Seismic Evaluation and Retrofit 

of Multi-Unit Wood-Frame 

Buildings With Weak First 

Stories

FEMA P-807 / May 2012

FEMA

FEMA P-807 

Seismic Evaluation and Retrofit of Multi-Unit 

Wood-Frame Buildings With Weak First Stories 

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 

Cathleen Carlisle, Project Monitor 

Daniel Shapiro, Technical Monitor 

Washington, D.C. 

TASK ORDER CONTRACT MANAGEMENT 

Christopher Rojahn (Project Executive Director) 

Thomas R. McLane (Project Manager) 

Jon A. Heintz (Project Quality Control Monitor) 

William T. Holmes (Project Technical Monitor) 

PROJECT REVIEW PANEL 

Chris Poland (Chair) 

Tony DeMascole 

Laurence Kornfield 

Bret Lizundia 

Joan MacQuarrie 

Andrew Merovich 

Tom Tobin 

PROJECT MANAGEMENT COMMITTEE 

David Mar (Project Technical Director) 

David Bonowitz 

Kelly Cobeen 

Dan Dolan 

Andre Filiatrault 

John Price 

ANALYSIS CONSULTANTS 

Maikol Del Carpio 

Mike Korolyk 

May 2012 
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. 

Cover Photo: Near-collapse of typical weak-story wood-frame buildings in the 1989 Loma Prieta earthquake.
FEMA P-807 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 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. 

In recent earthquake events, FEMA has observed that multi-unit wood-frame 

buildings with a weak first story represent a significant risk in highly seismic 

regions of the United States because of their high potential for collapse. This 

risk is magnified by the sheer numbers of these buildings that still exist and 

the numbers of people who occupy them. This collapse potential is due 

primarily to their soft or weak first-story walls, which have often been 

weakened by large numbers of openings such as garages or store front 

windows. 

FEMA worked with ATC to develop these guidelines to address seismic 

retrofit requirements for weak-story wood-frame buildings in seismically 

active regions of the United States, with a particular focus on Northern and 

Southern California and the Pacific Northwest. The guidelines focus on 

multi-family, multi-story buildings with weak first stories, such as those 

damaged in the Marina District of San Francisco in the 1989 Loma Prieta 

earthquake, and apartment buildings with tuck-under parking, such as those 

damaged in Southern California in the 1994 Northridge earthquake. 

These seismic retrofitting guidelines are the first to focus solely on the weak 

first story and to provide just enough additional strength to protect the first 

floor from collapse but not so much as to drive earthquake forces into the 

upper stories, placing them at risk of collapse. They are also the first to take 

into account the strength provided by existing non-structural walls. Both of 
iv Foreword FEMA P-807 

these steps will make seismic retrofitting more affordable. This methodology 

does presume, however, that the upper stories are basically regular and do 

provide enough strength to match the retrofitted first story. 

FEMA is indebted to the Project Management Committee of David Mar 

(Project Technical Director), David Bonowitz, Kelly Cobeen, Dan Dolan, 

Andre Filiatrault, and John Price, for preparing this report, and to Mike 

Korolyk, who as the Analysis Consultant conducted the computer analyses to 

validate the guidelines. We also wish to thank the Project Review Panel of 

Chris Poland (Chair), Tony DeMascole, Laurence Kornfield, Bret Lizundia 

(ATC Board Representative), Joan MacQuarrie, Andrew Merovich, and Tom 

Tobin, who provided expert review and guidance throughout the 

developmental effort. Without their dedication and hard work, this project 

would not have been possible. 

– Federal Emergency Management Agency 
FEMA P-807 Preface v 

Preface

In May 2009 the Applied Technology Council (ATC), with funding from the 

Federal Emergency Management Agency (FEMA) under Task Order 

Contract HSFEHQ-08-D-0726, commenced development of simplified 

guidelines for the seismic retrofit of weak-story wood-frame buildings—one 

of several projects in a task order series to develop written guidance for 

FEMA on the creation, update, and maintenance of seismic evaluation 

and rehabilitation documents for existing buildings.

Multi-unit wood-frame buildings with a weak first story represent a 

significant risk in highly seismic regions of the United States, not only 

because of their damage and collapse potential, but also because of their size, 

prevalence and the high numbers of people who occupy them. In San 

Francisco, for example, approximately 4,400 older, pre-seismic-code, woodframe residential buildings have been inventoried that contain five or more 

living units and are 3 or more stories in height (ATC, 2009a). Most of these 

buildings have potentially soft or weak ground floor (first story) walls, as do 

an expectedly high but unknown number of pre-seismic-code 3-to-5 story 

wood-frame commercial buildings, and similar buildings constructed after 

1974 not included in the San Francisco inventory. 

FEMA and ATC agreed that the retrofit guidelines development project 

should address seismic retrofit requirements for weak-story wood-frame 

buildings in seismically active regions of the United States, focusing 

primarily on Northern and Southern California and the Pacific Northwest. 

Configurations to be addressed included multi-family, multi-story buildings 

with weak first stories, such as those prevalent in San Francisco, and 

apartment buildings with tuck-under parking, such as those significantly 

damaged by the 1994 Northridge earthquake in Southern California. The 

project team was also charged with developing practical, model code 

provisions for seismic retrofit of weak-story wood-frame buildings that can 

be adopted by cities such as San Francisco and that are written to ensure that 

application and enforcement is uniform and enforceable. 

This Guidelines document sets forth the framework for procedures for 

seismic evaluation and retrofit of weak-story wood-frame buildings. 

Throughout this document the term weak-story is used to describe a 

building’s vulnerability, rather than soft-story. The reason is that while both 
vi Preface FEMA P-807 

flexibility and strength contribute to the structure’s response, strength is the 

more dominant characteristic. 

ATC is indebted to the ATC Project Management Committee, which 

consisted of David Mar (Project Technical Director), David Bonowitz, Kelly 

Cobeen, Dan Dolan, Andre Filiatrault, and John Price, for their efforts in 

researching and preparing this report; to Mike Korolyk, who served as the 

Analysis Consultant and conducted thousands of computer analyses to 

support and validate the guidelines; to Maikol Del Carpio, who assisted in 

the data analysis; and to the Project Review Panel, which consisted of Chris 

Poland (Chair), Tony DeMascole, Laurence Kornfield, Bret Lizundia (ATC 

Board Representative), Joan MacQuarrie, Andrew Merovich, and Tom 

Tobin, who provided expert review and guidance throughout the 

developmental effort. Thomas R. McLane served as Project Manager, 

William Holmes served as the Project Technical Monitor, and Peter Mork 

provided report production services. The affiliations of these individuals are 

provided in the list of Project Participants. 

ATC also gratefully acknowledges the input, support, and guidance provided 

by Michael Mahoney (FEMA Project Officer), Cathleen Carlisle (FEMA 

Project Monitor), Robert Hanson (FEMA Subject Matter Expert), and Daniel 

Shapiro (FEMA Technical Monitor). 

Jon A. Heintz Christopher Rojahn 

ATC Director of Projects ATC Executive Director 
FEMA P-807 Table of Contents vii 

Table of Contents

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

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

List of Figures ............................................................................................. xiii 

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

Glossary ...................................................................................................... xxv 

1. Introduction ..........................................................................................1 

1.1 Earthquake Risks of Multi-Unit Weak-Story Wood-Frame 

Buildings ......................................................................................1 

1.2 Weak-Story Building Characteristics ...........................................2 

1.2.1 The Critical Deficiency: A First Story Lacking 

Adequate Strength or Stiffness ........................................3 

1.3 Engineering Codes and Standards ................................................4 

1.3.1 The Guidelines as an Alternative ....................................5 

1.4 Purpose and Intended Use of the Guidelines ................................6 

1.4.1 Policy Options .................................................................7 

1.4.2 Selecting Performance Objectives ...................................8 

1.5 Validation ................................................................................... 10 

1.6 The Weak-Story Tool ................................................................. 10 

1.7 Guidelines Organization and Content ........................................ 10 

2. Technical Overview ............................................................................ 13 

2.1 Statistical Basis........................................................................... 15 

2.2 Modeling Actual and Surrogate Structures ................................ 15 

2.2.1 The Surrogate Models ................................................... 15 

2.2.2 Characterizing an Existing Building ............................. 17 

2.3 Acceptability Criteria ................................................................. 18 

2.3.1 Performance Measure .................................................... 18 

2.3.2 Performance Objective .................................................. 18 

2.3.3 Relationship to Other Codes and Standards .................. 19 

2.4 Critical Deficiencies ................................................................... 21 

2.5 Retrofit Design Philosophy ........................................................ 22 

2.5.1 Cost-Effective, First-Story Retrofit ............................... 22 

2.5.2 Bounded Design and Relative Strength ......................... 24 

2.6 Limitations and Eligibility Requirements .................................. 25 

2.6.1 General Eligibility Requirements .................................. 26 

2.6.2 Upper-Story Eligibility Requirements ........................... 26 

2.6.3 First-Story, Basement, and Foundation Eligibility 

Requirements ................................................................. 27 

2.6.4 Floor and Roof Diaphragms Eligibility 

Requirements ................................................................. 28 
viii Table of Contents FEMA P-807 

3. Simplified Evaluation ........................................................................ 33 

3.1 Purpose ...................................................................................... 33 

3.1.1 Limitations .................................................................... 33 

3.2 Simplified Evaluation Procedure ............................................... 33 

3.3 Building Survey ......................................................................... 34 

3.3.1 First-Story Survey ......................................................... 34 

3.3.2 Upper-Story Survey ...................................................... 35 

3.4 Building Characterization .......................................................... 35 

3.4.1 Total Building Weight, W ............................................. 36 

3.4.2 Shear Strengths of First-Story Walls ............................ 36 

3.4.3 Shear Strength of First Story ........................................ 37 

3.4.4 Center of Strength (COS1) of First Story ...................... 37 

3.4.5 Center of Strength (COS2) of Upper Stories ................. 38 

3.4.6 Eccentricity ................................................................... 38 

3.4.7 Simplified Torsion Coefficient, CTs .............................. 38 

3.5 Simplified Evaluation of Seismic Performance ......................... 39 

3.5.1 Site-Specific Spectral Acceleration Demand ................ 39 

3.5.2 Story-Height Factor, Qs ................................................ 40 

3.5.3 Simplified Spectral Acceleration Capacity, Scs ............ 40 

3.5.4 Comparison of Demand Versus Capacity ..................... 40 

4. Structure Characterization for Detailed Evaluation ...................... 41 

4.1 Introduction................................................................................ 41 

4.2 Wall Materials ........................................................................... 42 

4.3 Detailed Building Survey .......................................................... 42 

4.4 Load-Drift Curves for Common Sheathing Materials ............... 43 

4.5 Wall Line Load-Drift Curves ..................................................... 47 

4.5.1 Load-Drift Curves for Combinations of Sheathing 

Materials ....................................................................... 49 

4.5.2 Adjustment Factor for Openings in the Wall Line ....... 50 

4.5.3 Adjustment Factor for Overturning .............................. 53 

4.5.4 Drift Ratio Adjustment for First-Story Wall Line 

Height ........................................................................... 56 

4.6 Determine Strength of Each Story ............................................. 57 

4.6.1 Translational Load-Drift Curve .................................... 57 

4.6.2 Peak Strength ................................................................ 58 

4.6.3 Drift Ratio at Peak Strength .......................................... 59 

4.6.4 Center of Strength ......................................................... 60 

4.6.5 Torsional Eccentricity at the First Story ....................... 61 

4.6.6 Load-Rotation Curve .................................................... 61 

4.6.7 Torsional Strength ........................................................ 63 

4.6.8 Torsional Demand ........................................................ 64 

4.7 Characteristic Coefficients ......................................................... 64 

4.7.1 Normalized First-Story Strength ................................... 64 

4.7.2 Normalized Upper-Story Strength ................................ 65 

4.7.3 Weak-Story Ratio, AW ................................................... 66 

4.7.4 Strength-Degradation Ratio, CD.................................... 66 

4.7.5 Torsion Coefficient, CT ................................................. 66 

4.7.6 Story Height Factor, Qs ................................................. 67 

5. Detailed Evaluation ........................................................................... 69 

5.1 Evaluation Steps ........................................................................ 69 

5.2 Calculate the Median Spectral Acceleration Capacity ............... 71 
FEMA P-807 Table of Contents ix 

5.3 Calculate the Spectral Acceleration Capacity ............................ 72 

5.4 Evaluate the Existing Structure .................................................. 74 

5.4.1 Compare the Spectral Acceleration Capacity with 

Site-Specific Demand .................................................... 74 

5.4.2 Calculating the Probability of Exceedance .................... 75 

6. Retrofit ................................................................................................ 77 

6.1 Retrofit Scope ............................................................................. 77 

6.2 Retrofit Strength ......................................................................... 79 

6.2.1 Estimated Minimum Required Strength of the 

Retrofitted First Story .................................................... 80 

6.2.2 Estimated Maximum Acceptable Strength of the 

Retrofitted First Story .................................................... 81 

6.2.3 Estimated Ranges of Acceptable Retrofit Strength ....... 83 

6.3 Locating Retrofit Elements ........................................................ 85 

6.3.1 Retrofit Element Location to Minimize Torsion ........... 86 

6.3.2 Retrofit Element Location to Ensure Eligibility ............ 87 

6.4 Confirmed Performance of the Retrofitted Structure ................. 88 

6.4.1 Retrofits Intended to Satisfy the Performance 

Objective ....................................................................... 90 

6.4.2 Optimized Retrofits that Do Not Satisfy the 

Performance Objective .................................................. 90 

6.5 Retrofit Element Selection and Design ...................................... 91 

6.5.1 Load Path Components ................................................. 93 

6.5.2 Second Floor Diaphragm............................................... 93 

6.5.3 Wood Structural Panel Shear Walls .............................. 93 

6.5.4 Steel Moment Frames .................................................... 94 

6.5.5 Steel Braced Frames ...................................................... 94 

6.5.6 Concrete or Reinforced Masonry Shear Walls .............. 95 

7. Alternative Performance Assessment ............................................... 97 

7.1 Purpose ....................................................................................... 97 

7.2 Assessment Background ............................................................. 97 

7.3 Interstory Drift Limits ................................................................ 97 

7.4 Spectral Acceleration Capacity .................................................. 98 

7.5 Estimating the Drift Limit Probability of Exceedance ............... 99 

Appendix A: Guide to Weak-Story Tool ................................................. A-1 

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

A.2 Obtaining the Weak-Story Tool .............................................. A-1 

A.3 System Requirements .............................................................. A-1 

A.4 Weak-Story Tool Installation .................................................. A-1 

A.5 Basic Controls ......................................................................... A-2 

A.6 General Building Properties and Geometry ............................ A-2 

A.7 CAD Interface ......................................................................... A-4 

A.7.1 Analytical Entities ...................................................... A-4 

A.7.2 Non-Analytical Entities .............................................. A-4 

A.7.3 Other CAD Tools ....................................................... A-6 

A.8 Defining Sheathing Assemblies .............................................. A-7 

A.9 Assigning Level Properties and Laying Out Walls ............... A-11 

A.9.1 The Shearwall Layout Tab ....................................... A-12 

A.9.2 Shearwall Table ........................................................ A-15 
x Table of Contents FEMA P-807 

A.10 Evaluation and Retrofit Summary ......................................... A-15 

A.10.1 Evaluation Data Tab ................................................. A-15 

A.10.2 Backbone Curves Tab ............................................... A-17 

A.10.3 Performance Data Tab .............................................. A-17 

Appendix B: Model Provisions for Mitigation Programs ...................... B-1 

B.1 Targeted Mitigation Programs ................................................. B-1 

B.1.1 Planning and Program Development .......................... B-2 

B.1.2 Screening .................................................................... B-3 

B.1.3 Evaluation ................................................................... B-3 

B.1.4 Retrofit Prioritization .................................................. B-4 

B.1.5 Retrofit ........................................................................ B-5 

B.2 Program Performance Objectives ............................................ B-5 

B.3 Model Provisions and Commentary ........................................ B-7 

Appendix C: Example Calculations ......................................................... C-1 

C.1 Simplified Evaluation (Chapter 3) ........................................... C-3 

C.2 Structure Characterization and Evaluation (Chapters 4 

and 5) ....................................................................................... C-7 

C.3 Retrofit (Chapter 6) .................................................................. C-9 

C.4 Torsion Calculations (Chapters 3 and 4) ............................... C-17 

Appendix D: Characterization of Existing Materials ............................ D-1 

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

D.2 Research Addressing Wall Bracing Materials ......................... D-1 

D.3 Load-Deflection Backbone ...................................................... D-5 

D.3.1 Plaster on Wood Lath ................................................. D-6 

D.3.2 Horizontal Lumber Sheathing ..................................... D-8 

D.3.3 Diagonal Lumber Sheathing ....................................... D-9 

D.3.4 Stucco ....................................................................... D-11 

D.3.5 Gypsum Wallboard ................................................... D-13 

D.3.6 Plaster on Gypsum Lath ............................................ D-15 

D.3.7 Wood Structural Panel Siding .................................. D-17 

D.3.8 Wood Structural Panel Sheathing ............................. D-18 

D.4 Recommended Descriptions of Wall Bracing Materials ....... D-29 

D.5 Adjustment Factor for Combinations of Bracing Materials .. D-30 

D.6 Adjustment Factor for Openings in the Wall Line ................. D-32 

D.7 Adjustment Factor for Overturning ....................................... D-33 

D.8 Drift Adjustment for First-Story Wall-Line Height ............... D-34 

D.9 Descriptions of Damage versus Drift ..................................... D-35 

D.10 Recommended Future Research ............................................ D-54 

Appendix E: Detailed Analytical Background ....................................... E-1 

E.1 Purpose .................................................................................... E-1 

E.2 General ..................................................................................... E-1 

E.2.1 Overview and Limitations .......................................... E-1 

E.2.2 Building Characterization ........................................... E-1 

E.2.3 IDA Approach ............................................................ E-2 

E.2.4 Material Characterization ........................................... E-3 

E.2.5 Performance Criteria ................................................... E-5 

E.3 Modeling Details ..................................................................... E-7 

E.3.1 Software ...................................................................... E-7 
FEMA P-807 Table of Contents xi 

E.3.2 Typical Building Model .............................................. E-7 

E.3.3 Hysteretic Damping ..................................................... E-9 

E.3.4 Viscous Damping ...................................................... E-11 

E.3.5 P-Delta ....................................................................... E-11 

E.3.6 Accounting for Overturning Effects .......................... E-11 

E.4 Ground Acceleration Records ................................................ E-14 

E.5 Translational Analyses ........................................................... E-14 

E.5.1 Analysis Flow ............................................................ E-14 

E.5.2 Median Performance ................................................. E-15 

E.5.3 Interpolation for Intermediate Values of CD .............. E-18 

E.5.4 Adjustment for Uncertainty ....................................... E-20 

E.5.5 Assessment and Probability of Exceedance .............. E-26 

E.5.6 Retrofit Analyses ....................................................... E-29 

E.5.7 Effect of First-Story Retrofit ..................................... E-31 

E.5.8 Estimating the Minimum Retrofit for Achieving 

Desired Performance ................................................. E-33 

E.5.9 Wood-Sheathed Walls versus Moment Frame 

Retrofit ...................................................................... E-34 

E.5.10 First-Story Height ...................................................... E-36 

E.6 Torsional Analyses ................................................................. E-38 

E.6.1 Discussion on Torsional Behavior ............................ E-38 

E.6.2 Torsion Coefficient, CT ............................................. E-38 

E.6.3 Modeling ................................................................... E-39 

E.6.4 Response-History Input ............................................. E-39 

E.6.5 Assessing the Effect of Torsion ................................. E-41 

E.6.6 Simplified Torsion Coefficient, CTs .......................... E-42 

Appendix F: Validation of Analysis Methods .......................................... F-1 

F.1 Purpose ..................................................................................... F-1 

F.2 The Building Under Consideration .......................................... F-1 

F.3 Differences in Scope of Analysis ............................................. F-2 

F.3.1 Number of Stories ....................................................... F-3 

F.3.2 Sheathing Assemblies ................................................. F-3 

F.4 Differences in Analytical Methods ........................................... F-3 

F.4.1 Software ...................................................................... F-3 

F.4.2 Viscous Damping ........................................................ F-6 

F.4.3 Backbone of Increasing Retrofit .................................. F-7 

F.5 Comparison of Results ............................................................. F-8 

F.5.1 Existing Building ......................................................... F-9 

F.5.2 Retrofitted Building ................................................... F-10 

F.6 The Optimal Retrofit for Relative Strength ............................ F-11 

F.7 Conclusions ............................................................................ F-12 

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

Project Participants .................................................................................. H-1 

FEMA P-807 List of Figures xiii 

List of Figures

Figure 1-1 Photos illustrating near-collapse of typical weak-story 

wood-frame buildings in the 1989 Loma Prieta 

earthquake (left) and the 1994 Northridge earthquake 

(right) .....................................................................................1 

Figure 1-2 Exploded views of three common multi-unit wood-frame 

residential building styles (roof system, top row; 

first story, bottom row). .........................................................3 

Figure 2-1 Flow chart illustrating relationships between the 

Guidelines technical chapters .............................................. 14 

Figure 2-2 Plots of interstory drift versus shear force showing drift 

limits, L, used to develop fragility relationships from 

the surrogate models ............................................................ 17 

Figure 2-3 Plan diagrams of three weak-story buildings. ...................... 22 

Figure 2-4 Schematic response of a corner building subject to 

torsion under loads in either direction, due to open wall 

lines on two sides at the first story. ...................................... 23 

Figure 2-5 Schematic response of a building with a slightly weak 

story in the long direction and with torsion under loads 

in the long direction. ............................................................ 23 

Figure 2-6 Plots illustrating floor displacements and drift ratios in a 

building with constant upper-story strength and varying 

first-story strength. ............................................................... 25 

Figure 2-7 Floor plan schematic showing limits on eccentricity 

between the center of strength (Cs) of each upper story 

and the center of mass (Cm ) of the floor below it. ............... 27 

Figure 2-8 Floor plan schematic showing use of qualifying wall 

lines to meet diaphragm aspect ratio limits. ......................... 29 

Figure 2-9 Floor plan schematic showing locations of chords for 

cantilevered diaphragms that must satisfy eligibility 

rules ...................................................................................... 30 

Figure 2-10 Floor plan schematic showing reentrant corner limits and 

use of qualifying wall lines to satisfy eligibility rules. ........ 30 

Figure 2-11 Floor plan schematic showing diaphragm openings that 

must be limited in size to satisfy eligibility requirements. .. 31 
xiv List of Figures FEMA P-807 

Figure 3-1 Illustration of wall lengths for an example wall line ........... 37 

Figure 4-1 Unit load-drift curves for sheathing materials with 

high-displacement capacity ................................................. 45 

Figure 4-2 Unit load-drift curves for sheathing materials with 

low-displacement capacity .................................................. 45 

Figure 4-3 Unit load-drift curves for all sheathing materials 

considered; note the large differences in both peak 

strength and displacement capacities. ................................. 46 

Figure 4-4 Schematic of a typical wall assembly composed of 

various layers ...................................................................... 49 

Figure 4-5 Composite unit load-drift curve of a wall assembly 

comprising stucco, gypsum wallboard, and wood 

structural panels (structural plywood in figure), using 

100% of the wood structural panel (WSP) sheathing 

plus 50% of the other sheathing materials........................... 50 

Figure 4-6 Composite unit load-drift curve of a wall assembly 

comprising stucco, gypsum wallboard and wood 

structural panels (structural plywood in figure), using 

50% of the wood structural panel (WSP) sheathing 

plus 100% of the other sheathing materials ........................ 51 

Figure 4-7 Controlling unit load-drift curve of a wall assembly 

comprising stucco, gypsum wallboard, and wood 

structural panels .................................................................. 51 

Figure 4-8 Wall schematic showing variables in the adjustment 

factor for openings .............................................................. 52 

Figure 4-9 Wall schematic showing variables in the calculated 

adjustment factor for overturning ........................................ 55 

Figure 4-10 Wall schematics and load-drift curves illustrating drift 

adjustment parameters for varying first-story wall 

line heights .......................................................................... 57 

Figure 4-11 Wall-plan schematic and depiction of the first-story 

load-drift curve as the sum of first story wall line load 

drift curves, y-direction ....................................................... 59 

Figure 4-12 Wall-plan schematic showing location of center of 

strength at the first story ...................................................... 60 

Figure 4-13 Wall-plan schematic and related torsional-load rotation 

curves illustrating how the first story load-rotation curve 

is computed ......................................................................... 62 
FEMA P-807 List of Figures xv 

Figure 4-14 Wall-plan schematic depicting how the torsional 

demand on the first story is calculated ................................. 64 

Figure 4-15 Load-drift curve depicting determination of 

strength-degradation ratio, CD .............................................. 67 

Figure 5-1 Flowchart of typical evaluation procedure .......................... 70 

Figure 5-2 Plot showing variation in spectral acceleration capacity 

(spectral capacity) as a function of different existing 

building characteristics. ....................................................... 73 

Figure 6-1 Flowchart of typical retrofit procedure ................................ 78 

Figure 6-2 Plot of spectral acceleration capacity (spectral capacity) 

versus strength of retrofitted first-story, for buildings 

with strong upper stories ...................................................... 82 

Figure 6-3 Plot of spectral acceleration capacity (spectral capacity) 

versus strength of retrofitted first-story, for buildings 

with weak upper stories. ...................................................... 84 

Figure 6-4 Floor plan schematic showing use of retrofit elements to 

meet diaphragm aspect ratio limits. ..................................... 88 

Figure 6-5 Floor plan schematic showing use of retrofit elements to 

satisfy re-entrant corner limits, east-west analysis ............... 89 

Figure 6-6 Floor plan schematic showing use of retrofit elements to 

satisfy re-entrant corner limits, north-south analysis ........... 89 

Figure 6-7 Simplified load-drift curve for steel Special Moment 

Frame retrofit elements ........................................................ 94 

Figure 7-1 Illustration of drift limit definitions relative to two 

sheathing backbone curves with CD = 0.0 and 1.0, 

respectively. ......................................................................... 98 

Figure 7-2 Curves showing the relationship between as-built median 

spectral acceleration capacity, S, and base-normalized 

upper-story strength for various weak-story ratios, AW, 

and for the Onset of Damage set of drift limits.................. 100 

Figure 7-3 Curves showing the relationship between as-built median 

spectral acceleration capacity, S, and base-normalized 

upper-story strength for various weak-story ratios, AW, 

and for the Onset of Damage set of drift limits.................. 100 

Figure 7-4 Curves showing the relationship between as-built median 

spectral acceleration capacity, S, and base-normalized 

upper-story strength for various weak-story ratios, AW, 

and for the Onset of Strength Loss set of drift limits. ........ 101 
xvi List of Figures FEMA P-807 

Figure 7-5 Curves showing the relationship between as-built median 

spectral acceleration capacity, S, and base-normalized 

upper-story strength for various weak-story ratios, AW, 

and for the Onset of Strength Loss set of drift limits ......... 101 

Figure A-1 Screenshot of contents of WeakStoryTool folder 

containing installation files. .............................................. A-2 

Figure A-2 Screenshot of control buttons ............................................ A-2 

Figure A-3 Screenshot of General control ........................................... A-3 

Figure A-4 Reference geometrical input for sample building ............. A-6 

Figure A-5 Screen-shot of object snap menu ....................................... A-7 

Figure A-6 Screenshot of Assemblies control. ..................................... A-8 

Figure A-7 Screenshot of table of sheathing assemblies in 

Assemblies control ............................................................. A-9 

Figure A-8 Screenshot of form for defining assembly specifications 

for assemblies comprising standard sheathing layers ...... A-10 

Figure A-9 Screenshot of form for defining custom load-drift 

curves for retrofit assemblies .......................................... A-11 

Figure A-10 Screenshot of the Shearwall Layout tab in the Levels 

control for an example building ...................................... A-12 

Figure A-11 Screenshot of the perforation calculator form in the 

Levels/Shearwall Layout control ..................................... A-14 

Figure A-12 Screenshot of the Evaluation Data tab in the Summary 

control for an example building ...................................... A-16 

Figure A-13 Screenshot of the Backbone Curves tab in the Summary 

control for an example building showing first-story 

load-drift curve before retrofit ......................................... A-18 

Figure A-14 Screenshot of the Backbone Curves tab in the Summary 

control for an example building showing first-story 

load-drift curve after retrofit. .......................................... A-19 

Figure A-15 Screenshot of the Performance Data tab in the Summary 

control for an example building ...................................... A-20 

Figure A-16 Illustration of evaluation flow Upward from SMS. ........... A-21 

Figure A-17 Illustration of evaluation flow /Right from drift limit 

probability of exceedance. ............................................... A-21 
FEMA P-807 List of Figures xvii 

Figure C-1 Street elevation of example building ................................. C-1 

Figure C-2 Example building first-floor plan ....................................... C-3 

Figure C-3 Example building first-floor wall lengths and locations .... C-7 

Figure C-4 Example building upper-story wall lengths and 

locations ............................................................................. C-7 

Figure D-1 Load-drift data for plaster on wood lath ........................... D-7 

Figure D-2 Load-drift data for horizontal wood sheathing. ................ D-9 

Figure D-3 Load-drift data for diagonal lumber sheathing ............... D-11 

Figure D-4 Load-drift data for stucco................................................ D-13 

Figure D-5 Load-drift data for gypsum wallboard ............................ D-15 

Figure D-6 Load-drift data for plaster on gypsum lath...................... D-16 

Figure D-7 Load-drift data for wood structural panel siding. ........... D-17 

Figure D-8 Load-drift data for wood structural panel 8d@6............. D-20 

Figure D-9 Load-drift data for wood structural panel 8d@4............. D-22 

Figure D-10 Load-drift data for wood structural panel 8d@3............. D-24 

Figure D-11 Load-drift data for wood structural panel 10d@6 ........... D-25 

Figure D-12 Load-drift data for wood structural panel 10d@4 ........... D-27 

Figure D-13 Load-drift data for wood structural panel 10d@2 ........... D-29 

Figure D-14 Plotted load-deflection curves for combined materials .. D-32 

Figure D-15 Crack maps for stucco sheathing at 0.2% drift for 

(top) Wall 1 and (bottom) Wall 2. .................................. D-36 

Figure D-16 Crack maps for stucco sheathing at 0.4% drift for 

(top) Wall 1 and (bottom) Wall 2. .................................. D-37 

Figure D-17 Crack maps for stucco sheathing at 0.7% drift for 

(top) Wall 1 and (bottom) Wall 2. .................................. D-38 

Figure D-18 Crack maps for stucco sheathing at failure for 

(top) Wall 1 and (bottom) Wall 2 ................................... D-39 

Figure D-19 Photos of characteristic cracking at 0.4% drift. .............. D-40 

Figure D-20 Photos of characteristic cracking at 1.5% drift ............... D-41 

Figure D-21 Photos of characteristic cracking at failure ..................... D-42 
xviii List of Figures FEMA P-807 

Figure D-22 Crack maps for gypsum wallboard sheathing at 0.2% 

drift for (top) Wall 1 and (bottom) Wall 2. ..................... D-43 

Figure D-23 Crack maps for gypsum wallboard sheathing at 0.4% 

drift for (top) Wall 1 and (bottom) Wall 2. ..................... D-44 

Figure D-24 Crack maps for gypsum wallboard sheathing at 0.7% 

drift for (top) Wall 1 and (bottom) Wall 2. ..................... D-45 

Figure D-25 Crack maps for gypsum wallboard sheathing at failure 

for (top) Wall 1 and (bottom) Wall 2 .............................. D-46 

Figure D-26 Photos of characteristic cracking at 0.4% drift ................ D-47 

