of 

+/- 0.005. Therefore the cumulative deformation (accounting for both 
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-11

Monotonic-Load Testing

positive and negative excursions) is 0.00375 x 12+ 0.005 x 2, or a cumulative 

deformation of 0.055. For a normalized deformation amplitude of 0.14 (xvalue on Figure B-4b), the normalized cumulative deformation is 

0.055/0.035 = 1.57 (y-value on Figure B-4b). This process is repeated to 

obtain the relationship between normalized cumulative deformation and the 

normalized deformation amplitude over the entire deformation range 

imposed during the test. When computing the cumulative deformation, 

elastic or nearly elastic cycles should not be included; this example assumes 

there are no such cycles. 

 

Figure B-4 Illustration of normalized cumulative deformation plot, showing 

(a) SAC loading protocol, (b) plot of normalized cumulative 

deformation vs. normalized deformation amplitude.

Equivalency between loading histories is judged based on the normalized 

cumulative deformation at the deformation amplitude corresponding to ∆U. 

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

Story Drift

0 5 10 15 20 25 30

Cycle No.

Deformation Amplitude : 

Drift = +/- 0.00375

Deformation Amplitude : 

Drift = +/- 0.005

Point A

0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1 1.2

Cumulative Deformation ΣΔ/Δu

Deformation Amplitude Δ/Δu

Point A

NCD
B-12 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

This value is denoted NCD. Since ∆U will rarely coincide with a deformation 

amplitude of the loading history, interpolation is needed to obtain the value 

of NCD, as illustrated in the figure. In Figure B-4b, the normalized 

cumulative deformation at the assumed ∆U of 0.035 is 15.6. 

Comparison of Loading Histories for Proposed and Reference 

Component Tests

The criteria of Section B.2.3 are illustrated in Figure B-5 for the case of a 

single reference component test and various options of loading protocols for 

proposed component tests.

In this example, it is assumed that the reference component test has been 

executed with the CUREE protocol and that the measured ∆U is 0.035 and is 

equal to the target value ∆control of the protocol. For this case, the normalized 

cumulative deformation plot is as shown in a bold line in Figure B-5, denoted 

RC (CUREE), and the NCDRC is equal to 13.3. For simplicity of illustration, 

it assumed that the median value, NCDRC  , accounting for all reference 

component tests, is also 13.3. Note that in an actual case there will be 

several reference component tests and each may have a different ∆U and a 

different NCD. According to the requirements of Equation B-3, these 

reference component test results impose a lower bound of 0.75 x 13.3 or 10.0 

on the NCDPC  . 

For the purposes of this illustration, suppose that a preliminary proposed 

component test has been executed and ∆U is equal to 0.035 in this case as 

well. In Figure B-5 several candidate protocols are considered; these plots 

are generated assuming control variables of ∆max = 0.035 or ∆Y = 0.01 (for 

illustration only, recognizing that the actual values of ∆max and ∆Y may be 

quite differentfrom the assumed ones). NCDPC can then be compared to 

for the candidate proposed component protocols. Of the other 

protocols shown in Figure B-5, the CEN-short protocol would not be 

acceptable to test the proposed component because the NCD value in the 

example is below the lower bound of 10.0. The SPD protocol is shown to be 

significantly more damaging (i.e., leading to a much larger value of NCD) 

and it should be carefully considered whether this protocol is appropriate for 

testing the proposed component. All other protocols shown in the example 

are acceptable according to Equation B.3.

Once a candidate proposed component protocol is selected, all proposed 

components are tested and NCD is computed for each individual test. These 

test data are then used to determine whether the requirements of Section 

B.2.3 are met. 
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-13

Monotonic-Load Testing

Figure B-5 Normalized cumulative deformation plots for an example 

reference component protocol (CUREE) and several candidate 

protocols. This plot is created based on specific assumptions 

about the proposed and reference component and is not generally 

applicable. 

B.2.6 Additional Considerations for Cyclic-Load Testing

The Component Methodology does not stipulate specific requirements for 

testing to deformation levels beyond ∆U. However, it is emphasized that 

testing should be performed to levels of deformations that permit full 

assessment of important force-deformation characteristics of component at 

all performance levels, including structural collapse. Although not required 

by the Component Methodology, tests can be continued to larger 

deformations at little or no additional expense. Users will find that these data 

may be very useful in the future, especially for efforts related to analytical 

modeling of component behavior. 

B.3 Monotonic-Load Test Data Considerations

The Component Methodology requires monotonic-load test data, in addition 

to the cyclic-load test data already described. Requirements for monotonicload test data are included for two reasons.

Firstly, the Component Methodology focuses on collapse resistance, so it is 

desirable that components are tested under displacement patterns 

representative of the response history experienced by a component in a 

seismic-force-resisting system that is near-collapse or collapsing during an 

earthquake. It has been shown that in many cases these displacement 

0

2

4

6

8

10

12

14

16

18

20

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Cumulative Deformation ΣΔ

/

Δu

Deformation Amplitude Δ/Δu

RC (CUREE)

PC (SAC)

PC (ATC-24)

PC (ISO)

PC (SPD/CoLA)

PC (FEMA 461)

PC (CEN Short)
B-14 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

patterns may be more similar to a monotonic push than a symmetric cyclicloading history. Experimental test results for both cyclic- and monotonicloading patterns, as required in the Component Methodology, are likely to 

bracket the true response, which depends on the frequency content and 

duration of the earthquake ground motion. 

Second, the cyclic envelope curve, created from cyclic-load test data, gives 

an incomplete representation of component collapse resistance because it 

mixes two different modes of strength deterioration. To more reliably 

quantify collapse resistance, monotonic-load test data are a necessary 

supplement to cyclic-load test data.

B.3.1 Importance of Monotonic-Load Test Data in Component 

Methodology

Cyclic-loading protocols generally prescribe a deformation history that is 

symmetric with respect to the undeformed structural or component 

configuration. For structures subjected to code design-level ground motions, 

story drift and component responses during earthquake shaking are mostly 

symmetric and cyclic-load testing provides a reasonable representation of 

loads and deformation in the structure (Krawinkler et al., 2001). When 

subjected to an earthquake large enough to cause collapse, however, patterns 

of story drift and component responses depend on the failure mode and on 

the frequency characteristics and strong motion duration of the seismic input. 

Component responses might be close to symmetric-cyclic until severe 

deterioration occurs, or they might be one-sided and more similar to 

monotonic response than symmetric-cyclic. In the latter case, for example, a 

structure may deform permanently in one direction because deformation 

reversals are not sufficiently large to return the building to its original 

position (Krawinkler and Lignos, 2009). This case deserves consideration in 

the context of component equivalency evaluation. The requirements for both 

monotonic-load and cyclic-load test data are therefore intended to ensure that 

components are tested with deformation histories that represent the range of 

deformation patterns that may be experienced by the component during an 

earthquake. 

In addition, there are two distinctly different modes of strength deterioration 

that may occur in a structure or component, and each has substantially 

different impacts on the collapse resistance. The use of an envelope curve, 

based on cyclic-load test data, mixes these two modes of strength 

deterioration and gives an incomplete representation of component or system 

collapse resistance. Monotonic-load test data serve to separate these two 
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-15

Monotonic-Load Testing

modes of component strength deterioration, thereby improving understanding 

of collapse performance, as illustrated in this section. 

The two different modes of strength deterioration that may be experienced by 

a component or structure are defined as follows and illustrated in Figure B-6. 

• Cyclic strength deterioration: Strength loss occurs between two cycles of 

loading. In this mode of strength deterioration, the element response 

maintains a positive tangent stiffness.

• In-cycle strength deterioration: Strength loss occurs during a single cycle 

of loading. In this mode of strength deterioration, the element response 

exhibits a negative tangent stiffness.

For purposes of illustration, Figure B-6 shows two components, one of which 

is experiencing only cyclic strength deterioration and the other only in-cycle 

strength deterioration. In reality, most component behavior reflects a 

combination of the two. 

Figure B-6 Cyclic behavior of an element experiencing (a) only cyclic 

strength deterioration, and (b) only in-cycle strength 

deterioration, figures from FEMA P-440A (FEMA, 2009). 

As a structure approaches collapse, components experience both strength 

deterioration modes. It has been shown that in-cycle strength deterioration is 

usually more important in bringing on global collapse than cyclic strength 

deterioration (Ibarra et al., 2005). The deformation at the onset of these 

important deterioration modes depends on the loading history applied to the 

component or structure. As a result, cyclic-load testing may not capture 

important differences in component response in a real earthquake history. 

The cyclic envelope curve used to summarize experimental results from 

cyclic-load testing combine the effects of in-cycle and between-cycle 

strength deterioration. 
B-16 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

B.3.2 Illustration: Limitations of Using Only Cyclic-Load Test 

Data for Component Equivalency

This example illustrates the possible problems that arise if equivalency 

criteria did not utilize both monotonic load and cyclic load testing. 

Figure B-7 shows the response of two components with different types of 

cyclic behavior. The cyclic envelope curves show that both components 

have approximately the same ∆U ≈ 0.06 [story drift]. The reference 

component behavior in this example, Figure B-7a, exhibits a combination of 

cyclic strength deterioration (for cycles with peak story drift ≤ 0.06) and incycle strength deterioration (for cycles with peak story drift > 0.06). This 

behavior is representative of many types of structural components. In 

contrast, the proposed component behavior, Figure B-7b, exhibits no cyclic 

strength deterioration, and the behavior is controlled entirely by in-cycle 

strength deterioration. 

Despite differences in strength deterioration and cyclic behavior of the 

proposed and reference components, equivalency comparisons based only on 

the cyclic-load test data (i.e., the cyclic envelope curve) would find the two 

components to be equivalent since the components have the same strength, 

ultimate deformation, ∆U, and stiffness.

Figure B-7 also shows results of monotonic-load tests for the proposed and 

reference components. Due to the observed differences in strength 

deterioration, the behavior of these two components under monotonic-load 

tests is quite different, with the reference component test data showing 

significantly larger monotonic ultimate deformation than the proposed 

component test data. These distinct differences in monotonic-loading curves 

call into question whether these proposed and reference components are truly 

equivalent. The scope of the Component Methodology is to ensure 

equivalency in collapse performance, so these components should only be 

deemed equivalent if they result in equivalent collapse performance.

In order to determine if the example proposed and reference components

have equivalent collapse performance, a single-degree-of-freedom (SDOF) 

model is created for each system. These models are subjected to an 

incremental dynamic analysis process (as described by Vamvatsikos and 

Cornell, 2002) to assess seismic collapse resistance, using a set of 20 farfield ground motions. The period of each SDOF oscillator is 1.0 second and 

the models have 5% damping, and are assigned a yield strength of 200kN

(equivalent to a yield Sa(1.0s) of 0.25g). 
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-17

Monotonic-Load Testing

Figure B-7 Hypothetical cyclic-load and monotonic-load test data for 

reference component (top) and proposed component (bottom) 

illustrating the importance of considering both cyclic and 

monotonic behavior. Identical cyclic test parameters may 

obscure differences in monotonic behavior due to differences in 

cyclic and in-cycle strength deterioration. 

Figure B-8 shows the time-history response for a single ground motion 

scaled to Sa(1.0s) = 1.0g. Under this ground motion, the SDOF calibrated to 

represent the reference component is substantially damaged (exhibiting 

permanent drift deformation of 0.05), but does not collapse. In contrast, the 

SDOF calibrated to represent the proposed component behavior collapses 

laterally, exhibiting very large interstory drifts. 

Collapse fragility curves generated from incremental dynamic analysis of all 

20 ground motions are shown for the proposed and reference component

SDOF models in Figure B-9. The results in Figure B-9 show that the 

proposed component is substantially more prone to collapse than the 

reference component, with median collapse capacities of 1.6g and 2.9g for 
B-18 B: Development of Requirements for Cyclic-Load and FEMA P-795

Monotonic-Load Testing

the proposed and reference component SDOF models, respectively. These 

results imply higher probabilities of collapse for the proposed component 

model for a specified level of ground motion intensity. 

This example illustrates that equivalency between the cyclic envelope curves 

may not be sufficient to demonstrate equivalency in collapse safety. 

Equivalency in the monotonic-loading curves is helpful to discern the relative 

amounts of in-cycle deterioration present in the component behavior. An 

approach based on equivalency of cyclic envelope curve properties alone could 

lead to the approval of a proposed component that has much lower collapse 

capacity than the reference component.

Figure B-8 Example time-history response of the proposed and reference 

component SDOF models subjected to a single ground motion 

scaled to Sa(1.0s) = 1.0g. 

Figure B-9 Collapse fragility curves for the proposed and reference 

component SDOF models subjected to 20 ground motions. 

Note that in developing this example, several simplifications were made 

including the use of idealized rather than actual test data and the 

0 5 10 15 20 25 30 35 40

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Time [sec]

Lateral Drift

SDOF based on RC Data

SDOF based on PC Data

0 1 2 3 4 5 6 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sa(T = 1.0 sec) [g]

P[collapse]

SDOF based on RC Data

SDOF based on PC Data

RC Median = 2.9g

PC Median = 1.6g
FEMA P-795 B: Development of Requirements for Cyclic-Load and B-19

Monotonic-Load Testing

representation of structural response using a SDOF system rather than a 

multiple-degree-of-freedom system. Most real components exhibit some 

combination of in-cycle and cyclic strength deterioration. The

simplifications in component behavior made in this example exaggerate the 

differences in collapse capacity between the two components, but the 

conclusions hold for less extreme comparisons also. For any comparison in 

which the proposed component exhibits relatively more in-cycle strength 

deterioration (and relatively less cyclic strength deterioration) as compared 

with the reference component, establishing equivalency based only on the 

cyclic envelope curves would be non-conservative. Such an approach could 

lead to the approval of a proposed component that has much lower collapse 

capacity than the reference component.

B.3.3 Monotonic-Load Test Data Requirements 

The Component Methodology requires both monotonic-load and cyclic-load 

test data for establishing equivalency of the proposed and reference 

components. 

Specifically, the monotonic-load ultimate deformation of the proposed 

component should equal or exceed the monotonic load ultimate deformation 

of the reference component, increased by the uncertainty penalty factor. 

These comparisons should be conducted for a subset of the proposed and 

reference component configurations. Detailed requirements are given in 

Section 2.8.4. 

FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-1

Appendix C

Development of Probabilistic 

Acceptance Criteria

C.1 Introduction

This appendix describes the development of probabilistic-based acceptance 

criteria expressed in Equation 2-1 for evaluating component equivalency, and 

provides a detailed description of the development of Tables 2-3 and 2-4.

Quantitatively, equivalent collapse safety implies that the 10th percentile 

collapse capacities are equivalent for proposed components and reference 

components, and this concept has been incorporated into the acceptance 

criteria of the Component Methodology. Requirements for relative strength 

and ultimate deformation capacity of proposed and reference components 

have been set to achieve this equivalent collapse probability, and have been 

adjusted considering the uncertainties inherent in estimation of collapse 

capacity. 

C.2 Collapse Capacity Fragilities and the Effects of 

Uncertainty

Figure C-1 illustrates two different collapse fragility curves relating ground 

motion intensity at collapse (normalized by the maximum considered 

earthquake (MCE) and denoted as the collapse margin ratio) to the 

probability of collapse. This appendix assumes that collapse capacities are 

lognormally distributed. 

These two fragility curves have identical 10th percentile collapse capacities, 

i.e., in both cases a collapse margin ratio of 1.0 corresponds to a 10 percent 

probability of collapse. Even though the 10th percentile collapse capacities 

are identical, the median collapse capacity values corresponding to a 50 

percent probability of collapse differ because of the differences in underlying 

uncertainty or variability, quantified by the standard deviation. While 

Collapse Distribution “A” has a logarithmic standard deviation, βTOT, of 0.50 

and a median collapse margin ratio of 2.0, Collapse Distribution “B” has a

logarithmic standard deviation of 0.70, which leads to the larger required 

median value of 2.58. 
C-2 C: Development of Probabilistic Acceptance Criteria FEMA P-795

Figure C-1 Illustration of two collapse capacity fragilities, with the same 10th

percentile collapse capacity but different variability and 

medians.

Thus, for a given 10th percentile collapse capacity, there is a relationship 

between the uncertainty in the fragility and the required median collapse 

capacity necessary to achieve the same 10th percentile collapse capacity. 

This relationship is an important component of the probabilistic acceptance 

criteria of the Component Methodology. 

Following the framework used in FEMA P-695 Quantification of Building 

Seismic Performance Factors (FEMA, 2009b), the variability in the collapse 

capacity fragility, βTOT, is assumed to come from four sources of uncertainty, 

as follows:

2 22 2 β β βββ TOT RTR DR TD MDL = +++

where βTOT is the total variability in collapse fragility, βRTR is the variability

in collapse capacity fragility associated with record-to-record variability, βDR

is the uncertainty associated with imperfect design requirements, βTD is the 

uncertainty associated with variation in test data, and βMDL is the uncertainty 

associated with the imperfect numerical modeling of the structure. Further 

detail regarding the approach to assigning values for these parameters can be 

found in FEMA P-695.

The above equation for evaluating the total uncertainty in the collapse 

fragility represents the uncertainty in collapse capacity for a complete class 

of structural systems. Accordingly, not all terms are needed for the simpler 

Component Methodology. The equation can be simplified by assuming β RTR

0 1 2 3 4 5 6

0

0.2

0.4

0.6

0.8

1

Collapse Margin Ratio

P[Collapse]

Collapse Distribution A

Collapse Distribution B

Median = 2.0

βTOT = 0.50

Median = 2.58

βTOT = 0.70
FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-3

= 0.40 for record-to-record variability (consistent with FEMA P-695). In 

addition, since structural modeling is not a direct part of the Component

Methodology, β MDL = 0.20 is assumed for the structural modeling (consistent 

with “Good” modeling in FEMA P-695). After these substitutions, the 

design requirement and test data uncertainty terms (β DR and β TD) remain to 

be evaluated for the proposed component as part of the Component 

Methodology, as follows:

( ) ( ) 2 2 2 2

, 0.40 0.20 β TOT PC = +++ β β DR TD

The subscript PC implies that this total uncertainty reflects our uncertainty in 

the prediction of the collapse resistance of the seismic force resisting system 

consisting of the proposed component. 

For purposes of equivalency, this β TOT,PC must have a basis to be compared 

against. This basis utilizes the same record-to-record and modeling 

uncertainty values used above, and assumes Good design requirement (β DR 

= 0.20), which allows the user a beneficial effect if the design requirements 

are rated as Superior, and Superior test data (β TD = 0.10). The numeric 

values of β DR and β TD are based on FEMA P-695. The basis value is 

calculated as follows:

( ) ( ) ( ) ( ) 2222

,Target 0.40 0.20 0.10 0.20 0.50 β TOT = +++=

The relationship between the variability in the collapse fragility and the 

required median collapse capacity, in order to achieve the same 10th

percentile collapse capacity, is quantified below:

μμ β β C PC C RC , , −= − 1.28( TOT PC TOT , ,Target) (C-1)

where μC,PC is the logarithmic mean collapse capacity for the proposed 

component and μC,RC is the logarithmic mean collapse capacity for the 

reference component. In this equation the median is defined in logarithmic 

terms, i.e., μC,PC is the natural logarithm of the median collapse capacity of 

the seismic force resisting system of interest. The use of Equation C-1 is 

illustrated below for the example shown in Figure C-1: 

ln 2.58 ln 2.00 1.28 0.70 0.50 ( ) −= − ( ) ( )

Equation C-1 shows how to relate the collapse capacity uncertainty to the 

required median collapse capacity, but this is not enough to create a 

methodology for component equivalency. Such a methodology also requires 

an approximate relationship between the collapse capacity and the 
C-4 C: Development of Probabilistic Acceptance Criteria FEMA P-795

component parameter values that are observable from test data (e.g., strength 

and deformation capacity). The focus of the next two sections is to establish 

such relationships. 

C.3 Effect of Changes in Deformation Capacity on the 

Collapse Fragility

In order to create a probabilistic component equivalency criterion, a 

quantitative link is needed between the ultimate deformation of a component 

type and the collapse capacity of the structural system containing that 

component. Admittedly, the relationship between component and system 

behavior depends on the type and characteristics of the structural system 

(e.g., building height, stiffness, irregularities), and it is impossible to provide 

a single relationship that is generally applicable to all cases. This section 

develops a single approximate relationship between the component 

deformation capacity and the system-level collapse capacity. 

To create this quantitative relationship, the literature review and sensitivity 

studies of Appendix A are utilized. Figure C-2 shows an example from the 

sensitivity study of a three-story wood light-frame building (Building No. 

10). As the ultimate deformation of the components increases, the collapse 

capacity of the structural system also increases. The significance of this 

trend depends on the gradient (slope) between the collapse capacity and the 

component parameter (i.e., deformation capacity in this case). 

To quantify the relationship between component ultimate deformation and 

system-level collapse capacity, the gradient in Figure C-2b is utilized, 

denoted a1. The gradient is the slope of a linear trend line relating the natural 

logarithm (LN) of the component deformation capacity to the natural 

logarithm of the collapse capacity. Here, the collapse capacity is expressed 

in terms of the adjusted collapse margin ratio (ACMR), as defined in FEMA 

P-695 and Appendix A. For the example shown in Figure C-2b, the value of 

a1 is 0.70 for a decrease in deformation capacity from the baseline value of 

0.025. Note that the a1 decreases slightly for larger values of ultimate 

deformation, but this is neglected for simplicity.
FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-5

Figure C-2 Relationship between component deformation capacity and system-level collapse 

capacity, for a three-story wood light frame building (from Figure A-4 of Appendix A).

A similar sensitivity study was completed for several other wood light-frame 

buildings, including configurations where all components were modified (full 

replacement of reference components by proposed components) and 

configurations where only a subset of components were modified in the 

structural system (mix-and-match of proposed and reference components). 

These sensitivity studies are documented in Appendix A, and Table C-1

reports the a1 values for each of the wood light-frame buildings. The median 

value of the gradient for the full replacement cases is 0.74 where the median 

gradient is lower for the mix-and-match cases, such that the overall median 

value is 0.64. There is significant scatter in the a1 value across the various 

buildings. 

Table C-2 presents similar results for the set of reinforced concrete special 

moment frame sensitivity studies completed in Appendix A. The moment 

frame results show a substantially lower median value of a1 = 0.36. 

A similar recent study by Zareian and Krawinkler (2010) found a1 values of 

0.66 on average for generic shear wall buildings failing in flexure. 

Additionally, a1 values of 0.32 were found for generic moment resisting 

frames. The Zareian and Krawinkler study considered only full replacement 

cases. 