Figure D-27 Photos of characteristic cracking at 0.7% drift. ............... D-48 

Figure D-28 Photos of characteristic cracking at 1.5% drift ................ D-49 

Figure D-29 Detailed photos of characteristic wall cracking at 

1.5% drift ......................................................................... D-50 

Figure D-30 Photos of characteristic cracking at 1.5% drift showing 

wallboard fastener popping ............................................. D-51 

Figure D-31 Photos of characteristic cracking at completion of 

Forest Products Lab testing. ............................................ D-53 

Figure E-1 Illustration of solution flow for Incremental Dynamic 

Analysis results ................................................................. E-3 

Figure E-2 Unit load-drift curves for materials with lowdisplacement capacity ....................................................... E-4 

Figure E-3 Unit load-drift curves for materials with highdisplacement capacity ....................................................... E-5 

Figure E-4 Load-drift curves for archetypical material forms ............ E-6 

Figure E-5 Schematics illustrating simplified building model bar 

elements............................................................................. E-8 

Figure E-6 Screen-shot of typical four-story simplified building 

model in Perform 3D. ........................................................ E-9 

Figure E-7 Plot showing hysteretic behavior of simplified structure 

models constrained by the backbone curve for the highdisplacement capacity material form ............................... E-10 

Figure E-8 Plot showing hysteretic behavior of simplified structure 

models constrained by the backbone curve for the lowdisplacement capacity material form ............................... E-10 
FEMA P-807 List of Figures xix 

Figure E-9 Schematic of fiber model showing how wall elements 

were modeled to capture overturning restraint and 

allow uplift ....................................................................... E-12 

Figure E-10 Schematic of building displaced shapes and related pushover 

curves used in study to determine overturning adjustment 

factor, Qot ......................................................................... E-13 

Figure E-11 Plots of acceleration spectra for selected 

response-history records .................................................. E-14 

Figure E-12 Flow chart used in translational analyses to optimize 

retrofit .............................................................................. E-16 

Figure E-13 Curve fits for IDA results relating median spectral 

acceleration capacity (considering Onset of Strength 

Loss drift criteria) to base-normalized upper-story 

strength, AU for various weak-story ratios AW .................. E-17 

Figure E-14 Curve fits for IDA results relating median spectral 

acceleration capacity (considering Onset of Strength Loss

drift criteria) to base-normalized upper-story strength, 

AU for various weak-story ratios AW ................................. E-17 

Figure E-15 Curve fits for IDA results using linear interpolation 

model for CD relating median spectral acceleration 

capacity (considering Onset of Strength Loss drift 

criteria) to base-normalized upper-story strength, 

AU for various values of strength degradation ratio, 

CD, and torsion coefficient, CT = 0.0 ................................ E-18 

Figure E-16 Curve fit for IDA results using cubic interpolation model 

for CD relating median spectral acceleration capacity 

(considering Onset of Strength Loss drift criteria) to 

base-normalized upper-story strength, AU, for various 

values of strength degradation ratio, CD, and torsion 

coefficient, CT = 0.0 ......................................................... E-19 

Figure E-17 Plots of error data, as a function of strength degradation 

radio, CD, and base-normalized upper-story strength, 

AU, for linear and cubic interpolation models for 

estimating median spectral acceleration capacity, Sμ ....... E-20 

Figure E-18 Plots showing stiffness variations in high-displacement 

capacity materials (left) and low-displacement capacity 

materials (right) as a function of normalized force 

(acceleration response) and drift ratio .............................. E-22 

Figure E-19 Plots showing strength variations in high-displacement 

capacity materials (left) and low-displacement capacity 

materials (right) as a function of normalized force 

(acceleration response) and drift ratio .............................. E-22 
xx List of Figures FEMA P-807 

Figure E-20 Plots showing variations in drift at loss of strength in 

high-displacement capacity materials (left) and lowdisplacement capacity materials (right) as a function 

of normalized force (acceleration response) and 

drift ratio .......................................................................... E-22 

Figure E-21 Plot showing effect of variation in stiffness, K, on 

 median spectral capacity, S, for various configurations 

of material form and upper-story strength ratio, AU ........ E-24 

Figure E-22 Plot showing effect of variation in peak strength, FU, 

on median spectral capacity, S, for various 

configurations of material form and upper-story 

strength ratio, AU ............................................................. E-25 

Figure E-23 Plot showing effect of variation in drift at strength loss, 

DL, on median spectral capacity, S, for various 

configurations of material form and upper-story 

strength ratio, AU ............................................................. E-26 

Figure E-24 Cumulative Distribution Function plots showing effect 

of increasing log-normal standard deviation, , as a 

function of spectral acceleration response ....................... E-27 

Figure E-25 Plots of ratio of spectral acceleration capacity, Sc, at 

varying values of drift limit POE to median spectral 

capacity ........................................................................... E-28 

Figure E-26 Lognormal distribution for standard deviations,  = 0.5 

and 0.6, for ratio of spectral acceleration demand to mean 

spectral acceleration capacity, over range of probabilities 

of exceedance, with linear fit (left) and the error 

(% difference) relative to the linear fit (right) ................. E-29 

Figure E-27 Retrofit backbone curves for various strength increments 

relative to the upper-story shear strength, VU .................. E-30 

Figure E-28 Plot illustrating hysteretic behavior of moment 

frame retrofit elements .................................................... E-30 

Figure E-29 Plots of spectral acceleration capacity (spectral capacity) 

as a function of total first-story retrofitted strength, Vr, 

divided by upper-story strength, VU, for four levels of 

base-normalized upper-story strength, AU, varying initial 

pre-retrofit weak-story ratios, AW, original construction 

having high-displacement capacity (CD = 1.0), and 

Onset of Strength set of drift limits ................................. E-31 

Figure E-30 Plots of spectral acceleration capacity (spectral capacity) 

as a function of total first-story retrofitted strength, Vr, 

divided by upper-story strength, VU, for four levels of 

base-normalized upper-story strength, AU, varying initial 
FEMA P-807 List of Figures xxi 

pre-retrofit weak-story ratios, AW, original construction 

having low-displacement capacity (CD = 0.0), and 

Onset of Strength set of drift limits .................................. E-32 

Figure E-31 Plot of maximum strength of total retrofitted first-story, 

Vr max, divided by upper-story strength, VU, as a function 

of base-normalized upper-story strength, along with a 

plot of a linear-fit equation .............................................. E-33 

Figure E-32 Plots comparing retrofit performance for moment 

frame (M.F.) verses plywood wall retrofit, as a function 

of earthquake shaking intensity, for base-normalized 

upper-story strength, AU = 0.4, and weak-story ratio, 

AW = 0.6 ............................................................................ E-35 

Figure E-33 Plots of median spectral acceleration capacity 

(spectral capacity) versus first-story height for four 

building models considered ............................................. E-36 

Figure E-34 Plots of normalized median spectral acceleration 

capacity (spectral capacity) versus first-story height 

for four buildings considered ........................................... E-37 

Figure E-35 Plots of normalized median spectral acceleration 

capacity (spectral capacity) versus first-story height 

for four buildings considered with linear fit .................... E-37 

Figure E-36 Schematic illustration of floor plans and values of 

weak-story ratio, AW, used in Perform 3D models of 

unretrofitted buildings for various torsion coefficients, 

CT ..................................................................................... E-40 

Figure E-37 Schematic illustration of floor plans and values of weakstory ratio, AW, used in Perform 3D models of retrofitted 

buildings for various torsion coefficients, CT .................. E-40 

Figure E-38 Plots of spectral acceleration capacity reduction versus 

torsion coefficient, CT, for the Onset of Strength Loss set 

of drift criteria, considering the longitudinal direction 

for various values of weak-story ratio, AW ....................... E-41 

Figure E-39 Plots of spectral acceleration capacity reduction versus 

CT, for the Onset of Strength Loss set of drift criteria, 

considering the transverse direction for various values 

of weak-story ratio, AW .................................................... E-42 

Figure E-40 Illustration of the simplified torsional strength, Ts ........... E-43 

Figure F-1 CUREE Apartment Building used in ATC-71-1 

Task 2 Analysis .................................................................. F-2 
xxii List of Figures FEMA P-807 

Figure F-2 Hysteretic behavior of wood-framed elements in 

SAWS ................................................................................. F-4 

Figure F-3 Hysteretic behavior of moment frame elements in 

SAWS ................................................................................. F-4 

Figure F-4 Hysteretic behavior of elements emulating wood-frame 

walls in Perform-3D, where the degradation ratio, 

CD = 0.0 ............................................................................. F-5 

Figure F-5 Hysteretic behavior of elements emulating wood-frame 

walls in Perform-3D, where the degradation ratio, 

CD = 1.0 ............................................................................. F-5 

Figure F-6 Hysteretic behavior elements emulating ductile moment 

frames in Perform-3D......................................................... F-6 

Figure F-7 Backbone curves for varying retrofits modeled in the 

Task 2 Analysis ................................................................... F-7 

Figure F-8 Backbone curves for varying retrofits modeled in the 

Broad-Scope Analysis ........................................................ F-8 

Figure F-9 Comparison of selected backbone curves for varying 

retrofits modeled ................................................................ F-8 

Figure F-10 Comparison of analysis results for the existing building ... F-9 

Figure F-11 Comparison of analysis results for the building with 

retrofit strength of Vy/V2 of 0.2 for Task 2 and emulation 

of Task 2 and Vu/V2 of 0.2 for the Broad-Scope 

Analysis ............................................................................ F-10 

Figure F-12 Comparison of backbone curves for Task 2 retrofit 

set with ratio Vy/V2 = 0.2, and Broad-Scope Analysis 

retrofit set at Vu/V2 = 0.4 ................................................... F-11 

Figure F-13 Comparison of results for Task 2 retrofit set with ratio 

Vy/V2 = 0.2, and Broad-Scope retrofit set at Vu/V2 = 0.4 .. F-12 
FEMA P-807 List of Tables xxiii 

List of Tables

Table 1-1 Embedded and Alternative Criteria in the Guidelines ...........8

Table 2-1 Comparison of the Guidelines to 2009 IEBC Chapter A4 ... 20 

Table 3-1 Drift Limit Probability of Exceedance (POE) Adjustment 

Factors for Low-Displacement Capacity Elements ............. 34 

Table 3-2 Strength Data for Sheathing Materials Considered .............. 35 

Table 4-1 Load-Drift Curve Data for Sheathing Materials 

[pounds/linear foot] .............................................................. 44 

Table 4-2 Simplified Adjustment Factor for Overturning .................... 53 

Table 5-1 Drift Limit Probability of Exceedance (POE) Adjustment 

Factors .................................................................................. 73 

Table 7-1 Curve-Fitting Coefficients (U, U, and W) for 

Calculating Spectral Acceleration Capacity ........................ 98 

Table C-1 Example Building Properties ............................................. C-2 

Table C-2 Example Building Weights ................................................ C-4 

Table C-3 Example Building Spectral Capacity Calculated in 

Various Ways ..................................................................... C-6 

Table D-1 Load-Drift Data for Plaster on Wood Lath ....................... D-6 

Table D-2 Load-Drift Data for Horizontal Wood Sheathing ............. D-8 

Table D-3 Load-Drift Data for Diagonal Lumber Sheathing ........... D-10 

Table D-4 Load-Drift Data for Stucco ............................................. D-12 

Table D-5 Load-Drift Data for Gypsum Wallboard ......................... D-14 

Table D-6 Load-Drift Data for Plaster on Gypsum Lath ................. D-16 

Table D-7 Load-Drift Data for Wood Structural Panel Siding ........ D-17 

Table D-8 Load-Drift Data for Wood Structural Panel 8d@6 ......... D-19 

Table D-9 Load-Drift Data for Wood Structural Panel 8d@4 ......... D-21 

Table D-10 Load-Drift Data for Wood Structural Panel 8d@3 ......... D-23 
xxiv List of Tables FEMA P-807 

Table D-11 Load-Drift Data for Wood Structural Panel 10d@6 ....... D-25 

Table D-12 Load-Drift Data for Wood Structural Panel 10d@4 ....... D-26 

Table D-13 Load-Drift Data for Wood Structural Panel 10d@2 ....... D-28 

Table D-14 Recommended Values for Estimated Capacity and 

Variability ....................................................................... D-30 

Table D-15 Data for Combined Materials .......................................... D-31 

Table D-16 Descriptions of Damage States and Drifts ...................... D-52 

Table E-1 Drift Criteria, Interstory Drift Ratios in Percent ............... E-7 

Table E-2 Computed Material Statistics: x = Log-Normal Standard 

Deviation of Variable x, and xy = Correlation Coefficient 

of the Natural Logarithm of Variable x and y ................. E-23 

Table E-3 Modified Material Statistics: x = Log-Normal Standard 

Deviation of Variable x, and xy = Correlation Coefficient 

of the Natural Logarithm of Variable x and y ................. E-24 

Table E-4 Summary of Composite Log-Normal Standard Deviation, 

total (also known as ) .................................................... E-26 
FEMA P-807 Glossary xxv 

Glossary

Acronyms 

ASCE American Society of Civil Engineers 

ATC Applied Technology Council 

BSE-2 Basic Safety Earthquake level 2, an earthquake hazard level with 

ground motions have a 2% probability of being exceeded in 50 

years 

CalTech California Institute of Technology 

CUREE Consortium of Universities for Research in Earthquake 

Engineering 

EERI Earthquake Engineering Research Institute 

FEMA Federal Emergency Management Agency 

IEBC International Existing Building Code

MCE Maximum Considered Earthquake 

OD onset of damage 

OSL onset of strength loss 

POE Probability of Exceedance, as used extensively throughout the 

Guidelines in the phrase, “drift limit POE” (i.e., drift limit 

Probability of Exceedance) 

SEI Structural Engineering Institute of ASCE 

WSP wood structural panel 

Symbol Definitions 

Ai = area of wall opening i. 

Ai = peak strength of story i divided by the total seismic weight of the 

building (base-normalized strength). 

A1,x = peak strength of the first story divided by the total seismic weight 

of the building (base-normalized strength), in the x-direction. 

AU = base-normalized upper-story strength, calculated separately for 

each direction. 
xxvi Glossary FEMA P-807 

AUx = base-normalized upper-story strength, in the x-direction. 

AW = weak-story ratio, calculated separately for each direction. 

CD = strength degradation ratio, calculated separately for each 

direction. 

CD,x = strength degradation ratio, in the x-direction. 

CD,y = strength degradation ratio, in the y-direction. 

Ci = peak strength of story i divided by the seismic weight carried by 

story i (story-normalized strength). 

C1,x = peak strength of the first story divided by the seismic weight 

carried by the first story (story-normalized strength), in the xdirection. 

CT = torsion coefficient. 

CTs = simplified torsion coefficient. 

CU = minimum of the story-normalized story strengths of any of the 

upper stories, calculated separately for each direction. 

CU,x = minimum of the story-normalized story strengths of any of the 

upper stories, in the x-direction. 

COSi = plan location, in x and y coordinates, of the center of strength of 

story i. 

COS1 = plan location, in x and y coordinates, of the center of strength of 

the first story. 

COS2 = plan location, in x and y coordinates, of the center of strength of 

the upper stories. 

COS2,x = x coordinate of the center of strength of the second story. 

COS2,y = y coordinate of the center of strength of the second story. 

COS1r,x = x coordinate of the center of strength of the retrofitted first story. 

COS1 , r y = y coordinate of the center of strength of the retrofitted first story. 

dw = distance at which wall line w acts to contribute to a story’s twist. 

dw,x = distance between the center of strength of wall w, and the center 

of strength of the first story, in the x-direction. 

dw,y = distance between the center of strength of wall w, and the center 

of strength of the first story, in the y-direction. 
FEMA P-807 Glossary xxvii 

D = uniform horizontal displacement at top of wall in direction of 

wall. 

ex, ey = x and y components, respectively, of the torsional eccentricity. 

fw = load-drift curve for wall line w. 

v w, f = total shear strength of wall line w. 

vwx , , f = component of shear strength of wall w, in x-direction. 

vwy , , f = component of shear strength of wall w, in y-direction. 

fw j    = load-drift curve for wall line w, at drift ratio increment j.

fw jh   = load-drift curve for wall line w, at drift ratio increment jh, the 

drift ratio increment adjusted for wall line height, h. 

Fi = load-drift curve for story i, calculated separately for each 

direction. 

h = floor-to-ceiling wall height of first-story wall line. 

hw = floor-to-ceiling height of wall line w. 

H = maximum floor-to-ceiling height of any first-story wall.

HF1 = maximum story height of the first story, floor to floor. 

H1 = floor-to-ceiling height of the tallest first story wall line, 

determined separately in each direction. 

i = a subscript index indicating floor or story; story i is between floor 

i and floor i+1. 

j = twist angle index ranging from 0 to 10. 

LD = moment arm for concentrated load, PD. 

Lw = length of wall line w. 

Lx = overall building dimension in the x direction. 

Ly = overall building dimension in the y direction. 

Mot = overturning moment demand on the wall line. 

Mr = overturning resistance capacity of the wall line. 

Ns = total number of stories in the building. 

w x, p = x-coordinate of the center of wall w.

w y, p = y-coordinate of the center of wall w. 

POE = probability of exceedance. 
xxviii Glossary FEMA P-807 

wa v ,

PD = concentrated dead load tributary to wall line. 

Qopen = adjustment factor for openings in a wall line. 

Qot = adjustment factor for overturning of a wall line. 

Qs = story height factor for the first story, calculated separately for 

each principal direction. 

Sc = spectral acceleration capacity, calculated separately for each 

direction. 

Sc0 = spectral acceleration capacity (adjusted for drift limit POE) for 

materials with low-displacement capacity (CD value of 0.0).

Sc1 = spectral acceleration capacity (adjusted for drift limit POE) for 

materials with high-displacement capacity (CD value of 1.0).

cs S = simplified spectral acceleration capacity. 

Scs,x = simplified spectral acceleration capacity, in x-direction.

Scs,y = simplified spectral acceleration capacity, in y-direction.

Sd = spectral acceleration demand.

MS S = default (embedded) spectral acceleration demand; the maximum 

considered earthquake (MCE) spectral acceleration for short 

periods from ASCE/SEI 7-05. 

S = median spectral acceleration capacity. 

S0 = median spectral acceleration capacity for strength degradation 

ratio, CD = 0.0. 

S1 = median spectral acceleration capacity for strength degradation 

ratio, CD = 1.0. 

ti = load-rotation curve for story i. 

Ti = torsional strength of story i. 

T1 = torsional strength of first story. 

THD = tension ultimate capacity of tie-down hardware, if applicable. 

 = unit shear strength of wall assembly for wall line w. 

s v = unit shear strength of sheathing material 

vw j    = unit load-drift curve for the wall line’s combination of sheathing 

materials at drift ratio increment, j. 
FEMA P-807 Glossary xxix 

vw jh   = unit load-drift curve for the wall line’s combination of sheathing 

materials at drift ratio increment, jh, the drift ratio increment 

adjusted for wall line height, h. 

V ,1 x = peak first-story strength, in the x-direction. 

V1, y = peak first-story strength, in the y-direction. 

Vi = story strength of story i, calculated separately for each direction. 

V1r = story strength of the retrofitted first story, calculated separately 

for each direction. 

Vr,min = estimated minimum required strength of the retrofitted first story. 

Vw = peak shear strength from the load-drift curve of the wall line, 

adjusted for openings. 

VU = story strength of the upper story that determines the value of CU. 

w = a subscript index indicating a single wall line. 

wD = uniform dead load tributary to wall line. 

W = total seismic weight of the building, equal to the sum of all the 

tributary floor weights. 

Wi = tributary floor weight of floor i. 

Wj = tributary floor weight of floor j. 

x = a subscript index indicating the x-direction, or in some cases, one 

of two principal directions. 

y = a subscript index indicating the y-direction. 

POE,0 = drift limit probability of exceedance (POE) adjustment factor for a 

CD value of 0.0. 

POE,1 = drift limit probability of exceedance (POE) adjustment factor for a 

CD value of 1.0. 

U = curve fitting coefficient used to calculate Sc, provided for CD

values of 1.0 and 0.0, onset of strength loss (OSL) drift limits, and 

onset of damage (OD) drift limits. 

W = curve fitting coefficient used to calculate Sc, provided for CD

values of 1.0 and 0.0, onset of strength loss (OSL) drift limits, and 

onset of damage (OD) drift limits. 

i = drift at which the story strength of story i occurs, in each 

direction. 
xxx Glossary FEMA P-807 

U = curve fitting coefficient used to calculate Sc, provided for CD

values of 1.0 and 0.0, onset of strength loss (OSL) drift limits, and 

onset of damage (OD) drift limits. 

1 = first story torsional demand. 

 j = drift ratio at increment j. 

 jh = drift ratio at increment j, adjusted for wall height, h, 

 = maximum angle of twist, in radians. 

 j = twist angle j. 
FEMA P-807 1: Introduction 1 

Chapter 1 

Introduction 

Multi-unit buildings make up a large portion of the housing stock of any city. 

In the western United States, thousands of multi-unit buildings are three- or 

four-story wood-frame structures designed and built to outdated seismic 

standards. The worst ones, with collapse-prone weak first stories, pose 

enormous safety risks to tenants, financial risks to owners, and recovery risks 

to local, state and federal governments. 

1.1 Earthquake Risks of Multi-Unit Weak-Story WoodFrame Buildings 

Recent earthquakes have proven the vulnerability of wood-frame residential 

buildings with weak first stories (Figure 1-1). The critical damage pattern, 

involving the concentration of lateral deformation within a relatively open first 

story, was seen as early as the 1971 San Fernando earthquake. In the 1989 

Loma Prieta earthquake, six of the seven collapsed buildings in San 

Francisco’s Marina District were four-story corner apartment buildings with 

first-story parking (Harris and Egan, 1992). In the 1994 Northridge earthquake, 

perhaps two hundred such buildings, containing thousands of residential units, 

suffered severe damage or collapsed (EERI, 1996, Chapter 6). 

Despite this history, thousands of these buildings remain. In San Francisco 

alone, about 2,800 buildings providing housing to 58,000 residents appear to 

have collapse-vulnerable open first stories (ATC, 2009a). These are 

Figure 1-1 Photos illustrating near-collapse of typical weak-story wood-frame buildings in the 1989 Loma 

Prieta earthquake (left) and the 1994 Northridge earthquake (right). 
2 1: Introduction FEMA P-807 

buildings with more than 80% open area on one first-story wall or more than 

50% open area on two adjacent first-story walls. In addition, there are (a) 

another 1,600 buildings in the same category (buildings with three or more 

stories and five or more residential units) that have smaller percentages of 

open area on the first-story walls, (b) an expectedly high but unknown 

number of 3-to-5 story pre-seismic-code commercial wood-frame buildings 

with potentially weak first stories, and (c) similar buildings constructed after 

1974 not included in the San Francisco inventory. 

Though anyone in a collapsing building is at risk, the primary safety risk in a 

weak-story building is to anyone who happens to be in the first story when 

the earthquake strikes. A recent evaluation program in Berkeley found that 

about three-quarters of the buildings considered had at least one first-story 

residential unit, and another ten percent had first-story shops or offices 

(Bonowitz and Rabinovici, in preparation). Adding to the safety risk is the 

financial risk to owners and tenants of weak-story buildings. 

Jurisdictions with hundreds or thousands of these buildings face problems of 

a different sort. Even if only a fraction collapse, the resulting damage and 

debris will strain a city’s ability to perform search and rescue, transport the 

injured to hospitals, and fight fires started by inevitable rupture to gas lines 

and short circuits in electrical systems. Many buildings that do not collapse 

will be unsafe to occupy until repairs are made, increasing the demand for 

shelter beds and slowing recovery overall. Even where multi-unit buildings 

are not a large portion of the total housing stock, they might provide a 

disproportionate percentage of a city’s low-income housing; extensive 

damage within just that category affects recovery of the work force and 

strains social services. For these and other reasons, weak-story residential 

buildings have been put forward as a top priority for mitigation (ATC, 2009a; 

SPUR, 2009). 

1.2 Weak-Story Building Characteristics 

Not every wood-frame multi-unit building has a weak story. This particular 

vulnerability is found most often where population density and land values 

led to mixed-use construction. In many such instances, some or all of the 

residential units have been moved to the upper stories to make space for 

parking or, on busier streets, for first-story shops and offices. But mixed uses 

alone did not cause weak stories; the problem arose because the nonresidential first-story uses called for different column grids or wall layouts 

and did not require the same number of room partitions as the apartments 

above. The result was buildings with distinct lateral stiffness and strength 

differences between their first story and their upper stories (Figure 1-2). 
FEMA P-807 1: Introduction 3 

Figure 1-2 Exploded views of three common multi-unit wood-frame residential building styles (roof 

system, top row; first story, bottom row). The left building is characteristic of 1950s or 1960s 

buildings with tuck-under parking accessible through a long open side. The middle building is 

a 1920s era corner building with garage doors lining large portions of both street-facing sides. 

The right building is a midblock configuration with typically few first-story transverse walls. In 

all cases, note the relatively high density of walls and partitions above the first story. 

In San Francisco, these differences can be seen even in Victorian and 

Edwardian era buildings with tall first-story storefronts, some of which predate the 1906 earthquake. A 1920s building boom saw the construction of 

hundreds, perhaps thousands, of apartment buildings with first stories 

dedicated to car parking. The Marina District buildings that collapsed in 

1989 were from this era. 

Most of the buildings addressed by these Guidelines, however, are in more 

recent suburban developments, such as those in the San Fernando Valley, 

where low-rise apartment houses addressed a burgeoning demand beginning 

in the 1950s (EERI, 1995, Chapter 10). Even in Berkeley, which grew 

rapidly after the 1906 earthquake and during World War II, about 70 percent 

of the multi-unit buildings evaluated in a recent program were built between 

1950 and 1970 (Bonowitz and Rabinovici, in preparation). 

1.2.1 The Critical Deficiency: A First Story Lacking Adequate 

Strength or Stiffness 

Earthquake shaking imposes lateral (sideways) forces and deformations on a 

building. When the building’s first story lacks adequate strength or stiffness, 

the lateral deformations become concentrated within that story, instead of 

being distributed efficiently over the height of the structure. When the 
4 1: Introduction FEMA P-807 

available first-story walls are not positioned effectively, as when one or two 

sides are essentially open to facilitate parking, the first-story deformations 

can be compounded by the building’s tendency to twist. In structures built of 

obsolete or archaic materials, excessive deformation leads to damage and, in 

extreme cases, collapse. 

Whether designers of the 1920s and 1960s recognized the structural effects 

of an open first story is unclear. If measures were taken to compensate for the 

open first story, they were not uniform. Building codes did not address 

“irregular” structures until the 1970s, and those early provisions left much to 

the judgment of the engineer (ATC, 1984). Quantitative definitions (and 

prohibitions) of weak-story and soft-story irregularities were not codified 

until the 1988 Uniform Building Code (ICBO, 1988). 

1.3 Engineering Codes and Standards 

Building codes for new construction, while often applied to existing 

structures, are often unsuited to that purpose. The prescriptive rules of the 

code make assumptions about structural materials, the configuration of 

structural elements, and the quality of construction that are not satisfied by 

many existing buildings. Further, the code’s purpose is to check the 

compliance of a design relative to fixed rules; it is not especially helpful for 

evaluating non-compliant conditions in relative terms or for gauging a design 

against alternative objectives. 

Codes and standards for use with existing buildings do exist. There is even a 

set of code provisions intended specifically for the buildings addressed by 

these Guidelines. All have some shortcomings, however, as described below. 

Appendix Chapter A4 of the International Existing Building Code (IEBC), 

titled “Earthquake Hazard Reduction in Existing Wood-Frame Residential 

Buildings with Soft, Weak or Open-Front Walls” (ICC, 2009b), is similar to 

the code for new construction, only with reduced design forces, a focus on 

the critical first story, and some rules to guide application to existing 

conditions. While useful and adopted by several California jurisdictions with 

nascent mitigation programs (including San Francisco, Oakland, Berkeley, 

and Alameda), Chapter A4 mostly covers the design of retrofit elements but 

does not yield a careful evaluation of existing conditions. As a code-based 

document, it is more about assuring compliance than measuring performance. 

Its retrofit provisions also ignore the possibility of over-strengthening the 

first story. 

The evaluation standard known as ASCE/SEI 31, Seismic Evaluation of 

Existing Buildings (ASCE, 2003), is based on identifying a building’s 
FEMA P-807 1: Introduction 5 

potential deficiencies and using three levels of analysis to determine if the 

deficiencies are significant to the performance of the structure. While the 

presence of weak-story or open-front conditions are tagged as potential 

deficiencies, the analysis methods cited to determine their significance are 

quite conservative. ASCE/SEI 31 also does not cover retrofit design directly. 

The retrofit standard known as ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (ASCE, 2006b), is a comprehensive document suitable for 

both evaluating and retrofitting these irregular structures. ASCE/SEI 41 is a 

tool box of procedures requiring application by a knowledgeable specialist 

and its breadth and complexity can make it cumbersome, as it does not 

address specific building or structure types the way IEBC Chapter A4 and 

ASCE/SEI 31 do. It also lacks the practicality of Chapter A4, which 

acknowledges the value of a first-story-only retrofit. 

The existing codes and standards share two other shortcomings as well. First, 

they lack a consistent set of default strength and stiffness values for archaic 

or non-conforming materials. Second, they lack the means to make the kind 

of quick screening assessment a city-wide mitigation program often needs. 

1.3.1 The Guidelines as an Alternative 

The Federal Emergency Management Agency (FEMA) and the Applied 

Technology Council (ATC) have developed these Guidelines as an 

alternative to current codes and standards. The Guidelines present a 

methodology that combines the thoroughness of a detailed analysis with a 

simplified procedure and a focus on cost-effective evaluation and retrofit. 

The features of the method include the following: 

 Like ASCE/SEI 41, the method is based on a sophisticated understanding 

of nonlinear material behavior and structural response. It therefore allows 

a more complete understanding of the existing structure than a codebased procedure such as IEBC Chapter A4. 

 Unlike ASCE/SEI 41, the method entails a simplified a procedure for one 

vulnerable building type with a dominant deficiency. An engineer need 

only characterize the structure’s materials and geometry, then compare 

key parameters to the results of nonlinear analyses of surrogate structures 

already performed and summarized by the Guidelines. 

 Like IEBC Chapter A4 (but unlike ASCE/SEI 31 and ASCE/SEI 41), the 

method focuses on the dominant collapse-vulnerable deficiency, 

considering cost-effective retrofit solutions that require work only in the 

first story, thereby minimizing disruption to upper story occupants. 
6 1: Introduction FEMA P-807 

 Unlike Chapter A4, the method considers the consequences of overstrengthening the first story. In certain buildings, adding too much 

strength to the weak first story can lead to excessive damage in an upper 

story. The Guidelines procedure finds those cases and limits the retrofit 

appropriately. 

 Unlike any of the current codes and standards, the method quantifies 

performance in probabilistic terms, as opposed to giving a pass-fail 

grade. The probabilistic method, based on estimated fragility, supports a 

wider range of mitigation policy options. 

The Guidelines also use the latest and most consistent knowledge base of 

applicable test results, filling a gap in current practice. 

From the code official’s perspective, perhaps the most significant feature of 

the Guidelines’ methodology is that it does not require the engineer to 

develop and analyze a complete nonlinear model of the specific building in 

question. Instead, it relies on the statistical representation of hundreds of 

surrogate models already analyzed in advance (see Chapter 2). This approach 

allows the Guidelines to account for important nonlinear behavior without 

requiring difficult and expensive modeling. Of course, a building-specific 

model that accounts for each non-conforming detail might offer a more 

accurate performance prediction, but it is impractical in many cases. The 

Guidelines are intended to represent an improvement over current code-based 

provisions and are expected to offer an appropriate balance of engineering 

rigor and cost-effective practice. 

1.4 Purpose and Intended Use of the Guidelines

The Guidelines have a policy purpose as well as a technical objective. 

Current codes and standards for potential weak-story buildings are either 

overly simplistic, and therefore address only a narrow (and vague) range of 

mitigation goals, or are too comprehensive and complex to be used 

effectively on a large-scale program. By providing an alternative or 

complement to current codes and standards, the Guidelines are intended to 

make a range of mitigation programs more feasible and adaptable to a 

jurisdiction’s needs. 

Earthquake risk mitigation can be voluntary, mandatory, or triggered. Larger 

programs often involve linked but separable phases for evaluation and 

retrofit. As discussed, the most common engineering criteria for multi-unit 

wood-frame residential buildings are those in IEBC Chapter A4, but they 

focus on retrofit (not evaluation) and, because they are code-based, they are 

most suited to triggered projects where compliance with a pre-set standard is 
FEMA P-807 1: Introduction 7 

the main objective. Meanwhile, it is not clear that the more generic and 

comprehensive standards, ASCE/SEI 31 and ASCE/SEI 41, would support 

cost-effective mitigation of a specific building type with a dominant 

deficiency. 

Thus, the Guidelines offer potential benefits for a range of retrofit projects 

and programs: 

 For voluntary retrofit, the Guidelines provide an alternative that can be 

applied with other codes and material standards much like IEBC Chapter 

A4. Where voluntary work is done to qualify for an incentive, the 

Guidelines provide clear metrics to gauge acceptability. Where the work 

is not targeted toward a minimum qualifying level, the Guidelines allow 

an owner and engineer to assess the existing condition in quantitative 

terms and to study the costs and benefits of various alternatives. 

 For code-triggered work, the Guidelines provide alternative criteria that a 

jurisdiction can accept at its discretion. (See Section 2.3.3.) 

 Mandatory programs are likely to benefit most from the Guidelines. The 

Guidelines are suitable for phased programs in which evaluations and 

retrofits might be scheduled or prioritized differently, or even keyed to 

different objectives. They also make possible a mitigation program with 

a tailored objective. Because the Guidelines are based on probabilistic 

fragility data, and not on pass-fail design criteria, they can also be used 

to support planning and policy studies in ways that current codes and 

standards cannot. 

1.4.1 Policy Options 

An important feature of the Guidelines is that they are adaptable. However, 

this means that an owner or jurisdiction must make some decisions in order 

to use them effectively. The main decisions involve the three components of 

the performance objective (see Section 2.3 for additional discussion): (1) the 

earthquake hazard of interest, (2) the desired performance level, and (3) the 

allowed probability of failing the objective. A unique feature of the 

Guidelines is that they acknowledge the benefit, as well as the liability, of 

sometimes not achieving the targeted performance objective in favor of more 

feasible first-story-only retrofits, which are referred to herein as “optimized” 

retrofits. Therefore, the owner or jurisdiction must also decide whether, and 

to what degree, to take the innovative approach of the Guidelines. 

Table 1-1 lists the issues that require user input, together with options either 

recommended by or embedded in the Guidelines. 
8 1: Introduction FEMA P-807 

Table 1-1 Embedded and Alternative Criteria in the Guidelines 

Issue Criteria Embedded 

in the Guidelines

Alternative Criteria Options

Hazard Level Maximum 

Considered 

Earthquake (MCE) 

(Section 5.4) 

Any hazard level may be used (Section 

5.4.1). While the MCE is the theoretical basis 

for code-designed new buildings, 

engineering criteria often use 2/3 (MCE) or a 

probabilistically defined hazard. 

Performance Level Onset of Strength 

Loss (OSL) drift 

levels (Sections 2.3.2 

and A2.5) 

Onset of Damage (OD) drift levels (Chapter 

7). The OD drift levels correspond to less 

damage than the OSL levels. 

Targeted Drift 

Limit Probability 

of Exceedance 

(POE) 

User may select any 

value (Section 5.3). 

20 percent is recommended if the objective 

is to be consistent with other codes and 

standards that use relaxed or reduced 

criteria for existing buildings (Sections 1.4.2 

and 2.3.3). 

Allowance of 

Optimized Retrofit

Recommended for 

many projects and 

programs (Section 

6.4.2). 

Optimized retrofit might not be suitable 

where high performance or strict compliance 

with other codes or standards is necessary 

(Section 6.2.3). 

Maximum 

Acceptable Drift 

Limit POE for 

Optimized 

Retrofits 

User may select any 

value greater or 

equal to the targeted 

drift limit POE. 

Assuming optimized retrofit is allowed, the 

maximum acceptable POE should depend 

on multiple factors. However, where a POE

less than 50 percent cannot be achieved, it 

suggests a very weak building that might 

warrant study outside the scope of the 

Guidelines (Section 6.4.2). 

1.4.2 Selecting Performance Objectives 

As suggested in Table 1-1, a common performance objective might call for a 

building to exceed the “onset of strength loss” drift limit in the Maximum 

Considered Earthquake (MCE) with a probability of no more than 20 

percent. One or more of these choices can be altered to define a different 

objective. For example, a less aggressive, more lenient objective, which 

would find more existing buildings acceptable, could be obtained by 

choosing an earthquake hazard smaller than the MCE, or a drift limit 

probability of exceedance (POE) greater than 20 percent. An objective such 

as “reaching onset of strength loss in the MCE event, allowing for a 50 

percent drift limit probability of exceedance” would be easier to achieve than 

the similar objective with a 20 percent targeted drift limit POE. Such an 

objective might be useful for a program targeting only the “worst of the 

worst” buildings. 

Model building codes for new construction are expected to result in buildings 

with a 10 percent probability of collapse, given the Maximum Considered 

Earthquake (Luco et al., 2007; FEMA, 2009). Many codes and standards set 

less aggressive criteria for existing buildings. IEBC Chapter A4, for example, 
FEMA P-807 1: Introduction 9 

allows the use of a 75 percent factor on design loads. This factor can be 

considered roughly consistent with the use of a 20 percent probability of 

collapse, as opposed to the 10 percent probability of collapse expected of 

new buildings (see ASCE/SEI 41-13, in preparation). 

The appropriate performance objective depends on what a project or program 

is trying to achieve, and possibly also on whether it is considering only a 

single building or a city- or region-wide building stock. 

For voluntary work on a single building, an objective can be selected to suit 

goals related to insurance coverage, or feasible repair costs, or the owner’s 

particular risk tolerance. Often, voluntary work is scoped to match a certain 

project budget, and whatever performance results from that work becomes 

the de facto performance objective. The Guidelines’ use of a drift limit 

probability of exceedance (POE) as a variable, as well as the Chapter 7 

procedure for alternative performance assessment, can now help the owner 

and design professional quantify the benefits of a retrofit scope selected in 

this way. 

For an incentivized voluntary program intended to achieve certain benefits 

citywide, the objective is best set by following the thought process for a 

mandatory program, below. 

For work triggered by the building code, it is important to match the code’s 

implied objectives. See Section 2.3.3. 

For a simple mandatory program with no quantitative goals, a jurisdiction 

could set almost any performance objective, including the Guidelines’

embedded hazard level (MCE) and drift performance level (onset of strength 

loss) criteria with any reasonable drift limit POE value, and expect to 

improve performance of individual buildings and of the jurisdiction as a 

whole. The cumulative effect of the mandated work on individual buildings 

could be estimated using the Guidelines together with ground motion data 

from one or more planning scenarios to account for variations in shaking in 

different parts of the city. That is, the effect of an arbitrarily chosen 

performance objective can be measured, but it might not correspond to any 

pre-set policy goal. 

For a more sophisticated mandatory program, the right performance 

objective is the one that achieves the overall quantitative program goals when 

applied to each individual building mandated by the program. 
10 1: Introduction FEMA P-807 

1.5 Validation 

Three validation studies were performed to confirm the Guidelines’ novel 

methodology. Starting from basic concepts, an in-depth analysis effort 

duplicated the method’s derivation, building and analyzing a range of 

surrogate models and deriving equations for evaluation and retrofit design. 

This effort confirmed the findings and conclusions developed during the 

surrogate model analyses as well as the equations in Chapters 5 through 7. 

Secondly, a practical validation enlisted engineers unfamiliar with the 

method and asked them to analyze and design retrofits for two actual 

buildings. The purpose of the study was partly to check the method’s results 

for their practical meaning, but mostly to confirm that the new definitions, 

equations, and procedures could be followed and properly applied by 

engineers seeing them for the first time. This study led to several 

clarifications and small technical revisions. 

Thirdly, example calculations were prepared (and included in these 

Guidelines) to illustrate some of the new concepts and engineering 

procedures. 

1.6 The Weak-Story Tool 

A Weak-Story Tool, similar to a graphical spreadsheet, was also developed 

as part of the project to help apply the rules and perform the calculations 

described in Guidelines Chapters 4 through 7. Guidance on the use of the 

Weak-Story Tool is provided in Appendix A. 

By incorporating the tables of material properties and the rules for applying 

them, the Tool’s initial benefit is simply to organize the user’s work. Once 

building data is entered, however, the Tool facilitates modifications and 

presentation of results. It also makes comparative studies of different retrofit 

schemes easy. Still, as with any such tool, results should be verified by 

appropriate checks and quality control measures. Proper application of the 

Tool and understanding of its workings and its output remain the 

responsibility of the user. 

The Weak-Story Tool is not needed to use the Guidelines. The text of the 

Guidelines contains all the data, formulas, and procedural background 

needed to apply the method without using the Tool. 

1.7 Guidelines Organization and Content 

These Guidelines are written and organized to serve as background, 

commentary, and technical content for future building codes and seismic 
FEMA P-807 1: Introduction 11 

mitigation programs. The Guidelines present new engineering procedures in 

seven chapters that generally follow the sequence in which existing buildings 

would be evaluated and retrofitted. Appendices provide greater detail on 

specific topics of interest to certain user groups. 

Chapter 1 provides non-technical background and describes the issues the 

Guidelines were developed to address. Since the Guidelines are adaptable, 

Chapter 1 also identifies the decisions that policy makers or mitigation 

planners will need to make when implementing the provisions, including the 

specification of a performance objective. 

Chapter 2 provides a technical overview of the engineering procedures of the 

Guidelines and their analytical basis. It also gives the limitations and 

conditions a candidate building must meet to be eligible for these procedures. 

Chapter 3 is the first of five technical chapters. As an abbreviated version of 

Chapters 4 and 5, it provides a simplified (and generally conservative) 

method for determining the capacity of a candidate building. 

Chapter 4 gives the definitions and rules for characterizing an existing 

building’s strength, displacement capacity and toughness, and potential 

deficiencies. It provides new default material data for typical wall sheathing 

types. Chapter 4 concludes by defining several characteristic coefficients 

used in the full evaluation procedure of Chapter 5. 

Chapter 5 provides the equations that define a building’s capacity, given its 

characterization by Chapter 4. Chapters 4 and 5 apply to retrofitted buildings 

as well as existing buildings. 

Chapter 6 describes the logic for selecting, bounding, and optimizing the 

appropriate retrofit strength for buildings found deficient relative to the 

performance objective. Chapter 6 recognizes that the best possible 

performance of a first-story retrofit might not achieve the targeted 

performance objective but might be cost-beneficial regardless. 

Chapter 7 provides alternative versions of the Chapter 5 and 6 capacity 

equations for a higher performance level (“onset of damage” as opposed to 

“onset of strength loss”). 

Appendix A is a user’s guide for the Weak-Story Tool described in Section 

1.6. 

Appendix B, intended for policy makers and code officials, discusses 

potential implementation of the Guidelines in mitigation programs, as well as 

a basis for setting performance goals. It also provides a code language 
12 1: Introduction FEMA P-807 

version of Chapters 4 through 6 to facilitate incorporation into building codes 

or regulations. 

Appendix C, intended primarily for engineering practitioners and code 

officials, illustrates some of the new procedures with numerical calculations 

representative of an actual building. 

Appendix D*

 describes the testing data used to derive the Guidelines’ criteria 

for characterizing the strength and ductility of sheathed wood-frame walls. It 

is intended primarily for engineering practitioners as background to the 

provisions in Chapter 4 and for researchers. 

Appendix E*

 provides a detailed technical explanation and derivation of the 

procedures in Chapters 3 through 7. It is intended for technical readers who 

want to understand the full engineering basis of the new procedures, 

including the fragility data from analyses of surrogate models. 

Appendix F*

 describes an independent validation study that confirmed the 

modeling and analysis presented in Appendix E. Like Appendix E, it is 

intended primarily for researchers and for reviewers of the new procedures. 

 

*

Appendices D, E, and F are not included in the printed version of the Guidelines, 

but can be found on the CD that accompanies these Guidelines. 
FEMA P-807 2: Technical Overview 13 

2Chapter 2 

Technical Overview 

The principal features of the methodology, which distinguish it from other 

codes and standards, include the following: 

 The methodology is statistical, not explicit. Once the structure is 

modeled, it is not analyzed directly. Rather, it is compared statistically 

with other similar structures already analyzed. 

 Acceptability is based on drift, not on internal force or stress levels. 

 Performance objectives explicitly include a targeted probability of 

exceedance relative to drift limits. 

 Cost-effective retrofit schemes that keep work and disruption within the 

critical first story are emphasized, even if a targeted performance 

objective is not fully achieved. 

This chapter presents an overview of the statistical basis of the underlying 

methodology (Section 2.1), an overview of the surrogate analyses that were 

conducted to form the technical basis for the methodology and the means for 

characterizing an existing building in terms related to the design space of the 

surrogate analysis models (Section 2.2), acceptability criteria and related 

performance objectives (Section 2.3), a description of the critical deficiencies 

in buildings of the type considered by the Guidelines (Section 2.4), an 

overview of the cost-effective retrofit design philosophy incorporated in 

these Guidelines (Section 2.5), and Guidelines limitations and building 

eligibility requirements (Section 2.6). 

Chapters 3 through 7 of the Guidelines present the details of the prescriptive 

methodology for modeling and evaluating existing structures, sizing retrofit 

elements, and quantifying the benefits of retrofit in probabilistic terms. The 

formulas and criteria in those chapters are premised on certain presumptions 

and limitations, discussed in this chapter. 

Figure 2-1 broadly illustrates the Guidelines content and expected application 

from the perspective of the engineer user. More detailed flowcharts for each 

broad step are given with the referenced chapters. 
14 2: Technical Overview FEMA P-807 

Figure 2-1 Flow chart illustrating relationships between the Guidelines technical 

chapters. 

YES 

Investigate, model, and 

characterize the existing 

structure. 

No retrofit 

necessary. 

Section 3.5.4 or 5.4.1 

Does the building pass 

the evaluation? 

Confirm and finalize 

retrofit design. 

YES 

NO

Section 2.6 

Chapter 4

Evaluate the existing 

structure. 

Chapter 5 

Estimate retrofitted strength needed to meet the 

performance objective or optimize a first-story 

retrofit. 

Section 6.2

Develop conceptual retrofit design. 

Section 6.3

Sections 6.4 and 6.5

Do simplified 

evaluation.

Try simplified 

evaluation? 

Does the 

building pass 

the evaluation?

Confirm that the building is eligible (or will be 

made eligible through retrofit) for consideration 

using the Guidelines. If not, the Guidelines are 

not applicable. 

NO 

Chapter 3

YES 

NO
FEMA P-807 2: Technical Overview 15 

2.1 Statistical Basis 

Unlike most evaluation and design methodologies, the Guidelines do not rely 

on an explicit structural analysis of the building in question. That is, they do 

not require the creation of a unique structural model, the application of loads 

to that model, or the calculation of reactions, deflections, or internal member 

forces. Instead, the structure in question is compared with hundreds of 

hypothetical similar structures, or surrogate models, each of which has 

already been assessed with nonlinear response history analysis. The 

comparison is made on the basis of a few key parameters, with regression 

formulas that represent the aggregate fragility of the surrogates. The 

characterization of the actual building strength and deformations is necessary 

for this comparison. A full description of the statistical basis and the 

development of fragility curves and regression formulas is provided in 

Appendix E. 

The reason for this statistical approach is to relieve the engineer (and owner) 

of burdensome (and costly) nonlinear analysis. Certainly it is possible to 

evaluate a wood-frame structure and to design its retrofit with explicit 

structural analysis, but it is also more difficult. As noted in Chapter 1, ease of 

evaluation and design is part of the cost-effectiveness intended by the 

Guidelines. To the extent that the statistical approach reliably captures the 

significant aspects of any eligible building, it offers a valuable alternative to 

traditional analysis. 

2.2 Modeling Actual and Surrogate Structures 

2.2.1 The Surrogate Models 

The fragility data against which a particular building is compared was 

derived from analyses of hundreds of surrogate models, described in detail in 

Appendix E. The surrogate models represent a wide design space that 

accounts for realistic variations of material ductility, first-story strength, ratio 

of first-story strength to upper-story strength, and other variables. 

The types of actual wood-frame buildings covered by the Guidelines

generally have obsolete or non-conforming conditions in addition to an open 

front or potentially weak story. For example, most walls in actual buildings 

lack the overturning restraint that would come from hold-downs or story-tostory ties. Also, existing buildings might have inadequate collectors, 

diaphragms, or other load path elements. The surrogate analyses did not 

explicitly model these load path gaps. 
16 2: Technical Overview FEMA P-807 

The surrogate models did not account for interaction with adjacent buildings 

(also called pounding), which can occur where large buildings are divided in 

plan by narrow seismic joints or where dense development patterns required 

essentially no gaps between buildings (as in parts of San Francisco). Recent 

work with 1920s-era buildings has suggested that weak-story structures at the 

end of a block might have a slightly increased fragility if subject to 

pounding, but that retrofit mitigates that effect (Maison et al., 2011). Similar 

studies with smaller buildings subject to pounding on two sides is ongoing, 

but in any case, the effects are not expected to be significant with respect to 

the Guidelines methodology. 

The key performance measure for the surrogate models is peak transient 

interstory drift—the maximum lateral deformation within a story over a full 

response history, divided by the story height. Two drift limits are used: 1.25 

percent for stories with only low-displacement capacity elements (with an 

assumed strength degradation ratio, CD, of 0.0; see Sections 4.4 and 4.7.4), 

and 4.0 percent for stories with high-displacement capacity elements (CD = 

1.0). 

The Guidelines focus primarily on extreme performance levels under severe 

loads. The two drift limits, however, are not associated explicitly with 

collapse because there is not a robust historical record relating collapse to 

predicted drift. Rather, the drift limits are derived from tests of various 

sheathing materials and represent the onset of strength loss, an elementspecific condition assumed to indicate a substantially increased potential for 

collapse. 

Figure 2-2 illustrates the two material models used in the surrogate 

structures. The use of two drift limits follows precedents in other codes and 

standards for existing buildings, such as ASCE/SEI 41 (ASCE, 2006b), 

which distinguishes between force-controlled and deformation-controlled 

elements and sets acceptability limits element by element. 

All stories are considered in checking the surrogate model drifts. For 

example, if a model has only low-displacement capacity elements, such as 

stucco, throughout its height, it is considered to have “failed” the fragility 

criteria if any story exceeds the 1.25 percent limit during a response history. 

If the same model is retrofitted with high-displacement capacity elements in 

the first story, such as wood structural panels, then it fails the criteria if either

the first-story drift exceeds 4.0 percent or any upper story drift exceeds 1.25 

percent. (See Appendix E for further details.) 
FEMA P-807 2: Technical Overview 17 

Figure 2-2 Plots of interstory drift versus shear force showing drift limits, L, 

used to develop fragility relationships from the surrogate models. 

Sheathing materials with strength degradation ratio, CD = 1, have 

high-displacement capacity, and those with CD = 0, have lowdisplacement capacity. 

2.2.2 Characterizing an Existing Building 

The surrogate models cover a wide range of material properties, story 

strengths, and other variables (collectively referred to as the “surrogate 

space”). When working with an actual specific building, however, it is 

important to characterize it accurately enough that its capacity can be 

estimated and located within the surrogate space. 

Like other codes and standards for existing buildings, the Guidelines assign 

strength and stiffness even to wall segments constructed with archaic 

materials and detailing. For new construction, such “non-conforming” 

elements would be designated as non-structural partitions and would not be 

allowed to count toward required strength. For potential weak-story 

structures, however, this practice can significantly underestimate story 

strength and lead to unconservative conclusions. Upper stories, with many 

interconnected walls and partitions, are often reasonably strong. 

The Guidelines therefore rely on realistic estimates of material strength and 

corresponding deformation. Chapter 4 gives default strength values for nonconforming sheathing materials over a range of story drifts. The strength 

values were derived from wall component tests, as documented in Appendix 

D. The Guidelines use “strength” to mean a complete load-drift relationship, 

not just a single peak value. Chapter 4 gives procedures for characterizing 

Interstory Drift

Shear Force

Sheathing material with 

C D = 0.0

L = 1.25%

Sheathing material with C D = 1.0

L = 4.0%
18 2: Technical Overview FEMA P-807 

and combining materials, wall assemblies, wall lines, and stories in a way 

that considers displacement capacity. 

To account for load path and configuration details, the Guidelines apply a 

series of factors to the estimated story strength. As described in Chapter 4, 

the Guidelines modify the story strength, and eventually the structure’s 

overall capacity, with factors that account for wall and story height, wall 

overturning and uplift, wall openings, and wall configuration as it affects 

torsional response. 

The Guidelines assume that story shear can induce torsion even with wood 

floor diaphragms and that the torsion will be resisted by walls with any 

orientation, as if the diaphragm were essentially rigid. While this is not 

traditional practice for wood diaphragms, it is consistent with the ASCE/SEI 

7 default requirement for new structures, and the Guidelines’ writers consider 

it a more realistic description of actual performance. Limitations on 

diaphragm span and configuration are expected to rule out extreme cases 

where this assumption would not hold. 

2.3 Acceptability Criteria 

2.3.1 Performance Measure 

As shown in Chapter 5, the Guidelines gauge the acceptability of a structure 

by calculating its capacity in terms of spectral acceleration, then comparing 

that capacity to a site-specific spectral acceleration demand. The capacity, 

however, is derived from fragility data that relate ground motion to interstory 

drift (see Appendix E). 

As described above, the intent of the Guidelines is to base acceptability on a 

severe condition such as near-collapse. Chapter 7 provides guidelines for 

adjusting the methodology for different drift limits. 

2.3.2 Performance Objective 

As in other performance-based standards, the Guidelines use a performance 

objective that combines a desired performance level with a presumed hazard 

level. The Guidelines’ default (embedded) performance objective may be 

stated as: “A given probability of not exceeding the drift limits associated 

with onset of strength loss, in a Maximum Considered Earthquake.” 

The Guidelines also allow users to select a targeted maximum probability of 

exceeding the drift limits, or, put another way, a confidence level for meeting 

the objective. Thus, if a 20-percent drift limit probability of exceedance 

(POE) is selected, a complete statement of the default performance objective 
FEMA P-807 2: Technical Overview 19 

would be: “80-percent confidence of not exceeding the drift limits associated 

with onset of strength loss, in a Maximum Considered Earthquake.” The 

Guidelines allow the user to set all three parts of the performance objective, 

to varying degrees: 

 The drift limit POE is selected and applied as part of the evaluation 

process, in Section 5.3. 

 Two performance levels are available. Drift limits for “onset of strength 

loss” are embedded in the evaluation and retrofit procedures in Chapters 

5 and 6 as the default. Chapter 7 provides alternative parameters with 

which to adjust the evaluation and retrofit equations for drift limits at the 

“onset of damage.” 

 Any demand level may be used. Chapter 5 presents evaluation criteria 

using the Maximum Considered Earthquake hazard defined in ASCE/SEI 

7-05 (ASCE, 2006a) as the default (embedded criteria), but the shortperiod spectral acceleration value from any hazard can be substituted to 

represent a different performance objective. 

2.3.3 Relationship to Other Codes and Standards 

With a drift limit probability of exceedance (POE) of 20 percent, the 

Guidelines default objective is expected to be similar to an ASCE/SEI 41 

(ASCE, 2006b) objective of “Collapse Prevention in a BSE-21

 event.” No 

correlation or performance equivalence studies between the Guidelines and 

“Collapse Prevention in a BSE-2 event,” however, have been made as part of 

the effort to develop these Guidelines. 

Currently, the technical criteria most commonly used for retrofit of weakstory wood-frame buildings are from Chapter A4 of the International 

Existing Building Code (ICC, 2009b). IEBC Chapter A4 does not state a 

performance objective. It relies on definitions of weak-story and soft-story 

irregularities from ASCE/SEI 7-05 and the code for new construction, so it is 

unclear how the Guidelines compare, especially with respect to evaluation 

(which is not Chapter A4’s primary focus). Table 2-1 compares the 

Guidelines with Chapter A4 on issues related to performance expectations 

for Guidelines-eligible buildings. 

While the Guidelines can be nominally aligned with Chapter A4 (or any 

other code or standard) by selecting the right drift limit POE, performance 

 

1

 BSE-2 denotes Basic Safety Earthquake level 2, an earthquake hazard level with 

ground motions have a 2% probability of being exceeded in 50 years. 
20 2: Technical Overview FEMA P-807 

Table 2-1 Comparison of the Guidelines to 2009 IEBC Chapter A4 

Issue Guidelines 2009 IEBC Chapter A4 

Drift Limit 

Probability of 

Exceedance 

At user’s discretion. 20 percent is 

recommended for comparison 

with code-based criteria for 

existing buildings. Full compliance 

may be waived to accommodate 

first-story-only retrofit. 

For evaluation: Not applicable. 

For retrofit: None stated, but 75 

percent factor is applied to codelevel earthquake hazard. 

Performance 

Level for 

Evaluation 

Onset of Strength Loss or Onset of 

Damage 

Code-based definitions of weak 

story, soft story, and open front. 

No performance-based criteria. 

Performance 

Level for Retrofit 

Onset of Strength Loss or Onset of 

Damage 

Code-level performance (with 

some exceptions), based on drifts 

and material strengths allowed for 

new construction. Upper stories 

not considered. 

Earthquake 

Hazard 

At user’s discretion. Maximum 

Considered Earthquake per 

ASCE/SEI 7-05 is recommended 

for collapse- or safety-based 

objectives. 

Code-level design basis 

earthquake: 2/3 of the Maximum 

Considered Earthquake per 

ASCE/SEI 7-05. 

Existing material 

and system 

characterization 

Peak strength and load-drift curves 

given. No resistance factors 

applied. 

None specified. Code-based 

standards for new construction 

apply by reference. 

Retrofit material 

and system 

characterization 

Retrofit elements must have highdisplacement capacity. Some 

systems disallowed. Allowed 

systems may be combined. 

No limits on systems, except for 

code-based rules on combining 

systems. 

Retrofit scope First story only, plus load path from 

second-floor diaphragm to soil. 

Retrofit calibrated to prevent 

upper-story failure. 

First story only, plus load path from 

second-floor diaphragm to soil. No 

check on upper-story performance. 

level, and hazard, the task is not straightforward. With respect to Chapter A4, 

Table 2-1 allows some observations on this point: 

 Chapter A4 uses “reduced” seismic loads (75 percent of those used for 

new buildings). Similarly, the Guidelines, with a 20 percent drift limit 

POE, allow a higher probability of exceedance than is expected of new 

construction (see Section 5.3, citing Luco, et al., 2007). 

 Assuming a 20 percent drift limit POE and the default objective of onset 

of strength loss in MCE-level shaking, the Guidelines appear to be more 

conservative than Chapter A4 regarding the hazard, but less conservative 

regarding the characterization of existing and retrofit elements. 

 Chapter A4 requires lateral-system improvements only in the critical first 

story. Similarly, the Guidelines stipulate cost-effective first-story 

retrofits, and even recommend waiving the targeted performance 

objective in favor of project feasibility. Importantly, however, the 

Guidelines are careful to check that strengthening the first story does not 
FEMA P-807 2: Technical Overview 21 

push the failure into the upper stories. Chapter A4 does not make this 

check. 

2.4 Critical Deficiencies 

The Guidelines are not a comprehensive code or standard for generalized 

seismic evaluation and retrofit design. Rather, they focus on a few 

characteristic deficiencies understood to be most responsible for 

unacceptable past performance of a certain building type. The premise of the 

Guidelines is that traditional or vernacular designs with relatively open first 

stories gave rise to buildings with inadequate strength and resistance to 

collapse. These buildings’ weak first-story deficiencies, often exacerbated by 

torsion, are the primary focus of the Guidelines, but building performance as 

a whole is also addressed. 

Seismic deformation concentrates in a weak first story. While the first story 

undergoes large deformations, the upper stories tend to respond as a stiff 

block over a weak and deformable base. This weak-story mode dominates 

the dynamic response, both in the elastic range, but especially in the inelastic 

range, where concentrated damage can lead to collapse. 

Figure 2-3 shows the differences in wall layout and density between first and 

upper stories in three representative buildings. In the figure, the top and 

bottom buildings are characteristic of dense urban development with access 

to first floor parking directly from the street. The top building is a midblock 

configuration (typical of Victorian- or Edwardian-era buildings in San 

Francisco) with garage access at one end only, ample longitudinal walls, and 

light wells that lead to a barbell-shaped diaphragm. The bottom building is a 

corner configuration (typical of 1920s-era San Francisco apartment houses) 

with garage doors along both street-facing sides. The middle building in 

Figure 2-3 is a more modern prototype (typical of 1960s buildings 

throughout the San Francisco Bay Area, Greater Los Angeles, and the Pacific 

Northwest). While its massing and block location are similar to the top 

building, it has a drive aisle along the side, leading to a wide-open tuck-under 

parking area. 

While all three buildings in Figure 2-3 have likely weak stories, the designs 

vary with a building’s location within a block and the nature of its street or 

sidewalk access. Different weak-story designs thus have different torsional 

sensitivities. Figures 2-4 and 2-5 illustrate how torsion can exacerbate the 

weak-story deficiency. The arrows show the center-of-strength2

 locations of 

 

2

 Center of strength is defined as the location of the force resultant of the wall 

strengths (see Section 3.4.4 for additional information).
22 2: Technical Overview FEMA P-807 

Figure 2-3 Plan diagrams of three weak-story buildings. Left: first story. Right: upper 

stories. 

the first and upper stories, respectfully. The distance between them indicates 

the eccentricity that gives rise to torsion in the first story. Figures 2-4 and 2-5 

also illustrate the difference between one-directional torsion and bidirectional torsion. 

2.5 Retrofit Design Philosophy 

2.5.1 Cost-Effective, First-Story Retrofit 

Fundamental to these Guidelines is the stipulation that retrofit work should 

be kept to the first story. This constraint follows from an understanding of 

the building type in question. The Guidelines have in mind a building with 

(or without) a dominant deficiency in the first story and an occupied status 

that makes retrofit work in the upper stories disruptive and expensive. 