Comparing the results above, there is a trend suggesting that component 

ultimate deformation capacity has a larger effect on collapse resistance of 

shear wall buildings (with a1 = 0.66 to 0.74) as compared to moment frame 

buildings (with a1 = 0.32 to 0.36).

0 0.02 0.04 0.06 0.08 0.1 0

1

2

3

4

5

∆cap,pl/story height

Collapse Margin Ratios

CMR

ACMR

(a)

(b)
C-6 C: Development of Probabilistic Acceptance Criteria FEMA P-795

Table C-1 Relationship Between Component Ultimate Deformation and 

System-Level Collapse Capacity for Wood Light-Frame Buildings

Wood Light-Frame Building Model Stories Modified In Sensitivity 

Study

Gradient a1

for Decrease 

in Component 

Deformation 

Capacity

Full Replacement Sensitivity Study

1-story, low aspect ratio (No. 1) All 0.43

1-story, high aspect ratio (No. 2) All 0.78

2-story, low aspect ratio (No. 5) All 0.74

2-story, high aspect ratio (No. 6) All 0.71

3-story, low aspect ratio (No. 9) All 1.15

3-story, high aspect ratio (No. 10) All 0.70

4-story, high aspect ratio (No. 13) All 1.05

5-story, high aspect ratio (No. 15) All 0.73

Median: 0.74

Mix-and-Match Sensitivity Study

3-story, high aspect ratio (No. 10) 1 0.56

3-story, high aspect ratio (No. 10) 2-3 0.42

5-story, high aspect ratio (No. 15) 1 0.44

5-story, high aspect ratio (No. 15) 1-2 0.44

5-story, high aspect ratio (No. 15) 2-5 0.29

5-story, high aspect ratio (No. 15) 3-5 0.28

Median (lower floors modified): 0.44

Median (upper floors modified): 0.29

Table C-2 Relationship Between Component Ultimate Deformation and 

System-Level Collapse Capacity for Reinforced Concrete Special 

Moment Frame Buildings

Reinforced Concrete Special Moment 

Frame Building Model

Stories Modified In Sensitivity 

Study

Gradient a1

for Decrease 

in 

Component 

Deformation 

Capacity

Full Replacement Sensitivity Study

2-story ID2064 (Perimeter Frame) All 0.42

4-story ID1003 (Perimeter Frame) All 0.30

4-story ID1010 (Space Frame) All 0.47

12-story ID5013 (Perimeter Frame) All 0.19

12-story ID2009 (Space Frame) All 0.49

20-story ID5020 (Perimeter Frame) All 0.20

Median: 0.36
FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-7

For purposes of the component equivalency criterion, a single a1 value is 

selected and applied to all types of structural systems. Therefore, in order to 

avoid underpredicting the effects of component ultimate deformation, the 

value of a1 = 0.65 is selected. This value corresponds to the lower range 

value for shear wall buildings. It is consistent with the findings of the more 

extensive study by Zareian and Krawinkler, and approximately consistent 

with the findings for wood light-frame walls in Appendix A. 

C.4 Effect of Changes in Strength on the Collapse 

Fragility

This section creates an approximate relationship between the strength of a 

component and the collapse capacity of the structural system. This 

relationship is analogous to that considered above, except component 

strength rather than component ultimate deformation is the underlying 

variable. 

Figure C-3 shows an example sensitivity study of the same three-story wood 

light-frame building. In both full replacement and mix-and-match 

configurations, a decrease in component strength leads to a decrease in the 

system-level collapse capacity. 

For increases in component strength, the collapse safety increases when all of 

the component strengths are increased uniformly (Figure C-3a). However, 

when the strengths are increased for only the upper story components (Figure 

C-3b), the damage localizes more in the first story, thus the increased 

strength is detrimental to the system-level collapse safety. Similarly to the 

approach used in the last section, these relationships are quantified by the 

gradient a2, which is the slope between the natural logarithm of the ACMR 

and the natural logarithm of the component strength.

When the Component Methodology is employed, any approved proposed 

component can be freely mixed-and-matched with the component for which 

it is a replacement (the reference component). Therefore, the observation 

that increased component strength may have a detrimental impact on collapse 

safety when mixing-and-matching occurs (i.e., using the proposed 

component and reference component together in an individual building) must 

be accounted for in the Component Methodology. Accordingly a different a2

value is used to represent the effects of component strength decrease versus 

component strength increase. For example, the a2 values for Figure C-3b are 

0.55 for a decrease in strength and -0.19 for an increase in strength.
C-8 C: Development of Probabilistic Acceptance Criteria FEMA P-795

Figure C-3 Relationship between component strength and system-level 

collapse capacity, for a three-story wood light-frame building 

showing the results for: (a) full replacement; and (b) mixing-andmatching when only stories 2-3 are replaced with the stronger 

components.

Table C-3 summarizes the results of sensitivity study for the full set of wood 

light-frame buildings that were presented in Appendix A. For decreases in 

the component strength, the median a2 value is 0.43 for the full replacement 

case, and the a2 values are similar for mixing-and-matching cases. For an 

increase in component strength, we focus on the mixing-and-matching cases 

where the strength is increased in only the upper stories; for this small subset 

of cases, the median a2 value is -0.40. The negative gradient suggests that 

increases in component strength can sometimes be just as detrimental as 

decreases in component strength. Even so, this is not always the case and 

these observations are based on only three buildings, so judgment must be 

applied when determining how this should impact the a2 values used in the 

Component Methodology.

For cases of full replacement, Zareian and Krawinkler found that a2 = 0.33 is 

appropriate for generic shear wall buildings failing in flexure and a2 = 0.73 is 

appropriate for generic moment resisting frame buildings. 

Based on the above results, there is again an observed difference between 

shear wall structures and frame structures. Reduced component strength has 

a smaller effect on the collapse capacity of shear wall buildings (with a2 = 

0.33 to 0.41) than moment frame buildings (with a2 = 0.65 to 0.73).

For purposes of the Component Methodology, a single set of a2 values must 

be selected (one for decreased strength and one for increased strength) and 

used as the approximate value for all types of structural systems. For 

decreases in component strength, the larger value for moment-resisting 

frames is utilized (a2 = 0.70), in order to avoid underpredicting the effects of 

component strength on system collapse performance. 

0 1 2 3 4 0

1

2

3

4

5

Vy/Vy,baseline

Collapse Margin Ratios

CMR

ACMR

0 1 2 3 4 0

0.5

1

1.5

2

2.5

3

Vy

/Vy,baseline

Collapse Margin Ratios

CMR

ACMR

(a) (b)
FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-9

Table C-3 Relationship Between Component Strength and System-Level Collapse 

Capacity for Wood Light-Frame Buildings

Wood Light-Frame Building Model Stories Modified In Sensitivity 

Study

Gradient a2

for 

Decrease 

in 

Component 

Strength

Gradient a2

for 

Increase in 

Component 

Strength

Full Replacement Sensitivity Study

1-story, low aspect ratio (No. 1) All -- --

1-story, high aspect ratio (No. 2) All 0.35 --

2-story, low aspect ratio (No. 5) All 0.62 --

2-story, high aspect ratio (No. 6) All 0.36 --

3-story, low aspect ratio (No. 9) All 0.41 --

3-story, high aspect ratio (No. 10) All 0.51 --

4-story, high aspect ratio (No. 13) All 0.44 --

5-story, high aspect ratio (No. 15) All 0.43 --

Median: 0.43 --

Mix-and-Match Sensitivity Study

3-story, high aspect ratio (No. 10) 1 0.20 --

3-story, high aspect ratio (No. 10) 2-3 0.55 -0.19

5-story, high aspect ratio (No. 15) 1 0.84 --

5-story, high aspect ratio (No. 15) 1-2 0.57 --

5-story, high aspect ratio (No. 15) 2-5 0.44 -0.58

5-story, high aspect ratio (No. 15) 3-5 0.22 -0.40

Median (lower floors modified): 0.57 --

Median (upper floors modified): 0.44 -0.40

For increases in component strength, the effect on collapse safety can be 

either beneficial (for the full replacement case) or detrimental (for the 

mixing-and-matching case with stronger upper stories). Even though both 

effects are possible, a single value of a2 is needed for developing the 

equivalency acceptance criterion. From the results of the wood light-frame 

sensitivity studies, it was suggested that increased component strength can 

sometimes be as detrimental as decreased strength implying that the use of a2

= 0.70 could be appropriate for both strength increases and decreases. 

However, the use of such a large value would be unfairly based on a small 

subset of the most detrimental building configurations. Therefore, after 

evaluating the results from sensitivity studies and then applying judgment, a 

value of a2 = -0.35 was utilized for strength increases (set as half of the value 

for decreased strength). This value accounts for the fact that increased 

component strength can be detrimental to the system-level collapse safety, 
C-10 C: Development of Probabilistic Acceptance Criteria FEMA P-795

but is not pessimistically based on only the worst-case building 

configurations.

C.5 Probabilistic Acceptance Criterion Used in 

Component Equivalency Methodology

C.5.1 Overall Approach

Establishing equivalency between proposed and reference components 

requires equivalency in the resulting 10th percentile system-level collapse 

capacities. Differences in these collapse capacities could arise from 

differences in one or more of the following:

• Differences in collapse capacity uncertainty (βTOT,PC ≠ βTOT,Target)

• Differences in component ultimate deformation ( ∆ ∆  

U,PC U,RC ≠ )

• Differences in component strength ( R R  

Q PC Q RC , , ≠ )

To account for each of the above differences between proposed and 

replacement components, each are related back to a requirement on the 

median deformation capacities of the proposed and reference components 

( ∆U PC ,  and ∆U RC ,  , respectively) in Equation 2-1, repeated below: 

∆ ∆  

U,PC U,RC U Q ≥ ⋅⋅ P P

The penalty factor for uncertainty, PU, is the ratio of ∆ ∆ U,PC U,RC

  that is 

required to offset the effects of any differences in collapse capacity 

uncertainty (βTOT,PC ≠ βTOT,Target), in order to ensure uniform collapse safety 

between the proposed and reference components. Similarly, the penalty 

factor for strength, PQ, is the ratio of ∆ ∆ U,PC U,RC

  that is required to offset 

the effects of any differences in strength ( R R  

Q PC Q RC , , ≠ ) between the 

proposed and reference components.

C.5.2 Development of the Penalty Factor for Differences in 

Uncertainty

The penalty factor for uncertainty, PU, accounts for the relationship between 

uncertainties in the collapse fragility and the required median collapse 

capacities. 

Differences in median collapse capacity are related to differences in the 

median component ultimate deformation, following the guidance of Section 

C.3 which related the logarithmic mean of the collapse capacity to the 

logarithmic mean of the deformation capacity, which leads to the following:

μμ ∆ ∆ C,PC C,RC a LN LN 1 ( U,PC ) ( U,RC ) −= −      
FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-11

Combining the above equation with a1 = 0.65 with Equation C-1 leads to the 

following, effectively determining the improvement in component 

deformation capacity necessary to make up for differences in collapse 

fragility uncertainty such that the same 10th percentile collapse capacity is 

achieved regardless of whether proposed or replacement components are 

used:

a LN LN 1 , (∆ ∆ ββ U,PC ) ( U,RC ) 1.28( TOT PC TOT,Target)   −= −    

which can then be algebraically manipulated into:

( ) ( ) ( , )

1

1 1.28 LN LN U,PC U,RC TOT PC TOT,Target a

∆ ∆ ββ     −= −      

 

( , )

1

1 exp 1.28 U,PC

TOT PC TOT,Target

U,RC a

∆

β β ∆

    =     −

   





Substituting the uncertainty values from Section C.2 results in the final 

equation defining the penalty factor for uncertainty, PU. This penalty factor 

defines the required ratio of ∆ ∆ U,PC U,RC

  that is needed to offset any 

difference in uncertainty, in order to maintain equivalent collapse safety.

( ) ( ) 2 2 2 2

1

1 exp 1.28 0.40 0.20 0.50 U,PC

U DR TD

U,RC

P

a

∆ β β ∆

                   

= = +++ − 



Table C-4 presents the resulting penalty factors for uncertainties, PU, for 

various levels of uncertainty associated with the proposed component test 

data, βTD, and proposed component design requirements, βDR. 

Table C-4 Penalty Factor to Account for Uncertainty

Penalty Factor for Uncertainty (PU)

Test Data Quality Rating 

(βTD)

Design Requirements Quality Rating (β DR)

Superior (0.10) Good (0.20) Fair (0.35)

Superior (0.10) 0.95 1.00 1.15

Good (0.20) 1.00 1.05 1.25

Fair (0.35) 1.15 1.25 1.40

In developing Table C-4, target values of 0.10 (Superior) and 0.20 (Good) 

were used for the uncertainties associated with reference component test data 

and design requirements, respectively. This allows the final penalty factor,

PU, to be evaluated from the table based only on the quality ratings 

associated with the proposed component. In order to better generalize how 

the design requirement ratings are handled, Table 2-3 of Chapter 2 uses a 
C-12 C: Development of Probabilistic Acceptance Criteria FEMA P-795

slightly different comparative rating (Better, Same, Worst) for the proposed 

versus reference component design requirements.

C.5.3 Development of the Penalty Factor for Differences in 

Strength

The penalty factor for strength, PQ, is developed similarly to the penalty 

factor for uncertainty, PU. Equations below show how collapse capacity is 

affected by differences in component ultimate deformations and differences 

in component strengths, respectively.

μμ ∆ ∆ C,PC C,RC a LN LN 1 ( U,PC ) ( U,RC ) −= −      

,

, ,2

,

Q PC

C PC C RC

Q RC

R

a LN

R μ μ

    − =            





For equivalency in collapse safety, any reduction in collapse capacity caused 

by a difference in the component strengths must be offset by an increase in 

collapse capacity caused by a difference in component deformation 

capacities. This can be accounted for by setting the above equations equal to 

one another, as follows:

( ) ( ) ,

1 2

,

Q PC

U,PC U,RC

Q RC

R

a LN LN a LN

R

∆ ∆

      − =              

   

Rearranging leads to the theoretical penalty factor for strength, as follows:

2 ,

1 ,

exp U,PC Q PC

U,RC Q RC

a R

LN

a R

∆

∆

      =                

 

 

However, if the load (strength) ratio of the proposed component is similar to 

the reference component, i.e., R R Q,PC Q,RC

  is close to 1.0, there is no

penalty factor for component strength. It was determined that a range of 

0.9 ≤ R R Q PC Q RC , ,   ≤ 1.2 should be allowable with no penalty, so the revised 

equations are as follows:

If , , 0.9 R R  

Q PC Q RC < , then 2 ,

1 ,

exp 0.9

Q PC

Q

Q RC

a R

P LN

a R

      =              





If , , 1.2 R R  

Q PC Q RC > , then 2 ,

1 ,

exp 1.2

Q PC

Q

Q RC

a R

P LN

a R

      =              




FEMA P-795 C: Development of Probabilistic Acceptance Criteria C-13

Otherwise, ( ) 2

1

exp 1.0 1.0 Q

a P LN

a

  =     =    

Table C-5 presents penalty factors for strength, PQ, calculated with 

a2= -0.35, and provides the basis for Table 2-4 in Chapter 2.

Table C-5 Penalty Factor to Account for Differences in Strength

Penalty Factor for Differences in Strength (PQ)

PQ PQ

0.50 1.88 1.10 1.00

0.60 1.55 1.20 1.00

0.70 1.31 1.30 1.04

0.80 1.14 1.40 1.09

0.90 1.00 1.50 1.13

1.00 1.00 1.80 1.24

1.10 1.00 2.00 1.32

R R Q PC Q RC , ,   R R Q PC Q RC , ,  

FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-1

Appendix D

Test Application: Stapled Wood 

Shear Wall Components

D.1 Introduction

This appendix illustrates the application of the Component Methodology to 

the possible substitution of stapled wood shear wall components for nailed 

wood shear wall components in wood light-frame construction. The 

objective is to determine whether or not a stapled wood shear wall 

component is equivalent to line A.15 in Table 12.2-1 of ASCE/SEI 7-10, 

Minimum Design Loads for Buildings and Other Structures (ASCE, 2010), 

which reads “Light-framed (wood) walls sheathed with wood structural 

panels rated for shear resistance or steel sheets.” This example assumes that 

the stapled wood shear wall component is not currently approved by the 

building code, and is being proposed as an alternative to the code-recognized 

wood shear wall seismic-force-resisting system listed in Table 2306.3 of the 

2009 IBC International Building Code (ICC, 2009).

The steps in this test application follow directly from the requirements of the 

Component Methodology defined in Section 2.2 through Section 2.8 

D.2 Description of Stapled Wood Shear Walls

The stapled wood shear walls are designed and detailed with the approach 

proposed by Talbot et al. (2009), which includes specific detailing 

requirements that are intended to address common weaknesses and failure 

modes in the stapled wood shear wall component. Additionally, the 

associated cyclic-load test data from Talbot et al. (2009) is utilized in this 

example; these data include four geometric configurations and a total of 13

component tests. Table D-1 summarizes the tested components, providing 

general information about dimensions, sheathing thickness, and staple 

spacing. More complete information about the test specimens, including 

specific detailing information, is presented in Section D.5.2.

Table D-1 shows that the dominant failure mode in the tested stapled wood 

shear walls is progressive staple withdrawal, leading to separation of the 

sheathing from the framing. Other failure modes were also observed, such as 

splitting of the sill plate and failure of the anchor rod, failure of the anchor 
D-2 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

rod due to pullout from concrete and staple shear failure at the blocking 

locations. The staple shear failure mode at the blocking was corrected in the 

latter tests (denoted with superscript 1 in Table D-1) by doubling the number 

of staples in the blocking region. Figure D-1 illustrates most of these failure 

modes.

Table D-1 Overview of Stapled Wood Shear Wall Configurations Tested 

(after Talbot et al. 2009)

Wall 

Number

Wall 

Dimensions 

(HxL)

OSB 

Sheathing 

Thickness 

Staple Spacing 

(edge/field) Failure Mode2

3-A#1 8' x 3' 7/16" 2"/4" SW

3-A#2 8' x 3' 7/16" 2"/4" SW

3-B 8' x 3' 7/16" 2"/4" SW

3-C 8' x 3' 7/16" 2"/4" SW

4-A 8' x 4' 7/16" 2"/4" SW

4-B 8' x 4' 7/16" 2"/4" AR

4-C 8' x 4' 7/16" 2"/4" SW, EP

8-A 8' x 8' 7/16" 2"/4" SSB

8-B 8' x 8' 7/16" 2"/4" SSB

8-C1 8' x 8' 7/16" 2"/4" AR, SPS

12-A1 8' x 12' 7/16" 2"/4" SW, STP

12-B1 8' x 12' 7/16" 2"/4" STR, EP

12-C1 8' x 12' 7/16" 2"/4" SW

Note 1: Twice as many staples in the blocking region.

Note 2: Failure Modes: SW - staple withdrawal, STP - splitting of top plate, SSB - staple 

shear at blocking, EP - end-post, SPS - sill plate splitting, AR - anchor rod pull-out, 

STR - strap failure.

The breadth of the stapled wood shear wall data set is limited (one staple 

type/length, one stapling pattern, one sheathing type/thickness, and four 

geometric configurations). As such, if this example shows that stapled wood 

shear walls are equivalent to nailed wood shear walls, this conclusion would 

only apply to the configurations that were included in the stapled wood shear 

wall testing program. Accordingly, the stapled wood shear wall design 

requirements must be written to “reasonably restrict” the usage of the stapled 

wood shear walls to the range of configurations that were considered in 

testing (see Section 2.5.4); this is addressed later in Section D.5.4.
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-3

Figure D-1 Failure modes of stapled wood shear wall test specimens showing: (a) staple 

withdrawal for wall number 4-C; (b) staple and splitting of top plate for wall 

number 12-A; (c) anchor rod failure and splitting of sill plate for wall number 

8-C; and (d) staple shear and blocking failure for wall number 8-B (from 

Talbot et al., 2009).

D.3 Evaluation of Applicability Criteria

The Component Methodology is applicable for evaluating the possible 

equivalency between stapled wood shear walls and nailed wood shear walls. 

This is based on the criteria of Section 2.3, including the acceptable quality 

ratings of the test data and design requirements. As described in Section

D.7.1, the quality rating of the nailed wood shear wall test data is Superior 

(d)

(c)

(a) (b)
D-4 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

and the stapled wood shear wall test data are rated as Good. As described in 

Section D.7.2, the nailed and stapled wood shear wall design requirements 

are rated as Good and Superior, respectively. Based on these quality ratings,

both the reference component and the proposed component meet the 

minimum requirements for test data and design requirements. In addition, 

the stapled and nailed wood shear wall components can be isolated from the 

remainder of the seismic-force-resisting system by a clear component 

boundary.

D.4 Reference Component Test Data

D.4.1 Define the Reference Component Design Space 

The reference component is a nailed wood shear wall with the following

expected representative configurations:

• Wall height: 8’

• Aspect ratio (height/length): 1:1

• Sheathing: 

o OSB and STR1

o 3/8” to 15/32”

• Nails: 8d and 10d hand driven common nails

• Nail spacing (on-center): 

o Edge spacing: 2” to 6”

o Field spacing: 6” to 12”

• Openings: No openings are considered in the test data set. While 

openings are likely to occur in any wood light-frame building, the 

proposed component design requirements will require that only full 

height piers (without openings) be considered as part of the seismic 

force-resisting system. Accordingly, the proposed components will be 

tested without openings, so this reference component data set will be 

consistent.

D.4.2 Compile or Generate Reference Component Test Data 

The reference component data set is established based on available published 

information. The reference component data set for this test application is 

based on work by Pardoen at the University of California at Irvine (COLA, 

2001). This database includes 108 tests on 8’x8’ shear walls consisting of 36 

configurations with three tests per configuration. 
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-5

In this test application, tests that employ Sequential Phased Displacement 

(SPD) loading protocol (Porter, 1987) are used. This is done for consistency 

with the loading protocol used for testing of the proposed component. The 

final reference component data set includes a total of 63 tests (on 21 

configurations) that represent the remaining data after removal of data on 

gypsum wallboard, screws, stucco, and sheathing on both sides of the panel.

The reference component data set generally requires sets of both cyclic-load

and monotonic-load data (Section 2.2). In this example, the monotonic-load

data set is not compiled because monotonic-load data are not available for 

the proposed component data set. As such, this example is incomplete. Even 

so, this example is continued with the assumption that all acceptance criteria 

associated with monotonic-load data are fulfilled (Section 2.8.5), and the 

quality rating of the test data (Section 2.7.1) is not degraded due to the 

exclusion of monotonic-load data.