Open Front, Tuck-under Building: Weak with torsion due to earthquake 

loads in the long direction 

Corner Building: Weak with bi-directional torsion due to earthquake loads 

in either direction 

Mid-Block Building: Weak with minor torsion 
FEMA P-807 2: Technical Overview 23 

Figure 2-4 Schematic response of a corner building subject to torsion under loads in either direction, due

to open wall lines on two sides at the first story. The distance between the arrows indicates 

the eccentricity that gives rise to torsion in the first story. The light arrow denotes the center of 

strength of upper stories; the dark arrow denotes the center of strength of the first story. 

Figure 2-5 Schematic response of a building with a slightly weak story in the long direction and with 

torsion under loads in the long direction. The distance between the arrows indicates the 

eccentricity that gives rise to torsion in the first story. The light arrow denotes the center of 

strength of upper stories; the dark arrow denotes the center of strength of the first story. 
24 2: Technical Overview FEMA P-807 

Limiting retrofit to the first story recognizes the need, discussed in Chapter 1, 

to provide adequate benefit for minimal cost. This means that a retrofit in 

accordance with the Guidelines might knowingly leave less dominant upperstory deficiencies in place while limiting the displacement demand they 

experience. Such a retrofit might not achieve the same performance as a 

comprehensive top-to-bottom upgrade and might not satisfy the letter of 

other applicable codes or standards, something that needs to be approved by 

the authority having jurisdiction. Nevertheless, this is a tradeoff that may 

sometimes be found to be in the interest of owners, tenants, and jurisdictions 

because it allows the work to be done while the building is occupied. 

2.5.2 Bounded Design and Relative Strength 

For most weak-story buildings, a first-story retrofit is expected to address 

what is by far the structure’s weakest link. Upper stories might have 

unaddressed deficiencies, but as long as they are not made worse, the firststory retrofit improves the building’s overall seismic performance in a costeffective way. 

But what if the first-story retrofit does make upper stories more vulnerable? 

This is possible because the weak first story, by absorbing all the lateral 

deformation, protects the upper stories. When the weak story is strengthened, 

the structure becomes more regular, with deformations no longer 

concentrated in one story. So when the first story is strengthened, upper 

stories will have to sustain higher forces and drifts. 

Figure 2-6 illustrates this effect. The different lines represent similar fourstory structures with different first-story strengths. In the existing structure, 

the first-story drift far exceeds even a 4-percent limit, while corresponding 

drifts in the upper stories are small. As the first story is made stronger, the 

first-story drift decreases, but corresponding upper-story drifts increase. 

Eventually, the second-story drift exceeds its limit of 1.25 percent; this is the 

unintended consequence of an overly strong retrofit. 

The acceptable retrofits are those that reduce the first-story drift enough to 

satisfy the 4-percent drift limit (a high-displacement capacity) but keep the 

upper stories under their 1.25-percent limit (assuming the upper stories have 

low-displacement capacity). The least-cost retrofit is the acceptable retrofit 

that satisfies both criteria by adding the least amount of material to the first 

story. The best-performance retrofit is the one that reduces the first-story 

drift the most, while keeping upper stories within their drift limits. 

Chapter 6 provisions give the retrofit strength corresponding to these two 

bounding cases. The first bound—the minimum required strength of the 
FEMA P-807 2: Technical Overview 25 

Figure 2-6 Plots illustrating floor displacements and drift ratios in a building with constant upper-story strength 

and varying first-story strength. (E) Structure = Existing Structure. 

retrofitted first story—is that required to reduce the first-story drift to an 

acceptable level. The second bound—the maximum acceptable strength of 

the retrofitted first story—essentially sets a limit on the relative strength of 

the first and second stories. 

In certain buildings, the overall structure may be so weak that the two bounds 

will be in conflict, and it will be impossible to satisfy both conditions with a 

first-story-only solution. In these cases, the upper bound, based on the 

relative strength of the first and second story, is used to control the design. 

This cap on relative strength is a key feature of the Guidelines methodology. 

2.6 Limitations and Eligibility Requirements 

Because the Guidelines are based on statistical data and do not require 

customized modeling and analysis of a particular building, they only apply 

reliably to the range of conditions considered in developing the fragility 

relationships. For most of the limitations described below, eligibility is 

restricted only because the ineligible condition was not explicitly studied, not 

because the methodology has been shown not to work. 
26 2: Technical Overview FEMA P-807 

Buildings eligible for evaluation or retrofit using the Guidelines satisfy all of 

the following conditions. A building may be altered in accordance with 

Chapter 6 to make the building eligible. Unless noted otherwise, the same 

rules apply to both an existing building being evaluated and to the retrofitted 

building being designed or checked. 

2.6.1 General Eligibility Requirements 

 The building has no more than four wood-frame above-grade stories or 

partially above-grade stories. 

 The building does not have an above-grade concrete (or similarly stiff) 

podium structure (e.g., concrete-wall structure) supporting the woodframe stories. 

 There is no restriction on soil type or site class. However, it is important 

to note that the surrogate analyses on which the methodology is based 

used the ground motions considered in the development of the FEMA P695 Report, Quantification of Building Seismic Performance Factors

(FEMA, 2009), which considered ground motion records from site 

classes C and D, but not site classes B, E, or F. To the extent that soft 

soil records would have significantly changed the response of the 

surrogate models, use of the Guidelines for such sites could be 

unconservative. Even so, it is the judgment of the Guidelines’ writers 

that code-prescribed site coefficients (Fa), if applied when selecting the 

spectral acceleration demand used to check the building in Chapter 5, are 

sufficient to account for soil effects. The selection of Fa to adjust for site 

class effects, rather than Fv, is because Fa provides the most consistent 

and straightforward basis for comparing the actual building to the 

surrogate analyses. (See Appendix E for details on the surrogate 

analyses.) 

2.6.2 Upper-Story Eligibility Requirements 

 The primary components of the upper-story seismic-force-resisting 

system are wood-frame stud walls. 

 The upper-story heights (floor-to-floor) are between 8 feet and 12 feet, 

and the height of any upper story is constant within that story. 

 No upper story is prone to significant torsion. The methodology assumes 

that inertial forces from upper stories transfer to the first story near the 

geometric center of the second floor. As an approximate rule, this 

assumption may be considered satisfied if in each upper story, the 

distance from the story’s center of strength (see Section 4.6.4) to the 
FEMA P-807 2: Technical Overview 27 

center of mass of the floor below it is no more than 25 percent of the 

corresponding building dimension, as illustrated in Figure 2-7. 

Figure 2-7 Floor plan schematic showing limits on eccentricity between the 

center of strength (Cs) of each upper story and the center of 

mass (Cm) of the floor below it. 

2.6.3 First-Story, Basement, and Foundation Eligibility 

Requirements 

 The upper stories have no vertical mass or geometric irregularities as 

defined by ASCE/SEI 7-05 Table 12.3-2 (Irregularity Types 2 and 3). 

 The maximum first-story height (top of foundation to top of second 

floor) is between 8 feet and 15 feet. The first-story height may vary 

within the story. 

 The primary components of the first-story seismic force-resisting system 

are wood-frame stud walls or combine wood-frame walls with steel 

moment frames. 

 The first-story walls have continuous concrete or masonry perimeter 

foundations, or concrete slab-on-grade foundations. 

 If the wood-frame walls and steel frames are partial-height over stiff 

(concrete or masonry) retaining walls or foundation stem walls, the 

wood-frame or steel portion is at least four feet tall (top of stem wall to 

underside of second floor framing). 

 The first-story seismic force-resisting system does not include any fullheight concrete or masonry walls. 

 If the building has a basement below the first story, the basement walls 

and the floor diaphragm just above them are capable of transferring 
28 2: Technical Overview FEMA P-807 

seismic forces between the foundation and the first wood-frame story. 

The basement story is laterally stronger than the first story above it. 

 If the first floor is partly slab-on-grade and partly raised over a crawl 

space, the crawl space has concrete stem walls to the underside of the 

framing and does not have wood cripple walls (braced or unbraced). 

2.6.4 Floor and Roof Diaphragm Eligibility Requirements 

The Guidelines methodology was developed by studying structures 

dominated by weak-story deficiencies. The effects of significant diaphragm 

or load path deficiencies were not explicitly considered. As a general rule, 

then, any structure in which a diaphragm or load-path deficiency would 

control the response should not be eligible for the Guidelines without either 

separate careful study or remediation. The rules below, while rational and 

appropriate, were not derived from the surrogate analyses. Therefore, while 

the quantitative limits reflect the judgment of the Guidelines’ writers, they 

should also be considered open to modification, and subject to the reasoned 

judgment of the engineer and building official. 

As noted above, an ineligible building may be made eligible through 

alteration or retrofit. That is, if the alteration would correct the deficiency, 

the building may be assumed eligible for purposes of applying the 

Guidelines, with the understanding that the correction will be implemented 

even if the existing building, treated as eligible, already satisfies the 

performance objective. 

An ineligible diaphragm can often be made (or considered) eligible if it can 

be broken (figuratively) into a series of eligible sections divided by 

qualifying walls or frames. In order to qualify to divide a diaphragm for this 

purpose, a wall or frame line must contribute significantly to the peak firststory strength in the direction of interest. There is no analysis-based rule for 

what it means to “contribute significantly,” but the concept is that a nominal 

length of wall that would otherwise not be considered an important part of 

the seismic force-resisting system probably should not qualify to help make 

the diaphragm perform more regularly. As an approximate rule, any wall line 

contributing, say, at least half as much strength as the strongest parallel wall 

line may be considered as qualifying. In any case, some judgment is 

appropriate here, and any qualifying wall line should be confirmed as 

capable of delivering its assumed properties. 

With this understanding, the recommended eligibility rules for diaphragms 

are as follows: 
FEMA P-807 2: Technical Overview 29 

 The second floor diaphragm has an aspect ratio not greater than 2:1. 

Diaphragms with larger aspect ratios are eligible if each section of the 

diaphragm between qualifying wall lines has an aspect ratio not greater 

than 2:1. See Figure 2-8. 

Figure 2-8 Floor plan schematic showing use of qualifying wall lines to 

meet diaphragm aspect ratio limits. D denotes diaphragm. 

 The second floor diaphragm does not cantilever more than 25 feet from a 

qualifying wall line. 

 If the second floor diaphragm has a cantilevered span greater than 10 

feet, diaphragm chords are adequate to develop the lesser of the strength 

of the diaphragm or the diaphragm forces associated with the peak 

strength of the qualifying “supporting” wall line. See Figure 2-9. 

 No floor or roof diaphragm has a reentrant corner irregularity, defined as 

a condition in which both plan projections beyond a reentrant corner are 

longer than 15 percent of the plan dimension of the structure in the 

corresponding direction, except that diaphragms with reentrant corners 

are eligible if each leg of the diaphragm satisfies the aspect ratio and 

cantilever rules above. See Figure 2-10. The eligibility rules for 

buildings with reentrant corners might be more conservative than the > 0.15y

> 0.15x

East-West Analysis

D

D

Qualifying wall lines

y y

y / x < 2

y / x < 2

E

S

W

N

x

x

y
30 2: Technical Overview FEMA P-807 

Figure 2-9 Floor plan schematic showing locations of chords for 

cantilevered diaphragms that must satisfy eligibility rules. 

requirements of ASCE/SEI 31, which in some cases do not identify 

reentrant corners as problematic in seismic performance. The eligibility 

requirements are included to ensure that diaphragm demands are limited. 

 No floor or roof diaphragm has a vertical offset (a stepped or split level, 

for example), unless load path components are present and adequate to 

develop the diaphragm strength across the offset. 

Figure 2-10 Floor plan schematic showing reentrant corner limits and use of 

qualifying wall lines to satisfy eligibility rules. D denotes diaphragm. 

L

Cantilevered

Diaphragm

Chord capacity must be

checked if L > 10 feet.

> 0.15y

x

> 0.15x

North-South Analysis

D

D

Qualifying wall lines

x / y < 2

x / y < 2

x x

E

S

W

N

y

y
FEMA P-807 2: Technical Overview 31 

 No floor or roof diaphragm has excessive cutouts or openings within it. 

Excessive openings are deemed to exist if, along any line across the 

diaphragm, the sum of the opening widths along that line is more than 25 

percent of the overall diaphragm dimension along that line. See Figure 

2-11. 

Figure 2-11 Floor plan schematic showing diaphragm openings that must be 

limited in size to satisfy eligibility requirements. D denotes 

diaphragm. 

Depending on the width, this portion

may be considered a separate

sub-diaphragm, D

D D

W

W

W

FEMA P-807 3: Simplified Evaluation 33 

3Chapter 3 

1 Simplified Evaluation 

3.1 Purpose 

This chapter provides a simplified evaluation procedure that requires less 

building surveying and less computation than the full evaluation procedure of 

Chapters 4 and 5. Certain assumptions and simplifications make the 

simplified procedure somewhat more conservative but less time-consuming. 

Chapter 3 will be clearly advantageous when the building would likely meet 

the performance objective if it were to be evaluated using Chapters 4 and 5. 

The conditions where this would be the case would include some 

combinations of: 

 The existing building has wood structural panel sheathing as its primary 

later-force-resisting system, 

 The targeted drift limit probability of existence (POE) is 20%, and 

 The site is located in a region of moderate or low seismicity. 

3.1.1 Limitations 

This procedure only applies if: 

 The upper-story strengths are clearly stronger than the first-story 

strength, 

 The building meets the eligibility rules of Section 2.6, and 

 The selected performance level involves drift limits associated with onset 

of strength. 

3.2 Simplified Evaluation Procedure 

The simplified evaluation procedure comprises the following steps: 

1. Perform a detailed survey of the first story and a cursory survey of the 

upper stories in accordance with Section 3.3. 

2. Compute characterizing coefficients in accordance with Section 3.4. 

3. Select a targeted drift limit probability of exceedance for the building 

and determine the drift limit probability of exceedance (POE) adjustment 

factor using Table 3-1, which provides POE adjustment factors for low- 
34 3: Simplified Evaluation FEMA P-807 

Table 3-1 Drift Limit Probability of Exceedance (POE) Adjustment Factors 

for Low-Displacement Capacity Elements 

Targeted Drift Limit Probability of 

Exceedance (POE)

Adjustment Factor for Low-Displacement 

Capacity Elements*, POE,0

2% 0.29 

5% 0.37 

10% 0.46 

20% 0.60 

50% 1.00 

60% 1.16 

70% 1.37 

80% 1.66 

*Elements for which CD, strength degradation ratio, is assumed to be 0.0 

displacement capacity elements (i.e., those with an assumed strength 

degradation ratio of 0.0). 

4. Evaluate estimated seismic performance in comparison with spectral 

acceleration demand in accordance with Section 3.5. 

3.3 Building Survey 

The goal of the survey is to gather the information necessary to perform the 

simplified analysis and evaluation. The survey of the first story will require 

attention to detail similar to that required in Chapter 4 for the full evaluation. 

The upper-story survey, however, is intended to be much more limited. 

3.3.1 First-Story Survey 

The locations and lengths of the walls in the first story should be recorded. 

Only wall segments conforming to all of the following conditions should be 

considered: 

 Wall segments 

1. Are full-height from floor to floor, 

2. Are greater than two feet long, 

3. Have height-to-width ratios less than 8:1, 

4. Are structurally connected to the floor above, and 

5. Show no signs of significant deterioration or damage. (Deteriorated 

wall segments can be left out of the calculations.) 

The layers of material that make up each wall should also be recorded and 

categorized using the sheathing types listed in Table 3-2. If the exact 
FEMA P-807 3: Simplified Evaluation 35 

Table 3-2 Strength Data for Sheathing Materials Considered 

Material ID Strength (pounds/linear foot) 

Stucco L01 330 

Horizontal wood sheathing or wood siding L02 170 

Diagonal wood sheathing L03 910 

Plaster on wood lath L04 540 

Plywood panel siding (T1-11) L05 570 

Gypsum wallboard L06 210 

Plaster on gypsum lath L07 400 

Wood structural panel 8d@6” on center L08 840 

Wood structural panel 8d@4” on center L09 1,110 

Wood structural panel 8d@3” on center L10 1,690 

Wood structural panel 8d@2” on center L11 2,190 

Wood structural panel 10d@6” on center L12 1,070 

Wood structural panel 10d@4” on center L13 1,500 

Wood structural panel 10d@3” on center L14 1,990 

Wood structural panel 10d@2” on center L15 2,510 

Source: Table 4-1 (maximum strength values rounded to nearest 10 pounds per linear 

foot). 

sheathing type is not tabulated, the engineer may use judgment to choose the 

closest matching sheathing type. Some destructive investigation might be 

needed. 

3.3.2 Upper-Story Survey 

A survey of the upper stories should be only as detailed as necessary for the 

engineer to estimate the weight of the upper stories and the center of strength 

of the upper stories. This may include: 

1. Overall building geometry, including plan dimensions and story heights, 

2. The amount and composition of partitions contributing to the weight of 

the building, and 

3. Floor assemblies. 

3.4 Building Characterization 

This section outlines the computations necessary to determine a few 

coefficients that characterize the building in preparation for the evaluation in 

Section 3.5. The task is to synthesize the information gathered during the 

building survey into numerical quantities that characterize the building. 
36 3: Simplified Evaluation FEMA P-807 

These values will be used in Section 3.5 to evaluate the expected seismic 

performance. 

3.4.1 Total Building Weight, W 

The total weight of the building should be estimated. The engineer should 

use conventional assumptions for weights of building materials. The 

calculations should be consistent with the geometry and other information 

gathered about the building during the building survey. 

3.4.2 Shear Strengths of First-Story Walls 

Each conforming first-story wall identified in the building survey comprises 

one or more of the sheathing types listed in Table 3-2. The unit strength, vs, is 

tabulated for each sheathing type (Table 3-2, right column). For walls with 

the same finish on each face, vs for each face is to be included. Each wall 

segment should be assigned a unit strength, va, based on the sum of the 

strengths of each layer: 

aw s , v v  (3-1) 

where: 

 = unit shear strength of the wall assembly for wall w, and 

s v = sum of unit shear strengths of all the sheathing types in the 

wall assembly. 

For simplicity reasons, this method of combining the strengths for each layer 

neglects the fact that test results indicate various finish layers reach their 

strength at different drift levels. The detailed evaluation method described in 

Chapter 4 does not neglect such behavior. While the above-specified method 

of combining is effectively non-conservative, the overall simplified 

procedure described in this chapter is considered conservative. 

The total shear strength of each wall, fv, should be calculated as the unit 

strength of the wall assembly times the wall length: 

 vw aw w , , f  v L (3-2) 

where: 

 = shear strength of wall w, and 

 = Length of wall w; examples shown in Figure 3-1. 

wa v ,

wv f ,

Lw
FEMA P-807 3: Simplified Evaluation 37 

Figure 3-1 Illustration of wall lengths for an example wall line. In this case, 

Lw = L1 + L2 + L3.

3.4.3 Shear Strength of First Story 

The shear strength of the first story is computed for each direction as the sum 

of the strengths of the walls parallel to the direction under consideration. For 

walls at an angle to the primary wall directions, the projected length of the 

direction being considered should be used. The shear strength of the first 

story, V1, is given by: 

V f 1,x  vwx , , 3-3 

where: 

V1,x = first-story shear strength in the direction x, and 

vwx , ,  f = sum of shear strengths of all walls parallel to the x-direction. 

The first-story shear strength and the sum of shear strength of all walls in the 

y-direction are calculated similarly. 

3.4.4 Center of Strength (COS1) of First Story 

The center of strength of the first story, COS1, is defined to be the location of 

the force resultant of the wall strengths. For each wall, there is the point in 

plan, pw, through which forces in that wall will act. This is the center of each 

wall. The position in plan that defines the center of strength in each story is 

given by: 

H

Floor to Ceiling

L12 3 L L

Openings

Length of

Full-height Wall

Segments
38 3: Simplified Evaluation FEMA P-807 

,, , ,, ,

1 1

1

1, 1,

,

N N walls walls

vwy wx vwx wy

w w

y x

fp fp

COS

V V

 

   



 

 

 (3-4) 

where: 

COS1 = center of strength of the first story, 

vwx , , f = component of shear strength of wall w, in direction x, 

vwy , , f = component of shear strength of wall w, in direction y, 

w x, p = x-coordinate of the center of wall w, and 

w y, p = y-coordinate of the center of wall w. 

3.4.5 Center of Strength (COS2) of Upper Stories 

For the purposes of the simplified evaluation, the center of strength of the 

upper stories, COS2, may be assumed to be the same as the geometrical 

centroid of the floor/roof diaphragm above the second floor. 

3.4.6 Eccentricity 

Typically, the centers of strength of the first story and upper stories will not 

be in the same location. If they are not, an eccentricity exists in one or both 

directions. The eccentricity is the absolute value of the difference in each 

component of the centers of strength: 

x 2, 1, x x e COS COS   (3-5) 

where: 

ex = eccentricity in direction x, 

COS1,x = x-component center of strength of first story, and 

COS2,x = x-component center of strength of upper stories. 

A corresponding calculation is made to determine the eccentricity in 

direction y.

3.4.7 Simplified Torsion Coefficient, CTs

The simplified torsion coefficient takes into account the eccentricity of the 

structure under consideration. It is used in the evaluation to modify the 

expected seismic performance in Section 3.5.3. The simplified torsion 

coefficient is given by: 
FEMA P-807 3: Simplified Evaluation 39 

4 x y

Ts

x y

e e

C

L L

  

 (3-6) 

where: 

Lx = Length of the building in direction x, and 

Ly = Length of the building in direction y. 

3.5 Simplified Evaluation of Seismic Performance 

The seismic performance is evaluated by comparing the simplified spectral 

acceleration capacity, Sc, which estimates the spectral acceleration at which 

unacceptable damage occurs, to the selected site-specific spectral 

acceleration demand. If the spectral-acceleration capacity is larger than the 

selected site-specific spectral acceleration demand, the building is deemed to 

satisfy the default (embedded) performance objective. 

3.5.1 Site-Specific Spectral Acceleration Demand 

The spectral acceleration demand is the short-period spectral acceleration 

corresponding to the earthquake hazard level of interest, as described in 

Section 3.2.2. The default (embedded) spectral acceleration demand is the 

MCE spectral acceleration for short periods (SMS) from ASCE/SEI 7-053

. At 

sites classified as Site Class F, ASCE/SEI 7-05 requires the development of a 

site-specific acceleration design spectrum because its default spectrum might 

not be well-suited to soft or liquefiable soil. It was beyond the scope of these 

Guidelines to study the response of structures to soft-soil ground motions. 

However, it is expected that the conclusions and recommendations provided 

herein would still apply based on the following reasoning: the analytical 

study indicates that weak-story buildings behave much like single-mode 

structures, i.e., the relatively strong upper structure may be idealized as a 

rigid mass atop the weak first story. This single-mode behavior would be 

expected regardless of the ground-motion input, but the spectral acceleration 

demand on a soft-soil site may be larger at longer periods than at shorter 

periods. Thus, it is recommended that the maximum site-specific spectral 

acceleration (i.e., the largest spectral acceleration at any period) be used for 

the spectral acceleration demand. For sites classified Site Class F, the 

maximum site-specific spectral acceleration may be established in 

accordance with ASCE/SEI 7-05 Chapter 21. 

 

3

 Conceptually, the equivalent definitions in ASCE/SEI 7-10 for MCE and SMS could 

also be used to define spectral acceleration demand. 
40 3: Simplified Evaluation FEMA P-807 

3.5.2 Story Height Factor, Qs

The seismic performance of a weak-story building is related to the height of 

the first story (see Appendix E for further discussion). The story height 

factor accounts for this. It is given by: 

0.55 0.0047 Q H s   (3-7) 

where: 

H = Tallest height of any first-story wall, from floor to ceiling, in 

inches. 

3.5.3 Simplified Spectral Acceleration Capacity, Scs

The simplified spectral acceleration capacity should be computed in each 

direction. It is given by: 

 

0.6

1,

, ,0 1.47 0.73 x

cs x POE Ts s

V

S CQ W



       

 (3-8) 

where CTs, Qs, V1,x, and W are defined above, and 

POE,0 = drift limit probability of exceed (POE) adjustment factor for 

low displacement capacity elements, with strength 

degradation ratio, CD = 0.0, and

Scs,x = simplified spectral acceleration capacity in direction x.

This formulation requires the selection of a drift limit probability of 

exceedance (POE) level for the building, which is then used to determine the 

POE adjustment factor, POE,0 (see Table 3-1), used in Equation 3-8. 

3.5.4 Comparison of Demand Versus Capacity 

The spectral acceleration capacity in each direction should be compared with 

the spectral acceleration demand consistent with the performance objective. 

Equation 3-9 and Equation 3-10 use the Guidelines default (embedded) 

performance objective and therefore use the MCE spectral acceleration for 

short periods (SMS) from ASCE/SEI 7-05 as the demand; for further 

discussion on performance objectives, see Section 2.3.2 and Chapter 5. 

cs x MS , S S  (3-9) 

cs y MS , S S  (3-10) 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 41 

Chapter 4 

Structure Characterization 

for Detailed Evaluation 

4.1 Introduction 

Chapter 4 provides the procedure for characterizing the structure for the 

evaluation procedure of Chapter 5. The structure is characterized by five 

values: 

 Base-normalized upper-story strength, AU, 

 Weak-story ratio, AW, 

 Strength degradation ratio, CD, 

 Torsion coefficient, CT, and 

 Story height factor, Qs. 

Calculating these values requires information about the existing building 

collected in accordance with Section 4.3 and development of load-drift and 

load-rotation curves in accordance with Sections 4.4 through 4.6. 

The Guidelines use the following conventions to designate specific floors 

and stories: 

 The first story is the story being investigated as a potential weak story. It 

is frequently the ground story—that is, the story immediately at grade—

but not always so, due to sloped sites, partial basements, or other 

conditions. 

 The upper stories include all the stories above the first story. Frequently 

the second story is the most critical of these, but the Guidelines allow for 

the possibility that a story further up in the building might influence the 

evaluation results or the retrofit design. 

 Story i is between floor i and floor i+1. Thus, story 1—the first story—is 

between floors 1 and 2. For the common condition where the first story is 

adjacent to grade on a flat site, ground level is the first floor, or floor 1. 

 The subscript i is generally used to denote a floor or story. 
42 4: Structure Characterization for Detailed Evaluation FEMA P-807 

 The subscript x is generally used to denote a plan direction, with the 

understanding that a building has two principal orthogonal directions, x

and y. 

4.2 Wall Materials 

Buildings eligible for the Guidelines will have walls with a wide variety of 

sheathing materials. Wall materials likely to be encountered in older 

buildings include horizontal wood siding, horizontal and diagonal lumber 

sheathing, plaster over wood or gypsum lath, and stucco. Additional wall 

materials likely to be encountered in newer or remodeled buildings include 

gypsum wallboard and wood structural panel sheathing. While some of these 

are no longer common in new construction, all provide some level of strength 

and stiffness that should be considered in the evaluation and retrofit of 

existing buildings. Their contribution to strength and stiffness is particularly 

vital to the Guidelines methodology, in which story-to-story comparison of 

properties is paramount. 

4.3 Detailed Building Survey 

The purpose of the survey is to collect information required to calculate the 

building seismic weight and develop load-drift and load-rotation curves in 

accordance with Sections 4.4 through 4.6. Available drawings should be used 

to supplement the survey effort, but conditions depicted must still be fieldverified. 

An important part of data collection is identification and description of wall 

elements that contribute to the lateral strength and stiffness of the structure in 

each story. The following information is generally needed: 

1. Wall locations and the size of wall openings. Wall segments less than 

one-foot long, or with height-to-width ratios greater than 8:1, should be 

neglected, as these are treated as openings when calculating wall line 

load. 

2. Floor, roof, and wall assembly descriptions, to determine seismic weight, 

and to calculate overturning resistance where the simplified overturning 

adjustment factor is not applicable. 

3. Diaphragm geometry, including locations of significant openings. 

4. Wall sheathing materials. 

5. Where sheathing is wood structural panel (WSP) or where sheathing 

load-drift data depends on nailing (see Section 4.4), nail size, and edgenail spacing. 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 43 

6. Condition of walls, with attention to any deterioration or damage. 

Quality of construction can also affect capacity; see Section 4.4. 

7. Direction of floor and roof framing. This is necessary for the second 

floor and recommended at other floors for determining overturning 

resistance. 

8. In buildings where hold-down hardware is anticipated, the locations of 

hold-down hardware and the adequacy of installation of representative 

hold-down types. Judgment should be exercised regarding the level of 

effort needed to identify the pattern of placement and representative 

locations. 

9. Confirmation that walls are structurally connected for in-plane shear 

transfer at wall top and bottom. Check representative locations in the first 

story. Check representative locations in upper stories where there is 

reason to suspect walls might not be structurally connected. For nonWSP sheathing, the intent is to confirm that fastening reasonably 

conforms to conventional construction requirements. For existing WSP 

shear walls with nail spacing closer than six inches, it should be 

confirmed at representative locations that shear wall top and bottom 

connection capacity is reasonably in balance with the sheathing capacity. 

10. Anchor bolts. At the base of the first story, verify that anchor bolts exist 

or that anchor bolts will be added as part of an alteration or retrofit. 

11. Confirmation that walls have a load path to pick up or mobilize tributary 

dead load used to resist overturning. Check representative locations in 

the first story. Check representative locations in upper stories where 

there is reason to believe walls might not have bearing load path, such as 

conditions involving infill walls or long-span truss systems. 

Some destructive investigation might be needed, especially to determine the 

construction of representative wall assemblies. For example, a typical interior 

wall could have two layers of lath and plaster or two layers of gypsum 

wallboard. A perimeter wall could consist of a layer of stucco, diagonal 

siding, and gypsum wallboard. Only intact lengths of sheathing should be 

counted toward the strength of a wall. Any portion along the length of a fullheight pier of any layer of wall sheathing where capacity-reducing 

deterioration or damage exists should be excluded. 

4.4 Load-Drift Curves for Common Sheathing Materials 

The Guidelines rely on the concept of load-drift (or backbone) curves. A 

piecewise-linear curve is defined by a set of drift ratios and corresponding 

loads (lbs) or unit-loads (pounds per linear foot, plf) based on available test 
44 4: Structure Characterization for Detailed Evaluation FEMA P-807 

information. The interstory drift ratios at the top of Table 4-1 represent the 

set of expected deformations, j. Load-drift curve data for each sheathing 

material considered are tabulated in Table 4-1 and plotted in Figure 4-1, 

Figure 4-2, and Figure 4-3. As seen in Figures 4-1 and 4-2, the curves have 

been grouped into materials with high- and low-displacement capacity. See 

Appendix E for further discussion of this categorization. 

Table 4-1 Load-Drift Curve Data for Sheathing Materials [pounds/linear foot] 

The load-drift curves are based on available information from numerous 

sources described in Appendix D. As part of the Guidelines developmental 

project, engineering judgment was applied to reconcile the data, accounting 

for differences in loading protocol and testing conditions. Cautions are 

needed regarding several of the materials listed in Table 4-1. 

 Values for plywood panel siding (often called “T1-11”) are for fastening in 

accordance with APA recommendations, which require one nail to connect 

two lapped sheets at vertical edges. Inadequate nailing is frequently and 

widely observed. Where nailing is inadequate, sheathing capacity should 

be reduced for calculations, or nailing should be corrected. 

Sheathing Material ID 

Interstory Drift Ratio, j [%] 

0.5 0.7 1.0 1.5 2.0 2.5 3.0 4.0 5.0 

Stucco L01 333 320 262 0 

Horizontal wood 

sheathing or wood siding L02 85 96 110 132 145 157 171 0 

Diagonal wood sheathing L03 429 540 686 913 0 

Plaster on wood lath L04 440 538 414 391 0 

Plywood panel siding 

(T1-11) L05 354 420 496 549 565 505 449 0 

Gypsum wallboard L06 202 213 204 185 172 151 145 107 0 

Plaster on gypsum lath L07 402 347 304 0 

WSP, 8d@6” on center L08 521 621 732 812 836 745 686 0 

WSP, 8d@4” on center L09 513 684 826 943 1,018 1,080 1,112 798 0 

WSP, 8d@3” on center L10 1,072 1,195 1,318 1,482 1,612 1,664 1,686 1,638 0 

WSP, 8d@2” on center L11 1,393 1,553 1,713 1,926 2,096 2,163 2,192 2,130 0 

WSP, 10d@6” on center L12 548 767 946 1,023 1,038 1,055 1,065 843 0 

WSP, 10d@4” on center L13 707 990 1,275 1,420 1,466 1,496 1,496 1,185 0 

WSP, 10d@3” on center L14 940 1,316 1,696 1,889 1,949 1,990 1,990 1,576 0 

WSP, 10d@2” on center L15 1,120 1,568 1,999 2,248 2,405 2,512 2,512 2,231 0 

Source: Appendix D, Table F-14. 

Notes: Values in the shaded areas are interpolated or extrapolated from existing data. 

 WSP: Wood structural panel 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 45 

Figure 4-1 Unit load-drift curves for sheathing materials with high-displacement capacity. Wall-panel nailing 

notation: nail size (e.g., 8d) @ distance between center of nails in inches. 

Figure 4-2 Unit load-drift curves for sheathing materials with low-displacement capacity. 

0

500

1,000

1,500

2,000

2,500

3,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Unit Force, plf

Horizontal wood sheathing

Gypsum wall board

Wood structural panel 8d@6

Wood structural panel 8d@4

Wood structural panel 8d@3

Wood structural panel 8d@2

Wood structural panel 10d@6

Wood structural panel 10d@4

Wood structural panel 10d@3

Wood structural panel 10d@2

0

100

200

300

400

500

600

700

800

900

1,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Unit Force, plf

Stucco

Diagonal wood sheathing

Plaster on wood lath

Plywood panel siding

Plaster on gypsum lath
46 4: Structure Characterization for Detailed Evaluation FEMA P-807 

Figure 4-3 Unit load-drift curves for all sheathing materials considered; note the large differences in 

both peak strength and displacement capacities. Wall-panel nailing notation: nail size 

(e.g., 8d) @ distance between center of nails in inches. 

 Stucco over self-furring lath has performed poorly in some cases, often 

due to poor quality construction. Several investigations after the 

Northridge earthquake found that the stucco was applied over the face of 

the wire rather than engaging it and penetrating behind it. Where a 

significant proportion of building, story, or wall-line capacity is provided 

by stucco with self-furring lath, the adequacy of construction should be 

verified, and where inadequacies are found, sheathing capacity should be 

reduced to reflect these inadequacies. 

Finally, some materials should be ignored for the purpose of establishing 

load-drift curves. 

 Hardboard siding has been tested by Pardoen, et al. (2003) as part of the 

CUREE-Caltech Woodframe Project and found to have negligible 

capacity. 

 Steel sheet was used in the past to provide fire resistance for garage walls 

(especially in San Francisco), but its nailing is typically too light to make 

a contribution to wall strength. 

0

500

1,000

1,500

2,000

2,500

3,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Unit Force, plf

Stucco

Horizontal wood sheathing

Diagonal wood sheathing

Plaster on wood lath

Plywood panel siding

Gypsum wall board

Plaster on gypsum lath

Wood structural panel 8d@6

Wood structural panel 8d@4

Wood structural panel 8d@3

Wood structural panel 8d@2

Wood structural panel 10d@6

Wood structural panel 10d@4

Wood structural panel 10d@3

Wood structural panel 10d@2
FEMA P-807 4: Structure Characterization for Detailed Evaluation 47 

 Veneer test results were not reviewed for inclusion in Table 4-1. In 

general, brick veneer should be ignored for purposes of calculating wall 

assembly and wall line strength. While the veneer itself might have 

significant strength and stiffness, the shear load path and connection to 

the rest of the wall assembly is insufficient, as it typically involves only 

weak wire ties incapable of transferring substantial forces. 

See Appendix D for discussion of methods to develop load-drift curves for 

materials not included in Table 4-1. 

4.5 Wall Line Load-Drift Curves 

To quantify the load-drift behavior for each story and direction, wall 

segments within each story are assigned to wall lines, and a load-drift curve 

is established for each wall line. Wall segments combined into one wall line 

must meet all of the following requirements: 

 Wall segments must occur in a single line, or have out-of-plane offsets 

not exceeding four feet. 

 Wall segments must occur within continuous wall framing (top plates 

and studs). Where wall framing stops, wall segments on either side are to 

be assigned to separate wall lines. Party walls, with or without staggered 

studs may be considered the same wall line, provided the top and bottom 

of the wall are connected adequately to provide compatible deformations. 

 Wall segments must be of constant height. Wall segments with varying 

height should be assigned to separate wall lines. 

 Wall segments must be of a single sheathing assembly (that is, a single 

combination of sheathing materials). 

 Steel moment frames should be considered to have their own wall lines. 

The length of a wall line length should be taken as the longest possible length 

that satisfies these criteria. Where hold-downs exist at each end of a wall 

segment, that wall segment may be considered a separate wall line. 

Where bay windows exist, the segments of wall within the common plane are 

considered to be in the same wall line, but the wall segments within the 

cantilevered portions of the bay are not counted toward the wall line 

capacity. 

Once wall lines are defined, a load-drift curve is established for each wall 

line, adjusting for combinations of sheathing materials, openings, overturning 

restraint, and, for first-story walls, wall line height. 
48 4: Structure Characterization for Detailed Evaluation FEMA P-807 

The load-drift curve for each upper story wall line is given by: 

fw j w j w open ot    v LQ Q        (4-1) 

where: 

f w j   = load-drift curve for wall line w, at drift ratio increment, j,

v w j   = unit load-drift curve for the wall line’s combination of 

sheathing materials at drift ratio increment, j, using default 

load-drift material data provided in Section 4.4, or other 

technically substantiated load-drift data 

Lw = length of wall line, out-to-out, including openings within the 

defined wall line, 

Qopen = adjustment factor for openings in accordance with Section 

4.5.2, and 

Qot = adjustment factor for overturning in accordance with Section 

4.5.3. 

The load-drift curve for each first-story wall line is given by: 

fw jh w jh w open ot    v LQ Q        (4-2) 

where parameters have the same meaning as in Equation 4-1, except: 

f w jh   = load-drift curve for wall line w, at drift ratio increment jh, the 

drift ratio increment adjusted for wall line height, h, in 

accordance with Section 4.5.4, and 

v w jh   = unit load-drift curve for the wall line’s combination of 

sheathing materials at drift ratio increment, jh, using default 

load-drift material data provided in Section 4.4, or other 

technically substantiated load-drift data. 

As discussed in Section 4.4, wall capacity should be adjusted (by judgment) 

based on the extent of deterioration, damage, or inadequate construction, 

recognizing that it is not necessarily conservative to disregard questionable 

sheathing in the first story. As with the Guidelines eligibility rules in Section 

2.6, these condition assessment discounts may be ignored in calculations if 

all relevant conditions are to be remediated through an alteration or retrofit 

project. 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 49 

4.5.1 Load-Drift Curves for Combinations of Sheathing Materials 

In general, the unit load-drift curve for an assembly of several sheathing 

types is constructed by simply adding the unit load-drift curves of each layer, 

taking the full value of each layer. 

Assemblies that include wood structural panels, however, must be treated 

differently. Figure 4-4 shows such an assembly comprising three layers: 

gypsum wallboard sheathing, wood structural panels, and stucco. Tests have 

shown that when wood structural panels are combined with other sheathing 

materials in a wall assembly, the total strength is less than the sum of the 

strengths of individual layers. Wood structural panels can withstand high 

drift ratios before losing strength. Finish materials often lose strength at a 

drift ratio of 2 percent or less. Appendix Section D.5 discusses available data. 

The composite load-drift curve for a wall assembly including wood structural 

panels is derived by constructing two load-drift curves, and selecting the one 

that has the larger peak strength. The two load-drift curves are: 

 An assembly load-drift curve using 50 percent of the strength of the 

wood structural panel layers and 100 percent of the other sheathing 

materials, and 

 An assembly load-drift curve using 100 percent of the strength of the 

wood structural panel layers and 50 percent of the other sheathing 

materials. 

Figure 4-4 Schematic of a typical wall assembly composed of various 

layers. The capacity of the assembly is derived by combining the 

load-drift curves of the individual layers, while accounting for 

reductions due to interaction between wood structural panel 

(WSP) sheathing and other sheathing materials. 

Gypsum wallboard sheathing 

Wood structural panel 

Stucco 
50 4: Structure Characterization for Detailed Evaluation FEMA P-807 

Figure 4-5 illustrates the composite unit load-drift curve for an example wall 

assembly made of three sheathing layers—wood structural panel sheathing, 

gypsum wallboard, and stucco—taking 100 percent of the wood structural 

panel unit loads plus 50 percent of the other layers’ unit loads. Figure 4-6 

shows the composite load-drift curve taking 50 percent of the wood structural 

panel plus 100 percent of the other layers’ unit loads. Figure 4-7 shows both 

of the composite curves. In this example, the curve with 100 percent wood 

structural panel material plus 50 percent other materials has the higher peak 

load and it should be used to represent the load of this wall assembly at all 

drift levels (even those at which it drops below the other curve, as at drift 

ratios above 4 percent in Figure 4-7). 

Figure 4-5 Composite unit load-drift curve of a wall assembly comprising stucco, 

gypsum wallboard, and wood structural panels (structural plywood in figure), 

using 100% of the wood structural panel (WSP) sheathing plus 50% of the 

other sheathing materials. 

4.5.2 Adjustment Factor for Openings in the Wall Line 

When wall piers are part of a common wall line as shown in Figure 4-8, the 

segments interact because of headers and sills that behave like coupling 

beams. Thus, a group of in-line wall segments linked at the top or bottom of 

an opening should be treated as one long wall, but with the capacity reduced 

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Drift Ratio, %

Unit Force, plf

(0.5) Gypsum 

wallboard

(0.5) Stucco

Structural plywood 

with 8d @ 6" o.c.

Composite
FEMA P-807 4: Structure Characterization for Detailed Evaluation 51 

Figure 4-6 Composite unit load-drift curve of a wall assembly comprising stucco, gypsum wallboard and 

wood structural panels (structural plywood in figure), using 50% of the wood structural panel 

(WSP) sheathing plus 100% of the other sheathing materials. 

Figure 4-7 Controlling unit load-drift curve of a wall assembly comprising stucco, gypsum wallboard, and 

wood structural panels. 

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Drift Ratio, %

Unit Force, plf

Gypsum wallboard

Stucco

(0.5) Structural plywood 

with 8d @ 6" o.c.

Composite

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Drift Ratio, %

Unit Force, plf

Load-deflection curve with larger peak strength: 

100% Wood Structural Panels + 50% Other

Peak 

50% Wood Structural

Panels + 100% Other
52 4: Structure Characterization for Detailed Evaluation FEMA P-807 

Figure 4-8 Wall schematic showing variables in the adjustment factor for 

openings. A denotes area. 

to account for door and window openings. The adjustment factors are based 

on the area of openings relative to the area of full height wall segments. The 

reduction factor accounting for perforations, Qopen, is given by: 

2 3 0.92 0.72 0.80 Qopen      (4-3) 

 where: 

i

1

A

1

H Li

      

 





 (4-4) 

and where: 

Ai = sum of the areas of the openings, 

H = Maximum floor-to-ceiling wall height, and 

Li = sum of the lengths of the full-height wall segments. 

Where wall segments are less than one-foot long or have a clear height to 

length ratio of greater than 8:1, the area of the wall segment shall be included 

as an opening in Ai. 

The load-drift curve of a given wall is modified to account for openings by 

multiplying the unit force at each increment of drift ratio by Qopen as shown 

in Equations 4-1 and 4-2. Where the value, , for a given wall line is less 

L

H

Floor to Ceiling

w

L12 3 L L

Openings

A = A + A i 12 L = L + L + L i 1 23

Full-height wall

segments

A1

A2
FEMA P-807 4: Structure Characterization for Detailed Evaluation 53 

than 0.5, the wall line must be broken into separate walls so that the value, , 

for any wall line is greater than 0.5. This requirement is to keep walls 

reasonably compact so that the overturning adjustments calculated in Section 

4.5.3 remain valid. See Appendix D, Section D.6, for further discussion of 

the adjustment factor for openings. 

4.5.3 Adjustment Factor for Overturning 

Because older buildings often do not have hold-down rods or straps to 

provide overturning resistance, the walls rely on other mechanisms to resist 

overturning demands. These include dead load, coupling beam effects above 

and below openings, and “shell effects” due to the interaction between 

perpendicular walls and floors. The unit load-drift curves defined in Section 

4.4 presume full restraint against overturning (as would occur with an 

adequate hold-down device at each end of each shear-wall segment). Thus, 

wall line loads need to be adjusted in cases where the overturning restraint is 

insufficient to develop the peak shear strength. 

Following adjustment for materials and openings, each wall line load-drift 

curve is adjusted for overturning in accordance with either Section 4.5.3.1 or 

4.5.3.2. 

4.5.3.1 Simplified Adjustment Factor for Overturning 

The simplified adjustment factor for overturning, Qot, listed in Table 4-2, is 

applicable to upper stories only. The load drift curve for a given wall is 

modified by multiplying the unit force at each increment of drift ratio by the 

simplified factor for overturning given in Table 4-2. Tabulated values 

depend on the number of stories above the story under consideration and the 

span direction of floor or roof framing in the framing level immediately 

above the walls being considered. 

Table 4-2 Simplified Adjustment Factor for Overturning 

The simplified adjustment factors for overturning restraint were developed 

for conditions typical of residential occupancies characterized by frequent 

and well-distributed interior walls. Due to complex mechanisms including 

wall coupling and shell effects, available overturning restraint is generally 

Simplified Adjustment Factor For Overturning, Qot , for Upper Story Wall Lines 

Number of stories above Perpendicular to 

Framing

Parallel to 

Framing 

Unknown or 

mixed 

Two or more 0.95 0.85 0.85 

One 0.85 0.80 0.80 

None (Top story) 0.75 0.75 0.75 
54 4: Structure Characterization for Detailed Evaluation FEMA P-807 

not well captured in standard engineering overturning calculations. The 

simplified factors provided in Table 4-2 were derived from push-over 

analysis of a four-story building model, described in Appendix E. Use of the 

simplified adjustment factor is recommended for upper stories unless the 

building does not have frequent and well-distributed interior walls, in which 

case use of the calculated adjustment factor for overturning restraint is 

recommended. The simplified adjustment factors should not be used for 

retrofit elements. 

4.5.3.2 Calculated Adjustment Factor for Overturning 

The calculated adjustment factor is used when the simplified adjustment 

factor of Section 4.5.3.1 is not used or does not apply. 

The load-drift curve of a given wall line is modified by multiplying the unit 

force at each increment of drift ratio by Qot. 

0.4 1 1.5 r

ot

ot

M Q M

 

      (4-5) 

2

2

D w

r D D HD w

w L M   PL T L (4-6) 

Mot w V H (4-7) 

where: 

Mr = overturning resistance capacity of the wall line, 

wD = uniform dead load tributary to wall line, 

wD = uniform dead load tributary to wall line, 

PD = concentrated dead load tributary to wall line, 

LD = moment arm for concentrated load, PD, 

THD = tension ultimate capacity of tie-down hardware, if applicable, 

Mot = overturning moment demand on the wall line, 

Vw = peak shear strength from the load-drift curve of the wall line 

under consideration, adjusted for openings (Section 4.5.2), and 

H = the floor-to-ceiling height of the wall line. 

The overturning resistance includes potential contributions from hold-down 

hardware and tributary dead load (see Figure 4-9). For the contribution of the 

hold-down hardware, it is acceptable to use the ultimate capacity. Uniform 

and concentrated dead load contributions to resisting moment should be 

consistent with common design practice. The dead load tributary to the wall 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 55 

Figure 4-9 Wall schematic showing variables in the calculated adjustment 

factor for overturning. 

line under consideration may include contributions from intersecting walls in 

the same story. 

Equation 4-6 shows the general form of the formula for overturning 

resistance. In practice, the calculation should include as many uniform loads, 

wD, and concentrated loads, PD, as are needed to reflect the existing dead 

load, consistent with common engineering practice. 

Following common engineering practice, the ratio Mr/Mot may be calculated 

in either of two ways: 

 Values of Mr and Mot may be calculated considering only the story under 

consideration and loads tributary to the floor immediately above it, 

ignoring any overturning or resisting effects associated with stories 

further up the building, or 

 Values of Mr and Mot may be calculated considering the story under 

consideration and all floors and stories above it. In this case, Mr is a 

function of dead loads accumulated from multiple stories, and Mot is a 

function of the strengths of stacked wall lines, each multiplied by the 

appropriate height (the overturning moment arm) above the base of the 

wall line under consideration. The strengths of the wall lines above 

contributing to Mot should be adjusted for openings and overturning. 

In no case should the ratio Mr/Mot be taken greater than 1.0. 

L

H

Floor to Ceiling

Load-drift curve for wall line,

adjusted for perforations

Peak shear capacity, V, of wall

line, adjusted for openings

Dead load resultant, P

V

D

Overturning

work-point

THD

Distributed dead load

tributary to wall line, wD

w

Overturning arm
56 4: Structure Characterization for Detailed Evaluation FEMA P-807 

4.5.4 Drift Ratio Adjustment for First-Story Wall Line Height 

If the first story includes wall lines with varying heights, and the story sways 

laterally without rotation, the shorter wall lines will experience greater drift 

ratios than the taller wall lines. To account for this effect, the load-drift 

curves for shorter wall lines need to be adjusted. The Guidelines do this by 

mapping the standard load-drift curve data from Table 4-1 onto a narrower 

range of drift values. The modified, or narrowed, drift increment values are 

given by: 

0.7

jh j

h

H

         (4-8) 

where: 

 jh = drift ratio at increment j, adjusted for wall height, h, 

 j = standard drift ratio at increment j (see Table 4-1), 

h = floor-to-ceiling wall height of first-story wall line under 

consideration, with h < H, and 

H = floor-to-ceiling wall height of the tallest wood-frame wall in the 

first story. 

Figure 4-10 illustrates the effect of concentrating a uniform story 

displacement within the height of a shortened wall. Though wall line 1 and 

wall line 2 (recall, per Section 4.5, that wall segments of different heights are 

assigned to separate wall lines) have the same basic load-drift data and are 

subject to the same second floor displacement, they experience different 

amounts of distortion, or drift, relative to their height. The amplified drifts in 

wall line 2 are approximated by squeezing its load-drift curve into the heightadjusted drift range. See Appendix Section D.8 for further discussion. 

The height adjustment in this section applies to every first-story wall line 

shorter than the tallest first-story wall line. That is, while Figure 4-10 shows 

two wall lines that happen to be actually aligned with each other, the 

adjustment of Equation 4-8 also applies to parallel wall lines anywhere 

within the first story. 

An overall adjustment for a tall or short story is made separately, in Section 

4.7.6, to adjust the first story as a whole relative to the standard story height 

of 8 ft on which most load-drift curve data are based. 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 57 

Figure 4-10 Wall schematics and load-drift curves illustrating drift adjustment parameters for 

varying first-story wall line heights. 

4.6 Determine Strength of Each Story 

4.6.1 Translational Load-Drift Curve 

The load-drift curve for each story in each orthogonal direction is obtained 

by adding the loads in the load-drift curves for each wall line parallel to the 

direction of consideration at each increment of drift ratio, assuming twisting 

in plan is restrained. The load-drift curve for each story in each direction is 

H

H

Tallest wall in first story

2

H2

Drift ratio, 1 = D / H

Drift ratio, 2 2 = D / H



Adjusted Drift Ratio

1  2

Actual Drift Ratio

 2

1

1  2  = D / H

 2

 1

Unit load-drift curve for

the wall assembly

Unit load-drift curve of

Wall 1, equal to the

unadjusted unit load-drift

curve of the assembly

Wall 2

Wall 1

Unit load-drift curve adjusted

for height of Wall 2

H

Tallest wall in first story

Wall 2

Wall 1

Stepped concrete

foundation

Displacement, D

Displacement, D
58 4: Structure Characterization for Detailed Evaluation FEMA P-807 

defined by the sum of the individual wall line load-drift curves in that 

direction: 

, ,

1

() ()

Nwalls

ix j wx j

w

F f  



  (4-9) 

where: 

F, xi = load-drift curve for story i in direction x, over the range of drift 

ratio increments,  j , 

xwf , = component of load-drift curve for wall line w, in the x direction, 

over the range of drift ratio increments,  j , and 

Nwalls = total number of wall lines. 

The load drift, Fi,y, for story i in direction y, is calculated similarly as the sum 

of the individual wall line load-drift curves in that direction. 

Where all the wall line load-drift curves are mapped to the same set of drifts, 

the summation in Equation 4-9 is straightforward. Where some first-story 

wall lines have load-drift curves mapped to a height-adjusted set of drifts, per 

Section 4.5.4, load values at the standard drift increments, j, should be 

determined by linear interpolation. Once interpolated values are calculated, 

the various load-drift curves can again be added in a straightforward way 

based on the standard drift increments. 

Where a wall is not parallel to an orthogonal direction, the load-drift curve 

should be split into components aligned with the orthogonal directions. 

As discussed in Section 2.6, existing structures with steel frames in the first 

story are eligible for the Guidelines methodology. In such cases, the story 

strength and load-drift curve would include a contribution from the steel 

frame as well. It is important that the characterization accurately account for 

actual or expected strength, and base fixity. For example, designating a 

“pinned” base is not conservative when assessing a semi-rigid condition. 

4.6.2 Peak Strength 

The peak translational strength of a story in each orthogonal direction is 

defined as the maximum load of the load-drift curve for that story (see Figure 

4-11). 

, , max ( ) V F i x ix j       (4-10) 

where: 

Vi x, = peak translation strength of story i in direction x, and , ( ) Fix j  is 

defined above; , , Vi y peak translation strength of story i in 

direction y, is calculated similarly. 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 59 

Figure 4-11 Wall-plan schematic with depiction of the first-story load-drift curve as 

the sum of first-story wall line load drift curves, y-direction. 

4.6.3 Drift Ratio at Peak Strength 

The drift ratio at peak strength, for a given story and direction, is: 

  ix j ,  at which , , ( ) F V ix j ix   (4-11) 

where: 

i x, = drift ratio at peak strength for story i, in direction x. 
60 4: Structure Characterization for Detailed Evaluation FEMA P-807 

Values in direction y are calculated similarly. 

In each orthogonal direction, the drift ratio at peak strength is a single value 

that applies to an entire story. This drift ratio could be more or less than the 

drift corresponding to the peak strength of any individual wall line, as shown 

in Figure 4-11. 

4.6.4 Center of Strength 

A story’s center of strength is the location of the force resultant of the forces 

in the individual wall lines (under translation and allowing no rotation) at the 

drift ratio at peak strength, defined in Section 4.6.3. It is similar to the 

familiar concept of the center of rigidity, but with a focus on strength instead 

of stiffness. See Figure 4-12. 

Figure 4-12 Wall-plan schematic showing location of center of strength at the first story. Wall lines 

in the y-direction determine the x-component of the center of strength. 

The center of strength, COSi, is computed for each story. For each wall in the 

story under consideration, there is the point in plan, pw, through which forces 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 61 

in that wall will act. This defines the center of each wall. Each wall line is 

assigned the force from its load-drift curve corresponding to the drift ratio at 

the story’s peak strength, . The coordinates of the story’s center-of-strength 

are then given by: 

,, , ,, ,

1 1

, ,

() ()

,

N N walls walls

wy iy wx wx ix wy

w w

i

iy ix

fp fp

COS

V V

 

 

 

 



 

 

 (4-12) 

where fw,x, and i,x, are defined above and: 

fw,y = component of load-drift curve for wall line, w, in the y-direction, 

i,y = drift ratio at peak strength for story i, in direction y, 

COSi = center-of-strength of story i, 

pw,x = x-coordinate of the center of wall w, and 

pw,y = y-coordinate of the center of wall w. 

4.6.5 Torsional Eccentricity at the First Story 

The torsional eccentricity for a story is the distance between the centers of 

strength of that story and the story above. Thus, for the first story, the two 

components of the eccentricity are: 

x 2, 1, x x e COS COS   (4-13) 

y yy 2, 1, e COS COS   (4-14) 

where: 

COSi,x = x-coordinate of the center of strength of story i, 

x e = x-component of the torsional eccentricity 

y e = y-component of the torsional eccentricity 

This strength-based definition of torsional eccentricity differs from the 

conventional definition based on rigidity. However, both address the 

tendency of the second floor to twist relative to the ground. 

4.6.6 Load-Rotation Curve 

The load-rotation curve of the first story gives the torque required to twist the 

first story about its center-of-strength, assuming that the base of each firststory wall line is fixed. See Figure 4-13. This is similar to a story load-drift 

curve, except for twist instead of translational drift. The range of twist angles 

to be considered depends on the geometry of the wall layout. 
62 4: Structure Characterization for Detailed Evaluation FEMA P-807 

Figure 4-13 Wall-plan schematic and related torsional-load rotation curves illustrating how the first story 

load-rotation curve is computed. 

The distance, d, at which each wall line acts to contribute to a story’s twist is 

defined, in the case of direction x, as: 

wx wx x , , 1, d p COS   (4-15) 

Center of strength

at first story

j

Torsional moment that

causes a twist of  for the

first story, t ( )

A

B

C

D

E

1,x

 dj

 j d A,y

1,x

j d1,x

j f at 



d1,x 1,y

j d2,x j d3,x j d4,x

j f at 



d2,x 2,y

j f at 



d3,x 3,y

j f at 



d4,x 4,y

1 j

j

d

d

2,x d

d

3,x

4,x

d

d

d

d

d

B,y C,y

D,y A,y

E,y

j fA,x at  dA,y

j f

B,x at  dB,y

j f

C,x at  dC,y

j f

D,x at  dD,y

j f

E,x at  dE,y

t (1  )

j 1

Maximum twist angle to

consider for the first story

j

j

T1

Torsional strength of

the first story

Twist level 2 by

the twist angle,  j

First story torsional

load-deflection curve, t1

Torsional moment that

causes a twist of  for

the first story

Wall line: 1 32 4

First story torsional 

load-rotation curve, t1
FEMA P-807 4: Structure Characterization for Detailed Evaluation 63 

where pw,x and COSi,x are defined above, and: 

xw d , = distance between the center of strength of wall w, and the center 

of strength of the first story, in the x-direction. 

The distance between the center of strength of wall w, and the center of 

strength of the first story, in the y-direction, dw,y, is calculated similarly. 

The maximum angle of twist considered by the Guidelines is related to a 5 

percent translational drift ratio and is given by: 

 

1

1

0.05

max walls

F

w w N

H

d



 

 (4-16) 

where: 

 = maximum angle of twist to consider, in radians 

HF1 = maximum story height of the first story, floor to floor 

dw = distance between the centers of strength of the first story and 

wall w.

Equation 4-16 ensures that the wall farthest in plan from the center of 

strength is evaluated well past its peak strength. A horizontal deflection of 

0.05 times the story height produces a 5 percent drift for the farthest wall. All 

other walls would have less than 5 percent drift. To understand the 

relationship of story torsion as the twist angle increases and wall lines reach 

their peak strengths, it is necessary to consider a number of twist angles 

between zero and the maximum. In most cases a set of angles in ten even 

increments is convenient and is expected to be sufficient: 

10 j

j    (4-17) 

where: 

 j = twist angle j, at which to evaluate the load-rotation curve. 

j = index ranging from 0 to 10. 

The first-story load-rotation curve is given by: 

, ,

1 ,, ,,

1 1 1

( )

Nwalls

wy j wx j

j wy wx wx wy

w F F

d d

t df df H H

 





   

           (4-18) 

where all variables are defined above. 

4.6.7 Torsional Strength 

The torsional strength of the first story, T1, is the maximum torque from the 

load-rotation curve: 
64 4: Structure Characterization for Detailed Evaluation FEMA P-807 

1 1 max ( ) T t  j      (4-19) 

4.6.8 Torsional Demand 

The torsional demand on the first story is calculated by multiplying the 

translational strength of the first story by the eccentricity, as illustrated in 

Figure 4-14. It is given by: 

1 1, 1, x y yx   eV eV  (4-20) 

where all variables are defined above. 

Figure 4-14 Wall-plan schematic depicting how the torsional demand on the first story is 

calculated.

4.7 Characteristic Coefficients 

In this section, various coefficients are defined based on the properties and 

relationships described in Section 4.6. These coefficients are used in Chapter 

5 to evaluate the structure and in Chapter 6 to estimate the appropriate 

retrofit strength. 

4.7.1 Normalized First-Story Strength 

The Guidelines use two methods to normalize story strength: 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 65 

 The story-normalized strength, Ci, is the peak strength of story i divided 

by the seismic weight carried by story i. Thus, the normalizing value—

the carried weight—varies from story to story. 

 The base-normalized strength, Ai, is the peak strength of story i divided 

by the total seismic weight of the building. The normalizing value is the 

same no matter which story is being considered. 

At the first story, where the seismic weight carried by the story is the seismic 

weight of the whole building, the two values are the same. In the x-direction, 

the value is given by: 

1,

1, 1, 1

2

s

x

x x N

j

j

V

C A

W





 



 (4-21) 

where: 

Ns = total number of stories in the building 

V ,1 x = the peak first-story strength in the x direction 

Wj = seismic weight tributary to or assigned to floor j. 

The value in the y-direction is calculated similarly. 

4.7.2 Normalized Upper-Story Strength 

The smallest of the Ci values for any of the upper stories is given a special 

designation, CU. In the x-direction it is given by: 

,

, 1

1 2

min s

s

i x

U x N

j

j i i N

V

C

W



   

   

    

      

 (4-22) 

In typical regular buildings, the story strengths are roughly the same in all the 

upper stories, and the seismic weight is greater toward the lower stories, so 

CU,x is usually the story-normalized strength of the second story, C2,x. 

The term AU refers to the base-normalized strength of the controlling upper 

story (that is, the story that defines CU): 

,

,

U x

U x

V

A

W  (4-23) 

where: 
66 4: Structure Characterization for Detailed Evaluation FEMA P-807 

VU,x = the strength, in the x-direction, of the upper story that defines 

CU,x

W = total seismic weight of the building. 

Comparable parameters for the y-direction are calculated similarly. 

4.7.3 Weak-Story Ratio, AW

The weak-story ratio, AW, compares the first-story strength to the critical 

upper-story strength. In the x-direction, it is given by: 

1,

,

,

x

W x

U x

V

A

V

 (4-24) 

where V1,x and VU,x are defined above. 