D.4.3 Interpret Reference Component Test Results 

The test data are interpreted in accordance with the requirements of Section 

2.4.3 and Section 2.2 (with related illustrative examples in Section 3.2.2). 

The utilized force quantity is the horizontal shear force in the shear wall, and 

the displacement quantity is the lateral drift of the wall (lateral displacement 

divided by height) (Section 2.2). Per Section 2.2.2, the value of ∆U would be 

affected if the vertical load carrying ability of the specimen were 

compromised. Modification of the value of ∆U was not necessary in this 

example. 

Table D-2 summarizes the configuration of each test specimen, as well as the 

observed failure modes. Table D-3 provides values of important response 

quantities, such as strength, stiffness, ductility, and deformation capacity, for 

each specimen of the reference component data set. According to the 

guidelines of Section 2.4.4, the data are placed into a single performance 

group. 
D-6 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

Table D-2 Summary of Nailed Wood Shear Wall Configurations in the 

Reference Component Data Set

Test

Index Group

Wall 

Dimensions 

(HxL)

OSB Sheathing Fastener

Fastener 

Spacing 

(edge/field)

1

1 8' by 8' 3/8" STR I 8d hand driven 

common 2 6"/12"

3

4

2 8' by 8' 3/8" STR I 8d hand driven 

common 5 4"/12"

6

7

3 8' by 8' 15/32" STR I 10d hand 

driven common 8 6"/12"

9

10

4 8' by 8' 15/32" STR I 10d hand 

driven common 11 4"/12"

12

13

5 8' by 8' 3/8" STR I 8d hand driven 

common 14 4"/12"

15

16

9 8' by 8' 15/32" STR I 10d hand 

driven common 17 2"/12"

18

19

10 8' by 8' 7/16" OSB 8d hand driven 

common 20 4"/12"

21

22

11 8' by 8' 15/32" OSB 10d hand 

driven common 23 6"/12"

24

25

12 8' by 8' 15/32" OSB 10d hand 

driven common 26 4"/12"

27

28

13 8' by 8' 15/32" OSB 10d hand 

driven common 29 2"/12"

30

31

22 8' by 8' 15/32" STR I 10d hand 

driven common 32 4"/12"

33

34

23 8' by 8' 15/32 " STR I 10d hand 

driven common 35 4"/12"

36

37

24 8' by 8' 15/32" STR I 10d hand 

driven common 38 4"/12"

39

40

25 8' by 8' 3/8" STR I 8d hand driven 

common 41 2"/12"

42
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-7

Table D-2 Summary of Nailed Wood Shear Wall Configurations in the 

Reference Component Data Set (continued)

Test

Index Group

Wall 

Dimensions 

(HxL)

OSB Sheathing Fastener

Fastener 

Spacing 

(edge/field)

43

26 8' by 8' 15/32" STR I 8d hand driven 

common 44 4"/12"

45

46

27 8' by 8' 3/8" STR I 8d hand driven 

common 47 4"/6"

48

49

28 8' by 8' 3/8" STR I 8d hand driven 

common 50 4"/6"

51

52

29 8' by 8' 15/32" STR I 10d hand 

driven common 53 4"/12"

54

55

30 8' by 8' 15/32" STR I 10d hand 

driven common 56 4"/12"

57

58

31 8' by 8' 15/32" STR I 10d hand 

driven common 59 4"/12"

60

61

32 8' by 8' 15/32" STR I 10d hand 

driven common 62 4"/12"

63

Table D-3 Summary of Important Component Parameters for the Reference Component Data Set

Test

Index

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD (lb) RQ = 

VM / VD

KI

(lb/in) KD (lb/in) RK = KI / KD

ΔY,eff

(in/in) μeff ΔU (in/in)

1 5,299 2,240 2.4 15,019 10,481 1.4 0.004 5.4 0.020

2 5,481 2,240 2.4 11,849 10,481 1.1 0.005 4.0 0.019

3 5,632 2,240 2.5 14,649 10,481 1.4 0.004 5.2 0.021

4 7,433 2,240 3.3 13,879 23,903 0.6 0.006 4.2 0.024

5 7,214 2,240 3.2 15,161 23,903 0.6 0.005 5.1 0.025

6 8,144 2,240 3.6 17,002 23,903 0.7 0.005 4.5 0.022

7 6,567 2,720 2.4 18,020 14,246 1.3 0.004 6.8 0.026

8 6,509 2,720 2.4 16,558 14,246 1.2 0.004 6.2 0.025

9 7,136 2,720 2.6 16,599 14,246 1.2 0.004 5.9 0.026

10 9,770 4,080 2.4 18,276 19,300 0.9 0.006 n/a n/a

11 9,331 4,080 2.3 21,438 19,300 1.1 0.005 5.0 0.022

12 8,337 4,080 2.0 16,020 19,300 0.8 0.005 5.1 0.028

13 6,417 3,440 1.9 15,202 14,842 1.0 0.004 n/a n/a

14 6,879 3,440 2.0 17,444 14,842 1.2 0.004 4.4 0.018

15 6,774 3,440 2.0 16,150 14,842 1.1 0.004 5.2 0.023

16 15,450 6,960 2.2 25,806 30,969 0.8 0.006 4.5 0.028

17 14,718 6,960 2.1 20,649 30,969 0.7 0.007 n/a n/a

18 15,362 6,960 2.2 26,146 30,969 0.8 0.006 4.7 0.029
D-8 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

Table D-3 Summary of Important Component Parameters for the Reference Component Data Set

(continued)

Test

Index

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD (lb) RQ = 

VM / VD

KI

(lb/in) KD (lb/in) RK = 

KI / KD

ΔY,eff

(in/in) μeff ΔU (in/in)

19 6,784 3,040 2.2 26,079 13,466 1.9 0.003 6.7 0.018

20 5,727 3,040 1.9 29,593 13,466 2.2 0.002 6.9 0.014

21 5,735 3,040 1.9 28,749 13,466 2.1 0.002 6.5 0.014

22 4,234 2,480 1.7 23,651 13,677 1.7 0.002 8.4 0.016

23 4,583 2,480 1.8 22,915 13,677 1.7 0.002 7.2 0.015

24 4,567 2,480 1.8 22,256 13,677 1.6 0.002 7.7 0.016

25 8,371 3,680 2.3 31,967 18,457 1.7 0.003 8.2 0.023

26 8,515 3,680 2.3 29,687 18,457 1.6 0.003 6.9 0.021

27 8,635 3,680 2.3 34,538 18,457 1.9 0.003 7.7 0.020

28 13,986 6,160 2.3 37,323 30,692 1.2 0.004 n/a n/a

29 15,273 6,160 2.5 32,303 30,692 1.1 0.005 5.4 0.027

30 15,275 6,160 2.5 30,689 30,692 1.0 0.005 4.4 0.023

31 8,855 4,080 2.2 22,834 19,300 1.2 0.004 5.6 0.022

32 8,560 4,080 2.1 22,096 19,300 1.1 0.004 5.5 0.022

33 9,096 4,080 2.2 24,271 19,300 1.3 0.004 6.0 0.023

34 8,836 4,080 2.2 22,196 19,300 1.2 0.004 6.1 0.025

35 9,391 4,080 2.3 25,056 19,300 1.3 0.004 5.9 0.023

36 8,642 4,080 2.1 20,970 19,300 1.1 0.004 4.3 0.018

37 9,807 4,080 2.4 21,793 19,300 1.1 0.005 n/a n/a

38 10,512 4,080 2.6 25,254 19,300 1.3 0.004 4.5 0.019

39 10,012 4,080 2.5 22,286 19,300 1.2 0.005 5.1 0.024

40 14,037 5,840 2.4 20,816 28,092 0.7 0.007 3.1 0.022

41 13,776 5,840 2.4 21,833 28,092 0.8 0.007 3.2 0.021

42 14,815 5,840 2.5 23,255 28,092 0.8 0.007 3.2 0.021

43 7,797 3,440 2.3 19,812 20,027 1.0 0.004 n/a n/a

44 7,832 3,440 2.3 17,440 20,027 0.9 0.005 n/a n/a

45 7,389 3,440 2.1 22,905 20,027 1.1 0.003 n/a n/a

46 7,099 3,440 2.1 20,075 20,027 1.0 0.004 4.6 0.017

47 6,626 3,440 1.9 21,281 20,027 1.1 0.003 5.2 0.017

48 7,605 3,440 2.2 20,972 20,027 1.0 0.004 4.4 0.016

49 7,771 3,440 2.3 17,268 20,027 0.9 0.005 3.5 0.016

50 8,206 3,440 2.4 20,194 20,027 1.0 0.004 3.8 0.016

51 8,245 3,440 2.4 21,987 20,027 1.1 0.004 4.5 0.018

52 8,513 4,080 2.1 21,283 19,300 1.1 0.004 5.3 0.022

53 8,498 4,080 2.1 20,926 19,300 1.1 0.004 n/a n/a

54 8,511 4,080 2.1 18,654 19,300 1.0 0.005 n/a n/a

55 9,157 4,080 2.2 22,891 19,300 1.2 0.004 n/a n/a

56 9,177 4,080 2.2 20,699 19,300 1.1 0.005 n/a n/a

57 9,768 4,080 2.4 20,650 19,300 1.1 0.005 n/a n/a

58 8,981 4,080 2.2 11,579 19,300 0.6 0.008 2.1 0.017

59 9,137 4,080 2.2 13,279 19,300 0.7 0.007 3.1 0.022

60 8,746 4,080 2.1 7,547 19,300 0.4 0.012 1.9 0.023

61 8,744 4,080 2.1 9,742 19,300 0.5 0.009 2.5 0.023

62 9,012 4,080 2.2 6,755 19,300 0.4 0.014 n/a n/a

63 8,720 4,080 2.1 12,803 19,300 0.7 0.007 3.3 0.023

Median: 2.3 RQ =  1.04 RK =  4.8 μeff = 0.021 ∆U = 

Variability: 0.13 σ RQ = 0.36 σ RK = , 0.33 σ μ eff = 0.19 σ ∆U =
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-9

D.4.4 Define Reference Component Performance Groups

In accordance with Section 2.4.4, the reference component data were all 

placed into a single performance group. 

D.4.5 Compute Summary Statistics 

The summary statistics for each component parameter are computed in 

accordance with Section 2.4.5, assuming an underlying lognormal 

distribution of the data. Table D-4 presents the summary statistics for the 

data set, which is information repeated from the bottom of Table D-3.

Table D-4 Summary Statistics for the Reference Component 

Parameters

Summary 

Statistic

RQ

(=VM / VD)

RK

(=KI / KD) μeff ∆ U (in/in)

Median 2.3 Q R =  1.04 K R =  4.8 μeff  = 0.021 U ∆ = 

Variability 0.13 σ RQ = 0.36 σ RK = , 0.33 σ μ eff = 0.19 σ ∆U =

D.5 Proposed Component Design Requirements

Design requirements for stapled wood shear walls are based on a 

combination of requirements in 2006 IBC International Building Code (ICC, 

2006) and ANSI/AF&PA SDPWS-2005 Special Design Provisions for Wind 

and Seismic Standard with Commentary (AF&PA, 2005), with detailing 

requirements proposed by Talbot et al. (2009) and additional requirements 

pertaining to the connections, construction, inspection, and maintenance. 

In an actual application of the Component Methodology, code requirements 

for the proposed component may not exist, and such requirements would 

need to be developed.

D.5.1 Component Design Strength and Stiffness

The proposed allowable stress design (ASD) strength of the stapled wood 

shear walls is taken from the provisions of the 2006 IBC. Based on IBC 

Table 2306.4.1, the ASD design shear strength is 395 lb/ft for a blocked 

shear wall with 11⁄2” 16 gauge staples which are spaced at 2” on-center and 

have larger than 1” penetration. This 395 lb/ft design strength applies only to

walls with a maximum aspect ratio of 2:1 (i.e., 4’, 8’, and 12’ long walls). 

Walls 3 feet in length exceed the 2:1 aspect ratio limit, and have a lower 

design shear strength of 296 lb/ft, which accounts for the 25% strength 

reduction in Section 4.3.4 of ANSI/AF&PA SDPWS-2005. 
D-10 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

Design requirements are also needed for the prediction of initial stiffness. 

For stapled wood shear walls, Equation 23-2 from 2006 IBC is used here for 

computing the wall displacement at the design load, as shown below.

Another viable option would be to consider the use of Equation 4.3-1 of 

ANSI/AFPA SDPWS-2005.

3 8 0.75 n a

vh vh h he d

Eab Gt b

∆ = ++ +

where:

a = area of boundary element (in2

)

b = wall width (feet)

da = vertical elongation of overturning anchorage at the design shear 

load (v) (inches)

E = elastic modulus of boundary element (pounds/inch/inch)

en = staple or nail deformation (inches)

Gt = panel rigidity through the thickness (pounds/inch)

h = wall height (feet)

v = maximum shear due to design loads, applied at the top of the wall 

(pounds/foot)

The IBC requirements only contain en values for 2-inch, 14 gauge staples 

(IBC Table 2305.2.2(1)). To fulfill the stiffness-related requirements of the 

acceptance criteria in Chapter 2, it is proposed that the en values for 2-inch,

16 gauge staples be a factor of 2.0 larger than the values in the IBC table for 

14 gauge staples. This 2.0 factor is a calibrated value based on test data, 

such that the stiffness ratio R R K PC K RC , ,   is equal to unity.

D.5.2 Component Detailing Requirements

The stapled wood shear wall design requirements adopt many detailing 

requirements proposed by Talbot et al. (2009). The stapled wood shear wall 

test data utilized in Section D.6 are consistent with the use of these detailing 

requirements.

The detailing requirements for the stapled wood shear wall components are

summarized as follows:

• Douglas fir-larch 2x4 studs spaced at 16” on-center (or 18” on-center for 

the 8’x3’ wall).

• Top and sill plates consist of double studs.

• Two rows of staples along perimeter of double studs (4” on-center 

providing the equivalent 2” spacing).
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-11

• Simpson Strong-Tie RSP4 type 1 connectors (SST, 2009) used for stud 

to sill plate connection (see Figure D-2). This detail was used in the tests 

to simulate the effects of vertical loads (to prevent uplift of studs from 

sill plate) so this detail would not be required for site-built shear walls 

that are expected to carry vertical load.

• Simpson Strong-Tie PHD5 hold-downs (SST, 2009) (see Figure D-2).

• Backup anchor bolt (see Figure D-2).

Figure D-2 Illustration of several stapled wood shear wall detailing 

requirements, including hold-down, stud-to-sill plate connector, 

and backup anchor bolt. Photo from Talbot et al. (2009).

• Vertical studs (3x3) at adjoining panel edges (these are only needed for 

the 8’x12’ wall).

• End post detail to minimize bending of end post with Simpson StrongTie flat strap ST6224 connecting end post to bottom sill plate (see Figure 

D-1a):

o 45-degree cut at end of the sill plate bottom stud, done to reduce 

slack in the strap and reduce crushing of the sill plate bottom stud 

(see Figure D-1a and the right side of Figure D-2).

o Strap attached by anchor bolt (on bottom) and 16 to 18 Simpson 

Strong-Tie N10 nails (SST, 2009).

• Blocking details:

o Douglas fir-larch 2x4 blocks cut 14” long and placed with the longer 

dimension against the sheathing joint (see Figure D-1d). Blocking is 

secured by two rows of staples (one on each panel) at 2” on-center. 
D-12 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

This detailing requirement applies only to the 8’x3’, 8’x 4’, and 

8’x8’ walls.

o Special provisions for the blocking region of the 8’x12’ wall, 

requiring four rows of staples (two on each panel) at 2” on-center. 

Note that this detailing requirement was changed in the middle of the 

testing program, and the new detail was only utilized for wall 

numbers 8C and 12A-12C. Talbot et al. (2009) propose this 

detailing requirement for all wall geometries. 

D.5.3 Component Connection Requirements

Both the framing members of the stapled wood shear wall and the 

connections between the wall and the rest of the structural system are 

designed to resist induced seismic forces per the design methods listed in 

Section 2.1.2 of ANSI/AF&PA SDPWS-2005. Boundary elements of the 

wall, such as end studs, are also designed to transfer design tension and 

compression forces to the rest of the structural system.

Though not explicitly demonstrated in this example, it is assumed that these 

connection requirements ensure that the inelastic behavior occurs in the 

proposed shear wall components and not in the connections between the wall 

and the balance of the seismic-force-resisting system.

D.5.4 Limitations on Component Applicability and Use

The Component Methodology requires that the configurations of the 

proposed stapled wood shear wall component be reasonably restricted to the 

range of configurations that were considered in the testing program (i.e.,

usage must be restricted to the component design space). Accordingly, the 

stapled wood shear wall component can only be used within the range of 

configurations outlined in Section D.6.1.

Additionally, since the tests were completed without applied vertical loads, 

the proposed component design provisions include a restriction to the use of 

the component to ensure that applied vertical loads would not tangibly affect 

the behavior and performance of the component. In this example, the current 

height limits in ASCE/SEI 7-10 (i.e., 65’ in high seismic regions) were 

deemed sufficient to meet the requirements of Section 2.5.4.

D.5.5 Component Construction, Inspection, and Maintenance 

Requirements

The construction, inspection, and maintenance requirements for stapled wood 

shear walls are proposed to be consistent with the general requirements for 

nailed wood shear walls contained in Chapter 23 of the 2006 IBC.
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-13

D.6 Proposed Component Test Data

The work by Talbot et al. (2009) outlined in Section D.2 is used as the source 

of data for the proposed stapled wood shear wall component. 

D.6.1 Define Proposed Component Design Space

The proposed component design space includes walls that conform to the 

detailing requirements of Section D.5.2 with the following range of 

configurations:

• Wall height and length: 8’x3’ to 8’x12’

• Aspect ratio (height/length): 2.67:1 to 0.67:1. This range is broader than 

the reference component data set, but such differences are permitted 

when the transfer of forces across the component boundary is not 

significantly affected.

• Sheathing: 7/16” OSB, Exposure 1

• Staples: 2” long, 1/2” crown, 16 gauge galvanized

• Staple spacing (on-center): 2” edge, 4” field

• Openings: No openings are included in test specimens. While openings 

are expected in wood light-frame buildings, since only full height piers 

(without openings) were tested, only full height piers will be considered 

as part of the seismic-force-resisting system. 

D.6.2 Select Component Configurations for Testing

The component configurations selected for testing should span the 

component design space, in accordance with Section 2.6.2. In this example, 

the configurations tested by Talbot et al. (2009) are utilized. Within these 

configurations, the only variable is wall length, which is varied to 3’, 4’, 8’, 

and 12’. For a more complete evaluation of stapled wood shear walls, 

additional variables such as staple spacing, staple length, sheathing thickness,

can be included.

D.6.3 Perform Cyclic-Load and Monotonic-Load Tests

The Component Methodology requires that both cyclic-load and monotonicload data sets are provided for the proposed component. In this test example, 

only the cyclic-load data set is utilized, and monotonic-load data are not 

compiled because monotonic-load data are not available. This test 

application assumes that all acceptance criteria associated with monotonicload data are fulfilled, and the quality rating of the test data has not been

degraded due to the exclusion of monotonic-load data.
D-14 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

The Talbot et al. (2009) tests were conducted at a rate of one cycle per 

second (with a sampling rate of 50 samples/second) utilizing the SPD loading 

protocol. The nailed wood shear wall tests were done with lower strain rates

than the stapled shear wall tests, but this is judged to be acceptable according 

to the requirements of Section 2.2. Figure D-3 shows an example of the 

cyclic response for specimen 8C, which is an 8’x8’ wall. The stapled wood 

shear wall data was interpreted in the same manner as the nailed wood shear 

wall data.

Figure D-3 Illustration of cyclic response of stapled wood shear wall 

specimen 8C (Talbot et al., 2009).

D.6.4 Interpret Proposed Component Test Results

Data were compiled for each of the 13 stapled wood shear wall tests and 

Table D-5 presents important component parameters for each of the tests. 

The data in Table D-5 technically fulfill the minimum test data requirements 

of Section 2.2.2, which specifies that a minimum of four configurations (with 

at least two specimens per configuration) are needed for each component 

performance group. Even so, the proposed component design space that is 

defined in Section D.6.1 and sampled by these component configurations is 

extremely narrow. The component configurations adequately sample this 

narrow design space, but additional component configurations would still be

desirable to provide more confidence that the test results accurately reflect 

the behavior of the design space for stapled wood shear walls. 

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

-15

-10

-5

0

5

10

15

Drift (in/in)

Force (kips)

Cyclic Response
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-15

Table D-5 Summary of Important Component Parameters for Proposed Component Data Set

Wall 

Number

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD (lb) RQ = 

VM / VD

KI

(lb/in)

KD

(lb/in)

RK = 

KI / KD

ΔY,eff

(in/in) μeff

ΔU 

(in/in) ∆ Uj

3-A#1 2,900 888 3.3 5,015 4,307 1.2 0.006 3.7 0.022

0.025

3-A#2 3,900 888 4.4 2,714 4,307 0.6 0.015 1.7 0.026

3-B 3,900 888 4.4 4,603 4,307 1.1 0.009 2.8 0.025

3-C 3,700 888 4.2 3,085 4,307 0.7 0.012 2.3 0.029

4-A 5,500 1,580 3.5 4,461 6,463 0.7 0.013 1.8 0.024

4-B 5,200 1,580 3.3 4,384 6,463 0.7 0.012 1.6 0.020 0.021

4-C 4,800 1,580 3.0 7,038 6,463 1.1 0.007 2.7 0.019

8-A 8,700 3,160 2.8 16,734 13,461 1.2 0.005 2.4 0.013

0.013

8-B 10,100 3,160 3.2 20,694 13,461 1.5 0.005 2.6 0.013

8-C1 11,300 3,160 3.6 21,917 13,461 1.6 0.005 2.9 0.016 --

12-A1 21,700 4,740 4.6 27,079 20,474 1.3 0.008 2.4 0.020

12-B 0.019 1 19,900 4,740 4.2 21,239 20,474 1.0 0.010 1.7 0.017

12-C1 22,400 4,740 4.7 26,786 20,474 1.3 0.009 2.2 0.019

Median: 3.7 RQ =  1.04 RK =  2.3 μeff = 0.020 ∆U = 

Variability: 0.18 σ RQ = 0.32 σ RK = , 0.25 σ μ eff = 0.25 σ ∆U =

Note 1: Twice as many staples in the blocking region.

D.6.5 Define Proposed Component Performance Groups and 

Compute Summary Statistics

The proposed component data are all placed into a single performance group, 

consistent with the requirements of Section 2.6.5, and also consistent with 

the approach taken for the reference component data set. Table D-6 presents 

the summary statistics for the stapled wood shear wall test data.

It should be noted that the design requirements change slightly between 

various wall configurations in the data set, with the 3’ wide wall having a 

slightly different design strength (due to an aspect ratio exceeding 2:1), and 

the 12’ wall having an additional detailing requirement of twice the staples in 

the blocking region. Although strength and stiffness values differ between 

various wall configurations, these differences were considered to be minor so 

that the test data need not be separated into multiple performance groups. 
D-16 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

Table D-6 Summary Statistics for Proposed Component 

Parameters

Summary 

Statistic

RQ

(=VM / VD)

RK

(=KI / KD) μeff ∆ U (in/in)

Median 3.7 QR =  1.04 K R =  2.3 μeff  = 0.020 U ∆ = 

Variability 0.18 σ RQ = 0.32 σ RK = , 0.25 σ μ eff = 0.25 σ ∆U =

D.7 Evaluate Quality Ratings

D.7.1 Quality Rating of Test Data

According to the requirements of Section 2.7.1, the quality of the reference 

component test data is rated as Superior. This comes from a high rating for 

completeness and robustness and a high rating for confidence in the test 

results. The high rating for completeness and robustness is based on all of 

the important testing issues being addressed and the expectation that all 

important failure modes were uncovered in the testing. The high rating for 

confidence in the test results is based on the large number of test data, as well 

as multiple researchers and labs being involved in completing the testing. 

The quality of the proposed component test data is rated as Good, based on a 

high rating for completeness and robustness, and a medium rating for

confidence in the test results. The medium confidence rating is based on the 

limited number of tests – only four configurations and 13 specimens, and the 

fact that the same researcher and lab completed all of the tests used for 

evaluation. Note that data from Talbot et al. (2009) are limited with respect 

to the Component Methodology (e.g., numbers of tests) because the 

experimental program was developed for other purposes.

As noted previously, the data set does not include monotonic-load data, 

which is required for the proposed component. For the purpose of this test 

application, this shortcoming in available data has been overlooked, and was

not considered in the quality rating of the test data.

D.7.2 Quality Rating of Design Requirements

According to the requirements of Section 2.7.2, the quality of the reference 

component design requirements is rated as Good. This slightly lower rating 

is due to nailed wood shear walls having less stringent detailing 

requirements, as compared with the extensive detailing requirements used in 

the design of stapled wood shear walls.

The quality of the proposed component design requirements is rated as

Superior. This is based on high ratings for both completeness and robustness 
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-17

and confidence in the design requirements, based on the extensive detailing 

requirements being enforced for the stapled wood shear walls (see Section 

D.5.2), as well as the substantial amount of experience and mature 

construction practices that exist for nailed wood shear wall components.

D.8 Evaluate Component Equivalency 

D.8.1 Overview 

This section discusses the acceptance criteria of the Component 

Methodology and evaluates the possible equivalency between stapled and 

nailed wood shear walls.

D.8.2 Requirements Based on Cyclic-Load Test Data: Strength 

and Ultimate Deformation 

The median ultimate deformation of each proposed component performance 

group is required to fulfill Equation 2-1, as follows: 

∆ ∆  

U,PC U,RC U Q ≥ P P

When evaluating the above equation, the median ultimate deformation,

∆U RC ,  , from the reference component data set is 0.021 (from Table D-4). 

The uncertainty penalty factor, PU, is based on the quality ratings discussed 

in Section D.7.1. Incorporating these quality ratings into Table D-7 shows 

that the uncertainty penalty factor, PU, equals 1.00.

The penalty factor for strength is based on the median proposed and 

reference component strength ratios, as follows:

3.7 1.6

2.3

Q,PC

Q,RC

R

R = =





Linear interpolation based on Table D-8 results with strength penalty factor, 

PQ, as 1.17. Incorporating these values leads to the following requirement 

check, showing that the median ultimate deformation value of 0.020 does not 

meet this requirement.

0.020 0.021 1.00 1.17 0.025 < = ( )( )( ) FAIL
D-18 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

Table D-7 Penalty Factor to Account for Uncertainty (from 

Table 2-3)

Penalty Factor for Uncertainties (PU)

Quality Rating of 

Proposed Component 

Test Data

Quality Rating of Proposed Component Design 

Requirements Relative to Reference Component 

Design Requirements

Higher Same Lower

Superior 0.95 1.00 1.15

Good 1.00 1.05 1.25

Fair 1.15 1.25 1.40

Table D-8 Penalty Factor to Account for Difference in Component 

Strengths (from Table 2-4)

Penalty Factor for Differences in Strength (PQ)

PQ PQ

0.50 1.88 1.10 1.00

0.60 1.55 1.20 1.00

0.70 1.31 1.30 1.04

0.80 1.14 1.40 1.09

0.90 1.00 1.50 1.13

1.00 1.00 1.80 1.24

1.10 1.00 2.00 1.32

The median value of ultimate deformation for each geometric configuration,

∆Uj,PC

 , must meet the requirement of Equation 2-2, as shown below. 

According to Table D-4, the variability in ultimate deformation, σ ∆U,RC , is 

0.19 for the reference component data.

Since the ratio of the median and proposed reference component strengths is 

greater than 1.2 but not greater than 2.0, the exception of Section 2.8.2 would 

be invoked. Accordingly, provisions would need to be added to the proposed 

component design requirements stating that the force-controlled and 

capacity-designed components of the reference SFRS must be designed for 

the expected strength of the proposed components (i.e., the component 

design strength scaled up by a factor of RQ,PC

 ).

∆ σ∆  

Uj,PC ≥ − (1 1.5 ∆U,RC U,RC U Q )( ) P P

∆Uj PC , ≥ −  ⋅ 1 1.5 0.19 0.021 1.00 1.17 0.018 ( ) ( ) ( )( ) =   

Table D-9 summarizes the above acceptance criteria checks being applied to 

the full performance group and to each individual geometric configuration. 

R R Q,PC Q,RC

  R R Q,PC Q,RC 
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-19

The stapled wood shear walls fail the basic ultimate deformation acceptance 

criterion for the full performance group; they also fail the individual 

configuration check for the 8’x8’ panel configuration. 

Table D-9 Evaluation of Equivalency Acceptance Criteria for Stapled Wood 

Shear Walls

Wall 

Number

Deformation Capacity Acceptance Check

∆ U

Median ∆ U And 

∆ Uj

 Accept. Criteria Pass/ Fail

Perf. Group I: 0.020 ∆

U = 0.025 FAIL

3-A#1 0.022

0.025 0.018 Pass

3-A#2 0.026

3-B 0.025

3-C 0.029

4-A 0.024

4-B 0.020 0.021 0.018 Pass

4-C 0.019

8-A 0.013

0.013 0.018 FAIL

8-B 0.013

8-C 0.016 -- -- --

12-A 0.020

12-B 0.017 0.019 0.018 Pass

12-C 0.019

D.8.3 Requirements Based on Cyclic-Load Test Data: Effective 

Initial Stiffness

To fulfill the requirements of Section 2.8.3 (Equation 2-3), design provisions 

for initial stiffness were calibrated based on the observed stiffness values of 

the proposed and reference components. In this example, this was done by 

adjusting the en value for staple slip in the design displacement equation, as

discussed in Section D.5.1. By completing the calibration of the 

displacement prediction equation, the ratio was made equal unity. A value of 

1.0 easily falls within the range of 0.75 to 1.33 determined by Equation 2-3, 

so the design stiffness provisions fulfill this acceptance criterion.

0.75 1.33 K,PC

K,RC

R

R

≤ ≤ 



1.04 0.75 1.33

1.04

≤ ≤ OK
D-20 D: Test Application: Stapled Wood Shear Wall Components FEMA P-795

D.8.4 Requirements Based on Cyclic-Load Test Data: Effective 

Ductility Capacity 

In order to fulfill the requirements of Section 2.8.4 (Equation 2-4), and to 

ensure at least rough parity between the post-yield deformation capacity (and 

energy dissipation capacity) of the proposed and reference components, the 

median ductility capacity of the proposed components, μeff,PC  , must be at least 

half as large as the median ductility capacity of the reference components,

μeff,RC  . In this example, μeff,PC  = 2.3 and μeff,RC  = 4.8, so this requirement is 

not met. 

Because Equation 2-4 was not fulfilled, the exception in Section 2.8.4 would 

be invoked in this example, and the design requirements would need to limit 

the lateral force in proposed component to less than 25% of the design 

seismic force along any framing line in the building. 

D.8.5 Requirements Based on Monotonic-Load Test Data: 

Ultimate Deformation

As discussed previously, monotonic-load test data for stapled wood shear 

wall components were not available, so monotonic criteria were not 

evaluated. 

D.8.6 Summary of Component Equivalency Evaluation

In summary, the stapled wood shear wall components passed the acceptance 

criteria related to initial stiffness but failed the criteria related to ultimate 

deformation capacity. Stapled wood shear wall components also failed the 

ductility capacity criterion, but this can be addressed though modification of 

design requirements. 

D.9 Iteration: Evaluate Component Equivalency with 

Modifications

In order to demonstrate equivalency stapled wood shear wall design 

requirements would need to be modified, or stapled wood shear wall test data

would need to be expanded. Possible alternative approaches include the 

following:

• Changes to reduce the strength penalty factor, PQ, to 1.0. One approach 

would be to refine the stapled wood shear wall design strength 

requirements (Sections 2.5.1 and D.5.1). Since the proposed component 

is stronger than the reference component, another approach would be to 

modify the stapled wood shear wall design provisions to prohibit mixing 

of the reference and proposed components in a building (Sections 2.8.2

and D.5.4).
FEMA P-795 D: Test Application: Stapled Wood Shear Wall Components D-21

• Generation of more stapled wood shear wall data to achieve a data 

quality rating of Superior and a resulting value of PU = 0.95.

• Identification of the behavioral problem with the 8’x8’ panel 

configuration, fix the problem, and perform more 8’x8’ panel testing to 

prove that the problem has been resolved.

• Improvement in stapled wood shear wall detailing requirements to 

achieve larger ultimate deformations in tested wall components.

Data in this chapter suggest that stapled wood shear wall components could 

pass the component equivalency criteria if the above items were 

implemented.

D.10 Summary of Component Equivalency Evaluation of 

Stapled Wood Shear Walls

Possible equivalency between stapled wood shear walls and nailed wood 

shear walls was evaluated. Due to limitation in available data this 

application focused on a narrow range of possible stapled wood shear wall

configurations. Additionally, monotonic-load test data were not available. 

Results are summarized in Table D-10. Overall, stapled wood shear wall 

components were not found to be equivalent to nailed wood shear wall 

components based on the criteria of the Component Methodology.

Table D-10 Summary of Acceptance Criteria Evaluation for Proposed Stapled Wood Shear 

Component

Acceptance Criteria Equation 

Reference

Pass/Fail

Requirement Based on Cyclic-Load Test Data

Ultimate Deformation Capacity 

(performance group) ∆ ∆  

U,PC U,RC U Q ≥ P P 2-1 Fail

Ultimate Deformation Capacity 

(individual configurations) , (1 1.5 , , )( ) ∆ σ∆  

Uj PC ≥ − ∆U RC U RC U Q P P 2-2 Pass 3,

Fail 1

Initial Stiffness Ratio 0.75 1.33 K,PC

K,RC

R

R

≤ ≤ 

 2-3 Pass

Effective Ductility Capacity eff ,PC eff ,RC ~ . ~

μ ≥ 0 5μ 2-4 Fail

Requirements Based on Monotonic-Load Test Data

Ultimate Deformation Capacity

(Option 1) ∆ ∆  

UM PC UM RC U Q , , ≥ P P 2-5 n/a

Ultimate Deformation Capacity

(Option 2) , , 1.2 ∆ ∆ UM PC ≥ D PP C U RC U Q    2-6 n/a

FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-1

Appendix E

Test Application: BucklingRestrained Brace Components

E.1 Introduction

This appendix illustrates the application of the Component Methodology to 

the possible substitution of buckling-restrained braces for conventional 

braces in a special steel concentrically-braced seismic-force-resisting system.

The objective is to determine whether or not equivalency based on 

comparison of test data for the proposed component (buckling-restrained 

braces) and the reference component (conventional braces) can be achieved. 

This test application assumes that buckling-restrained braces (BRBs) are not 

currently approved, and that they are proposed as an alternative to 

conventional braces in the code-approved special steel concentrically braced 

frame system listed in Table 12.2-1 of ASCE/SEI 7-10 Minimum Design 

Loads for Buildings and Other Structures (ASCE, 2010). Seismic design 

coefficients for the reference system are R = 6, Cd = 5, and Ωo = 2. 

The findings of this test application are presented with two caveats. First, 

differences between buckling-restrained braces and conventional braces may 

warrant a system-level evaluation approach, as outlined in the FEMA P-695

Methodology, rather than the component-level approach of the Component 

Methodology. A detailed evaluation of system behavior may be appropriate

because of: (1) differences in the transfer of forces from the component to the 

system for BRBs as compared with conventional braces; and (2) the 

potentially important role of beams, columns and connections in the overall 

behavior of braced frame systems. Second, available data are limited, and 

conventional brace (reference component) data do not reflect the full range of 

the possible brace designs and properties and may represent a lower bound 

on brace ductility and performance. More data are needed for a complete 

evaluation.

The steps in this test application follow the requirements of the Component 

Methodology defined in Section 2.2 through Section 2.8.
E-2 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

E.2 Description of Buckling-Restrained Braces 

In steel braced frame seismic-force-resisting systems lateral forces create 

axial forces in brace components, and energy is dissipated through the

hysteretic response of the braces. Conventional braces typically have 

significant strength and deformation capacity under tensile loading, but can

buckle in compression, leading to a reduction in compressive load-carrying 

capacity and energy dissipation in the member. Under repeated cycles of 

loading, braces can fracture, leading to a redistribution of loads to the beams 

and columns in the framing system. On the other hand, buckling-restrained 

braces (BRBs), in use in Japan since the mid-1980s (Black et al., 2002), have

exhibited nearly symmetric behavior under tension and compression loads. 

Failure can occur if deformations are large enough to fracture the core plate

or exceed compression deformation limits. Figure E-1 shows typical force 

deformation response from cyclic loading on conventional and bucklingrestrained braces.

Figure E-1 Conventional (left) and buckling-restrained (right) braces under 

cyclic loading (from Kumar et al., 2007).

Steel braces can be made of wide-flange or HSS sections with bolted or 

welded gusset plate connections to beams and columns. Buckling-restrained

braces consist of a ductile steel core that carries the entire axial load in the 

member with a mortar- or concrete-filled steel tube confining the core. The 

concrete in the tube restrains the steel core from buckling, but is prevented 

from bonding with the core so that axial loads cannot be transferred to outer 

steel tube. Isolation of the steel core is accomplished with a layer of 

unbonding material. Figure E-2 illustrates the different parts of a BRB.

This test application considers buckling-restrained braces designed according 

to AISC 341-10 Seismic Provisions for Structural Steel Buildings (AISC, 

2011). These design provisions ensure that the braces are able to permit 

axial elongation and shortening in the steel core up to deformations 

corresponding to twice the design story drift. The design strength is based on 

the size and strength of the steel core material, and must be sufficient to resist 

relevant load combinations. In order to show that a buckling-restrained brace
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-3

meets the requirements for strength and inelastic deformation, individual 

braces and brace assemblages are required to undergo cyclic qualification 

testing according to Section K3 of AISC 341-10. Design of brace 

connections and adjoining members of the braced frame is based on the 

maximum strength of the buckling-restrained brace. Buckling-restrained 

braces are not designed to be part of the gravity framing system.

Figure E-2 Features of a typical buckling-restrained brace (from Tsai and 

Hsiao, 2008). 

E.3 Evaluation of Applicability Criteria

The Component Methodology applicability criteria address the suitability of 

the reference SFRS, the adequacy of the reference and proposed component 

design criteria and test data, and the characteristics of the proposed 

component. The adequacy of the design criteria and test data for the 

reference and proposed component data are assumed to be sufficient for the 

purpose of establishing equivalency in the Component Methodology. 

An important part of evaluating the applicability of the Component 

Methodology is the definition of the component boundary, which separates

the component of interest from the seismic-force-resisting system. As 

illustrated in Figure E-3, the reference component is defined as a pair of 

braces. Pairs of braces (rather than individual braces) were selected because 

conventional braces have very different behavior in the tensile and 

compressive directions, and a single brace (acting in either tension or 

compression) will not have the same seismic response as a pair of braces. 

Furthermore, AISC 341-10 requires that in special steel concentrically braced 

frames “along any line of bracing braces shall be deployed in alternate 

directions such that, for either direction of force parallel to the bracing, at 

least 30%, but no more than 70% of the total horizontal force is resisted by 
E-4 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

tension braces.” Although there are various design alternatives that meet this 

requirement, a pair of braces with one brace acting in compression and one

acting in tension is a commonly used solution. The compressive strength of 

braces with slenderness ratios used in special concentrically braced frames 

have approximately 30% to 40% of the strength of a pair of tension and 

compression braces. 

Defining the reference component as a pair of braces ensures that the 

component boundary and transfer of forces across the component boundary

are as similar as possible for reference and proposed components. Based on 

this definition, it is assumed that the reference component can be tested either 

in pairs of braces (e.g., X-brace configurations) or as single braces assumed 

to resist lateral forces in parallel with another identical single brace. 

Figure E-3 Illustration of reference component and definition of 

component boundary (Engelhardt, 2007). 

In this test application, the proposed component is defined as a single 

buckling-restrained brace and its end connections, as shown in Figure E-4. 

Provided that gusset plates and connections are designed for the maximum 

brace force, inelastic action is expected to occur in the BRB. 

With the component boundaries of proposed and reference components 

defined, the balance of seismic-force-resisting system is essentially 

unchanged by the replacement of reference components with proposed 

components. In both cases, the inelastic deformation occurs primarily in the 

braces through compression buckling or tension and compression yielding.

In actuality, buckling-restrained and conventional braces may induce 

significantly different axial forces in columns because of differences in 

configuration and angle between the proposed and reference component. In 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-5

addition, beams, columns, and beam-column connections may influence 

structural response. These differences are set aside in order continue with the 

test application. Nevertheless, there are significant questions as to whether 

the applicability criteria are fully satisfied in this example.

Figure E-4 Illustration of proposed component and definition of 

component boundary (Photo from Star Seismic).

E.4 Reference Component Test Data

This section describes the conventional brace reference component test data 

set compiled specifically to include braces that may be employed in the 

special steel concentrically braced frame system. 

E.4.1 Define Reference Component Design Space 

In this test application, the reference component design space is intended to 

represent the range of possible braces in the special steel concentrically 

braced frame system. The design space includes braces of varying size and 

strength, and braces with different sections, including wide-flange, angle, 

tube, and others. While brace detailing, brace slenderness, or width-tothickness ratios may also have a critical influence on the response, and 

should be considered, special steel concentrically braced frames must satisfy

limitations on width-to-thickness ratios for highly ductile members such that 

the range of sections that can be used is significantly restricted (AISC, 2011). 

The component design space is intended to represent conventional brace 

systems with any of the approved connection types, such as welded or bolted 

gusset plate connections. 

The reference component design space includes a variety of system 

configurations, including diagonal, chevron, V-brace, and X-brace 

configurations. However, since it is assumed that the primary configuration 

issue is the number of braces acting in tension and compression, the single-
E-6 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

brace and X-brace data collected are taken to be representative of the 

commonly used brace configurations. K-brace configurations are prohibited 

in special steel concentrically braced frames, and have been excluded from 

the reference component data set.

The reference component data set also has limited variation in section 

properties, size, and configuration such that it does not fully represent the full 

reference component design space. These limitations affect the test data 

quality ratings that are assigned. 

E.4.2 Define Reference Component Performance Groups 

Within the reference component design space, differences in brace 

slenderness, brace configuration, or section properties may lead to different 

failure modes and load-deformation responses. Such fundamental 

differences in behavior could lead to the assigment of different performance 

groups. However, performance groups defined for proposed and reference 

components should be compatible. Since conventional and bucklingrestrained braces have different failure modes and component strengths (e.g.,

buckling-restrained braces are often strong enough to replace several 

conventional braces), it is difficult to divide reference and proposed 

components into an analogous set of performance groups that can be

systematically compared. Therefore, all buckling-restrained braces are seen 

as a potential substitute for conventional braces in the special steel 

concentrically braced frame system, allowing all conventional braces to be

placed in a single performance group. In addition, all buckling-restrained 

braces are also placed in a single proposed component performance group.

E.4.3 Compile or Generate Reference Component Test Data 

In this test application, data on “special” or similar conventional braces are 

obtained from Johnson (2005), Kotulka (2007), Clark, (2009) and Powell 

(2010). Much of the available test data, however, including Astaneh-Asl et 

al. (1982), El-Tayem and Goel (1985), Aslani and Goel (1989), and 

Wakabayashi et al. (1977 and 1980) were not included in the reference 

component data set because the characteristics of the tested braces or 

connections might not satisfy AISC 341-10 provisions for special braces. 

As a result, a limited set of brace tests that includes special or similar braces 

for the Component Methodology equivalency comparison were assembled. 

Even so, in some cases, specific specimens may have characteristics that 

differ from those that would be permitted in AISC 341-10. These limitations 

should be considered in interpreting the reference component data. 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-7

The data gathered include 19 configurations, summarized in Tables E-1 and 

E-2. Most configurations include just one specimen, although two 

configurations have two or more identical specimens. Among the X-brace 

tests listed in Table E-1, both tube and wide flange sections are used for test 

specimens, all with welded gusset plate connections. The single brace tests

listed in Table E-2 include tubular and wide flange sections, with either 

welded or bolted gusset plate connections with varying properties. 

Table E-1 Summary of Conventional Brace Configurations in the Reference Component Data Set: 

X-Brace Tests

Test 

Index

Test Specimen 

ID

Area 

(in2)

Length 

(in) Brace Section* Connection Type Failure Mode

1 TCBF1-HSS-R 6.15 275.7 HSS 125x125x9 Gusset Plate(Weld) Brace Buckling

2 TCBF1-HSS-T 6.15 275.7 HSS 125x125x9 Gusset Plate(Weld) Brace Buckling

3 TCBF1-WF-R 7.94 275.7 H 175x175x7.5x11 Gusset Plate(Weld) Brace Buckling

* Section properties defined in millimeters.