The weak-story ratio in the y-direction , ( ) AW y is calculated similarly, using 

V1,y and VU,y values. 

4.7.4 Strength Degradation Ratio, CD

The strength degradation ratio, CD, characterizes the ability of the first story 

to maintain strength over large drifts. The loss of lateral strength at high drift 

ratios has a significant impact on seismic performance. CD is the ratio of the 

strength at 3 percent drift (a convenient value to distinguish stories that can 

achieve high deformation from those that cannot) divided by the peak 

strength from the load-drift curve (see Figure 4-15). In the x-direction it is 

given by: 

1,

,

1,

( 3%) x

D x

x

F

C

V

   (4-25) 

where F1,x and V1,x are defined above. 

The strength degradation ratio in the y-direction, CD,y, is calculated similarly, 

using values of F1,y and V1,y as defined above. 

4.7.5 Torsion Coefficient, CT

The torsion coefficient, CT, is the ratio of torsional demand to torsional 

strength in the first story. It characterizes the vulnerability to lateral 

instability due to twist, where a larger ratio represents greater vulnerability. It 

is given by: 

1

1

CT T



 ; need not be taken greater than 1.4 (4-26) 
FEMA P-807 4: Structure Characterization for Detailed Evaluation 67 

Figure 4-15 Load-drift curve depicting determination of strength degradation ratio, CD. 

where T1 and 1 are determined as given in Sections 4.6.7 and 4.6.8, 

respectively. 

4.7.6 Story Height Factor, Qs 

The Guidelines methodology relies on performance data from laboratory 

tests of various sheathing materials and assemblies (see Appendix D). Most 

of these data were derived from, or have been adjusted to, standard wall 

heights of 8 ft. As discussed further in Appendix E, buildings with different 

story heights will perform differently under the same ground motions or 

imposed displacements; shorter stories will exceed pre-set drift limits at a 

higher rate. 

The Guidelines account for this effect with a story height factor, Qs, which 

adjusts the actual story height relative to the 8-ft height used in the tests and 

the surrogate models. It is given by: 

Qs = 0.55 + 0.0047 H (4-27) 

where: 

H = tallest height of any first-story wall, floor to ceiling, in inches. 

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Drift Ratio, %

Unit Force, plf

Load-Deflection Curve

Peak Strength, V

Strength at 3% Drift, V3%

Strength Degradation Ratio,

Shear force, plf 

C D = V 3% /V
68 4: Structure Characterization for Detailed Evaluation FEMA P-807 

The adjustment of Equation 4-27 applies to a whole story. Relative 

adjustment for wall lines of varying heights within the first story is addressed 

in Section 4.5.4. 
FEMA P-807 5: Detailed Evaluation 69 

5Chapter 5 

Detailed Evaluation

This chapter uses the parameters defined in Chapter 4 to evaluate an existing 

structure. Figure 5-1 illustrates the content of the chapter and its relationship 

to other Guidelines chapters. 

5.1 Evaluation Steps 

The Guidelines evaluate an existing structure by comparing its capacity, 

estimated from the parameters defined in Chapter 4, with a demand. This is 

done in three steps that reflect components of the performance objective. As 

discussed in Section 2.3, the Guidelines measure performance in terms of 

transient interstory drift. Using a fragility-based methodology, the Guidelines

address a performance objective stated as a maximum probability of 

exceeding certain drift limits at a specified level of ground motion. Thus, the 

three evaluation steps cover the three quantities that must be specified— the 

drift limits, the allowed probability of exceeding them, and the ground 

motion of interest: 

 Calculate the median capacity of the structure (Section 5.2). Given in 

spectral acceleration terms, the median capacity is the level of shaking at 

which the specified drift limits are exceeded with 50 percent confidence. 

The Guidelines’ formulas for the median spectral acceleration capacity 

have embedded in them a set of default drift limits representing the onset 

of strength loss. 

 Calculate the spectral acceleration capacity of the structure, accounting 

for the targeted probability of exceeding the drift limits (Section 5.3). 

This calculation is made by applying an adjustment factor to the median 

capacity. 

 Compare the spectral acceleration capacity to the site-specific 

acceleration demand (Section 5.4.1). 

The Guidelines evaluation provisions focus on the strength of vertical 

elements of a structure’s seismic force-resisting system. Satisfactory 

performance of any structure also requires adequate performance of 

diaphragms and load path components, as well as reliable detailing and 

construction quality in the walls themselves. The Guidelines do not require 

explicit evaluation of these issues. Instead, they assume that the eligibility 
70 5: Detailed Evaluation FEMA P-807 

Figure 5-1 Flowchart of typical evaluation procedure. 

Is the building being 

evaluated relative to drifts 

representing “onset of 

strength loss”? 

NO 

YES

Verify eligibility of building (in retrofitted state). 

Section 2.6

Calculate median capacity. 

Survey and characterize the structure. 

Sections 4.3 through 4.7

Is the intent to evaluate to 

a known or given POE? 

Estimate POE for calculated 

median capacity and known 

spectral acceleration demand. 

Section 5.4.2

Does the spectral 

capacity exceed the 

spectral acceleration 

demand in both 

directions? 

Building meets the 

performance objective. Make 

alterations as needed to 

ensure presumed eligibility. 

Building does not meet 

performance objective. Consider 

retrofit per Chapter 6. 

Section 5.4.1

NO 

YES

YES NO 

Chapter 7

Section 5.2

Calculate spectral 

acceleration capacity. 

Section 5.3

Determine alternative coefficients 

for drift limits of interest. 
FEMA P-807 5: Detailed Evaluation 71

requirements in Section 2.6 and the building survey scope in Section 4.3 

provide an implicit evaluation. Corrections, improvements, or assumptions 

required by those sections are expected to be sufficient to support the 

evaluation procedure in this chapter. This assumption is expected to hold for 

the Guidelines’ default performance objective involving the onset of strength 

loss drift limits, especially where the purpose of evaluation is to find 

buildings with dominant weak-story or open-front deficiencies. If a more 

conservative evaluation objective is applied, or if the evaluation program is 

intended to be more general and comprehensive, more thorough load path 

evaluation and condition assessment might be warranted. This is because 

higher performance (for example, involving onset of damage drift limits) or 

general evaluation (for example, involving nonstructural components or 

upper story deficiencies) might rely on conditions considered secondary here. 

5.2 Calculate the Median Spectral Acceleration 

Capacity 

The median spectral acceleration capacity, S, is calculated for the two 

extreme values of the strength degradation ratio, CD, in each of the two 

directions, x and y: 

   0.48

1 0.525 2.24 1 0.5 W Ts U S AC    Q A for 1.0 CD  (5-1) 

   0.60

0 0.122 1.59 1 0.5 W Ts U S AC    Q A for 0.0 CD  (5-2) 

where: 

AW = weak-story ratio, defined in Section 4.7.3 

AU = base-normalized upper-story strength, defined in Section 4.7.2 

CT = torsion coefficient, defined in Section 4.7.5 

Qs = story height factor, defined in Section 4.7.6 

(The median spectral acceleration capacity for intermediate values of CD can 

be calculated using an interpolation similar to Equation 5-5, but that step is 

not strictly necessary because the interpolation will be done on the spectral 

acceleration capacity, as shown below.) 

Equations 5-1 and 5-2 are essentially regression relationships that relate the 

structure in question to the surrogate models. Their derivation is described 

further in Appendix E. Embedded within these equations are default limits on 

interstory drift. As described in Section 2.2.1 and Appendix E, the default 

limits (1.25 percent for CD = 0.0 and 4.0 percent for CD = 1.0) correspond to 

the onset of strength loss for each of the two material models. Onset of 

strength loss is an element-specific condition assumed to indicate a 
72 5: Detailed Evaluation FEMA P-807 

substantially increased potential for collapse. Chapter 7 provides factors to 

adjust the capacity formulas for different drift limits. 

Equations 5-1 and 5-2 show that a structure’s median spectral acceleration 

capacity is related to its upper-story strength, its weak-story ratio, its 

torsional vulnerability and its propensity to degrade. Median capacity most 

strongly corresponds to high first-story strength, low torsional demands and 

ductile materials (CD near 1). Capacity increases as: 

 weak-story ratio, AW, increases, i.e., as the first- and upper-story 

strengths become closer, 

 the base-normalized upper-story strength, AU, increases, 

 the strength degradation ratio, CD, increases, and 

 the torsion coefficient, CT, decreases. 

5.3 Calculate the Spectral Acceleration Capacity 

Determination of the spectral acceleration capacity requires the selection of a 

drift limit probability of exceedance (POE). As discussed in Section 3.2.2, 

the drift limit POE is part of a defined performance objective. 

In each direction, the spectral acceleration capacity, Sc, is then calculated for 

the two extreme values of the strength degradation ratio, CD, by applying a 

drift limit probability of exceedance (POE) adjustment factor to the 

corresponding median spectral acceleration capacity, as shown in Equations 

5-3 and 5-4. The spectral acceleration capacity for the structure’s actual 

value of CD is determined by interpolation with Equation 5-5. 

c POE 1 ,1 1 S S   for 1.0 CD  (5-3) 

c POE 0 ,0 0 S S   for 0.0 CD  (5-4) 

  3 3

1 0 1 c Dc D c S CS C S   for intermediate values of CD (5-5) 

where POE,1 and POE,0 are the drift limit POE adjustment factors taken from 

Table 5-1 with linear interpolation as needed for intermediate values of the 

targeted POE. 

Figure 5-2 shows how spectral acceleration capacity varies for different 

combinations of the key parameters AU, AW, and CD. All four of the curves in 

the figure assume a drift limit POE of 20%. 

The drift limit POE adjustment factors come from the fragility curves 

derived from the surrogate model analyses (see Appendix E). Each fragility 

curve is a log-normal cumulative distribution function of the spectral 
FEMA P-807 5: Detailed Evaluation 73

Table 5-1 Drift Limit Probability of Exceedance (POE) Adjustment Factors

Targeted POE Targeted Confidence Level 

(100% – Targeted POE) 

POE,1 POE,0

2% 98% 0.36 0.29 

5% 95% 0.44 0.37 

10% 90% 0.53 0.46 

20% 80% 0.66 0.60 

50% 50% 1.00 1.00 

60% 40% 1.14 1.16 

70% 30% 1.30 1.37 

80% 20% 1.52 1.66 

Figure 5-2 Plot showing variation in spectral acceleration capacity (spectral capacity) as a 

function of different existing building characteristics, i.e., different strength 

degradation ratios (CD) and different weak-story ratios (AW) (POE = 20%, CT = 

0.0, Qs = 1.0). 

acceleration at which the structure fails the drift criteria. Away from the 

median, values on the fragility curve are functions of uncertainties in the 

surrogate models, represented by the standard deviation, , of the log-normal 

curve. The values selected for  are 0.5 and 0.6 for CD = 1.0 and 0.0, 

respectively. For these values, the tabulated drift limit POE adjustment 

0

0.5

1

1.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Upper-Story Strength Ratio, A U

Spectral Capacity, 

Sc

C D = 1.0

A W = 0.2

A W = 1.0

C D = 0.0

Base-Normalized Upper-Story Strength, AU
74 5: Detailed Evaluation FEMA P-807 

factors give points on the fragility curve relative to the median capacity. The 

lower the targeted drift limit POE, the lower the spectral acceleration 

capacity. 

For example, consider a targeted drift limit POE of 20 percent. This 

represents a fairly conservative objective, seeking 80-percent confidence that 

the drift limits will not be exceeded under the specified shaking. The table of 

drift limit POE adjustment factors shows that the spectral acceleration 

capacity will be a bit less than two-thirds of the median capacity. This does 

not mean that the structure is actually weaker because higher confidence is 

sought. Rather, it means that the only way there will be an 80-percent chance 

of staying under the drift limits is if the demand is lower than this reduced 

value. That is, if you want high confidence, you need to assume a capacity 

lower than what it probably is. Of course, as you evaluate to a higherconfidence (lower drift limit POE) objective, it becomes more difficult to 

pass the evaluation, as shown in Section 5.4. 

As discussed in Sections 1.4 and 2.3.2, the appropriate drift limit probability 

of exceedance (POE) can vary. For voluntary work, a target POE can be set, 

or the actual POE can be derived by working the equations backward (see 

Section 5.4.2). For a mandatory or incentivized program, the targeted drift 

limit POE will generally be given as a matter of policy. For work triggered 

by a building code, it is important to use the POE that most closely reflects 

the intent of the code. 

5.4 Evaluate the Existing Structure 

5.4.1 Compare the Spectral Acceleration Capacity with SiteSpecific Demand 

To represent seismic demand, the Guidelines use the short-period spectral 

acceleration corresponding to the site-specific Maximum Considered 

Earthquake (MCE), SMS, as defined by ASCE/SEI 7-05 (ASCE, 2006a, 

Section 11.4.3)—the default hazard level of the Guidelines. The structure is 

deemed to satisfy the evaluation objective if Equation 5-6 is satisfied in both 

directions. 

Sc  SMS (5-6)

Where Equation 5-6 is not satisfied, retrofit is required. 

The short-period spectral acceleration corresponds to a fundamental period of 

0.2 seconds. Many soft- or weak-story wood-frame buildings have periods 

longer than 0.2 seconds, especially when responding beyond their elastic 

range. Nevertheless, the short-period spectral value is to be used as the 
FEMA P-807 5: Detailed Evaluation 75

demand of interest. The reason is not because it best represents the response 

of an actual building, but because it provides the most consistent and 

straightforward basis for comparing the actual building to the surrogate 

analyses. 

Equation 5-6 uses SMS because it corresponds to the Guidelines’ default 

(embedded) performance objective. As discussed in Sections 1.4 and 2.3.2, 

however, a performance objective could use a different level of shaking, 

resulting in a higher or lower demand. In such cases, the short-period spectral 

acceleration of the selected shaking level should be used in place of SMS. 

5.4.2 Calculating the Probability of Exceedance 

Where a drift limit POE value is set in advance of the evaluation, as in the 

case of most triggered or mandatory work, the evaluation focuses on whether 

the existing structure can meet the corresponding performance objective. 

Guidelines Section 5.4.1 addresses that question. 

In other cases, where the drift limit POE is not specified, it can be useful to 

think of the evaluation from a different perspective. That is, given the median 

spectral acceleration capacity, S, and the demand, SMS, what confidence do 

they provide that drifts will remain below the critical levels? This question is 

of interest to voluntary projects where the decision to retrofit, or the scope of 

retrofit, depends on an owner’s individual risk tolerance. It is also potentially 

valuable to a phased mandatory mitigation program of the sort described in 

Appendix B. 

In general, the drift limit POE can be estimated by trial and error using the 

equations in Section 5.3, iterating on the value of POE until the spectral 

acceleration capacity just matches the demand. For a broad range of drift 

limit POE values, however, the relationship of the drift limit probability of 

exceedance (POE) adjustment factors to POE is very nearly linear and can 

therefore be estimated closely with closed-form linear equations. 

If the ratio SMS /S is between 0.5 and 1.25, the drift limit POE may be 

estimated in each principal direction using Equations 5-7 and 5-8. Linear 

interpolation may be used for intermediate values of CD. The two equations 

should be used to calculate drift limit POE (%) separately for each principal 

direction, x and y. The drift limit POE of the building is then taken as the 

minimum of the two directional values. If the value of drift limit POE

computed this way is between 5% and 70%, the estimate is valid based on 

the assumed linear fit. 
76 5: Detailed Evaluation FEMA P-807 

84.0 0.41 , MS S POE

S

     

 

for 1.0 CD  (5-7) 

75.2 0.33 , MS S POE

S

     

 

for 0.0 CD  (5-8) 
FEMA P-807 6: Retrofit 77 

Chapter 6 

Retrofit 

This chapter presents the measures that comprise a complete retrofit in 

accordance with the Guidelines. Figure 6-1 illustrates the content of the 

chapter and its relationship to other Guidelines chapters. 

6.1 Retrofit Scope 

In these Guidelines, retrofit to satisfy the selected performance objective 

involves all of the following measures in accordance with this chapter and 

with other codes or standards, as referenced: 

 Addition or replacement of vertical elements of the seismic forceresisting system to increase first-story strength and reduce torsion 

(Sections 6.2 and 6.3); 

 Providing new or replacement elements as needed to satisfy the 

eligibility rules in Guidelines Section 2.6 (Section 6.3.2); 

 Detailing of any new, replacement, and enhanced vertical elements of the 

seismic force-resisting system (Section 6.5); 

 Checking or providing detailed load path elements from the diaphragm 

immediately above the retrofitted story to the supporting ground (Section 

6.5.1); 

 Checking or strengthening of the diaphragm immediately above the 

retrofitted story (Section 6.5.2); and 

 Providing new or replacement elements as needed to satisfy the condition 

assessment provisions in Guidelines Section 4.3. 

Note that diaphragms, foundations, load path elements, deterioration, and 

construction defects were exempt from explicit evaluation in Chapter 5. If 

retrofit is performed, however, these items should be included in the scope 

where they would affect the intended performance of the retrofit. The 

purpose of evaluation under the Guidelines is to find dominant weak-story 

and open-front conditions. Where those are present, these other deficiencies 

are secondary. Where retrofit is being performed to remove the dominant 

deficiencies, however, the secondary deficiencies become significant and 

should be addressed to ensure completeness with respect to the performance 

objective. 
78 6: Retrofit FEMA P-807 

Figure 6-1 Flowchart of typical retrofit procedure. 

Estimate the minimum required and maximum acceptable 

strength of the retrofitted first story, Vr, min and Vr, max. 

Is Vr, min < Vr, max ? 

Section 6.2.3

Sections 6.2.1 and 6.2.2

NO 

Section 6.2.3

YES 

Locate retrofit elements to minimize torsion. 

Section 6.3.1

Complete the conceptual design as needed to correct 

irregularity and condition assessment issues as needed. 

Section 6.3.2

Characterize the conceptual design per Chapter 4. 

Section 6.4

Is the design expected to 

meet the performance 

objective? 

Section 6.4

YES 

For optimized design, is 

the drift limit POE less than 

the maximum acceptable 

drift limit POE? 

Guidelines not applicable. Use 

other retrofit procedure. 

Section 6.4

NO 

Section 6.4

YES

Complete the design, considering load 

path, element detailing. 

Section 6.5

Meet performance objective: Develop 

conceptual design to provide first-story 

strength between Vr, min and Vr, max. 

Optimize: Develop conceptual design 

to provide optimized first-story 

strength between 0.9Vr, max and 1.1Vr, 

Confirm the design by evaluating 

the retrofit per Chapter 5. 

Confirm that the retrofit design 

meets eligibility, strength, and 

eccentricity limits. 

NO 
FEMA P-807 6: Retrofit 79

6.2 Retrofit Strength 

As shown in Chapter 5, existing buildings that do not satisfy the performance 

objective generally fail because of inadequate first-story strength (though 

torsion can play a significant role as well). This section discusses the 

Guidelines’ approach to bounding and optimizing the strength of a retrofitted 

first story. Ultimately, however, a proposed retrofit design is assessed not by 

the estimating equations provided here, but by evaluating that design with the 

procedures in Chapter 5. 

As discussed in Section 2.5.1, the Guidelines attempt to balance structural 

benefit with project cost by stipulating that retrofit work be limited to the 

first story. An ideal retrofit under the Guidelines would meet the 

performance objective with a first-story-only retrofit. As shown in this 

section, however, the ideal is sometimes not possible. In certain buildings, 

the retrofit needed to limit drifts in the first story would over-strengthen the 

first story, forcing upper stories to exceed their drift limits. 

In these cases, the Guidelines offer the option of an optimized retrofit that 

reduces torsion and adds as much strength as possible to the first story, 

maximizing spectral acceleration capacity, without causing excessive drifts 

in upper stories. This solution gives the maximum confidence of not 

exceeding the drift limits while maintaining the feasibility of a first-story 

retrofit. Whether this optimized retrofit would provide acceptable 

performance remains a question for the owner or the jurisdiction. See 

Sections 6.2.3 and 6.4.2. 

Most “weak-link” retrofit methodologies set the minimum scope necessary to 

mitigate a dominant deficiency, leaving the impression that anything more 

than the minimum is necessarily better. The Guidelines take a more complete 

approach; they consider not only the minimum retrofit strength, but also the 

potentially adverse effects of providing too much retrofit strength. 

Section 6.2 of the Guidelines provides the means to estimate the minimum 

and maximum story strengths that will satisfy a given performance objective: 

 The minimum required strength of the retrofitted first story is the 

minimum strength needed to meet the specified performance objective, 

considering only first-story drifts. It is estimated (Section 6.2.1) from 

regression relations similar to those used to evaluate the existing 

structure in Chapter 5. 

 The maximum acceptable strength of the retrofitted first story is the 

strength at which upper-story drift becomes more critical than first-story 
80 6: Retrofit FEMA P-807 

drift, given the performance objective. It is estimated (Section 6.2.2) with 

an empirical formula derived from the results of surrogate analyses. 

In other words, the minimum and maximum strengths correspond to the twopart drift criteria embedded in the fragility definition. The minimum strength 

is set by the need to improve the first story. The maximum strength is set by 

the need to protect the un-retrofitted upper stories. 

If the minimum required strength is less than the maximum acceptable 

strength, then any value between them will satisfy the performance objective. 

Within this range, lower values represent lower retrofit costs, and higher 

values represent better performance and higher confidence against 

unacceptable drifts. 

If the minimum required strength is greater than the maximum acceptable 

strength, then it is unlikely that any first-story-only retrofit will satisfy the 

performance objective. In this case, the Guidelines provide the option to use 

the maximum acceptable strength as the basis for retrofitting the first story. 

This is the optimized retrofit, though the resulting drift limit probability of 

exceedance (POE) will exceed the targeted drift limit POE of the 

performance objective. 

In either case, the equations below merely estimate the minimum and 

maximum values. This is because the design process is iterative and because 

the equations are empirical. Therefore, in either case, the Guidelines call for 

evaluating a proposed retrofit using the methodology of Chapters 4 and 5 to 

confirm an acceptable spectral acceleration capacity or, in the case of an 

optimized retrofit, to determine the resulting drift limit POE. 

6.2.1 Estimated Minimum Required Strength of the Retrofitted 

First Story 

The estimated minimum required strength of the retrofitted first story, Vr,min, 

is the total first-story strength (that is, existing strength plus retrofit strength) 

needed to satisfy the performance objective, considering only first-story 

drifts. Equations 6-1 through 6-5 incorporate the Guidelines’ default 

(embedded) performance objective, which combines a targeted drift limit 

POE, story drifts at the onset of strength loss, and the spectral acceleration 

demand SMS. (See Section 2.3 for discussion of performance objectives; 

Chapter 7 provides the means to account for different drift limits.) Vr,min, 

which is to be calculated in each direction, is derived from the surrogate 

analyses, much like the evaluation equations in Chapter 5. 
FEMA P-807 6: Retrofit 81

 

 

3 3

2 2

,min 3 3

1 1

1

1

MS D D

r U

D D

S XC Y C

V V

XC Y C

    

 (6-1) 

where: 

  0.48

0 ,1 1 0.5 X AQ C    POE U s T (6-2) 

1 0 X  2.24X and 2 0 X  0.525X (6-3) 

  0.6

0 ,0 1 0.5 Y AQ C    POE U s T (6-4) 

1 0 Y Y 1.59 and 2 0 Y Y  0.122 (6-5) 

and where VU is the controlling strength of the upper stories, AU is the basenormalized upper-story strength as defined in Section 4.7.2, Qs is the story 

height factor as defined in Section 4.7.6, POE,1 and POE,0 are the drift limit 

probability of exceedance (POE) adjustment factors as described in Section 

5.3, and the strength degradation ratio, CD, and the torsion coefficient, CT, are 

determined as described below. 

In applying Equations 6-1 through 6-5, values of CD and CT for the preretrofit structure may be used. These values will give an initial estimate of 

the minimum required strength. When retrofit elements are added, however, 

the values of these parameters will tend to change, reflecting the improved 

ductility and torsional strength of the retrofitted structure, so the value given 

by Equation 6-1 will change as well. (Appendix C provides an example of a 

building for which improved CD and CT values made a significant difference, 

allowing the retrofit design to achieve the performance objective without the 

need for optimized design.) One or two iterations are expected to result in a 

final estimate of the minimum required strength, but such a refined estimate 

is not really needed. Even the initial estimate might be enough to guide the 

retrofit design. Final acceptability of any retrofit design will be based on 

evaluation of its spectral acceleration capacity (Section 6.4), not on its 

relation to the estimated minimum strength. Alternatively, to arrive at an 

estimate with less iteration, one may guess at final values of CD and CT for 

use in Equations 6-1 through 6-5. In either case, the final design will be 

confirmed in the same manner. Note that the Weak-Story Tool (Section 1.6) 

automatically recalculates these values as retrofit elements are added to the 

model, eliminating much of the burden of iteration.

6.2.2 Estimated Maximum Acceptable Strength of the Retrofitted 

First Story 

As shown by the grey curves in Figure 6-2, varying the first-story retrofit 

strength changes the spectral acceleration capacity. The different sets of 
82 6: Retrofit FEMA P-807 

Figure 6-2 Plot of spectral acceleration capacity (spectral capacity) versus strength of retrofitted 

first-story, for buildings with strong upper stories. Grey lines show how varying the 

first-story retrofit strength changes the spectral acceleration capacity for different 

combinations of base-normalized upper-story strength, AU, and weak story ratio, 

AW. Sc is spectral acceleration capacity, and SMS is short-period spectral acceleration 

demand. 

curves represent different values of base-normalized upper-story strength, 

AU. Within each set, separate curves represent different initial, unretrofitted 

values of the weak story ratio, AW. Subsequent points along each curve 

represent changes in AW due to different retrofits. These curves were derived 

from the fragility curves associated with the surrogate models—fragility 

curves that consider the possibility of excessive drift in either the first story 

or an upper story. The peak in each curve represents the point at which the 

response shifts from a first-story failure (left of the peak) to an upper-story 

failure (right of the peak). The peak, then, represents the maximum strength 

retrofit, that is, the retrofit that adds the most strength without inducing 

unacceptable drift in the upper stories. 

The precise location of the peak varies with different values of AU and initial 

AW. Equation 6-6 approximates this point for a broad range of combinations, 

giving Vr,max, the total retrofitted strength (that is, the combined strength of 

existing and new elements). 

  ,max 0.11 1.22 V AV r UU    (6-6) 

Strength of Retrofitted Ground-Story

Spectral Capacity, 

Sc

Au = 0.4, Aw = 0.6

Maximum Strength, V r max

(Best Performance)

Minimum Strength, V r min

(Achieves Performance Objective) 

Acceptable Retrofit Range

Sc =  POE S = S MS

Strength of Retrofitted First Story
FEMA P-807 6: Retrofit 83

where AU and VU are defined above. 

Since AU and VU are independent of first-story conditions, Vr,max does not 

change as a retrofit design goes through iterations. Nevertheless, it is still an 

estimate because Equation 6-6 is a simple, but reasonable, linear fit through 

data with various values of CD, as discussed further in Appendix E. Note that 

for typical buildings, AU is less than 0.5, so the maximum acceptable strength 

of the first story, assuming the default (embedded) performance objective, 

will generally be between 1.2 and 1.3 times VU. In other words, when the first 

story is more than about 1.3 times the strength of a brittle upper story, initial 

failure in the upper story controls performance. 

6.2.3 Estimated Ranges of Acceptable Retrofit Strength 

In buildings with sufficiently strong upper stories, Vr,max will be greater than 

Vr,min, and either value, as well as any strength value between them, should 

satisfy the performance objective. This is illustrated in Figure 6-2. Each 

curve in the figure represents a building with CT equal to 0.0 and Qs equal to 

1.0, evaluated to the default (embedded) performance objective with a drift 

limit POE at 20 percent. The dark curve represents an existing building with 

a relatively high base-normalized upper-story strength, AU, of 0.4. At the left 

end of the dark curve, the weak-story ratio, AW, is 0.6. Moving to the right, 

adding retrofit strength to the first story increases spectral acceleration 

capacity, and where the retrofitted strength reaches Vr,min, the spectral 

acceleration capacity, Sc, equals the spectral acceleration demand, SMS, 

indicating the minimum retrofit that meets the default performance objective. 

As more retrofit strength is added, the spectral acceleration capacity 

continues to increase until it reaches a peak at roughly Vr,max. Increasing the 

first-story strength beyond Vr,max would lead to unacceptable drift and related 

damage in one or more upper stories. 

In buildings with weak upper stories, however, even the minimum required 

first-story strength will be beyond the peak of the curve. This is illustrated in 

Figure 6-3. The dark curve represents another existing building, but this time 

with a low base-normalized upper-story strength, AU, of 0.1. In this case, the 

spectral acceleration capacity again increases as retrofit strength is added, but 

it reaches its peak before the minimum required strength is obtained. A 

spectral acceleration capacity equal to the spectral acceleration demand 

would only be achievable if the upper stories did not begin to control the 

response, as suggested by the dotted line. Thus, Vr,max, representing the peak 

of the dark curve, turns out to be less than Vr,min, at the far right edge of the 

figure. In this case, no first-story-only retrofit will satisfy the performance 

objective. Instead, an owner or jurisdiction might consider either: 
84 6: Retrofit FEMA P-807 

Figure 6-3 Plot of spectral acceleration capacity (spectral capacity) versus strength of 

retrofitted first-story, for buildings with weak upper stories. Grey lines show 

how varying the first-story retrofit strength changes the spectral acceleration 

capacity for different combinations of base-normalized upper-story strength, 

AU, and weak story ratio, AW. Sc is spectral acceleration capacity, and SMS is 

short-period spectral acceleration demand. 

 An optimized first-story-only retrofit that maximizes the spectral 

acceleration capacity by providing a first-story strength roughly equal to 

Vr,max. Such a solution would not meet the performance objective but 

would make the most of a first-story-only retrofit. 

 A retrofit scheme that strengthens one or more upper stories as well as 

the first story, as needed to meet the performance objective. Such a fullbuilding solution would be outside the scope of the Guidelines. 

The Guidelines, which are premised on the idea of practical, cost-effective 

mitigation, recognize the value of the latter approach involving optimized 

retrofit. While the decision to waive the performance objective and accept 

such retrofits is ultimately a policy decision for the owner or jurisdiction, it is 

the judgment of the Guidelines’ writers that if the optimized retrofit would 

provide a significant measure of improvement (see Section 6.4.2), it could be 

an appropriate solution for many mitigation projects and programs. In 

particular, if the alternative—a full building retrofit—would prove so costly 

and disruptive as to make the mitigation program infeasible, then optimized 

Strength of Retrofitted Ground-Story

Spectral Capacity, 

Sc

Optimized Retrofit Range

Au = 0.1, Aw = 0.6

1.1V r max 0.9V r max 

S MS

S c

Strength of Retrofitted First Story
FEMA P-807 6: Retrofit 85

first-story retrofit seems the better choice. On the other hand, if consistency 

with the performance objective is crucial, then optimized first-story retrofits 

might be unsuitable. 

Importantly, Figure 6-3 also illustrates the ineffectiveness of overly strong 

first-story-only retrofits. Beyond the peak at Vr,max, additional first-story 

strength does not bring a structure with weak upper stories any closer to 

meeting the performance objective. More strength merely adds cost to the 

retrofit project with no benefit. In fact, if enough strength is added, the 

spectral acceleration capacity decreases. It is this effect that a simplified 

retrofit code such as IEBC Chapter A4 can miss. 