Table E-2 Summary of Conventional Brace Configurations in the Reference Component Data Set: 

Single Brace Tests 

Test 

Index

Test Specimen 

ID

Area 

(in2)

Length 

(in) Brace Section* Connection Type Failure Mode

4 HSS-01 6.94 134.6 HSS-5x5x3/8 Gusset Plate(Weld) Weld Fracture

5 HSS-02 6.94 157.8 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

6 HSS-03 6.94 157.8 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

7 HSS-05 6.94 157.8 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

8 HSS-04 6.94 153.7 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

9 HSS-12 6.94 134.6 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

10 HSS-13 6.94 157.3 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

11 HSS-17 6.94 157.3 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

12 HSS-14 6.94 157.7 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

13 HSS-15 6.94 162.1 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

14 HSS-16 6.94 131.3 HSS-5x5x3/8 Bolted Splice Plate Fracture

15 HSS-18 6.94 157.7 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

16 HSS-19 6.94 103.6 HSS-5x5x3/8 Gusset Plate(Bolt) Plate Fracture

17 HSS-20 6.94 157.7 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

18 HSS-21 6.94 157.7 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

19 HSS-22 6.94 157.3 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

20 WF-23 7.34 158.7 W 6x25 Gusset Plate(Weld) Weld Fracture

21 HSS-24 6.94 157.7 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

22 HSS-25 6.94 148.8 HSS-5x5x3/8 Gusset Plate(Weld) Brace Fracture

* Section properties defined in inches.
E-8 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

All specimens have slenderness ratios, Kl/r, between 49 and 100. For braces 

in V or inverted-V configurations in special concentrically braced frames, the

ratios are limited to /4/ Kl r E F ≤ y . For 50 ksi steel, this limit 

corresponds to a maximum slenderness ratio of 96. Width-to-thickness 

ratios, b/t, of the specimens are all approximately 13 to 14. Since the 

prescribed maximum b/t for highly ductile compression elements is 

0.55 / 13.2 E Fy = in AISC 341-10, these specimens are near the maximum 

allowable slenderness and width-to-thickness ratios for special steel 

concentrically braced frames. 

This data set satisfies the requirement that the reference component include 

at least four tested configurations per performance group. The Component 

Methodology also requires a minimum of two identical test specimens for 

each component configuration. The data compiled do not meet this 

requirement, as few of the configurations have been tested repeatedly. Even 

so, the lack of repeated configurations may be acceptable according to the 

provisions in Chapter 2, provided that there is no significant variation in the 

response among the different test specimens. Otherwise, more data may be 

needed. 

There are no monotonic-load data included in the reference component test 

data set but the Component Methodology permits the use of reference 

component data with cyclic-load data only. Examples of reference 

component test data are shown in Figures E-5 and E-6. The data were 

available graphically (rather than digitally) so key force and deformation 

quantities were digitized from plots of cyclic-load test data. 

Figure E-5 Illustration of cyclic response of X-brace configuration tested by 

Clark (2009) for a two-story frame configuration. 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-9

Figure E-6 Illustration of cyclic response of single HSS-section brace from 

Kotulka (2007) for a 1-story, 1-bay frame. 

E.4.4 Interpret Reference Component Test Results 

Figure E-7a shows the cyclic response of one X-brace test, with the cyclic 

envelope curve drawn according to the requirements of Section 2.2.2 

superimposed. The envelope curve is used to determine the parameters that 

are utilized in the acceptance criteria of the Component Methodology. 

The force quantity used to compare response between the reference and 

proposed component is the axial force in the brace or the total axial force in 

the X-braces (kips). The displacement quantity is the axial elongation in the 

brace, l, normalized by the length of the brace, i.e., in/in. In Figure E-7b, the 

cyclic envelope curve has been converted from horizontal force and 

deformation quantities obtained from frame tests to axial force and 

normalized axial deformation quantities. This estimation assumes that the 

lateral force is taken entirely by the brace and that all lateral deformation in 

the frame comes from brace axial elongation and shortening. The axial 

force, FA, is calculated as F F A H = / cos(θ ) where FH is the horizontal force

on the frame and θ is the brace orientation angle measured counterclockwise 

from horizontal to brace axis. FA is approximately 1.41FH for θ = ° 45 . The 

axial deformation, DA, can be computed from the horizontal deformation, DH,

as D D A H = cos . (θ ) If the horizontal deformation is reported as lateral drift

(such that D h H H = ∆ ) and the axial deformation is normalized by brace 

length l (such that / ), ∆A A = D l A H cos 0.707 ( ) H h h

l l ∆ = ∆θ ∆ ≈ .

For tests conducted in a frame, these assumptions overly simplify the actual 

behavior as the frame members will carry some of the lateral force and 

connections and other members contribute to the total frame deformation.

For example, the test data in Figure E-5 show very little strength loss after 
E-10 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

brace buckling, likely because the moment resistance of frame members is 

significant. As a result, when force and deformation quantities of the frame

are converted to force and deformation quantities of a brace under the 

assumptions described above, the values obtained overestimate both the force 

and the deformation in the brace. For the reference component, 

overestimating the ultimate brace deformation is conservative, since it 

requires that the proposed component data satisfy a higher ultimate 

deformation threshold. 

(a)

(b)

Figure E-7 Cyclic test data for X-brace specimen TCBF-HSS-R (Test Index 

1) tested by Clark (2009) showing: (a) cyclic response and cyclic 

envelope curve; and (b) cyclic envelope curve and component 

response quantities, in terms of brace axial force and 

elongation. The frame height and width are 6660 mm. 

Lateral
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-11

The specimen in Figure E-7 has maximum axial strength in positive and 

negative directions of 717.6 kips and 743.4 kips, respectively, for an average 

QM = 730.5 kips. For consistency, units were converted from kN to kips. 

The design strength, QD, of the braces is computed as the sum of the brace 

design strength in tension and compression, because the component is 

defined as a pair of braces, one in compression and one in tension. The 

design tensile strength is given by AISC 341-10 as follows:

φ φ tn t y g P FA =

where t = 0.90, Fy is the nominal yield stress of the type of steel being used,

and Ag is the gross area of the member. The design compressive strength is 

φ φ c n c cr g P FA =

where c = 0.90. Fcr is the flexural buckling stress and depends on the 

slenderness ratio of the brace, Kl /r. For braces, the effective length factor, 

K, is equal to 1.0. For specimens with / 4.71 / , Kl r E F F ≤ y cr is determined 

from:

[0.658 ]

y

e

F

F F F cr = y

The elastic critical buckling stress, Fe, is: 

2

2 ( ) e

E F Kl

r

π =

For the example in Figure E-7, the yield stress is 46 ksi, the area is 6.15 in2

, 

l/r is 78, and QD = 424 kips. The ratio of maximum strength to design 

strength, RQ = QM/QD, is 1.72.

Initial stiffness is computed as the secant stiffness at 40% of the peak 

strength, and the average of the positive and negative loading directions is KI

= 1327 kips/in. The design stiffness, KD, is computed simply as the stiffness 

of brace itself, i.e., K = EA/L. For the specimen of interest and the simple 

assumption, K is calculated as 646.5 kips/in. Since there are two braces

acting in parallel to resist the lateral force, KD is 1293 kips/in and RK, the ratio 

of measured to design stiffness, is 1.03. (Note that these computations ignore 

the influence of other frame elements on lateral stiffness. The calculation of 

design stiffness could easily be improved by estimating the stiffness of the 

entire frame/brace/connection specimen that was tested). 

The ultimate deformation, ∆U, is 3.84 inches in the negative loading direction 

and 3.94 inches in the positive loading direction. The final average ultimate 
E-12 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

deformation is 3.89 inches, which corresponds to ∆U = 0.014 in/in for this 

specimen, when normalized. Per Section 2.2.2, the value of ΔU would be 

affected if the vertical load carrying ability of the specimen was

compromised. Since braces are assumed to carry no gravity load, 

consideration of vertical load carrying capacity is not relevant. 

The Component Methodology also requires determination of the effective 

yield displacement, ∆Y,eff. For this specimen, ∆Y,eff is computed separately in 

the positive and negative directions and the average value is ∆Y,eff = 0.55 in. 

When normalized by brace length, ∆Y,eff = 0.0020 in/in. Chapter 2 defines 

effective ductility capacity as the ratio of the ultimate deformation, ∆U, to the 

effective yield displacement, ∆Y,eff, in each direction. The specimen shown 

has an average effective ductility capacity, μeff = 7.1. 

Figure E-8a shows the cycle response of one of the single-brace tests with the 

cyclic envelope curve drawn according to the requirements of Chapter 2. 

Because seismic-force-resisting system requirements in AISC 341-10 do not 

allow single braces to be used, the single-brace test data are modified to 

represent a pair of braces. Assuming that there is no significant interaction 

between the two braces, we assume that, for any given level of deformation, 

the response in the compressive and tensile directions can be added to 

represent the behavior of a pair of braces. This process is illustrated in 

Figure E-8b, where the total backbone curve represents the sum of the cyclic 

envelope curves in the two loading directions. The design values of strength 

and stiffness are determined as before. (Note: In some tests, the brace 

buckles before any excursions in the tensile direction occur. In such a case, 

estimates of initial stiffness are based only on the first loading cycle in the 

compressive direction). 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-13

(a)

(b)

Figure E-8 Plot of test data for specimen HSS-12 (Test Index 9) from Kotulka 

(2007) showing: (a) cyclic response and cyclic envelope curve; and 

(b) combination of response in the positive and negative direction 

for calculation of component parameters for single brace specimen,

tested in a 1-bay, 1-story frame with height and width of 12 ft. 

For each of the tests included in the reference component data set, a cyclic 

envelope curve was drawn similar to those in Figures E-7 and E-8 in order to 

obtain component parameters for establishing equivalency. Table E-3 

provides values of important response quantities, such as strength, stiffness,

ductility, and deformation capacity, for each specimen of the reference 

component data set. 

E.4.5 Compute Summary Statistics

The summary statistics for each component parameter are computed 

according to the requirements of Chapter 2 and presented in Table E-4. 

Statistical values of component parameters combine data from X-braces and 

single braces (converted to pairs).

-3 -2 -1 0 1 2 3

-400

-200

0

200

400

600

800

Axial Displacement (in)

Axial Force (kips)

QM = 768 kips

0.8QM 

∆u = 1.4 in

0.4QM 

KI = 1962 kips/in

∆y,eff = 

0.39 in
E-14 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

Table E-3 Summary of Important Component Parameters for the Reference Component Data Set

Test 

Index

Strength Stiffness Ductility Deformation 

Capacity

QM

(kips)

QD

(kips)

RQ KI

(kip/in)

KD

(kip/in)

RK ∆Y,eff

(in/in)

μeff ∆U (in/in)

1 730 424 1.7 1327 1293 1.0 0.0020 7.1 0.014

2 642 429 1.5 1398 1293 1.1 0.0017 11.3 0.019

3 668 573 1.2 1653 1670 1.0 0.0015 14.5 0.021

4 747 459 1.6 2204 2802 0.79 0.0025 4.9 0.012

5 709 465 1.5 2025 2551 0.79 0.0022 4.5 0.010

6 742 465 1.6 1841 2551 0.72 0.0026 3.9 0.010

7 708 465 1.5 1643 2551 0.64 0.0027 4.3 0.012

8 695 470 1.5 1803 2618 0.69 0.0025 4.0 0.010

9 768 490 1.6 1962 2990 0.66 0.0029 3.6 0.010

10 715 466 1.5 2106 2559 0.82 0.0022 6.1 0.013

11 719 466 1.5 1617 2559 0.63 0.0028 4.9 0.014

12 716 465 1.5 1704 2552 0.67 0.0027 5.0 0.013

13 696 461 1.5 1562 2483 0.63 0.0028 4.1 0.011

14 628 493 1.3 1447 3066 0.47 0.0033 6.3 0.021

15 665 471 1.4 2650 2552 1.04 0.0016 6.6 0.010

16 439 424 1.0 2317 3885 0.60 0.0018 2.0 0.004

17 708 489 1.4 2804 2552 1.10 0.0016 6.7 0.011

18 717 472 1.5 2391 2552 0.94 0.0019 5.4 0.010

19 604 465 1.3 2330 2559 0.91 0.0016 5.8 0.010

20 683 481 1.4 2681 2683 1.00 0.0016 9.4 0.015

21 698 496 1.4 2412 2552 0.95 0.0018 6.7 0.012

22 814 590 1.4 3824 2705 1.41 0.0014 4.0 0.006

Table E-4 Summary Statistics for the Reference Component

Summary 

Statistic

Perf. 

Group

RQ

(=QM / QD)

RK

(=KI / KD)

μeff

(= ∆ U/ ∆ y,eff)

∆ U

(in/in)

Median ALL 1.45 Q R =  0.79 K R =  5.5 μeff  = 0.011 ∆ U = 

Variability ALL 0.11 σ RQ = 0.26 σ RK = , 0.42 σ μ eff = 0.38 σ ∆U =

E.5 Proposed Component Design Requirements

The buckling-restrained brace design requirements are based on AISC 341-

10. In an actual application of the Component Methodology, code 

requirements may not exist for the proposed component, and such 

requirements would need to be created. Necessary design requirements 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-15

include design strength and stiffness requirements, as well provisions to 

ensure that the component has adequate deformation capacity and detailing. 

E.5.1 Component Design Strength and Stiffness

According to AISC 341-10 the steel core is designed to resist the total axial 

force in the brace. The brace design axial strength is

φ φ P FA ysc ysc sc =

where is Fysc is the specified minimum yield stress of the steel core or actual 

yield stress of the steel core as determined from a coupon test, Asc is the net 

area of steel core, and φ = 0.90. In the evaluation that follows, the design 

strength is taken as QD = Pysc, using the specified minimum yield stress.

Design requirements are also needed to predict the initial stiffness. The total 

elastic stiffness of the BRB is the in-series sum of the individual stiffnesses 

of the different brace segments as proposed by Black et al. (2002): 

total

1

111 2 2

y con tr

K

KK K

=     + +

 

where Ky = EAy/Ly is the elastic stiffness of the yielding portion, Kcon = 

EAcon/Lcon is the stiffness of the connection portion and Ktr = EAtr/Ltr is the 

stiffness of the transition portion. The “yielding,” “connection,” and 

“transition” portions of a BRB are illustrated in Figure E-9.

Figure E-9 Dimensions needed for computing the design stiffness for BRBs

(Figure from Black et al., 2002). 

For the 28 specimens studied, there was insufficient information about the 

dimensions needed to compute Ktotal. Instead, an approximate relationship

proposed for typical buckling-restrained brace dimensions, story heights, and 

bay widths (Nippon Steel Engineering) was used:

0.83 y

total

y

A E

K

L 

This approximation has been shown to provide good agreement with the 

original equation for BRB specimens of typical sizes. The design stiffness 

value KD is taken equal to Ktotal.
E-16 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

E.5.2 Component Detailing Requirements

Detailing provisions follow AISC 341-10. The primary requirement is that 

buckling-restrained braces are able to permit axial elongation and shortening 

in the steel core without failure up to deformations that are twice the design 

story drift. Additional requirements specify the minimum stiffness and notch 

toughness requirements for the steel core plates. 

E.5.3 Component Connection Requirements

According to AISC 341-10, the required strength of columns, beams and 

connections must be designed to include the amplified seismic load, which 

accounts for the adjusted strength of BRBs in tension and compression. The 

adjusted brace strength is based on qualification testing and accounts for 

differences in strength in compression and tension. These connection and 

load transfer design requirements ensure that the inelastic behavior occurs in 

the BRB and fulfill the connection capacity design requirements of Section 

2.5.3.

In using the AISC 341-10 requirements for buckling-restrained braces as the 

basis for the proposed component design requirements, it is assumed that if 

buckling-restrained braces were substituted for conventional braces in the 

special concentrically braced frame system, the design of the rest of the 

system would also comply with the AISC 341-10 specifications for bucklingrestrained braces. Specifically, connection design in the balance of the 

system would need to account for the large overstrength that is associated 

with the use of buckling-restrained braces.

E.5.4 Limitations on Component Applicability and Use

The Component Methodology requires that the design provisions restrict the 

design space to the range of configurations that are considered in the testing

program. Since the test data described in Section E.6 cover the range of size 

and other properties of BRBs that may be reasonably expected in practice, 

there are no specific additional limitations on component applicability and 

use.

E.5.5 Component Construction, Inspection, and Maintenance 

Requirements

Construction, inspection, and maintenance requirements for BRBs follow 

AISC 341-10 provisions for quality assurance which include requirements 

for written description of qualifications, procedures, quality inspections, 

resources, and records to be used to provide assurance that the structure 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-17

complies with the engineer's quality requirements, specifications, and 

contract documents.

E.6 Proposed Component Test Data

Experimental work conducted by a variety of researchers provided test data 

for the proposed component. These data include 33 geometric configurations 

and a total of 46 component tests. Table E-5 summarizes the components

tested, providing general information about core plates, dimensions, and 

failure modes. Configurations of identical specimens are grouped by the 

color of rows. 

The following references were used to collect the BRB data in this section:

Black et al. (2002), Merritt et al. (2003a), Merritt et al. (2003b), Reaveley et 

al. (2004), Newell et al. (2005), Christopulos (2005), Newell et al. (2006), 

Benzoni and Innamorato (2007), Kim et al. (2010), and Sim et al. (2010). 

Data were provided by a number of researchers and includes experimental 

tests of products from three major BRB manufacturers: CoreBrace, Star 

Seismic and Nippon Steel. 

Although a number of tests do not show any failure, commonly occurring 

failure modes included core plate fracture or local buckling at end plates. 

Figure E-10 illustrates the fracture that can occur in buckling-restrained 

braces.

Table E-5 Summary of Buckling-Restrained Brace Configurations in the Proposed Component Data Set

Test

Index

Test Specimen 

ID

Number of 

Core 

Plates/Shape

Area of Core 

Plate (in2)

Length, 

Ly (in) Connection Type Tube Section Failure Mode

1 PC1100A-1 3/Flat 24.1 185.9 Pin Rectangular Not failed

2 PC1100B-1 3/Flat 24.1 185.9 Pin Rectangular Not failed

3 PC1000A-1 2/Flat 23.6 185.9 Pin Rectangular Core plate rupture

4 1D 1/Flat 10.0 133.0 Pin (with cruciform 

gusset bracket) Rectangular Core plate fracture

5 2D 1/Flat 10.0 133.0 Pin (with cruciform 

gusset bracket) Rectangular Core plate fracture

6 3D 1/Cruciform 16.0 131.0 Pin (with cruciform 

gusset bracket) Rectangular Core plate fracture

7 4D 1/Cruciform 16.0 131.0 Pin (with cruciform 

gusset bracket) Rectangular Core plate fracture

8 5D 1/Cruciform 23.1 130.0 Pin (with cruciform 

gusset bracket) Rectangular Core plate fracture

9 6D 1/Cruciform 23.1 130.0 Pin (with cruciform 

gusset bracket) Rectangular Core plate fracture

10 1E 1/Flat 4.0 100.2 Gusset Plate (with bolt) Rectangular Core plate fracture

11 2E 1/Flat 4.0 73.8 Gusset Plate (with bolt) Rectangular Core plate fracture

12 3E 1/Flat 9.0 92.7 Gusset Plate (with bolt) Rectangular Gusset plate bending

13 4E 1/Flat 9.0 65.8 Gusset Plate (with bolt) Rectangular Core plate fracture
E-18 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

Table E-5 Summary of Buckling-Restrained Braces in the Proposed Component Data Set (continued)

Test

Index

Test Specimen 

ID

Number of 

Core 

Plates/Shape

Area of Core 

Plate (in2)

Length, 

Ly (in) Connection Type Tube Section Failure Mode

14 5E 1/Cruciform 20.0 54.5 Gusset Plate (with bolt) Rectangular Gusset plate bending

15 6E 1/Cruciform 20.0 54.5 Gusset Plate (with bolt) Rectangular Gusset plate bending

16 1F 1/Cruciform 27.0 144.5 Gusset Plate (with bolt) Rectangular Core plate fracture

17 2F 1/Cruciform 27.0 144.5 Gusset Plate (with bolt) Rectangular Core plate fracture

18 1G 1/Flat 12.0 132.5 Gusset Plate (with bolt) Rectangular Not failed

19 2G 1/Flat 12.0 132.5 Gusset Plate (with bolt) Rectangular Not failed

20 3G 1/Cruciform 27.0 144.4 Gusset Plate (with bolt) Rectangular Core plate rupture

21 4G 1/Cruciform 27.0 144.4 Gusset Plate (with bolt) Rectangular Not failed

22 H1 1/Flat 4.0 179.9 Pin Circular Buckling at end of plates

23 H2 1/Flat 11.5 125.8 Pin Rectangular HSS Casing damaged

24 H3 1/Flat 18.0 113.2 Pin Rectangular Test stopped

25 H4 1/Flat 27.0 178.8 Pin Rectangular Core plate rupture

26 J2 1/Flat 2.0 217.0 Gusset Plate (with weld) Circular Core plate rupture

27 J3 1/Flat 6.0 203.0 Gusset Plate (with weld) Rectangular Core plate fracture

28 J4 1/Flat 18.0 176.0 Gusset Plate (with weld) Circular Core plate rupture

29 Star - 1 2/Flat 3.8 176.0 Pin 1-Rectangular Core plate fracture

30 Star - 2 2/Flat 6.0 179.4 Pin 1-Rectangular Core plate fracture

31 Star - 3 2/Flat 8.3 183.3 Pin 1-Rectangular Not failed

32 Star - 4 2/Flat 12.7 185.1 Pin 1-Rectangular Not failed

33 Star - 5 4/Flat 17.9 184.2 Pin 2-Rectangular Not failed

34 Star - 6 6/Flat 17.9 179.4 Pin 2-Rectangular Not failed

35 Star - 7 6/Flat 28.5 185.2 Pin 2-Rectangular Not failed

36 Star - 8 8/Flat 28.6 181.3 Pin 4-Rectangular Not failed

37 99-1 1/Flat 4.5 121.7 Gusset Plate (with bolt) Rectangular Not failed

38 99-2 1/Flat 6.0 117.7 Gusset Plate (with bolt) Rectangular Not failed

39 99-3 1/Cruciform 8.0 135.8 Gusset Plate (with bolt) Rectangular Not failed

40 00-11 1/Cruciform 11.0 134.3 Gusset Plate (with bolt) Rectangular Not failed

41 00-12 1/Cruciform 11.0 134.3 Gusset Plate (with bolt) Rectangular Not failed

42 REF-BRB 1/Flat 4.8 93.2 Gusset Plate (with bolt) Rectangular Core plate yielding

43 BRB02 1/Flat 4.8 93.2 Gusset Plate (with bolt) Rectangular Core plate yielding

44 BRB03 1/Flat 4.8 93.2 Gusset Plate (with bolt) Rectangular Core plate yielding

45 BRB04 1/Flat 4.8 93.2 Gusset Plate (with bolt) Rectangular Core plate yielding

46 BRB01 1/Flat 4.8 93.2 Gusset Plate (with bolt) Rectangular Core plate yielding
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-19

Figure E-10 Photo of steel core after fracture in buckling-restrained brace

specimen (Merritt et al., 2003a).

E.6.1 Define Proposed Component Design Space

The proposed component design space includes buckling-restrained braces

that comply with the design and detailing requirements of Section E.5. 

Buckling-restrained braces used in practice vary in terms of:

• Steel core length,

• Cross-sectional area and geometry of the steel core plates,

• Type of connection,

• Cross-section of the steel brace section ,

• The presence of mortar fill as the buckling-restraining mechanism, and

• Failure mode.

E.6.2 Select Component Configurations for Testing

Component configurations selected for testing should span the component 

design space in accordance with Section 2.6.2. In this test application, the 

configurations listed in Table E-5 are utilized. The specimens cover the 

reasonable range of configurations for key variables, including steel core 

plate length, which varies from 54.5 to 217 inches, the type of the 

connection, which includes pins, gusset plates with different cross-sectional 

shape and bolts or welds, different numbers and geometries of core plates, 

including both flat and cruciform plates, core cross-section areas ranging 

from 4 in2 to 28.62 in2

, and shape. 
E-20 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

All buckling-restrained brace specimens considered are mortar-filled. 

Therefore, the findings of the Component Methodology should be applicable 

only to these mortar-filled tubes, unless it can be shown that specimens 

without concrete or mortar filling have comparable performance. 

E.6.3 Perform Cyclic-Load and Monotonic-Load Tests 

In this test application, only cyclic-load test data are utilized because 

monotonic-load test data were not found in the available references. 

Although monotonic-load test data for the proposed component are required 

in most cases, under certain conditions, the cyclic-load data can be used in 

lieu of monotonic-load test data. 

Figure E-11 shows an example of the cyclic response for Specimen 3, which

has 2 flat plates in the steel core. This specimen failed because of core plate 

rupture during the test. 

Most of the tests were conducted according to the loading protocol specified 

in AISC 341-10 for cyclic qualification of buckling-restrained braces (Section 

K3). This loading history is defined by the axial deformation in the brace,

∆b, and depends on the value of axial deformation corresponding to the 

design story drift, ∆bm, and the value of axial deformation at first significant 

yield of the test specimen, ∆by. The loading history imposed can be shown to 

be equivalently damaging to the histories used in the reference component 

tests, as described in Section E.9. 

Figure E-11 Illustration of cyclic response of buckling-restrained brace 

Specimen 3 (Benzoni and Innamorato, 2007). 

2500

2000

1500

1000

500

0

-500

-1000

-1500

-2000

-2500-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-21

E.6.4 Interpret Proposed Component Test Results

An example cyclic envelope curve is shown in Figure E-12 illustrating the 

calculation of component response quantities. The component parameters 

are obtained from experimental data following the same steps described 

previously for the reference component data.

Figure E-12 Illustration of cyclic response, cyclic envelope curve and 

calculation of component response quantities of BRB Specimen

1 (Benzoni and Innamorato, 2007). 

Important component parameters were compiled for each of the 46 bucklingrestrained brace tests, and summarized in Table E-6. As was done with the 

reference component data, proposed component data was placed in one 

performance group, implying that any of the buckling-restrained braces are 

conceived as a replacement for any of the conventional brace components. 

Note that some configurations have only one test specimen. According to the 

Component Methodology, each proposed component configuration should 

have at least two identical test specimens. Repeated specimens would 

therefore need to be added to the data set to complete this example.

Most of the braces were tested axially and test data were provided in terms of 

axial force and deformation. However, specimens 42 through 46 were tested 

in a frame including beam, columns, and connection. These test results have 

been converted from lateral force-story drift to axial force and deformation in 

accordance with the formulas provided in Section E.4.4 for comparison with 

component parameters from other tests. 

2500

2000

1500

1000

500

0

-500

-1000

-1500

-2000

-2500

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
E-22 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

Table E-6 Summary of Important Component Parameters for the Proposed Component 

Data Set

Test 

Index

Strength Stiffness Ductility Deformation 

Capacity

QM

(kips)

QD

(kips) RQ

KI

(kips/in)

KD

(kips/in) RK

∆Y,eff

(in/in) μeff

∆U

(in/in)

∆U l



1 1850 780 2.4 3107 3118 1.0 0.00300 7.0 0.021

0.021

2 1780 780 2.3 3270 3118 1.0 0.00279 7.5 0.021

3 1816 763 2.4 2988 3051 1.0 0.00302 8.5 0.026 0.026

4 700 324 2.2 1751 1846 0.9 0.00276 10.7 0.029

0.029

5 706 324 2.2 1843 1846 1.0 0.00270 10.8 0.029

6 1139 518 2.2 2844 2610 1.1 0.00291 10.3 0.029

0.029

7 1140 518 2.2 2839 2610 1.1 0.00287 10.1 0.029

8 1495 749 2.0 4474 3664 1.2 0.00248 10.0 0.024

0.026

9 1630 749 2.2 3930 3664 1.1 0.00309 9.6 0.029

10 294 130 2.3 931 961 1.0 0.00317 10.7 0.034 0.034

11 286 130 2.2 1040 1304 0.8 0.00366 7.1 0.025 0.025

12 602 292 2.1 1836 2336 0.8 0.00356 8.6 0.029 0.029

13 655 292 2.2 2140 3292 0.6 0.00457 8.9 0.040 0.040

14 1291 648 2.0 5860 8833 0.7 0.00413 7.2 0.030

0.030

15 1313 648 2.0 5613 8833 0.6 0.00433 7.0 0.029

16 1985 875 2.3 4723 3869 1.2 0.00299 12.5 0.037

0.037

17 1897 875 2.2 4329 3869 1.1 0.00253 14.0 0.036

18 894 389 2.3 1974 1522 1.3 0.00344 10.2 0.035

0.034

19 940 389 2.4 1533 1522 1.0 0.00423 8.0 0.034

20 1826 875 2.1 4015 3721 1.1 0.00306 10.4 0.031

0.034

21 1934 875 2.2 4228 3721 1.1 0.00300 12.2 0.036

22 345 130 2.7 501 535 0.9 0.00364 9.5 0.033 0.033

23 813 373 2.2 2166 2201 1.0 0.00273 12.0 0.033 0.033

24 1205 583 2.1 3905 3828 1.0 0.00265 11.1 0.029 0.029

25 1622 875 1.9 3292 3636 0.9 0.00234 9.2 0.020 0.020

26 200 65 3.1 216 232 0.9 0.00307 9.0 0.027 0.027

27 475 194 2.4 645 726 0.9 0.00319 9.2 0.029 0.029

28 1406 583 2.4 2467 2173 1.1 0.00274 12.1 0.033 0.033

29 306 123 2.5 428 571 0.7 0.00404 6.1 0.024 0.024

30 447 193 2.3 636 845 0.8 0.00357 7.1 0.024 0.024

31 525 270 1.9 1000 1118 0.9 0.00319 5.9 0.019 0.019

32 915 410 2.2 1430 1625 0.9 0.00374 6.7 0.025 0.025
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-23

Table E-6 Summary of Important Component Parameters for the Proposed Component 

Data Set (continued)

Test 

Index

Strength Stiffness Ductility Deformation 

Capacity

QM

(kips)

QD

(kips) RQ

KI

(kips/in)

KD

(kips/in) RK

∆Y,eff

(in/in) μeff

∆U

(in/in)

∆Ul

33 1359 578 2.3 2142 2291 0.9 0.00409 6.5 0.027 0.027

34 1378 579 2.4 1875 2438 0.8 0.00418 6.2 0.026 0.026

35 1787 924 1.9 2000 3529 0.6 0.00371 5.2 0.019 0.019

36 1764 927 1.9 2500 3660 0.7 0.00359 5.3 0.019 0.019

37 325 146 2.2 949 976 1.0 0.00282 7.1 0.020 0.020

38 328 194 1.7 994 1265 0.8 0.00281 7.4 0.021 0.021

39 599 259 2.3 1681 1528 1.1 0.00262 7.6 0.020 0.020

40 725 358 2.0 1997 2083 1.0 0.00253 8.6 0.022

0.021

41 719 358 2.0 2531 2083 1.2 0.00203 10.1 0.020

42 475 155 3.1 1043 1244 0.8 0.00384 6.0 0.023

0.022

43 445 155 2.9 1043 1244 0.8 0.00437 5.9 0.026

44 459 155 3.0 1043 1244 0.8 0.00490 4.6 0.022

45 464 155 3.0 1043 1244 0.8 0.00490 5.0 0.025

46 409 155 2.6 1043 1244 0.8 0.00490 3.2 0.016

E.6.5 Compute Summary Statistics

The summary statistics for buckling-restrained brace data are computed in 

accordance with the requirements of Section 2.6.5, and reported in Table E-7. 

Table E-7 Summary Statistics for the Proposed Component

Summary 

Statistic

Perf. 

Group

RQ

(=QM / QD)

RK

(=KI / KD)

μeff

(=∆U/∆y,eff)

∆U

(in/in)

Median ALL 2.27 Q R =  0.92 K R =  8.1 μeff  = 0.026 ∆ U = 

Variability ALL 0.13 σ RQ = 0.19 σ RK = , 0.31 σ μ eff = 0.22 σ ∆U =

E.7 Evaluate Quality Ratings

E.7.1 Quality Rating of Test Data

Judged according to the criteria described in Section 2.7, the quality of 

reference component test data was rated as Fair. Although there is good 

agreement between test results and numerical and analytical predictions of 

test data, the test specimens do not cover the range of possible component 

configurations that would be used in practice, such that the data set was
E-24 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

assigned a medium confidence rating. In addition, because frame data were

used to approximate axial force and elongation parameters, the dataset was 

also rated with medium completeness and robustness. According to the 

Component Methodology, reference component test data with a Fair quality 

rating are not acceptable. As a result, more testing of reference component 

specimens would be required. However, for the purpose of this test 

application, the reference data quality rating has been artificially inflated to a 

rating of Good. 

The quality of proposed component test data was rated as Superior. This 

rating is based on high confidence in test results due to the large number of 

tests completed by independent investigators. Tests represent a reasonable 

range of design parameters to be representative of design practice. There is 

substantially smaller uncertainty in the buckling-restrained brace data than 

the conventional brace data. The completeness and robustness of the test 

data were also judged to be high. Material component and connection 

behavior is well understood, and there is good agreement between 

experimental testing and analytical modeling. The primary limitation in the 

data set is the lack of configurations with two or more test specimens. 

E.7.2 Quality Rating of Design Requirements

The quality rating for proposed and reference component design 

requirements depends on the completeness and robustness of requirements 

and the confidence in the underlying methods and design data. 

For conventional braces there is high confidence in design requirements 

because there are extensive experimental data and analytical studies, and 

good agreement between the two. Completeness and robustness of design 

requirements is also high since the usage of capacity design requirements 

ensures that inelastic action concentrates primarily in braces. Seismic 

compactness requirements delay brace buckling in compression. On the 

basis of these evaluations, the reference component design requirement 

quality rating was judged to be Superior.

The proposed component design requirements were also assigned a quality 

rating of Superior. Extensive experimental data and analytical studies 

provide high confidence that the material properties, strength criteria and 

other parameters are representative of actual behavior. In addition, BRB 

design is based on prototype testing that demonstrates that the component has 

good performance (no failure) up to deformations that are twice the design 

displacement level of the structure. Fabrication, erection, and other 

construction issues are carefully controlled by BRB manufacturers. 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-25

E.8 Evaluate Component Equivalency

E.8.1 Overview

This section discusses the acceptance criteria and evaluates whether the 

conventional and buckling-restrained braces can be judged to be equivalent 

according to the Component Methodology. If equivalent, the proposed 

components could hypothetically be substituted for brace components of the 

reference seismic-force-resisting system, subject to design requirements and 

seismic design category restrictions on the use of the reference seismic-forceresisting system. 

E.8.2 Requirements Based on Cyclic-Load Test Data: Strength 

and Ultimate Deformation 

The median ultimate deformation of each proposed component performance 

group is required to fulfill Equation 2-1, as follows: 

∆ ∆  

U,PC U,RC U Q ≥ P P

In this example, the reference and proposed components are each treated as a 

single performance group. 

As reported in Table E-4, the median ultimate deformation, ∆U RC ,  , of the 

reference component data set is 0.011 in/in. The uncertainty penalty factor, 

Pu, is based on the quality ratings discussed in Section E.7.1. Incorporating

design requirement ratings of Superior and test data ratings of Good and 

Superior, the uncertainty penalty factor Pu = 1.00. The penalty factor for 

strength is based on the ratio of the median proposed and reference 

component strength ratios, as follows:

2.27 1.57

1.45

Q,PC

Q,RC

R

R = =





Based on linear interpolation in Table 2-4 with a strength ratio of 1.57, the 

penalty factor to account for differences in strength, PQ, is 1.21. The ratio of 

R R Q PC Q RC , ,   exceeds the limit of 1.2, but is allowed because bucklingrestrained brace design provisions ensure that force-controlled and capacitydesigned components are designed for the expected strength of the 

component. 

Incorporating these values leads to the following requirement:

0.026 0.011 1.00 1.21 0.013 ∆

U PC < = ≥ ××=
E-26 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

This requirement is easily satisfied since the median ultimate deformation 

obtained from buckling-restrained brace data is 0.026 (from Table E-7). 

The ultimate deformation for each geometric configuration, ∆Uj,PC

 , must also

meet the requirement of Equation 2-2, repeated here: 

, (1 1.5 , , )( ) ∆ σ∆  

Uj PC ≥ − ∆U RC U RC U Q P P

According to Table E-4, the variability in ultimate deformation for the 

reference component, σ ∆U RC , , is 0.38. Since σ ∆U RC , exceeds 0.3, 0.3 is used. 

Therefore, each proposed component configuration must exceed the lower 

bound: 

∆

Uj PC , ≥− × (1 1.5 0.30 0.011 1.00 1.21 0.0074 )( ) × =

Referring back to Table E-6, all proposed component configurations have 

median ultimate deformation capacities of 0.0074 or larger, and therefore 

satisfy the requirement. 

E.8.3 Requirements Based on Cyclic-Load Test Data: Effective 

Initial Stiffness

The median value of the proposed component initial stiffness ratio, RK,PC

 ,

should be within the range specified in Equation 2-3, and repeated here:

,

,

0.92 0.75 1.14 1.33

0.81

K PC

K RC

R

R

≤ = =≤





The stiffness ratio computed is 1.14, which falls within the allowable range.

E.8.4 Requirements Based on Cyclic-Load Test Data: Effective 

Ductility Capacity

The median value of the effective ductility capacity of the proposed 

component should not be less than 50% of the median value of the effective 

ductility capacity of the reference component, such that 

8.1 0.5 0.5(5.5) 2.75 μ μ eff,PC =≥ = = eff,RC  

The median effective ductility for the reference brace component is 5.5 from 

Table E-4. The median effective ductility for the proposed component is 8.1 

from Table E-7, satisfying the effective ductility capacity requirement. 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-27

E.8.5 Requirements Based on Monotonic Load Test Data: 

Ultimate Deformation

As discussed previously, the proposed and reference component data 

compiled in this test application do not include monotonic data. When 

monotonic data for the reference component are not available, the monotonic 

load test data requirements in Equation 2-6 specify that: 

, , 1.2 ∆ ∆ UM PC ≥ D PP C U RC U Q   

However, since monotonic test data are not available, it is allowable to take 

∆UM PC ,  as equal to ∆U PC ,  , which is 0.026. As before ∆U RC ,  = 0.011, PU = 

1.00, and PQ = 1.21. The median value of the cumulative damage factor, 

DC

 , depends on the number of cycles in the reference component testing 

protocols. In this data set, the reference components are tested with a 

number of different loading histories but an average of 35 cycles before 

failure. Therefore, according to Section 2.8.5, DC

 = 1.5. Substituting these 

values into Equation 2-6 results in

, 0.026 1.2 (1.5)(0.011)(1.00)(1.21) 0.024 ∆

UM PC = ≥ =

Since the median cyclic deformation capacity for the proposed component 

exceeds this limit with 0.026, the monotonic load test data requirements are 

implicitly met. 

If Equation 2-6 were not satisfied with the cyclic data, at a minimum, 

monotonic data would be required for selected BRB configurations. Ideally, 

experimental monotonic load testing would be conducted on selected 

reference component configurations as well, though this is not required. 

Monotonic load test data provide important insights into the seismic behavior 

of new components. 

E.8.6 Summary of Component Equivalency Evaluation

In summary, buckling-restrained brace components passed all acceptance 

criteria, including those related to ultimate deformation capacity, initial 

stiffness, and effective ductility. Results are summarized in Table E-8. 

Based on the criteria of the Component Methodology, buckling-restrained

braces are equivalent to conventional braces, and could be substituted into 

the special steel concentrically braced frame seismic-force-resisting system. 

This substitution is contingent on incorporation of the design rules proposed 

for buckling-restrained braces in Section E.5.
E-28 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

Table E-8 Summary of Acceptance Criteria and Equivalency Evaluation

Acceptance Criteria Equation 

Reference

Pass/Fail

Requirement Based on Cyclic-Load Test Data

Ultimate Deformation Capacity 

(performance group) ∆ ∆  

U,PC U,RC U Q ≥ P P 2-1 Pass

Ultimate Deformation Capacity 

(individual configurations) , ,, (1 1.5 )( ) ∆ σ∆  

Uj PC ≥ − ∆U RC U RC U Q P P 2-2 Pass

Initial Stiffness Ratio 0.75 1.33 K,PC

K,RC

R

R

≤ ≤



 2-3 Pass

Effective Ductility Capacity , , 0.5 μ μ eff PC ≥ eff RC   2-4 Pass

Requirements Based on Monotonic-Load Test Data

Ultimate Deformation Capacity

(Option 1) ∆ ∆  

UM PC UM RC U Q , , ≥ P P 2-5 N/A

Ultimate Deformation Capacity

(Option 2) , , 1.2 ∆ ∆  

UM PC C U RC U Q ≥ D PP  2-6 Pass

E.9 Loading Protocol Suitability 

In order for the comparisons described above to be appropriate, the loading 

protocols used to test reference and proposed component test specimens must 

be equivalently damaging. The method described in Appendix B is used to 

compare the loading histories used in cyclic load testing for the bucklingrestrained and conventional brace specimens. According to the Component 

Methodology, other quantitative methods may also be used to compare cyclic 

loading protocols. 

In all cases, the reference components were tested with a cyclic loading 

protocol based on a combination of ATC-24 (ATC, 1992) and SAC Steel 

protocols (Clark et al., 1997). The control variable was based on the 

interstory drift angle of the frame at the first onset of yielding or buckling. 

Based on these loading histories, the normalized cumulative deformation 

(NCD) imposed before reaching the ultimate deformation was computed for 

each specimen. The median normalized cumulative deformation imposed in 

the reference component tests is 16.7, with a maximum computed value of 

24.5 (Specimen 19) and a minimum value of 12.2 (Specimen 15). 

Most of the proposed component tests were conducted according to the 

loading protocol specified in AISC 341-10 Section K3, as described in 

Section E.6.3. The median normalized cumulative deformation imposed in 

the proposed component tests is 15.4; individual specimen normalized 

cumulative deformations vary from 9.2 to 23.5. 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-29

The first criterion in Appendix B is that the normalized cumulative 

deformation demand from each test, NCDi, should fall within the range 

defined by either the equations below, such that

, 0.5 2 NCD NCD NCD RC ≤ ≤ RC i RC  

and 

, 0.5 2 NCD NCD NCD PC ≤ ≤ PC i PC  

For the median cumulative deformations calculated for the reference and 

proposed components, respectively, these limits become:

8.4 33.4 ≤ ≤ NCDRC,i

and

7.7 30.8 ≤ ≤ NCDPC,i

Although not reported here, all specimens tested have a normalized 

cumulative deformation value, NCDi, that fall within these ranges. 

The second criterion states that no tests with normalized cumulative 

deformation smaller than 6.0 are permitted, ensuring that all loading histories

are sufficiently damaging. The normalized cumulative deformation imposed 

on every test specimen exceeds this lower bound. 

Finally, the proposed component shall be tested under a loading protocol(s)

that imposes approximately the same, or more, normalized cumulative 

deformation on the component, compared to the loading histories used to 

establish the reference component data set. Quantitatively, this limit is 

provided in Equation B-3 and repeated here: 

NCDPC =≥ = = 15.4 0.75 0.75 16.7 12.5 NCDRC ( )( )  

This implies that proposed component specimens should be tested with a 

protocol that imposes (on average) at least a normalized cumulative 

deformation of 12.5. The median proposed component normalized 

cumulative deformation is 15.4, exceeding this lower bound. As a result, the 

cyclic loading histories imposed on the reference and proposed components 

are deemed equivalently damaging for use in the Component Methodology. 
E-30 E: Test Application: Buckling-Restrained Brace Components FEMA P-795

E.10 Summary of Component Equivalency Evaluation of 

Buckling-Restrained Braces 

Overall, the comparison of buckling-restrained braces to special steel braces 

found that the buckling-restrained braces have a larger median deformation 

capacity and satisfy Component Methodology equivalency criteria based on

deformation capacity. Although buckling-restrained braces have higher 

overstrength than conventional braces, connections are designed using a

capacity design philosophy that satisfies Component Methodology 

requirements for strength. Requirements based on stiffness and effective 

ductility capacity are also met. As a result, the evaluation concludes that 

buckling-restrained braces are equivalent to conventional braces in special 

steel concentrically braced frame systems.

E.11 Limitations of Test Application

This section summarizes limitations in the test application comparison 

between buckling-restrained braces and steel concentric braces, which limit 

the general applicability of the conclusions and the usability of the reference 

and proposed component data sets developed.

E.11.1 Reference Component Test Data Do Not Fully Represent 

the Design Space

The reference component data gathered in this example are based primarily 

on HSS sections of the same length and area, with different connection types. 

There are also a few wide flange tests. Most of the test specimens have 

section properties that are close to the limit in terms of allowable slenderness 

and width-to-thickness ratios. As a result, the reference component data set 

may present a pessimistic view of brace behavior that does not represent the 

typical behavior of braces in real buildings. In addition, some of these tests 

examine changes in connection design that may not be typical special 

concentrically brace frames as currently constructed in practice. 