Where optimized retrofit is pursued, the basis for the first-story retrofit 

strength is Vr,max. As Figures 6-2 and 6-3 show, the peak of each curve is 

relatively flat, so that similar performance can be expected for a range of 

strengths around Vr,max. With this in mind, and to provide the designer with 

some flexibility in sizing retrofit elements, the Guidelines recommend that 

the acceptable range of first-story retrofit strength, V1r, should be such that 

Equation 6-7 is satisfied. 

,max 1 ,max 0.9 1.1 VVV r rr   (6-7) 

In addition to satisfying Equation 6-7, an optimized retrofit should also 

locate the retrofit elements so as to minimize torsion, as discussed in Section 

6.3.1. 

Each principal direction should be considered separately when estimating the 

ranges of acceptable retrofit strength. It is possible that one direction will 

have strong enough upper-story walls to meet the performance objective, 

while the other direction will qualify only for an optimized design. 

Whichever combination applies, however, the effect of the two solutions 

acting together can affect the structure’s torsional response and must be 

confirmed, per Section 6.4. 

6.3 Locating Retrofit Elements 

The best performance will generally be achieved where retrofit elements are 

located in plan so as to minimize first-story torsion. This is especially 

important for optimized designs. In addition, eligibility for the Guidelines’

methodology (per Section 2.6) requires the mitigation of certain diaphragm 

irregularities, and retrofit elements may be located for this purpose as well. 
86 6: Retrofit FEMA P-807 

6.3.1 Retrofit Element Location to Minimize Torsion 

Where the retrofit satisfies the performance objective, the spectral 

acceleration capacity already accounts approximately (through the CT factor) 

for first-story eccentricities and torsion. Therefore, an explicit requirement to 

locate retrofit elements so as to minimize torsion is not necessary. Still, as the 

spectral acceleration capacity equations reflect, there are advantages to 

reducing torsion by design. Retrofits that minimize torsion achieve a higher 

capacity with the same amount of material (and cost), or can achieve the 

minimum required capacity with less material. 

For optimized retrofits that, by definition, do not satisfy the targeted 

performance objective, potential torsion must be addressed more explicitly, 

for two related reasons. First, the optimized strength is only truly optimized 

when the added retrofit elements minimize torsion. If the only requirement 

for optimized retrofit were to satisfy Equation 6-7, any arrangement of the 

retrofit elements would be satisfactory. But as the spectral acceleration 

capacity equations show, if torsion is minimized, a lower, optimized drift 

limit POE can be achieved for the same retrofit strength. Second, the 

empirical grey curves in Figures 6-2 and 6-3 were derived from surrogate 

models that assumed no torsion. Therefore, to best match the Guidelines’ 

assumptions, optimized retrofits should minimize torsion. 

As shown in Section 4.6, first-story torsion is a function of the eccentricity 

between the centers of strength of the first and second stories. When retrofit 

elements are added, the first-story center of strength can shift, so x and y

components of the eccentricity of the retrofitted first story, er,x and er,y,

become: 

r x, 2, 1 x rx, e COS COS   (6-8) 

r y, 2, 1, y ry e COS COS   (6-9) 

where: 

COS1r,x = x coordinate of the center of strength of the retrofitted first 

story, calculated in accordance with Section 4.6.4, 

COS2, x = x coordinate of the center of strength of the second story, 

calculated in accordance with Section 4.6.4, 

COS1 , r y = y coordinate of the center of strength of the retrofitted first 

story, calculated in accordance with Section 4.6.4, and 

COS2, y = y coordinate of the center of strength of the second story, 

calculated in accordance with Section 4.6.4. 
FEMA P-807 6: Retrofit 87

Potential torsion is minimized when the eccentricity is zero, so ideally, 

retrofit elements should be located so that both er,x and er,y are zero. Where 

the pre-retrofit eccentricity is large and the retrofit strength is limited by 

Equation 6-7, however, it might not be possible to eliminate the eccentricity 

completely—the retrofit elements would have to be located, theoretically, 

outside the building footprint. In this case, the perimeter of the building 

becomes the optimal location. But even then, retrofit elements cannot always 

be placed at the perimeter because of interference with existing utilities, 

egress ways, property lines, and other conditions. Therefore, to provide 

design flexibility and to reflect the Guidelines’ overall preference for 

feasible, cost-effective solutions, the logic of locating retrofit elements 

should work as follows: 

 Where possible, locate the retrofit elements so that er,x and er,y are zero. 

For design flexibility, er,x is acceptable if it is less than 10 percent of the 

building dimension Lx (and similarly in the y direction). 

 Where the foregoing rule cannot be satisfied, locate the retrofit elements 

along the perimeter lines that minimize er,x and er,y. For design flexibility, 

new retrofit elements are acceptable if they are a distance from the 

appropriate perimeter line less than 5 percent of the corresponding 

building dimension. 

There might be cases where all the necessary retrofit elements cannot be 

made to fit along a single perimeter wall line. In these cases, the design 

should follow the general rule and try to minimize eccentricity. If the 

remaining eccentricity still allows significant torsion and significantly limits 

the reduction in drift limit POE, the building official and engineer of record 

should consider whether the Guidelines methodology, which presumes 

minimal torsion for optimized retrofits, is really suitable to the building in 

question. 

Achieving the optimized story strength is more important than achieving the 

minimum eccentricity. Therefore, even if the eccentricity can be eliminated 

by adding more or stronger retrofit elements, that approach should not be 

taken if it increases the retrofitted first-story strength beyond the limit of 

Equation 6-7. 

6.3.2 Retrofit Element Location to Ensure Eligibility 

The Guidelines apply only to buildings—existing or retrofitted—that meet 

the eligibility criteria in Section 2.6, including the limits on diaphragm shape 

and plan irregularity in Section 2.6.4. As stipulated there, an ineligible 
88 6: Retrofit FEMA P-807 

existing building may be made eligible through retrofit measures that divide 

the diaphragm into eligible pieces with qualifying walls or frames. 

Figure 6-4 shows a diaphragm whose aspect ratio exceeds the limit of 2:1 

(from Section 2.6.4). Following the provision in Section 2.6.4, the building 

can be made eligible by placing a qualifying wall or frame element to reduce 

the diaphragm span as shown. 

Figures 6-5 and 6-6 show a building with an ineligible re-entrant corner. 

Following the provisions of Section 2.6.4, as shown in the figures, the 

building can be made eligible if qualifying existing or new wall or frame 

lines divide the diaphragm so that each diaphragm section, D1 or D2, has an 

aspect ratio less than 2:1. (In the Figure 6-5 and 6-6 examples, the cantilever 

limit does not apply because each extension of the diaphragm beyond the reentrant corner has a qualifying wall section at its edge and is therefore not 

cantilevered.) 

Figure 6-4 Floor plan schematic showing use of retrofit elements to meet 

diaphragm aspect ratio limits. The retrofit element between 

diaphragm D1 and D2 must be a qualifying wall or frame per 

Section 2.6.4. 

6.4 Confirmed Performance of the Retrofitted Structure 

While the equations in Section 6.2 estimate the range of acceptable retrofit 

strength, a final retrofit design is assessed by evaluating it with the 

procedures in Chapters 4 and 5. 

For this evaluation, the parameters AW, CD, CT, and related parameters should 

be recalculated for the proposed retrofit design, in each direction. The 

parameter AU (base-normalized upper-story strength) is not affected by the 

first-story-only retrofit. Note that the sizing and location of key elements in a 

D D

x

y

x : y > 2 : 1

x

x

x : y < 2 : 1 x : y < 2 : 1

This frame must support

lateral loads from both

diaphragms D and D

Direction of motion

considered
FEMA P-807 6: Retrofit 89

Figure 6-5 Floor plan schematic showing use of retrofit elements to satisfy 

re-entrant corner limits, east-west analysis. D denotes 

diaphragm. 

Figure 6-6 Floor plan schematic showing use of retrofit elements to satisfy 

re-entrant corner limits, north-south analysis. D denotes 

diaphragm.

> 0.15y

> 0.15x

East-West Analysis

D

D

Qualifying

frame/wall line

y y

y / x < 2

y / x < 2

E

S

W

N

x

x

y

> 0.15y

x

> 0.15x

North-South Analysis

D

D

Qualifying wall line

x / y < 2

x / y < 2

x x

E

S

W

N

y

y
90 6: Retrofit FEMA P-807 

final retrofit design must account not only for the necessary story strength, 

but also for any eligibility or condition assessment issues identified earlier in 

the process. Further, optimized retrofits should minimize torsion, as 

discussed in Section 6.3.1. The Weak Story Tool (Section 1.6 and Appendix 

A) can be helpful in these tasks. 

6.4.1 Retrofits Intended to Satisfy the Performance Objective 

If the retrofit is intended to satisfy the performance objective, the spectral 

acceleration capacity of the retrofitted structure should be determined and 

compared with the spectral acceleration demand per Sections 5.2 through 5.4. 

If the capacity exceeds the demand, the retrofit design is confirmed. 

(Alternatively, the drift limit probability of exceedance (POE) can be 

determined per Section 5.4.2 and compared with the targeted drift limit POE

of the performance objective.) 

6.4.2 Optimized Retrofits that Do Not Satisfy the Performance 

Objective 

If the retrofit is intended to optimize performance but not necessarily satisfy 

the targeted performance objective, three checks should be made: 

1 The peak story strength of the retrofitted first story, V1r, should be 

determined per Section 4.6.2 and shown to satisfy Equation 6-7. 

2 The center of strength of the retrofitted first story, COS1r, should be 

determined per Section 4.6.4 and shown to satisfy the eccentricity limits 

in Section 6.3.1. 

3 The drift limit probability of exceedance (POE) of the retrofitted 

structure should be determined per Section 5.4.2 and shown to be less 

than the maximum acceptable POE for optimized retrofits. 

The “maximum acceptable drift limit POE for optimized retrofits” is a matter 

of owner or jurisdiction judgment. The optimized retrofit does not satisfy the 

performance objective in quantitative terms. The acceptability of an 

optimized retrofit is therefore not a function of performance alone, but one of 

costs and benefits, in which improved performance is compared with fully 

satisfactory performance and weighed against the costs of retrofitting. 

To understand the issue, consider a performance objective that includes a 

targeted drift limit POE of 20 percent. Any retrofit that lowers the POE to 20 

percent or less fully satisfies the objective. Now consider a case in which a 

first-story-only retrofit would lower the drift limit POE from 60 percent to 40 

percent. Two questions arise: First, is 40 percent close enough to the targeted 

objective of 20 percent to ever be considered adequate, if not fully 
FEMA P-807 6: Retrofit 91

compliant? Second, is the improvement from 60 to 40 worth the cost of 

retrofit? 

Now consider a case in which a first-story-only retrofit would lower the drift 

limit POE from 90 percent to 40 percent. Even if 40 percent is still risky, the 

improvement is enormous and probably worthwhile, especially if the cost of 

getting all the way down to 20 percent with a full-building retrofit would 

make the project infeasible. 

Owners undertaking voluntary work must weigh the costs and benefits of 

full-building and first-story-only retrofits. As discussed in Section 1.4.2 and 

Appendix B, a jurisdiction designing a mitigation program should select the 

maximum acceptable drift limit POE considering the overall goals of its 

program and the composition of its building stock. 

It is clear, then, that the Guidelines cannot recommend a maximum 

acceptable drift limit POE that will apply in all cases. Nevertheless, it is the 

judgment of the Guidelines’ writers that if a drift limit POE less than 50 

percent cannot be achieved, it generally indicates extremely weak upperstory walls, and that fact argues strongly for a full-building retrofit. 

If the building is such that the optimized first-story retrofit cannot provide a 

drift limit POE less than the maximum acceptable value, then the retrofit 

cannot be designed using the Guidelines. Instead, a more comprehensive or 

building-specific approach will be needed. The Guidelines recommend 

ASCE/SEI 41 as the basis for such a retrofit. 

Importantly, the Guidelines recommend that IEBC Chapter A4 should not be 

used in these cases, since IEBC Chapter A4 makes some of the same 

assumptions as the Guidelines. In other words, if no acceptable retrofit can 

be found using the Guidelines, it is probably because the existing building is 

too weak in its upper stories for a first-story-only approach to work. Since 

IEBC Chapter A4 also stipulates a first-story-only approach, but does not 

explicitly check the upper stories as the Guidelines do, use of IEBC Chapter 

A4 could result in this weakness being overlooked, thereby providing a false 

sense of improvement. 

6.5 Retrofit Element Selection and Design 

For the Guidelines’ methodology to be reliable, the retrofit design must be 

consistent with Guidelines’ assumptions. Therefore, certain restrictions and 

design criteria apply to the selection of suitable retrofit elements. 
92 6: Retrofit FEMA P-807 

The surrogate modeling on which the Guidelines are based assumes that 

retrofit elements will be ductile enough to qualify for the high-displacement 

capacity designation illustrated in Figure 4-1. 

General guidelines for the design of retrofit elements, supplemented by 

material- and system-specific guidelines below, include: 

 New retrofit wall elements should be sized based on the strengths given 

in Table 4-1. Where principal retrofit elements (walls and frames) are 

sized based on unit strengths from codes or standards, the full expected 

capacity, without strength reductions or resistance factors, should be 

used. 

 The load-drift curve of each retrofit element type should be based on 

expected material properties, including overstrength. The full expected 

capacity, without strength reduction or resistance factors, should be 

assumed for purposes of establishing load-drift curves and peak 

strengths. 

 Each retrofit element should be such that a load-drift curve based on 

similar elements alone would have a strength degradation ratio, CD, 

greater than or equal to 0.8. 

 The load-drift curve of each retrofit element type should be defined up to 

5 percent interstory drift or as needed to fully characterize the retrofit 

design per Chapter 4. 

 Materials and systems for retrofit elements should be consistent with 

provisions of the building code for new construction. While codes for 

existing buildings typically allow “like materials” for repairs and 

alterations (for example, see 2009 IBC Section 3401.4.2), the Guidelines

presume that retrofit elements will be reliably ductile. This is consistent 

with code provisions for voluntary seismic upgrade (for example, see 

IBC Section 3404.5 or 2009 IEBC Section 707.6). 

 Detailing of retrofit wall and frame elements should be consistent with 

that applied to special seismic-force-resisting systems used in new 

construction for the corresponding occupancy and risk category. 

 Quality assurance measures should be applied. They should be consistent 

with those normally applied to special seismic-force resisting systems 

used in new construction for the corresponding occupancy and risk 

category. 
FEMA P-807 6: Retrofit 93

6.5.1 Load Path Components 

Reliable performance of retrofit elements relies on the presence of a designed 

and detailed load path from the second-floor diaphragm (or the diaphragm 

immediately above the retrofitted story) through the retrofit elements and 

their foundations, to the supporting soils. Load path elements should be 

designed to develop the full strength and the intended mechanism of the 

principal wall or frame elements. Therefore, to ensure reliability, appropriate 

strength reduction factors should be applied to the ultimate strengths of load 

path elements. Specific criteria may be derived from principles of capacity 

design or from other codes or standards, such as ASCE/SEI 41 or building 

code provisions involving the overstrength factor, 0. 

New foundation elements should be provided as needed to resist bearing, 

sliding, and overturning forces associated with the retrofit element acting at 

its peak strength. Ultimate material and soil strengths should be used. 

Connections and load path elements related to wall or frame overturning 

should not assume any acting dead load except for the self weight of the 

retrofit element (and its foundation, if adequately connected), unless the 

retrofit element incorporates existing gravity-load-carrying framing or unless 

the design and construction explicitly transfer existing dead load to the 

retrofit element. 

6.5.2 Second-Floor Diaphragm 

The second-floor diaphragm (or the diaphragm immediately above the 

retrofitted story) should be strengthened as needed to ensure that expected 

forces can be transferred between the diaphragm and the first-story elements. 

Diaphragm strengthening can sometimes be avoided by the careful placement 

of retrofit walls or frames. 

6.5.3 Wood Structural Panel Shear Walls 

Load-drift curves for retrofit designs employing wood structural panel shear 

walls may be based on Guidelines Sections 4.4 through 4.6. As noted in 

Section 4.5.3.1, however, the simplified overturning reduction factor should 

not be used for retrofit elements. 

Existing shear walls may be modified by replacing existing sheathing 

materials with new wood structural panels or by adding new wood structural 

panels onto existing wall framing or assemblies. 
94 6: Retrofit FEMA P-807 

6.5.4 Steel Moment Frames 

Steel retrofit elements may be designed and detailed, with reference to 

ASCE/SEI 7 (ASCE, 2006a or later), either as Moment-Resisting Frame 

Systems or as Cantilevered Column Systems, as long as the element 

configuration provides the minimum CD value of 0.8. Generally, retrofit 

elements that conform to the requirements of AISC 341-05 (AISC, 2005) 

Section 9 for Special Moment Frames or AISC 341-10 (AISC, 2011) for 

Special Cantilevered Column systems are most likely to meet this 

requirement. Intermediate and Ordinary systems are unlikely to do so, but the 

Guidelines do not specifically require, approve, or rule out any system. For 

complying systems, the load-drift curve may be approximated by the trilinear curve shown in Figure 6-7, where Zy and Fye are properties of the 

yielding member. 

Figure 6-7 Simplified load-drift curve for steel Special Moment Frame 

retrofit elements. Zy and Fye are properties of the yielding 

member. 

6.5.5 Steel Braced Frames 

Concentrically braced frame elements, including Ordinary or Special 

Concentrically Braced Frames, are not suitable for retrofit using the 

Guidelines. These systems involve buckling braces and are not expected to 

satisfy the requirement for a CD value of 0.8 with adequate reliability. 

Buckling-restrained Braced Frames, however, are suitable, provided that the 

load-drift curve of such a frame can provide the minimum CD value of 0.8. 

Frames that conform to the requirements of AISC 341-05 (AISC, 2005) 

Section 16 for Buckling-restrained Braced Frames are likely to meet this 

requirement. For such frames, the load-drift curve may be approximated by a 

tri-linear curve similar to that shown in Figure 6-7. lateral force, 

V

Vfy based on Z F

f

x ye

interstory drift ratio, 

 y + 4%

based on elastic

section properties

1.2Vfy

 y
FEMA P-807 6: Retrofit 95

6.5.6 Concrete or Reinforced Masonry Shear Walls 

Concrete or reinforced masonry shear walls are not suitable for retrofit using 

the Guidelines. While these systems are often adequately strong, their yield 

point and capacity are difficult to establish with precision, so they do not 

work well with the Guidelines methodology, which relies on predictable 

load-drift curves and limited first-story strength. 

FEMA P-807 7: Alternative Performance Assessment 97 

7Chapter 7 

Alternative Performance 

Assessment 

7.1 Purpose 

As described in previous Chapters, any performance objective involves a 

desired performance level, which the Guidelines characterize in terms of 

interstory drift limits. The equations in Chapters 5 and 6 assume the 

Guidelines' default objective, using drift limits associated with the onset of 

strength loss. This Chapter provides alternative equations suitable for tighter 

drift limits that correspond to less damage. 

7.2 Assessment Background 

The assessment approach presented here is conceptually the same as that 

presented in Chapter 5. As discussed in Chapter 5, a large number of 

nonlinear response history analyses form the basis for the evaluation 

empirical equations. Any set of drift criteria may be selected to represent the 

seismic performance of interest. Using these drift criteria, the analytical 

results can be queried to define equations that relate a building’s 

characteristics to its probability of exceeding the drift criteria at some 

earthquake intensity. This has been done for the two sets of drift criteria 

defined below. The building’s characteristics are quantified by the 

coefficients presented in Chapter 4, and the earthquake shaking intensity is 

quantified as a specified short-period spectral acceleration, Sd. 

7.3 Interstory Drift Limits 

In this chapter, two sets of drift criteria are considered: “onset of strength 

loss” (OSL) and “onset of damage” (OD). Figure 7-1 illustrates a comparison 

of the drift criteria in the context of the two archetypal sheathing material 

backbone curves representing degradation ratios of zero and one. The 

Guidelines use a drift limit of 1.0 % for OD for all materials. As shown in 

Figure 7-1, 1% represents near the yield limit and peak strength for high 

deformability materials (CD = 1), and is deemed to be close enough to the 

peak strength for low deformability materials (CD = 0). 
98 7: Alternative Performance Assessment FEMA P-807 

Figure 7-1 Illustration of drift limit definitions relative to two sheathing 

backbone curves with CD = 0.0 and 1.0, respectively. 

7.4 Spectral Acceleration Capacity 

Chapter 5 provides spectral acceleration capacity equations relative to the 

OSL drift criteria. The evaluation equation in Chapter 5 has the general form: 

   , , 1 0.5 U

c POE U W W x T s U x S AC Q A     (7-1) 

where the coefficients U , W , and U are computed to minimize the error of 

the fit to the analytical results. These coefficients depend on the drift criteria 

and may be modified to fit the analytical results queried relative to other drift 

criteria. The coefficients U, U, and W are tabulated in Table 7-1 for the 

OSL and OD drift limits. 

Table 7-1 Curve-Fitting Coefficients (U, U, and W) for Calculating 

Spectral Acceleration Capacity. 

U U W

Strength Degradation Ratio, CD = 0.0 

OSL 0.60 0.122 1.594 

OD 0.60 0.044 1.551 

Strength Degradation Ratio, CD = 1.0 

OSL 0.48 0.525 2.240 

OD 0.56 -0.027 1.537 

Note: OSL and OD refer to the Onset of Strength Loss and Onset of Damage drift 

limits, respectively.

Interstory Drift

Shear Force

Sheathing material with 

C D = 0.0

OSL for 

CD = 1.0 (4%)

OSL for 

CD = 0.0 (1.25%)

OD for any 

CD (1.0%)

Sheathing material with C D = 1.0
FEMA P-807 7: Alternative Performance Assessment 99 

Thus, the spectral acceleration capacity for the drift criteria under 

consideration is given by: 

c x POE x 1, ,1 1, S S   for CD = 1.0 (7-2) 

c x POE x 0, ,0 0, S S   for CD = 0.0 (7-3) 

   1

1, 1 1 , , 1 0.5 Ux U W Wx T s Ux S AC Q A     for CD = 1.0 (7-4) 

   0

0, 0 0 , , 1 0.5 Ux U W Wx T s Ux S AC Q A     for CD = 0.0 (7-5) 

  3 3

1 0 1 c Dc D c S CS C S   (7-6) 

where: 

S ,1 x = median spectral acceleration capacity in the x-direction for CD = 

1.0, 

S ,0 x = median spectral acceleration capacity in the x-direction for CD = 

0.0, 

S ,1 xc = spectral acceleration capacity (adjusted for drift limit POE) in 

the x direction for CD = 1.0, 

S ,0 xc = spectral acceleration capacity (adjusted for drift limit POE) in 

the x direction for CD = 0.0, 

 POE = drift limit POE adjustment factors defined in Chapter 5, 

S ,xc = spectral acceleration capacity in the x direction for intermediate 

values of CD, 

U1, U1, and W1 are as tabulated in Table 7-1 for CD = 1.0, 

U0, U0, and W0 are as tabulated in Table 7-1 for CD = 0.0, and 

Qs, story height factor, and AU, base-normalized upper-story strength, are 

defined earlier. 

Figures 7-2 through 7-5 show charts of median spectral acceleration capacity, 

S, for various values of base-normalized upper-story strength, AU, weakstory ratio, AW, and strength degradation ratio, CD, for the OD and OSL drift 

limits. The torsion coefficient, CT is zero in all cases. The plots are graphical 

representations of Equation 7-4 and Equation 7-5 showing the analytical 

results to which the curves are fitted. 

7.5 Estimating the Drift Limit Probability of Exceedance 

The drift limit probability of exceedance (POE) may be estimated using the 

same procedure presented in Chapter 5 for the specified short-period spectral 

acceleration demand, Sd. If the ratio, Sd/ S is between 0.5 and 1.25, the drift 
100 7: Alternative Performance Assessment FEMA P-807 

Figure 7-2 Curves showing the relationship between as-built median spectral 

acceleration capacity, S, and base-normalized upper-story strength for 

various weak-story ratios, AW, and for the Onset of Damage set of drift 

limits. Strength degradation ratio CD = 1.0. 

Figure 7-3 Curves showing the relationship between as-built median spectral 

acceleration capacity, S, and base-normalized upper-story strength for 

various weak-story ratios, AW, and for the Onset of Damage set of drift 

limits. Strength degradation ratio CD = 0.0. 

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Upper-Story Strength Ratio, A U

Median Spectral Capacity, 

S

  .0 56

1 .0 027 .1 54 AA UW S 

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Upper-Story Strength Ratio, A U

Median Spectral Capacity, 

S

  .0 60 S  0 .0 044  .1 55 AA UW
FEMA P-807 7: Alternative Performance Assessment 101 

Figure 7-4 Curves showing the relationship between as-built median spectral 

acceleration capacity, S, and base-normalized upper-story strength for 

various weak-story ratios, AW, and for the Onset of Strength Loss set of drift 

limits. Strength degradation ratio CD = 1.0. 

Figure 7-5 Curves showing the relationship between as-built median spectral 

acceleration capacity, S, and base-normalized upper-story strength for 

various weak-story ratios, AW, and for the Onset of Strength Loss set of drift 

limits. Strength degradation ratio CD = 0.0. 

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Upper-Story Strength Ratio, A U

Median Spectral Capacity, 

S

  .0 48

1 .0 525 .2 24 AA UW S   

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Upper-Story Strength Ratio, A U

Median Spectral Capacity, 

S

  .0 60

0 .0 122 .1 59 AA UW S   
102 7: Alternative Performance Assessment FEMA P-807 

limit probability of exceedance, POE, may be estimated in each direction 

using Equation 7-7 and Equation 7-8 for CD = 1.0 and 0.0, respectively. 

Linear interpolation may be used for intermediate values of CD. The drift 

limit POE of the building shall be the minimum value computed considering 

each direction independently. 

1

84.0 0.41 d S POE

S

     

 

, for CD = 1.0 (7-7) 

0

75.2 0.33 d S POE

S

     

 

, for CD = 0.0 (7-8) 

where: 

Sd = short-period spectral acceleration demand of interest (e.g., SMS), 

S 1 = median spectral acceleration capacity for strength degradation 

ratio, CD = 1.0, in accordance with Equation 7-4, and 

S0 = median spectral acceleration capacity for strength degradation 

ratio, CD = 0.0, in accordance with Equation 7-5. 
FEMA P-807 A: Guide to Weak-Story Tool A-1 

Appendix A 

Guide to Weak-Story Tool 

A.1 Introduction 

The Guidelines introduce topics that may be unfamiliar to some engineers. 

Though the calculations required in Chapters 4 and 5 are not conceptually 

difficult, the novelty of these concepts might be confusing. Also, there is a 

significant amount of number-crunching that must be done. This is the direct 

result of trying to take into account as much of the strength of the existing 

building as possible to make the retrofit economical. Each wall in the 

building will participate in resisting instability during an earthquake whether 

it is considered structural or not; thus each wall must be tabulated, assigned 

an assembly (and requisite load-drift curve), and be included in the 

calculations of the strength of each level in each direction and in torsion. 

The concept of the Weak-Story Tool is to provide a convenient means of 

tabulating the walls in a building with clear graphical feedback to clarify the 

calculations that are being done by the spreadsheet tool. It provides a 

relatively fast means of going from the building survey through checking if 

the first-story retrofit is applicable, and if so, to finding the required strength 

of the retrofitted first story. 

A.2 Obtaining the Weak-Story Tool 

The Weak-Story Tool is included on a CD accompanying this report. See 

Section A.4 for installation instructions. 

A.3 System Requirements 

The Weak-Story Tool was developed using Visual Basic.Net and should 

work on any Windows machine with Windows XP or later operating system. 

A.4 Weak-Story Tool Installation 

The installation files will come in the form of a folder called 

“WeakStoryTool.” (see Figure A-1) Inside the folder will be several items. 

To install the Tool, simply double-click the file setup.exe. The Tool may be 

removed from the system using the Control Panel as with any similar 

commercial tool. The Tool launches itself at the end of the installation 

process. It also places a shortcut in the Start Menu. 
A-2 A: Guide to Weak-Story Tool FEMA P-807 

A.5 Basic Controls 

When the Tool is launched, a new document will be created. The user must 

create a unique document for each distinct building to be analyzed. There are 

four buttons near the top of the screen (see Figure A-2) that determine which 

control is currently displayed. The following is a list of the controls and their 

purposes. 

1. General: Enter general buildings properties and reference geometry (e.g. 

gridlines and images) that might be relevant on more than one level. 

2. Assemblies: Combine sheathing layers into assemblies that can be 

assigned to walls. 

3. Levels: Define properties for each level including clear story height, wall 

layout, diaphragm shape, and unit weights. 

4. Summary: Review evaluation and performance results indicating the 

need for and acceptability of retrofit. 

Figure A-2 Screenshot of control buttons. 

A.6 General Building Properties and Geometry 

The General control (Figure A-3) is where the user enters information and 

geometry that apply to the building as a whole. On the top left of the drafting 

area, there is a control box where the building properties may be edited. The 

Figure A-1 Screenshot of contents of WeakStoryTool folder containing installation files. 
FEMA P-807 A: Guide to Weak-Story Tool A-3 

user may toggle an expanded view of the available properties by clicking the 

 (toggle expand) button. The properties are as follows: 

1. Number of Levels: The number of levels in the building. 

2. SMS: The short-period MCE acceleration for this building. Clicking on the 

 (calculator) button brings up a form that helps the user find sitespecific SMS based on zip code and site class as in ASCE/SEI 7-05. 

3. Typical Wall Thickness: The wall thickness that will appear when the 

user draws a wall when the Levels control is displayed. It has no affect 

on the calculations. 

4. Description: Text that describes this building. 

Figure A-3 Screenshot of General control. 
A-4 A: Guide to Weak-Story Tool FEMA P-807 

A.7 CAD Interface 

The calculations in the Guidelines require a detailed accounting of the 

locations of the various walls in plan. To accomplish this effectively, the 

Weak-Story Tool relies on a CAD (computer-aided drafting) interface as the 

means by which the user will layout the walls. 

A.7.1 Analytical Entities 

There are two analytical entities that the user can draw in the CAD interface 

in the Weak-Story Tool: shearwalls and diaphragms. Once the user draws 

these entities, they are part of the analytical model and will be included in the 

calculations once their input is valid. One may draw a shear wall or 

diaphragm when the Levels control is displayed (but not in the General

control) by clicking the appropriate button: 

1. : Draw shape of diaphragm; only available when Levels control is 

displayed and active level is an upper (not first) level. 

2. : Draw new shear wall; only available when Levels control is 

displayed. 

A.7.2 Non-Analytical Entities 

The CAD interface in the Weak-Story Tool also has a library of drafting 

entities that will help the user layout the walls and diaphragms but will not 

interact with the analysis. The user can create these entities by pressing the 

appropriate button in the tool strip to the right of the black drafting area. 

Referring to Figure A-3, the following is a list of commands available from 

top to bottom: 

1. : Draw point. 

2. : Draw line. Lines may be drawn to define gridlines for laying out the 

walls in the Levels control (see Figure A-4) 

3. : Draw circle. 

4. : Draw polyline (i.e., a line with multiple segments). 

5. : Draw closed shape. 

6. : Set text styles. 

7. : Insert text. 

8. : Edit text. 

9. : Draw leader 

10. : Draw leader with text attached. 
FEMA P-807 A: Guide to Weak-Story Tool A-5 

11. : Draw angular measurement. 