E.11.2 The Equivalency Evaluation May Not Adequately Account 

for System Differences 

While most of the buckling-restrained braces were tested in an axial test 

setup (with the exception of specimens 42-46), the reference component 

braces were tested in frames and the data recorded were in terms in lateral 

force and drift ratio. This difference in test setup poses problems in 

obtaining a consistent metric of force and deformation for comparison of 

proposed and reference components. In this evaluation, data obtained from 

frame tests were used to estimate the axial force and axial elongation in the 

brace assuming that the entire lateral force is taken by the brace. In fact, 
FEMA P-795 E: Test Application: Buckling-Restrained Brace Components E-31

depending on the properties of the frame and connection, some portion of the 

load is taken by the frame itself. For one specimen (Specimen 6), Johnson 

(2005) reported that about 85% of the horizontal load is in the brace. 

However, this information is not available for other specimens and the actual 

amount transferred depends on the frame and connection properties. In 

addition, the calculation of the ultimate deformation in the brace assumes 

that there is no significant deformation in the connections or other framing 

elements. When there is significant deformation in the connections, the 

ultimate deformation of the brace itself is overestimated. In this example, the 

overestimation occurs primarily with the reference component tests, 

introducing additional conservatism to the comparison and evaluation of the 

proposed components. The overstrength in the reference components is also 

overestimated. 

The differences in frame versus brace behavior also illustrate the important 

influence that frame and connection elements in special concentrically braced 

frame have on overall system behavior. For example, Figure E-6 shows that 

the frame tested shows very little strength loss after buckling, which occurs 

in the range of 0.2% to 0.5% drift. This ductility is likely provided by the 

moment resistance of frame members, and it is not clear whether the frame 

ductility evident in these tests is generally representative of buildings 

designed according to AISC 341-10. In addition, since a single bucklingrestrained brace may be used to replace more than one conventional brace, 

the transfer of forces across the component boundary and engagement of the

frame in the system behavior may be different for the two different 

components. These observations indicate that a system analysis of bucklingrestrained brace frames as described in FEMA P-695, and illustrated in NIST 

GCR 10-917-8 (NIST, 2010) may be more appropriate. 

E.11.3 Component Parameters are Approximate

Because component parameters were obtained from graphical interpretation 

of load-deformation plots, rather than digitized data. This approach may lead 

to errors in estimation of parameters, especially those related to initial 

stiffness and effective yield displacement. 

FEMA P-795 F: Test Application: F-1

Pre-Fabricated Wall Components

Appendix F

Test Application: Pre-Fabricated

Wall Components

F.1 Introduction

This appendix illustrates the application of the Component Methodology to 

the possible substitution of pre-fabricated wall components for nailed wood 

shear wall components in wood light-frame construction. In accordance with 

the request of the manufacturer, the specific product is not identified, but is 

representative of a number of proprietary wall products from different 

manufacturers, including Weyerhaeuser, Hardy Frames, Simpson Strong-Tie, 

and others. These products are typically slender elements with very highaspect ratios that are used at the boundaries of large openings where 

available wall length is limited (e.g., garage wall lines in residential 

construction), and are particularly common in regions of high seismicity or 

strong winds.

Available design information and test data were limited for the pre-fabricated 

wall component, consisting of cyclic-load testing on three specimens of one 

configuration. As such, these data are not sufficient to permit a complete 

application of the Component Methodology. Nonetheless, these data are 

useful in terms of testing the methods for construction of cyclic envelope

curves, extraction of key parameters from these curves, and the evaluation of 

component parameters using the acceptance criteria of Section 2.8.

Although incomplete as a full application of the Component Methodology, 

this test application illustrates a special case that might be consistent with a

preliminary check of equivalency during the development of a new product. 

In this case, prototypical specimens of a representative (or critical) 

configuration are constructed and cyclic-load tested, and key performance 

parameters evaluated, to determine if the product will have reasonably 

adequate deformation capacity and ductility. In such an application, at least 

two specimens should be tested to assess the repeatability of key parameters.

F.2 Description of Pre-Fabricated Wall Component

The pre-fabricated wall component is intended for use in wood light-frame 

construction. The component is 9 feet (108 inches) tall and is very short in 

length. The details of the materials and construction were not available. 
F-2 F: Test Application: FEMA P-795

Pre-Fabricated Wall Components

Figures F-1 and F-2 show typical applications of two similar high-aspect 

ratio, pre-fabricated wall products.

Figure F-1 Example residential building application of high-aspect ratio 

pre-fabricated wall components 

(www.sbebuilders.com/images/hardy-frame-2.jpg).

Figure F-2 Example commercial building application of high-aspect ratio, 

pre-fabricated wall components

(www.sbebuilders.com/images/strong-wall.jpg)

F.3 Evaluation of Applicability Criteria

The applicability of the Component Methodology is based largely on the

comparison of characteristics of components of the reference system, in this 

case, the light-frame (wood) wall system of line A.15 in Table 12.2-1 of 

ASCE/SEI 7-10 Minimum Design Loads for Buildings and Other Structures 
FEMA P-795 F: Test Application: F-3

Pre-Fabricated Wall Components

(ASCE, 2010) and those of the proposed component. While the applicability 

of the Component Methodology could not be rigorously evaluated, due to 

lack of specific design and configuration data, the Component Methodology 

is expected to generally apply to these types of pre-fabricated wall 

components.

Of particular importance to the applicability of high-aspect wall components 

is the definition of the component boundary, and related boundary 

conditions, which must be realistically represented by the test setup. Possible 

differences to consider would include additional overturning demands due to 

differences in aspect ratio between pre-fabricated wall components and 

typical configurations of nailed wood shear wall reference components. 

The boundary of pre-fabricated wall components is typically well defined by 

the manufacturer's drawings of typical details for anchoring and connecting 

these products to the balance of the seismic-force-resisting system. This test 

application presumes that these types of drawings would be available for 

evaluating force transfer at the component boundary and for establishing 

boundary conditions of tests.

F.4 Reference Component Test Data

The reference component test data in this example is taken as the same nailed 

wood shear wall data set developed for the example application in Chapter 4. 

Table F-1 shows the summary statistics for the reference component data set.

Table F-1 Summary Statistics for Reference Component 

Parameters (from Table 4-3)

Summary 

Statistic

RQ

(=VM / VD)

RK

(=KI / KD) μeff ∆ U (in/in)

Median 2.7 Q R =  1.00 K R =  6.3 μeff  = 0.035 U ∆ = 

Variability 0.11 σ RQ = 0.42 σ RK = , 0.38 σ μ eff = 0.16 σ ∆U =

F.5 Proposed Component Design Requirements

Design data and requirements were not available for the pre-fabricated 

component, other than an ASD design load of QD = 580 lbs, and a drift 

displacement of 0.38 inches (i.e., drift ratio of 0.0035 in./in.) at the ASD 

design load. This corresponds to a design stiffness of KD = 1,514 lbs/in.

In general, manufacturers of pre-fabricated wall components provide detailed 

product guides that describe installation requirements, including typical 

anchorage and connection details and construction requirements, and tables 
F-4 F: Test Application: FEMA P-795

Pre-Fabricated Wall Components

of design loads and other design criteria. This test application presumes that 

these types of design and construction requirements would be available for 

establishing design loads and evaluating the quality of design requirements.

F.6 Proposed Component Test Data

Cyclic-load test data were provided by the manufacturer for three specimens 

of one proposed component configuration. While this configuration is 

somewhat different from the configurations contained in the reference 

component data set, this is acceptable and does not violate any of the 

applicability criteria of Section 2.3. No monotonic-load test data were 

available. 

Cyclic-load test data were plotted, envelope curves fitted, and values of 

various load, deformation and related parameters determined from the 

envelop curves, as shown in Figure F-3.

Figure F-3 Illustration of cyclic-load testing data and cyclic envelope curve 

(from Figure 2-2).

Plots of the cyclic-load test data and envelopes are shown in Figures F-4, F-5 

and F-6 for the three test specimens. The test loops are very stable and 

similar for the three test specimens. Table F-4 summarizes values of 

strength, stiffness, ductility and deformation capacity parameters obtained for 

these three test specimens, and shows the summary statistics (median and 

variability) for these four parameters.

∆Y,eff+ ∆U

+

QM+

0.8QM+

0.4QM+

KI

+

KI

-

QM0.8QM0.4QM-

∆Y,eff ∆ - U

-

∆Y,eff+ ∆U

+

QM+

0.8QM+

0.4QM+

KI

+

KI

-

QM0.8QM0.4QM-

∆Y,eff ∆ - U

-
FEMA P-795 F: Test Application: F-5

Pre-Fabricated Wall Components

Figure F-4 Cyclic response and envelope curve for pre-fabricated 

component test specimen No.1.

Figure F-5 Cyclic response and envelope curve for pre-fabricated 

component test specimen No.2.

-0.1 -0.05 0 0.05 0.1

-3000

-2000

-1000

0

1000

2000

3000

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope

-0.1 -0.05 0 0.05 0.1

-3000

-2000

-1000

0

1000

2000

3000

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope
F-6 F: Test Application: FEMA P-795

Pre-Fabricated Wall Components

Figure F-6 Cyclic response and envelope curve for pre-fabricated 

component test specimen No.3.

Table F-2 Values of Strength, Stiffness, Ductility and Deformation Capacity Parameters and Summary

Statistics for the Proposed Component

Test

Index

Strength Stiffness Ductility Deformation 

Capacity

VM (lb) VD (lb) RQ = 

VM / VD

KI

(lb/in)

KD

(lb/in)

RK = 

KI / KD

ΔY,eff

(in/in) μeff

ΔU 

(in/in) ∆Uj

1 2,745 580 4.7 1,248 1,514 0.8 0.020 3.5 0.071

2 2,730 580 4.7 1,211 1,514 0.8 0.021 3.3 0.070 0.068

3 2,810 580 4.8 1,317 1,514 0.9 0.020 3.3 0.065

Median: 4.8 R

Q = 0.83 RK =  3.4 μeff = 0.068 ∆

U =

Variability: 0.02 σ RQ = 0.04 σ RK = , 0.03 σ μ eff = 0.05 σ ∆U =

F.7 Evaluate Quality Ratings

F.7.1 Quality Rating of Test Data

Consistent with the example of Chapter 4, reference component test data is 

rated as Superior.

There was not sufficient information to rate the quality of proposed 

component test data due to limited number of available test data. For the 

purpose of this test application, it was assumed that proposed component test 

data would be rated as Good, if all required cyclic-load and monotonic-load 

tests were performed. 

-0.1 -0.05 0 0.05 0.1

-3000

-2000

-1000

0

1000

2000

3000

Drift (in/in)

Force (lbs)

Cyclic Response

Cyclic Envelope
FEMA P-795 F: Test Application: F-7

Pre-Fabricated Wall Components

F.7.2 Quality Rating of Design Requirements

Consistent with the example of Chapter 4, the quality rating for the reference 

component design requirements is Good.

There was not sufficient information to rate the quality of proposed 

component design requirements. For the purpose of this test application, it 

was assumed that proposed component design requirements would be rated 

as Superior, if product information, including design and construction 

requirements, were comparable to that typically provided by manufacturers 

of pre-fabricated wall product. The higher quality rating of the proposed

component design requirements recognizes the greater control that can be 

achieved in pre-fabricated products that are manufactured in a controlled 

environment (rather that site-built), provided they are properly installed in 

the field.

F.8 Evaluate Component Equivalency

F.8.1 Overview

This section discusses the acceptance criteria of the Component 

Methodology and evaluates whether the proposed pre-fabricated component 

can be judged to be equivalent for use in light-frame wood construction. The 

evaluation of equivalency is necessarily incomplete due to the limited 

amount of available test data. Nonetheless, results provide a useful

evaluation of equivalency to the degree that a single configuration can

represent the balance of all possible configurations of the pre-fabricated wall 

component of interest.

The Component Methodology evaluates equivalency of proposed and 

reference components by performance group (components grouped in terms 

of comparable characteristics). In this test application, there is only one 

performance group, and the proposed component is represented by a single 

configuration with three test specimens. The summary statistics of the 

proposed component performance group are assumed to be the same as those 

of the three specimens of the single configuration.

If test data were available for all configurations of the proposed component, 

then the summary statistics of the proposed component performance group 

would likely be different from those based on the single configuration of this 

test application. In general, median values of parameters would be expected 

to vary modestly, while values of log standard deviation would be expected 

to increase significantly.
F-8 F: Test Application: FEMA P-795

Pre-Fabricated Wall Components

F.8.2 Requirements Based on Cyclic-Load Test Data: 

Strength and Ultimate Deformation 

Section 2.8.2 requires that the median ultimate deformation of each proposed 

component performance group satisfy Equation (2.1), as follows: 

∆ ∆  

U,PC U,RC U Q ≥ P P

The median ultimate deformation, , ∆ U,RC

 of the reference component, 

expressed in terms of drift ratio, is 0.035 in/in. (from Table F-1), and the 

median ultimate deformation, , ∆ U,PC

 of the proposed component, expressed 

in terms of drift ratio, is 0.068 in/in. (from Table F-2). The penalty factor for 

strength is based on the ratio of median strength ratios of proposed and 

reference components. The ratio of proposed component strength (i.e., 

overstrength) is 4.8 (from Table F-2) and the ratio reference component 

strength is 2.7 (from Table F-1) and the ratio of these values is:

,

,

4.8 1.78

2.7

Q PC

Q RC

R

R = =





Based on this ratio and from Table 2-4, the value of the penalty factor is PQ = 

1.24.

Since the ratio exceeds 1.2, Section 2.8.2 requires force-controlled and 

capacity designed elements of the reference SFRS to be designed to develop 

the expected strength of the proposed component (i.e., 4.8 x 580 lbs = 2,784 

lbs). Regardless of the value of this ratio, Section 2.5.2 requires the 

attachment of the proposed component to the balance of the reference SFRS 

to be strong enough to develop the full ultimate strength of the proposed 

component, such that inelastic behavior occurs in the proposed component, 

and not at the boundary between the proposed component and the balance of 

the reference SFRS.

From Table 2-3, based on the quality ratings described in Section F.7, the 

value of uncertainty factor is PU= 1.0. In this case, differences in the quality 

ratings of test data and design requirements of the proposed and the reference 

components essentially cancel out.

Incorporating these values into the first equation leads to the following check 

of ultimate deformation equivalency:

0.068 ≥ 0.035 (1.0) (1.24) = 0.043 OK

This requirement is easily satisfied since the median ultimate deformation 

capacity of the pre-fabricated wall is quite large.
FEMA P-795 F: Test Application: F-9

Pre-Fabricated Wall Components

In addition to the equivalency requirement for the median of each component 

performance group, , ∆ U,PC

 the median ultimate deformation of each 

configuration, , ∆ Uj,PC

 must meet the requirement of Equation (2-2), as 

follows:

(1 1.5 , )( ) ∆ σ∆  

Uj,PC ≥ − ∆U RC U,RC U Q P P

This equation checks for “outlier” configurations, which cannot be 

meaningfully evaluated without having summary statistics for all 

configurations of the proposed component.

F.8.3 Requirements Based on Cyclic-Load Test Data: 

Effective Initial Stiffness

Section 2.8.3 requires that the median initial stiffness ratio of the proposed 

component be reasonably similar to median initial stiffness ratio of the 

reference component, in accordance with Equation (2-3), as follows:

,

,

0.75 1.33 K PC

K RC

R

R

≤ ≤





As reported earlier, the median initial stiffness ratio, RK ,RC

~ , of the reference 

component is 1.00 (from Table F-1) and the median initial stiffness ratio,

RK ,PC

~ , of the proposed component is 0.83 (from Table F-2).

Incorporating these values leads to the following check of initial stiffness 

equivalency:

. OK .

. . 1 33

1 00

0 83 0 75 ≤ ≤

As shown, the initial stiffness requirement is satisfied. While the initial 

stiffness of the proposed component is much less than that of the reference 

component, the design stiffness of the proposed component is also much less 

than that of the reference component.

F.8.4 Requirements Based on Cyclic Test Data: Effective 

Ductility Capacity

Section 2.8.4 requires that the median effective ductility of the proposed 

component be not less than one-half of the median effective ductility of the 

reference component, in accordance with Equation (2-4), as follows:

eff ,PC eff ,RC ~ . ~

μ ≥ 0 5μ
F-10 F: Test Application: FEMA P-795

Pre-Fabricated Wall Components

The median effective ductility, eff ,RC ~

μ , of the reference component is 6.3 

(from Table F-1) and the median initial stiffness ratio, eff ,PC ~

μ , of the 

proposed component is 3.4 (from Table F-2).

Incorporating these values into Equation (F-7) leads to the following check 

of effective ductility:

3.4 ≥ (0.5)6.3 = 3.2 OK

As shown, the effective ductility requirement is satisfied, although with a 

modest margin, essentially using all of the proposed component's ultimate 

displacement capacity to meet the effective ductility criterion.

F.8.5 Requirements Based on Monotonic Load Test Data: 

Ultimate Deformation

Section 2.8.5 requires that monotonic-load data be used to show that the 

proposed component has some additional ultimate displacement capacity

with respect to the cyclic-load ultimate displacement capacity of the

reference component, in accordance with either Equation (2-5) or (2-6), as 

follows:

∆ ∆  

UM PC UM RC U Q , , ≥ P P

, , 1.2 ∆ ∆ UM PC ≥ D PP C U RC U Q  

Since monotonic data were not available, the latter equation was used to 

evaluate this requirement, where monotonic-based median ultimate 

displacement, ∆ UM PC ,  , is taken as equal to the cyclic-based median ultimate 

displacement, ∆ U PC ,  , of 0.068. The value of DC

 is 1.0, based on the use of 

CUREE cyclic-load test protocol to perform the cyclic-load tests of the 

reference component. Values of penalty factors, PU and PQ, are as previously 

defined.

Incorporating these values leads to the following check of ultimate 

displacement capacity for monotonic-loading:

0.068 ≥1.2(1.0)0.035(1.0)(1.24) = 0.052 OK

As shown, the check of monotonic ultimate displacement capacity is 

satisfied, using the cyclic-load test ultimate deformation of the proposed

component as a surrogate for the monotonic-load test ultimate deformation of 

the proposed component. This result shows that monotonic-load tests would 

not be required for the pre-fabricated wall component.
FEMA P-795 F: Test Application: F-11

Pre-Fabricated Wall Components

Table F-3 provides a summary of the acceptance criteria and the results of 

the evaluation of the equivalency of the pre-fabricated wall components and

nailed wood shear walls components.

Table F-3 Summary of Acceptance Criteria Evaluation for Pre-Fabricated Wall Components

Acceptance Criteria Equation 

Reference

Pass/Fail

Requirement Based on Cyclic-Load Test Data

Ultimate Deformation Capacity 

(performance group) ∆ ∆  

U,PC U,RC U Q ≥ ⋅⋅ P P 2-1 Pass

Ultimate Deformation Capacity 

(individual configurations) , (1 1.5 , , )( ) ∆ σ∆  

Uj PC ≥ − ∆U RC U RC U Q P P 2-2 N/A

Initial Stiffness Ratio 0.75 1.33 K,PC

K,RC

R

R

≤ ≤



 2-3 Pass

Effective Ductility Capacity , , 0.5 μ μ eff PC ≥ eff RC   2-4 Pass

Requirements Based on Monotonic-Load Test Data

Ultimate Deformation Capacity

(Option 1) ∆ ∆  

UM PC UM RC U Q , , ≥ P P 2-5 N/A

Ultimate Deformation Capacity

(Option 2) , , 1.2 ∆ ∆ UM PC ≥ D PP C U RC U Q    2-6 Pass

F.9 Summary of Component Equivalency Evaluation of 

Pre-Fabricated Wall Components

This test application of the Component Methodology for pre-fabricated wall 

components, although limited to the evaluation of just three cyclic-load test 

specimens on a single configuration, provided useful information on the 

Component Methodology when applied to the proposed substitution of a 

product that is inherently more flexible than that of the reference system. In 

this case, the high-aspect ratio pre-fabricated wall component is a relatively 

strong, short (slender) proprietary product intended for substitution in lightframe wood wall construction, and is representative of similar proprietary 

products from a number of manufacturers.

Overall, the test application found that the pre-fabricated wall component 

was equivalent. This finding is consistent with findings of the International 

Code Council Evaluation Services (ICC ES) for similar products using the 

acceptance criteria of AC322.

FEMA P-795 References G-1

References

ACI, 2001, Acceptance Criteria for Moment Frames Based on Structural 

Testing (ACI T1.1-01) and Commentary (ACI T1.1R-01), Innovation 

Task Group 1 and collaborators, American Concrete Institute, 

Farmington Hills, Michigan.

AF&PA, 2005, Special Design Provisions for Wind and Seismic Standard 

with Commentary, ANSI/AF&PA SDPWS-2005, American Forest & 

Paper Association, Washington, D.C.

AF&PA, 2009, Special Design Provisions for Wind and Seismic Standard

with Commentary, ANSI/AF&PA SDPWS-2008, American Forest & 

Paper Association, Washington, D.C.

AISC, 2011, Seismic Provisions for Structural Steel Buildings, ANSI/AISC 

341-10, American Institute for Steel Construction, Chicago, Illinois.

ASCE, 2005, Minimum Design Loads for Buildings and Other Structures, 

ASCE/SEI 7-05, American Society of Civil Engineers, Reston, 

Virginia.

ASCE, 2010, Minimum Design Loads for Buildings and Other Structures, 

ASCE/SEI 7-10, American Society of Civil Engineers, Reston, 

Virginia.

Aslani, F. and Goel, S.C., 1989, Experimental and Analytical Study of the 

Inelastic Behavior of Double Angle Bracing Members under Severe 

Cyclic Loading, Research Report UMEE 89-5, University of 

Michigan.

Astaneh-Asl, A., Goel, S.C., and Hanson, R.D., 1982, Cyclic Behavior of 

Double Angle Bracing Members with End Gusset Plates, Research 

Report UMEE 82R7, University of Michigan.

ASTM, 2009, Standard Test Method for Cyclic (Reversed) Load Test for 

Shear Resistance of Vertical Elements of the Lateral Load Force

Resisting System for Buildings, ASTM E2126-09, American Society 

for Testing and Materials International, West Conshohocken, 

Pennsylvania.
G-2 References FEMA P-795

ATC, 1992, Guidelines for Cyclic Seismic Testing of Components of Steel 

Structures, Report No. ATC-24, Applied Technology Council, 

Redwood City, California.

Benzoni, G. and Innamorato, D, 2007, StarSeismic Brace Tests. Mercy San 

Juan Hospital Project, Report No. SRMD-2007-05-rev2, University 

of California, San Diego.

Bernal, D., 1992, “Instability of buildings subjected to earthquakes,” Journal 

of Structural Engineering, American Society of Civil Engineers, 

Vol. 118, No. 8, pp. 2239-2260.

Bernal, D., 1998, “Instability of buildings during seismic response,” 

Engineering Structures, Vol. 20, No. 4-6, pp. 496-502.

Berry, M., Parrish, M., and Eberhard, M., 2004, PEER Structural 

Performance Database User’s Manual, Pacific Earthquake 

Engineering Research Center, University of California, Berkeley, 

California, 38 pp. Available at http://nisee.berkeley.edu/spd/ and 

http://maximus.ce.washington.edu/~peera1/.

Black, C., Makris, N., and Aiken, I., 2002, Component Testing, Stability 

Analysis and Characterization of Buckling-Restrained Unbonded

Braces, PEER Report 2002/08, Pacific Earthquake Engineering 

Research Center, University of California, Berkeley.

CEN, 1995, Timber Structures–Test Methods–Cyclic Testing of Joints Made 

with Mechanical Fasteners, IN TC 124.117, European Committee 

for Standardization, Brussels, Belgium.

Cheung, P.C., Pauley, T., Park, R., 1991, “New Zealand tests on full-scale 

reinforced concrete beam-column-slab sub-assemblages designed for 

earthquake resistance,” ACI Special Publication SP-123, Design of 

Beam-Column Joints for Seismic Resistance, American Concrete 

Institute, Detroit, Michigan, pp. 1-37.

Christopulos, A.S., 2005, Improved Seismic Performance of Buckling 

Restrained Braced Frames, M.Sc. Thesis, University of Washington.

Clark, K.A., 2009, Experimental Performance of Multi-Story X-Braced 

SCBF Systems, M.Sc. Thesis, University of Washington.

Clark, P., Frank, K., Krawinkler, H., and Shaw, R., 1997, Protocol for 

Fabrication, Inspection, Testing, and Documentation of BeamColumn Connection Tests and Other Experimental Specimens, SAC 

Steel Project Background Document, Report No. SAC/BD-97/02.
FEMA P-795 References G-3

Clough, R.W. and Johnston, S.B., 1966, “Effects of stiffness degradation on 

earthquake ductility requirements,” Proc. 2nd Japan Earthquake

Engrg. Symp., pp. 227–232.

CoLA, 2001, Report of a Testing Program of Light-Framed Walls with 

Wood-Sheathed Panels, final report to the City of Los Angeles 

Department of Building and Safety, by Structural Engineers 

Association of Southern California and COLA-UCI Light Frame 

Test Committee, Department of Civil Engineering, University of 

California, Irvine, California, 93 pp.

Dolsek, M. and Fajfar, P., 2004, “Inelastic spectra for infilled reinforced 

concrete frames,” Earthquake Engineering and Structural 

Dynamics, Vol. 33, pp. 1395–1416.

El Tayem, A. and Goel, S.C., 1985, Cyclic Behavior of Angle X-Bracing 

with Welded Connections, Research Report UMEE 85-4, University 

of Michigan.

Engelhardt, M., 2007, Teaching Principles of Seismic-Resistant Design of 

Steel Building Structures, prepared for the American Institute of 

Steel Construction. Available at 

http://www.aisc.org/content.aspx?id=21490. Last accessed February 

25, 2010.

Fardis, M.N. and Biskini, D.E., 2003, “Deformation capacity of RC 

members, as controlled by flexure or shear,” Proceedings, Otani 

Symposium, University of Tokyo, Japan, pp. 511- 530.

FEMA, 2007, Interim Testing Protocols for Determining the Seismic 

Performance Characteristics of Structural and Nonstructural 

Components, FEMA 461, prepared by the Applied Technology 

Council for the Federal Emergency Management Agency, 

Washington, D.C.

FEMA, 2009a, Effects of Strength and Stiffness Degradation on Seismic 

Response, FEMA P-440A, prepared by the Applied Technology 

Council for the Federal Emergency Management Agency, 

Washington, D.C.

FEMA, 2009b, Quantification of Building Seismic Performance Factors, 

FEMA P-695, prepared by Applied Technology Council for the 

Federal Emergency Management Agency, Washington, D.C.

Filiatrault, A., Wanitkorkul, A., and Constantinou, M.C., 2008, Development 

and Appraisal of a Numerical Cyclic Loading Protocol for 

Quantifying Building System Performance, Technical Report 
G-4 References FEMA P-795

MCEER-08-0013, Multidisciplinary Center for Earthquake 

Engineering Research, University at Buffalo, New York.

Folz, B., and Filiatrault, A., 2004a, “Seismic analysis of woodframe 

structures I: model formulation,” Journal of Structural Engineering,

American Society of Civil Engineers, Vol. 130, No. 8, pp. 1353-

1360. 

Folz, B. and Filiatrault, A., 2004b, “Seismic analysis of woodframe 

structures II: model implementation and verification,” Journal of 

Structural Engineering, American Society of Civil Engineers, Vol. 

130, No. 8, pp. 1361-1370.

Foutch, D.A. and Shi, S., 1998, “Effects of hysteresis type on the seismic 

response of buildings,” Proceedings of the Sixth U.S. National 

Conference on Earthquake Engineering, Seattle, Washington.

Gatto, K. and Uang, C.M., 2002, Cyclic Response of Woodframe Shearwalls: 

Loading Protocol and Rate of Loading Effects, CUREE Report No. 

W-16, Consortium of Universities for Earthquake Engineering 

Research, Richmond, California.

Gupta, A. and Krawinkler, H., 1998, "Effect of stiffness degradation on 

deformation demands for SDOF and MDOF structures,” 

Proceedings of the Sixth U.S. National Conference on Earthquake 

Engineering, Seattle, Washington.

Gupta, A. and Krawinkler, H., 1999, Seismic Demands for Performance 

Evaluation of Steel Moment-Resisting Frame Structures, John A. 

Blume Earthquake Engineering Center Technical Report No. 132, 

Stanford University, Stanford, California.

Haselton, C.B. and Deierlein, G.G., 2007, Assessing Seismic Collapse Safety 

of Modern Reinforced Concrete Frame Buildings, John A. Blume 

Earthquake Engineering Center Technical Report No. 156, Stanford 

University, Stanford, California.

Haselton, C.B., Mitrani-Reiser, J., Goulet, C., Deierlein, G.G., Beck, J., 

Porter, K.A., Stewart, J., and Taciroglu, E., 2008, An Assessment to 

Benchmark the Seismic Performance of a Code-Conforming 

Reinforced-Concrete Moment-Frame Building, PEER Report 

2007/12, Pacific Earthquake Engineering Research Center, 

University of California, Berkeley, California.

Ibarra, L., 2003, Global Collapse of Frame Structures Under Seismic 

Excitations, Ph.D. Dissertation, Department of Civil and 
FEMA P-795 References G-5

Environmental Engineering, Stanford University, Stanford, 

California.

Ibarra, L.F. and Krawinkler, H., 2005, Global Collapse of Frame Structures 

Under Seismic Excitations, PEER Report 2005/06, Pacific 

Earthquake Engineering Research Center, University of California, 

Berkeley, California, and John A. Blume Earthquake Engineering 

Center Technical Report No. 152, Department of Civil Engineering, 

Stanford University, Stanford, California.

Ibarra, L.F., Medina, R.A., and Krawinkler, H., 2005, “Hysteretic models 

that incorporate strength and stiffness deterioration,” International 

Journal for Earthquake Engineering and Structural Dynamics, Vol. 

34, No.12, pp. 1489-1511.

ICC, 2006, International Building Code, International Code Council, 

Washington, D.C.

ICC, 2009, International Building Code, International Code Council, 

Washington, D.C.

ICC-ES, 2007, Acceptance Criteria for Prefabricated, Cold-Formed, Steel 

Lateral-Force-Resisting Vertical Assemblies, AC322, International 

Code Council Evaluation Services, Whittier, California.

ISO, 2003, Timber Structures-Joints Made with Mechanical Fasteners –

Quasi-Static Reversed-Cyclic Test Method, ISO 16670:2003, 

International Organization for Standardization, Geneva, Switzerland. 

ISO, 2005, General Requirements for the Competence of Testing and 

Calibration Laboratories, ISO/IEC 17025:2005, International 

Organization for Standardization, Geneva, Switzerland.

Iwan, W.D., 1973, “A model for the dynamic analysis of deteriorating 

structures,” Proc. Fifth World Conference on Earthquake 

Engineering, Rome, Italy, pp. 1782-1791.

Iwan, W.D., 1977, “The response of simple stiffness degrading structures,” 

Proc. Sixth World Conference on Earthquake Engineering, pp. 

1094-1099.

Iwan, W.D., 1978, “The earthquake response of strongly deteriorating 

systems including gravity effects,” Proc. Sixth European Conference 

on Earthquake Engineering; pp. 23-30.

Johnson, S., 2005, Improved Seismic Performance of Special Concentrically 

Braced Frames, M.Sc. Thesis, University of Washington.
G-6 References FEMA P-795

Karacabeyli, E., 1998, “Lateral resistance of nailed shear walls subjected to 

static and cyclic displacements,” Forest Products Society 49th 

Annual Meeting, Portland, Oregon.

Kim, D.W., Sim, H.B., Uang, C.M., and Benzoni, G., 2010, Subassemblage 

Testing of CoreBrace Buckling-Restrained Braces (H series), Report 

No. TR 09-01, University of California, San Diego.

Kotulka, B.A., 2007, Analysis for a Design Guide on Gusset Plates used in 

Special Concentrically Braced Frames, M. Sc. Thesis, University of 

Washington.

Krawinkler, H., 2009, “Loading histories for cyclic tests in support of 

performance assessment of structural components,” Proceedings

3AESE Conference, San Francisco, California.

Krawinkler, H. and Lignos, D, 2009, “How to predict the probability of 

collapse of non-ductile building structures,” book chapter in Seismic 

Assessment and Retrofitting, Geotechnical, Geological, and 

Earthquake Engineering, Vol. 10, published by Springer, NY.

Krawinkler, H., Gupta, A., Medina, R., and Luco, N., 2000, Development of 

Loading Histories for Testing of Steel Beam-to-Column Assemblies, 

SAC Background Report SAC/BD-00/10.

Krawinkler, H., Parisi, F., Ibarra, L., Ayoub, A., and Medina, R., 2000, 

Development of a Testing Protocol for Woodframe Structures, 

CUREE Report No. W-02, Consortium of Universities for 

Earthquake Engineering Research, Richmond, California.

Kumar, G.R., Kumar, S.R., and Kalyanaraman, V., 2007, “Behaviour of 

frames with non-buckling bracings under earthquake loading,” 

Journal of Constructional Steel Research, Vol. 63, No. 2. 

Lee, L.H., Han, S.W., and Oh, Y.H., 1999, “Determination of ductility factor 

considering different hysteretic models,” Earthquake Engineering 

and Structural Dynamics, Vol. 28, 957–977.

Line, P., Waltz, N., and Skaggs, T., 2008, “Seismic equivalence parameters 

for engineered wood frame wood structural panel shear walls,” 

Wood Design Focus, Vol. 18 No. 2.

Mahin, S.A. and Bertero, V.V., 1981, “An evaluation of inelastic seismic 

design spectra,” Journal of the Structures Division, American 

Society of Civil Engineers, Vol. 107, No. 9, pp. 1777-1795.
FEMA P-795 References G-7

Medina, R. and Krawinkler, H., 2004, “Influence of hysteretic behavior on 

the nonlinear response of frame structures,” Proc. 13th World 

Conference on Earthquake Engineering, Vancouver, Canada. 

Merritt, S., Uang, C.M., and Benzoni, G., 2003a, Subassemblage Testing of 

CoreBrace Buckling-Restrained Braces, Report No. TR-03/01, 

University of California, San Diego. 

Merritt, S., Uang, C.M., and Benzoni, G., 2003b, Subassemblage Testing of 

StarSeismic Buckling-Restrained Braces, Report No. TR-03/04, 

University of California, San Diego.

Miranda, E. and Akkar, S.D., 2003, "Dynamic instability of simple structural 

systems," Journal of Structural Engineering, American Society of 

Civil Engineers, Vol. 129, No. 12, pp 1722-1727.

Newell, J., Uang, C.M., and Benzoni, G., 2005, Subassemblage Testing of 

CoreBrace Buckling-Restrained Braces (F series), Report No. TR05/01, University of California, San Diego.

Newell, J., Uang, C.M., and Benzoni, G., 2006, Subassemblage Testing of 

CoreBrace Buckling-Restrained Braces (G series), Report No. TR06/01, University of California, San Diego.

Nippon Steel Engineering, “Unbonded Brace: Basic Design Information,” 

Nippon Steel Engineering Co. Ltd., Building Construction and Steel 

Structures Div., Undated.

NIST, 2010, Evaluation of the FEMA P-695 Methodology for Quantification 

of Building Seismic Performance Factors, NIST GCR 10-917-8, 

prepared by the NEHRP Consultants Joint Venture, a partnership of 

the Applied Technology Council and the Consortium of Universities 

for Researh in Earthquake Engineering for the National Institute of 

Standards and Technology, Gaithersburg, Maryland.

OpenSees, 2009, Open System for Earthquake Engineering Simulation, 

Pacific Earthquake Engineering Research Center, University of 

California, Berkeley. Available at http://opensees.berkeley.edu/. 

Otani, S., 1981, “Hysteresis model of reinforced concrete for earthquake 

response analysis,” Journal, Fac. of Eng., University of Tokyo, 

Series B, Vol. XXXVI-11, 2, 407-441.

Panagiotakos, T.B., and Fardis, M.N., 2001, “Deformations of reinforced 

concrete members at yielding and ultimate,” ACI Structural Journal, 

Vol. 98, No.2.
G-8 References FEMA P-795

PEER/ATC, 2010, Modeling and Acceptance Criteria for Seismic Design 

and Analysis of Tall Buildings, PEER/ATC-72-1 Report, prepared 

by the Applied Technology Council in cooperation with the Pacific 

Earthquake Engineering Research Center, Redwood City, California.

Pincheira, J.A, Dotiwala, F.S., and D’Souza, J.T., 1999, “Spectral 

displacement demands of stiffness- and strength-degrading systems,” 

Earthquake Spectra, Vol. 15, No. 2, pp. 245–272.

Porter, M.L., 1987, “Sequential phased displacement (SPD) procedure for 

TCCMAR testing,” Proceedings, 3rd Meeting of the Joint Technical 

Coordinating Committee on Masonry Research, US-Japan 

Coordinated Research Program.

Powell, J.A., 2010, Evaluation of Special Concentrically Braced Frames for 

Improved Seismic Performance and Constructability, M.S.E. Thesis, 

University of Washington.

Rahnama, M. and Krawinkler, H., 1993, Effects of Soft Soil and Hysteretic 

Models on Seismic Demands, John A. Blume Earthquake 

Engineering Center Technical Report No. 108, Stanford University, 

Stanford, California.

Riddell, R. and Newmark, N.M., 1979a, Statistical Analysis of the Response 

of Nonlinear Systems Subjected to Earthquakes, Rep. No. UILIENG79-2016, Structural Research Series, Dept. of Civil 

Engineering, University of Illinois, Urbana.

Riddell, R. and Newmark, N.M., 1979b, “Force-deformation models for 

nonlinear analyses,” J. Struct. Div., American Society of Civil 

Engineers, 105, pp. 2773–2778.

Reaveley, L.D., Okahashi, T., and Farr, C.K., 2004, Corebrace Series E 

Buckling-Restrained Brace Test Results, University of Utah Report. 

Rosowsky, D., Elkins, L., and Carrol, C., 2004, Cyclic Tests of Engineered 

Shear Walls Considering Different Plate Washers, prepared by 

Oregon State University for the American Forest and Paper 

Association.

Ruiz-Garcia, J. and Miranda, E., 2005, Performance-Based Assessment of 

Existing Structures Accounting for Residual Displacements, John A. 

Blume Earthquake Engineering Center Technical Report No. 153, 

Stanford University, Stanford, California.

Sabelli, R., 2007, Teaching Principles of Seismic-Resistant Design of Steel 

Building Structures: Special Plate Shear Walls, prepared for the 
FEMA P-795 References G-9

American Institute of Steel Construction. Available at 

http://www.aisc.org/content.aspx?id=21490. Last accessed February 

25, 2010.

Sim, H.B., Kim, D.W., Uang, C.M., and G. Benzoni, G., 2010, 

Subassemblage Testing of CoreBrace Buckling-Restrained Braces (J 

series), Report No. TR-09/02, 2010, University of California, San 

Diego.

Song J.K. and Pincheira, J.A., 2000, “Seismic analysis of older reinforced 

concrete columns,” Earthquake Spectra, Vol. 16, No. 4, pp. 817–

851.

SST, 2009, Wood Construction Connectors Catalogue, Simpson Strong-Tie 

Company, Inc. Available at http://www.strongtie.com/literature

Talbot, K.C., Reaveley, L.D., and Pantelides, C.P., 2009, “Structural 

performance of stapled wood shear walls under dynamic cyclic

loads,” Earthquake Spectra, Vol. 25, No. 1, pp. 161-183.

. 

Last accessed November 20, 2009.

Tsai, K.C. and Hsiao, P.C., 2008, “Pseudo-dynamic test of a full-scale 

CFT/BRB frame—Part II: Seismic performance of bucklingrestrained braces and connections,” Earthquake Engineering and 

Structural Dynamics, Vol. 37, No. 7. 

Uang, C.M., Yu, K., and Gilton, C., 2000, Cyclic Response of RBS Moment 

Connections: Loading Sequence and Lateral Bracing Effects, 

Structural Steel Research Project Report No. SSRP-99/13.

Vamvatsikos, D. and Cornell, C.A., 2002, “Incremental Dynamic Analysis,” 

Earthquake Engineering and Structural Dynamics, Vol. 31, Issue 3, 

pp. 491-514.

Vian, D. and Bruneau, M., 2003, “Tests to structural collapse of single 

degree of freedom frames subjected to earthquake excitations,” 

Journal of Structural Engineering, American Society of Civil 

Engineers, Vol. 129, No. 112, pp. 1676-1685.

Wakabayashi, M., Nakamura, T., and Yoshida, N., 1977, “Experimental 

studies on the elastic-plastic behavior of braced frames under 

repeated horizontal loading: Part 1 experiments of braces with an Hshaped cross section in frame,” Bulletin of the Disaster Prevention 

Research Institute, Vol. 27, Part 3, No. 251. 

Wakabayashi, M., Nakamura, T., and Yoshida, N., 1980, “Experimental 

studies on the elastic-plastic behavior of braced frames under 
G-10 References FEMA P-795

repeated horizontal loading: Part 1 experiments of braces composed

of steel circular tubes, angle-shapes, flat bars and round bars,” 

Bulletin of the Disaster Prevention Research Institute, Vol. 29, Part 

3, No. 264. 

Zareian, F., 2006, Simplified Performance-Based Earthquake Engineering, 

Dissertation, Department of Civil and Environmental Engineering, 

Stanford University.

Zareian, F. and H. Krawinkler, 2010, “Structural system parameter selection 

based on collapse potential of buildings in earthquakes,” Journal of 

Structural Engineering, American Society of Civil Engineers, Vol. 

136, No. 8, pp. 933-943.
FEMA P-795 Project Participants H-1

Project Participants

ATC Management and Oversight

Christopher Rojahn (Project Executive)

Applied Technology Council

201 Redwood Shores Parkway, Suite 240

Redwood City, California 94065

Jon A. Heintz (Project Quality Control Monitor)

Applied Technology Council

201 Redwood Shores Parkway, Suite 240

Redwood City, California 94065

William T. Holmes (Project Technical Monitor)

Rutherford & Chekene

55 Second Street, Suite 600

San Francisco, California 94105

Ayse Hortacsu (Project Manager)

Applied Technology Council

201 Reddwod Shores Parkway, Suite 240

Redwood City, California 94065

FEMA Project Officer

Michael Mahoney

Federal Emergency Management Agency

500 C Street, SW

Washington, DC 20472

FEMA Technical Monitor

Robert D. Hanson

Federal Emergency Management Agency

2926 Saklan Indian Drive

Walnut Creek, California 94595

Project Management Committee

Charles Kircher (Project Technical Director)

Kircher & Associates, Consulting Engineers

1121 San Antonio Road, Suite D-202

Palo Alto, California 94303

Gregory Deierlein

Stanford University

Dept. of Civil & Environmental Engineering

John A. Blume Earthquake Engineering Center

Stanford, California 94305

Andre Filiatrault

University at Buffalo

Dept. of Civil, Structural & Environ. Engineering

134 Ketter Hall

Buffalo, New York 14260

James R. Harris

J.R. Harris & Company 

1776 Lincoln Street, Suite 1100

Denver, Colorado 80203

John Hooper

Magnusson Klemencic Associates

1301 Fifth Avenue, Suite 3200

Seattle, Washington 98101

Helmut Krawinkler

Stanford University

Dept. of Civil & Environmental Engineering

473 Via Ortega 

Stanford, California 94305

Kurt Stochlia

International Code Council

5360 Workman Mill Road

Whittier, California 90601

Christopher Rojahn (ex-officio)

William Holmes (ex-officio) 

Jon A. Heintz (ex- officio)

Ayse Hortacsu (ex- officio)
H-2 Project Participants FEMA P-795

Working Groups

Curt Haselton

Department of Civil Engineering

California State University, Chico

Langdon Hall, Room 209F

Chico, California 95926

Abbie Liel

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

University of Colorado

1111 Engineering Drive

Boulder, CO 80309

Seyed Hamid Shivaee

University of Colorado

1111 Engineering Drive

Boulder, CO 80309

Jackie Steiner

California State University, Chico

Langdon Hall

Chico, California 95926

Project Review Panel

S.K. Ghosh 

S.K. Ghosh Associates Inc.

334 East Colfax Street, Unit E

Palatine, Illinois 60067

Mark Gilligan

Structural Engineer

1327 Blake Street

Berkeley, California 94702

Ramon Gilsanz

Gilsanz Murray Steficek LLP

129 W. 27th Street, 5th Floor

New York, New York 10001

Ronald O. Hamburger

Simpson Gumpertz & Heger

The Landmark @ One Market, Suite 600

San Francisco, California 94105

Richard E. Klingner

University of Texas at Austin 

10100 Burnet Road

Austin, Texas 78758

Philip Line

URS Corporation

200 Orchard Ridge Drive, Suite 101

Gaithersburg, Maryland 

Bonnie E. Manley, P.E.

AISI Regional Director

41 Tucker Road

Norfolk, Maryland 02056

Rawn Nelson

R.F. Nelson and Associates

840 20th Street

Hermosa Beach, California 90254

Andrei M. Reinhorn

University at Buffalo

Dept. of Civil, Structural & Environ. Eng.

231 Ketter Hall

Buffalo, New York 14260

Rafael Sabelli 

Walter P. Moore

595 Market Street, Suite 950

San Francisco, California 94105