12. : Draw linear measurement. 

13. : Define block made of a group of entities. 

14. : Insert a block. 

15. : Insert an image. If a drawing exists, it may be scanned and inserted 

into the document as a background image for tracing the walls and 

diaphragms in the Levels control. After the image is inserted, it must be 

scaled and rotated so that distances in the image agree with measured 

distances from the reconnaissance (survey). 

16. : Edit layers. Drawing entities are drawn on layers. These layers may 

be manipulated in several ways. The line-type, thickness, and color may 

be changed. They may be hidden or locked against editing. 

17. : Move entities. 

18. : Copy entities. 

19. : Rotate entities 

20. : Mirror entities. 

21. : Scale entities. 

22. : Stretch entities. 

23. : Create a linear array of selected entities. 

24. : Offset line, circle or polyline entities. 

25. : Cut entities to clipboard. 

26. : Copy entities to clipboard. 

27. : Paste entities from clipboard. 

28. : Delete selected entities. 

29. : Undo. 

30. : Redo. 

31. : Zoom. 

32. : Set print area. 
A-6 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-4 Reference geometrical input for sample building. 

A.7.3 Other CAD Tools 

The CAD interface is equipped with “snapping” tools that can be toggled 

with the F3 key. The user can also access a particular snapping option by 

clicking Shift and Right-Click when the interface is awaiting a point as input. 

For example, snapping allows the user to draw a line whose endpoint is 

locked to the endpoint of another line. Other snapping options are available 

as illustrated in Figure A-5. 
FEMA P-807 A: Guide to Weak-Story Tool A-7 

Figure A-5 Screen-shot of object snap menu. 

The CAD interface also allows the user to draw lines constrained to a set of 

specified angles (e.g., 0 deg. or 90 deg.). This may be toggled with the F8

key, and the angle interval may be set by clicking Shift and Right-Click when 

the interface is awaiting a point as input as shown near the bottom of the 

menu in Figure A-5. 

Entities, including shear walls and diaphragms may be copied to and pasted 

from the clipboard. Type Control-C to copy entities to the clipboard and 

Control-V to paste from the clipboard. Entities may be copied from one level 

and pasted to another. 

A.8 Defining Sheathing Assemblies 

In the Assemblies control, the user may define assemblies that will be 

assigned to wall (or frame) elements in the Levels control. There are fifteen 

(15) pre-defined sheathing layer types including both finish and wood 

structural panel types. The list of available layer types appears on the top left 

(see Figure A-6). The load-drift curves for the default sheathing layer types 

are read-only. 
A-8 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-6 Screenshot of Assemblies control. 

On the top right is the table of sheathing assemblies. The user may create a 

new assembly by clicking the New Assembly button (Figures A-6 and A-7). 

The user must specify an assembly type. There are four types available: 

1. As-Built: This assembly is part of the original structure. It comprises 

layers from the list of sheathing layers. 

2. Retrofit using standard layers: This assembly is part of the retrofitted 

structure. It comprises layers from the list of sheathing layers. 

3. Retrofit with custom backbone and forces per unit length: This assembly 

is part of the retrofitted structure. The load-drift curve must be entered by 
FEMA P-807 A: Guide to Weak-Story Tool A-9 

the user, and the loads are expected to be unit loads (i.e. pounds per foot 

of wall). 

4. Retrofit with custom backbone and absolute forces: This assembly is part 

of the retrofitted structure. The load-drift curve must be entered by the 

user, and the loads are expected to be absolute loads (i.e., kips). This is 

the option that should be used to model a moment frame. 

For assembly types 1 through 3, the load-drift curve for a given wall will 

depend upon its length. The unit load-drift curve will be multiplied by the 

length of the wall and factored to account for overturning and perforations to 

find the load-drift curve for the wall. 

For assembly type 4, the load-drift curve for a given element (not wall in this 

case) will be independent of the length of the element. There will be no 

factors applied. 

Figure A-7 Screenshot of table of sheathing assemblies in Assemblies control. 

If assembly type 1 or 2 is selected, the user must input the assembly 

specification in the Assembly column. This specification is a formatted string 

in which multiple layer names are joined by plus (+) signs to form the 

assembly. Multiple layers of the same type may be specified using a number 

inside parentheses next to the layer name. For example, the string, L01+L02, 

indicates an assembly of one layer of L01 (Stucco) and one layer of L02

(Horizontal wood sheathing). The string, (2)L06+L08, indicates two layers of 

L06 (Gypsum wallboard) and one layer of L08 (Wood structural panel with 

8d nails @ 6” on center). 

As an alternate to entering the assembly string directly, if the user clicks the 

 (ellipsis) button at the right end of the cell, a form will come up that 

enables a more convenient method of building the assembly string (Figure A8). In the form, the user may add a layer to the assembly by either doubleclicking a layer or by clicking the plus (+) button after selecting a layer. 

When wood structural panels exist with finish materials in a wall assembly, 

the Weak-Story Tool automatically uses the combination rules described in 

Section 4.5. (The combined capacity is the weaker strength from either 50% 
A-10 A: Guide to Weak-Story Tool FEMA P-807 

of the structural wood panel layers and 100% of the finish materials, or 100% 

of the structural wood panel layers and 50% of the finish materials.) 

Figure A-8 Screenshot of form for defining assembly specifications for 

assemblies comprising standard sheathing layers. 

If assembly type 3 or 4 is selected, the user must click the (ellipsis) 

button at the right end of the cell to define the custom load-drift curve 

(Figure A-9). In this form, the user simply enters forces (or unit forces as 

applicable) for certain given drift ratios. After clicking OK, the load-drift will 

be saved to the assembly. 
FEMA P-807 A: Guide to Weak-Story Tool A-11 

Figure A-9 Screenshot of form for defining custom load-drift curves for retrofit assemblies. 

The Status column of the assembly table indicates whether an assembly 

definition is valid. It will have OK if the assembly is valid; otherwise, a 

message will appear indicating what is wrong. The analysis will not be 

performed while there are any invalid assemblies. 

A.9 Assigning Level Properties and Laying Out Walls 

In the Levels control, the user may draw walls, define diaphragms, and assign 

properties to each level including unit weight and story height. The combo 

box at the top of the control indicates which level is currently active; the First 

story is active in the screenshot in Figure A-10. The user may specify the 

number of levels in the General control. The user may activate another level 

by selecting it from the list or by clicking the (cycle) button. 
A-12 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-10 Screenshot of the Shearwall Layout tab in the Levels control for an example building. The first 

story is active. 

A.9.1 The Shearwall Layout Tab 

When the Shearwall Layout tab is selected, a set of options and controls 

appear in the control box on the top left of the drafting area. The user may 

toggle an expanded view of the available options by clicking the (toggle 

expand) button. The following is the list of options and controls: 

1. Assemblies: Shows the assembly that is currently active. When new shear 

walls are drawn, they will automatically be assigned the active assembly. 

If the user selects a different assembly, the selected walls will be 

assigned the new assembly. Retrofit assemblies will only appear in the 
FEMA P-807 A: Guide to Weak-Story Tool A-13 

list if the active level is the first story and the View Mode is set to After 

Retrofit. 

2. View Mode: Sets the view mode for the drafting area. When View Mode

is set to Before Retrofit, all walls assigned retrofit assemblies will be 

hidden; all other walls will be visible. When View Mode is set to After 

Retrofit, all walls marked Remove wall during retrofit will be hidden; all 

other walls will be visible. 

3. View Backbone Curve (button): Brings up a control showing backbone 

curves for the active level. If no walls are selected, backbone curves for 

all walls will show. If some walls are selected, than the load-drift curves 

of the selected walls will be highlighted. If the Add Curves checkbox is 

checked, the forces of the load-drift curves of the selected walls (or all 

walls if none are selected) will be added and displayed as a separate 

curve. This control is only relevant to the first story. 

4. View Level Properties (button): Brings up a control showing the 

properties of the level: unit weight, story height, and color scheme. Other 

read-only data for level will also be displayed for the user’s interest. 

5. Top Label: specifies the type of label that will appear above each wall. 

6. Bot. Label: specifies the type of label that will appear below each wall. 

7. Perforations/Total length of full-height segments: Specifies the total 

length of full-height segments for each of the selected walls. Clicking on 

the (calculator) button brings up a form (Figure A-11) that helps the 

user calculate the full-height segment length and open area. In this form 

the user adds openings of specified width and length, and after OK is 

clicked, the program computes the full-height segment length and open 

area values and assigns them to the selected walls. 

8. Perforations/Total open area: Specifies the total open area for each of 

the selected walls. 

9. Gravity Load: Allows user to specify the amount of gravity-load 

tributary to the selected walls. The load will be used only if the 

simplified overturning adjustment approach is not selected. If the 

simplified approach is used, the specified number of levels determines 

the overturning adjustment factor, Qot. 
A-14 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-11 Screenshot of the perforation calculator form in the 

Levels/Shearwall Layout control. 

10. Use simplified approach for overturning adjustment: If checked, the 

gravity load on a given wall is ignored and the simplified approach is 

used, given the specified number of levels. The framing direction is 

considered unknown. This option is only relevant to walls with nonretrofit assemblies. 

11. Wall height: Specifies the clear height of the selected walls if the 

Override story height option is checked. By default, walls will acquire 

their height from the level. The Wall height property is used to determine 

the drift ratio adjustment for walls in the first story with a height that is 

different than the maximum wall height. 

12. Hold-down strength: Specifies the hold-down strength at the end of each 

wall. This property is relevant only if the simplified approach for 

overturning adjustment is not selected. Any new retrofit walls must have 

sufficient hold-down strength to yield an overturning adjustment factor, 

Qot, of zero. 

13. Remove wall during retrofit: Determines if wall will remain after retrofit. 

In some cases, the user may wish to add wood structural sheathing to an 

existing wall. This is done by first copying the assembly of the existing 
FEMA P-807 A: Guide to Weak-Story Tool A-15 

wall, assigning it the retrofit type, and adding wood structural sheathing. 

The existing wall must be copied (but not moved). One of the duplicate 

walls must be marked Remove wall during retrofit and the other assigned 

the new retrofit assembly. This control is only relevant to the first story. 

Once a level is made active, any entities, including drafting entities like lines 

or images and analytical entities like shear walls will be added to that level. 

Those entities will only appear when that level is active. This is distinct from 

entities added on the General control. 

The user may draw a new wall by clicking the (draw shearwall) button at 

the top of the CAD tool strip on the right. If the active level is not the first 

story, the user may draw the diaphragm shape by clicking the (draw 

diaphragm) button. 

A.9.2 Shearwall Table 

The shearwall table lists all the walls on the active level with their properties. 

Many shear-wall properties may be edited in the table or graphically in the 

Shearwall Layout tab. 

A.10 Evaluation and Retrofit Summary 

As the user adds assemblies and walls to the model, the Weak-Story Tool is 

constantly checking whether the input is valid. Once the input has been 

validated, the Summary control button near the top of the screen will be 

enabled. If a change is made that causes the input to be invalid, the Summary

control button will be disabled until the input is again made valid. 

The combo box near the top right of the control sets the drift limit probability 

of exceedance considered in the evaluation. The following is a list of the 

three tabs in the Summary control and their relevance: 

1. Evaluation Data: Shows the textual summary of the analysis. 

2. Backbone Curves: Plots of the load-drift curves of the various levels. 

3. Performance Data: Written and graphical summary of predicted 

probabilistic seismic performance. 

A.10.1 Evaluation Data Tab 

In the Evaluation Data tab, the Evaluation Log is displayed (Figure A-12). It 

shows all the values calculated by the Weak-Story Tool that are relevant to 

the evaluation. The log consists of three sections: Torsion Properties, XDirection, and Y-Direction. 
A-16 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-12 Screenshot of the Evaluation Data tab in the Summary control for an example building. 

Under Torsion Properties, the user can find the data required to compute the 

Torsion Coefficient, CT, defined in Chapter 4 of the Guidelines. 

For each orthogonal direction, x and y, the following information is 

presented: 

1. Upper-story data: controlling story (i.e., the upper story with the smallest 

ratio of shear strength to weight above), upper-story shear strength, VU, 

base-normalized upper-story, AU, and minimum of the story-normalized 

strength, CU, of the controlling upper story. 
FEMA P-807 A: Guide to Weak-Story Tool A-17 

2. Table of relevant data before and after retrofit: First-story strength, V1, 

Base shear ratio, C1, strength degradation ratio, CD, weak-story ratio, AW, 

and spectral acceleration capacity evaluated at the specified drift limit 

probability of exceedance for the OSL (onset of strength loss) drift 

criteria. 

3. Retrofit data: If the structure before retrofit meets certain standards 

defined in the Guidelines, the Weak Story Tool will report that no retrofit 

is required. Otherwise, the program will note which standards were not 

met, give the range of the acceptable total (new plus existing) first-story 

strength after retrofit, and report whether the current retrofit is adequate. 

The minimum retrofitted strength is an estimate reported for the user’s 

convenience; the actual goal is to meet one of the following conditions: 

a. Get the spectral acceleration capacity after retrofit below the default 

(embedded) site-specific spectral acceleration demand, SMS, given the 

specified drift limit probability of exceedance, if this is possible 

without exceeding the maximum allowed retrofit strength, or 

b. Strengthen the retrofitted first-story to within ±10% of the maximum 

allowed to increase the spectral capacity as high as possible within 

the constraint of the first-story only retrofit. 

A.10.2 Backbone Curves Tab 

In the Backbone Curves tab, the user has the ability to view backbone curves 

of the various levels. For the first story, the user may compare backbone 

curves before (Figure A-13) and after (Figure A-14) the retrofit. There are 

plotting options to view the forces (y-axis) in terms of force story-normalized 

or base-normalized weak-story ratio. 

A.10.3 Performance Data Tab 

In the Performance Data tab (Figure A-15), the user can review the effect of 

the retrofit in probabilistic terms. There are two drift criteria considered as 

defined in the Guidelines: OSL (onset of strength loss), and OD (onset of 

damage). On the top left, there is a text console summarizing the retrofit 

effect. It is broken into four sections: 

1. Change in Drift Limit Probabilities of Exceedance due to Retrofit: 

Summarizes the change in drift limit probability of exceedance due to the 

retrofit for each set of drift criteria.
A-18 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-13 Screenshot of the Backbone Curves tab in the Summary control for an example building showing 

first-story load-drift curve before retrofit. 

2. Envelope of X- and Y-Direction: Table comparing drift limit probabilities 

of exceedance for each set of drift criteria before and after retrofit.

3. X –Direction: Table comparing values of lognormal standard deviation 

(), mean spectral acceleration capacity, and drift limit probability of 

exceedance for each set of drift criteria before and after retrofit in the xdirection of the building.

4. Y-Direction: Same as to X-Direction table but for the y-direction of the 

building.
FEMA P-807 A: Guide to Weak-Story Tool A-19 

Figure A-14 Screenshot of the Backbone Curves tab in the Summary control for an example building 

showing first-story load-drift curve after retrofit. 

On the bottom of the Performance Data tab are two charts. The left chart is 

for the x-direction of the building; the right is for the y-direction. Each chart 

shows two fragility curves relating drift limit probability of exceedance of 

the specified drift criteria (vertical axis) with spectral acceleration (horizontal 

axis). One curve corresponds to the building before retrofit, the other after 

retrofit. The user may change the drift criteria by selecting the desired option 

in the top right area of the Performance Data tab. 
A-20 A: Guide to Weak-Story Tool FEMA P-807 

Figure A-15 Screenshot of the Performance Data tab in the Summary control for an example building. 

The user may toggle the flow of the performance evaluation between 

Upward from SMS (Figure A-16) and Right from drift limit probability of 

exceedance (Figure A-17). In the first flow, the evaluation starts along the 

horizontal axis at the SMS spectral acceleration demand. A vertical line going 

up from there will intersect each fragility curve at two different drift limit 

probabilities of exceedance. The distance between these two intersections 

represents the change in drift limit probability of exceedance due to the 

retrofit. In the second flow (Figure A-17), the evaluation starts along the 

vertical axis at the specified drift limit probability of exceedance. A 

horizontal line going to the right from there will intersect each fragility curve 

at two different spectral accelerations. The distance between these two 

intersections represents the change in spectral acceleration capacity due to 

the retrofit. 
FEMA P-807 A: Guide to Weak-Story Tool A-21 

Figure A-16 Illustration of evaluation flow Upward from SMS. 

Figure A-17 Illustration of evaluation flow Right from drift limit probability of exceedance. 

FEMA P-807 B: Model Provisions for Mitigation Programs B-1 

Appendix B 

Model Provisions for Mitigation 

Programs 

This appendix extends ideas introduced in Guidelines Section 1.4 regarding 

targeted mitigation programs—mandatory programs or incentive-based 

voluntary programs. In these programs, the work must meet a defined 

standard (unlike purely voluntary work), but that standard may be different 

from the one implied by building codes. 

Despite differences from the building code, targeted mitigation programs still 

typically rely on provisions written in “code language” to ensure consistency 

and enforceability. This appendix presents the Guidelines evaluation and 

retrofit methodology in code language suitable for adoption through a local 

ordinance. 

B.1 Targeted Mitigation Programs 

As discussed in Section 1.4, seismic mitigation can generally be categorized 

as voluntary, mandatory, or triggered. Purely voluntary mitigation, by 

definition, need not satisfy any legislative, code, or regulatory requirements 

in terms of how, or how much, it improves earthquake performance. 

Triggered mitigation occurs only when some other intended project—a 

repair, a major alteration, or a change of occupancy, for example—requires it 

as a condition of code compliance. For an individual building, voluntary or 

triggered mitigation can be extremely effective and valuable. From the 

perspective of a jurisdiction thinking about a citywide building stock, 

however, voluntary and triggered work is comparatively piecemeal and 

unpredictable. It is very hard to know in advance how much earthquake risk 

will be reduced citywide by purely voluntary or triggered mitigation. 

By comparison, targeted mitigation—through a legislated program involving 

mandates and/or incentives—is generally more predictable and effective at a 

city scale. Targeted mitigation programs have other advantages as well: 

 They can be developed and coordinated as part of a larger earthquake 

risk reduction plan, for example, one that considers the vulnerability of 

different economic sectors, demographic groups, building uses, and 

geotechnical hazards. 
B-2 B: Model Provisions for Mitigation Programs FEMA P-807 

 They can be phased as needed to match the resources of the affected 

owners and tenants, as well as the regulators charged with their 

implementation. 

 They can be customized technically, with performance objectives 

different from those of the building code—specifically, with objectives 

linked to a city’s loss or recovery goals. 

The Guidelines, while suitable for voluntary use and adaptable to building 

code contexts, were developed especially to facilitate targeted programs. 

The following subsections discuss how the Guidelines might be used within a 

typical mandatory mitigation program administered by a local government. 

Not discussed are several preliminary or developmental phases, including 

raising public awareness, building political consensus, securing bond 

funding, and vetting legal issues. While important, even critical, these are 

outside the scope of the Guidelines. 

B.1.1 Planning and Program Development 

This initial phase should include an inventory effort, some initial loss or 

performance estimation based on that inventory, and some tentative goal 

setting. The overall purpose is to understand how the contemplated 

mitigation program for wood-frame multi-unit residential buildings would 

relate to broader jurisdiction goals regarding, for example, emergency 

management, housing recovery, or public safety. 

The initial inventory and loss estimation are important because the 

Guidelines recognize that certain buildings (those with especially weak upper 

stories) have only limited room for improvement with first-story-only 

retrofits. Understanding how many of these buildings a city has relative to its 

overall stock, and how little or how much they might be improved, will 

inform decisions about performance objectives. Case studies using 

Guidelines Chapters 3 through 7 can advance this understanding. 

The setting of program and project objectives, discussed further in Section 

B.2, should ask what performance would be needed from each building in the 

target class (multi-unit wood-frame) to meet the performance goal for the 

class as a whole. It should also consider the broader context of the program 

by asking what performance would be needed from the class to meet the 

goals for a broader sector (e.g., housing, small businesses) or for the 

jurisdiction as a whole. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-3 

B.1.2 Screening 

Typical mandatory retrofit programs define a target class of buildings. The 

current Oakland, California program, for example, requires compliance from 

any building built before 1990 with two or more stories, five or more units, 

and non-residential first-floor occupancy (Oakland Municipal Code, 2010). 

Since it is often impossible to know in advance precisely which owners will 

be mandated to act, a screening phase can be beneficial. A basic screening 

phase merely confirms that compliance notices were sent to the targeted 

buildings and owners. If an owner is supposed to be exempt from the 

program, the screening process should give her/him a quick and inexpensive 

means to show it. 

A more sophisticated screening process can also be used to triage the 

mandated buildings, culling those that would obviously pass or obviously fail 

a rigorous evaluation. In concept, any building that meets the screening 

objective would be deemed to comply with the requirements of the program 

and would be exempted from further work, except as needed to confirm any 

assumptions made by the screening. Buildings that failed the screening 

would move into the next phases of the program. 

Ideally, a predictive screening tool would be based on attributes that are easy 

to confirm, perhaps even without the need for professional consultants. 

Unfortunately, such a tool does not yet exist, and the simplified evaluation 

method in Guidelines Chapter 3 suggests that any reliable evaluation, even 

just for triage purposes, must consider actual building conditions in 

engineering terms (as opposed to simple measures of floor area or wall 

length). Nevertheless, Guidelines Chapter 3, which is intended to 

approximate a full evaluation with less effort and less cost, might be useful in 

a screening phase. 

B.1.3 Evaluation 

The evaluation and retrofit phases are the guts of a mitigation program. A 

separate evaluation phase, while not strictly necessary, offers several 

benefits. It simplifies the initial tasks for the mandated owner, allowing 

her/him to engage an engineer for a small and relatively certain scope. It 

provides an intermediate review step for the code official. It allows a 

jurisdiction to start the mitigation process without having all the logistics of 

the retrofit phase in place. Most important, it allows room to revise the 

retrofit scope or criteria based on analysis of the evaluation findings. 

Instead of requiring a pass/fail evaluation to a pre-set drift limit probability 

of exceedance (POE), a phased mitigation program using the Guidelines
B-4 B: Model Provisions for Mitigation Programs FEMA P-807 

could require each owner to report the building’s actual drift limit POE using 

concepts in Section 5.4.2. From the reported results, a jurisdiction could 

better estimate the benefits and costs of mandated retrofits, or could adjust 

the retrofit criteria to suit broad program objectives. 

While the Guidelines provide clear evaluation criteria, they only apply to 

eligible buildings (see Section 2.6). A mitigation program should provide 

suitable alternatives that would apply to any mandated building. Even where 

the Guidelines are adopted, ASCE/SEI 31, Seismic Evaluation of Existing 

Buildings, ASCE/SEI 41, Seismic Rehabilitation of Existing Buildings, and 

International Existing Building Code (IEBC) Chapter A4 remain available as 

more general criteria, assuming they support the program’s objective. 

However, as discussed in Guidelines Sections 6.2.3 and 6.4.2, Chapter A4 

can lead to over-strengthening of the first story without due regard for 

potential damage in upper stories. Therefore, while Chapter A4 might be 

suitable for some Guidelines-ineligible buildings, it is not recommended for 

buildings with very weak upper stories. 

As in the screening phase, any building that meets the evaluation objective 

would be deemed to comply with the requirements of the program and would 

be exempted from further work, except as needed to confirm any 

assumptions made by the evaluation. Buildings that failed the evaluation 

would move into the next phases of the program. 

Alternatively, owners might be given the option of moving straight to 

retrofit, bypassing any requirements to file a detailed evaluation of existing 

conditions. In the recent Berkeley, California program, this approach resulted 

in a significant number of retrofits even when no retrofit mandate was in 

place (Rabinovici, 2012). 

B.1.4 Retrofit Prioritization 

This optional phase offers an opportunity to adjust the program based on the 

findings of the evaluation phase. Conceivably, the retrofit mandate could be 

scheduled, funded, or otherwise fine-tuned based on the newly available 

information. Even the retrofit objective could be changed if evaluations 

reveal a much greater or smaller risk than anticipated. 

A separate prioritization phase represents a more deliberate (and probably 

longer duration) program in which the criteria and logistics of the retrofit 

phase might not be well-defined at the outset. If such a prioritization phase is 

not used, the evaluation and retrofit phases can still be separate, or they can 

be combined to any degree as might be convenient to the jurisdiction and the 

mandated owners. For example, some buildings might move straight to a 
FEMA P-807 B: Model Provisions for Mitigation Programs B-5 

retrofit mandate based on screening alone, or owners might be excused from 

the evaluation if they commit to perform a retrofit. 

B.1.5 Retrofit 

The final phase of the program involves the retrofit work itself, using 

Guidelines Chapter 6 (or appropriate alternative provisions for Guidelinesineligible buildings). If not done during the prioritization phase, the retrofit 

phase also involves confirming the retrofit objective and the maximum 

acceptable drift limit POE for optimized retrofits. 

B.2 Program Performance Objectives 

As described in Sections 1.4.1 and 2.3.2, the Guidelines require the selection 

of three parameters to define a performance objective—hazard level, 

performance level, and desired drift limit probability of exceedance (POE). 

In addition, the Guidelines support waiving the defined objective in some 

cases, in the interest of balancing the benefits and costs of a first-story-only 

retrofit. 

As applied in the Guidelines, however, this combination of parameters, 

waivers, and limits constitutes primarily the objective for an individual 

building. Whether established by a jurisdiction as part of a targeted program, 

or selected by an owner for a single voluntary project, the objective does not 

directly address the likely performance of the targeted class or of the building 

stock as a whole. Similarly, a recovery objective for a city does not always 

translate directly to a performance objective for individual retrofits. To relate 

program objectives to project objectives, one needs to consider how the 

targeted class of buildings relates to the housing (or building) stock as a 

whole and how the distribution of the targeted class relates to the sources of 

seismic risk (primarily by fault distance). 

To be sure, as noted in Guidelines Section 1.4.1, a jurisdiction that knows it 

has a significant number of obviously deficient buildings can probably 

achieve a measurable improvement with almost any program objective, even 

if that objective is not derived from a broader mitigation policy. For example, 

consider a program that mandates first-story retrofit of all three-story or taller 

wood-frame residential buildings to the following objective: 

No more than a 20 percent probability of exceeding the 

onset of strength-loss drift levels in a Maximum Considered 

Earthquake (MCE), with the exception that any optimized 

first-story-only retrofit will be deemed to comply as long as 

it does not have a drift limit POE greater than 50 percent. 
B-6 B: Model Provisions for Mitigation Programs FEMA P-807 

If a thousand buildings are retrofitted to that objective, there is no question 

that some measure of earthquake risk will have been reduced both for 

individual buildings and for the jurisdiction as a whole. However, the 

following questions, among others, remain: 

 Of the thousand buildings, how many ended up at the desired drift limit 

POE of 20 percent or less, and how many qualified for the exception and 

ended with a POE between 20 percent and 50 percent? How many 

residential units ended up in each group? 

 In most areas, the MCE is an aggregation of possible events from a 

number of different fault sources. Of the thousand retrofitted buildings 

and their residential units, what percentage is expected to see drifts 

exceeding the stated limits in an MCE event from source A west of the 

city? What is the percentage if the event is from source B east of the 

city? 

 Given a scenario event, if it can be projected that 70 percent of the 

thousand retrofitted buildings will experience drifts under the stated 

limits, how would that affect the performance of the citywide housing 

stock, which includes 50,000 buildings not covered by the program? 

If the jurisdiction has loss or recovery goals that look beyond one class of 

structures, it should perhaps be asking questions such as these when 

designing its mitigation programs. For example, a jurisdiction goal might be 

to preserve low-income housing, or to limit the need for emergency shelters. 

Meeting these goals will depend in part on the performance of wood-frame 

multi-unit buildings. But it will also depend on other structure types, and the 

programs needed to meet such goals will likely vary from city to city. 

A jurisdiction with a high proportion of wood-frame multi-unit housing will 

need most of those individual buildings to perform well in order to meet any 

overall goal for its housing stock. A jurisdiction with only a small percentage 

of its units in this building type can perhaps set a less aggressive objective 

and still meet its overall goal, assuming other housing types perform well. 

Also, a large target class of similar buildings spread across a city will 

perform better as a group than its worst-performing members, simply 

because ground shaking from any single earthquake varies from place to 

place. Therefore, it might sometimes be possible to set only a moderately 

aggressive performance objective for each building and still achieve 

acceptable performance from the class as a whole. 

To summarize, a performance objective, as applied in the Guidelines, is 

always for an individual building. A mitigation program, by contrast, seeks 
FEMA P-807 B: Model Provisions for Mitigation Programs B-7 

to achieve certain benefits for the jurisdiction as a whole. Therefore, when 

selecting a performance objective to be mandated by a program, the right 

objective is the one that achieves the overall quantitative program goals when 

applied to each individual building. 

B.3 Model Provisions and Commentary 

Most mitigation programs, even if they are enacted by legislation and not 

through the building code, rely on regulations written in code-like language. 

These will differ in style and content from the text of the Guidelines. This 

section provides regulatory language intended to help a jurisdiction implement 

the Guidelines’ ideas and recommendations. Where regulatory language is 

adopted, the Guidelines document remains a useful reference and commentary. 

As discussed in Guidelines Section 1.4.1, implementation of the Guidelines

requires selection of several parameters related to performance objectives: 

 Hazard level. The model language below leaves this as a variable to be 

selected. 

 Performance level. The model language below assumes the “onset of 

strength loss” level, which is also assumed by the equations in 

Guidelines Chapters 5 and 6. If the “onset of damage” level is preferred, 

certain provisions (including text in Section 1 below and equations in 

Section 6 and 7 below) will need to be adjusted in accordance with 

Guidelines Chapter 7. 

 Desired drift limit probability of exceedance (POE). The model language 

below leaves this as a variable to be selected. 

 Maximum acceptable drift limit POE for optimized retrofits. The model 

language below leaves this as a variable to be selected. 

Note that the two drift limit POE values may be kept the same through all 

phases of the mitigation program or may be strategically varied by phase. For 

example, the drift limit POE for evaluation could be set high (lenient) so as 

to catch only the worst buildings, while the drift limit POE for retrofit would 

be set lower (more strict) to ensure a significant improvement. Or, if the 

jurisdiction is prepared to allow optimized first-story retrofits to a maximum 

drift limit POE of, say 40 percent, it could set the drift limit POE for 

evaluation to match, but set the desired drift limit POE for retrofit at a lower, 

stricter level. (Similarly, though not reflected in the model language below, 

the drift limit POE for screening or triage using Guidelines Chapter 3 could 

be set at a high value to screen out all but the worst buildings or to 

compensate for conservatism inherent in the simplified evaluation rules.) 
B-8 B: Model Provisions for Mitigation Programs FEMA P-807 

Following, in code language and format, are proposed model provisions for 

implementing the basic provisions of the Guidelines. In some instances, the 

notation and terminology differ slightly from those in the Guidelines. The 

model provisions present the concepts and methods of Guidelines Chapters 4 

through 6. For clarity and brevity, the simplified evaluation equations of 

Guidelines Chapter 3 are not presented. Simplified evaluation per Guidelines

Chapter 3, which is advantageous in certain circumstances but which yields 

conservative estimates of capacity and drift limit POE, could be accepted by 

a jurisdiction as an alternative to model code Sections 4, 5, and 6 below. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-9 

CHAPTER 1. SEISMIC EVALUATION AND RETROFIT OF WEAKSTORY DEFICIENCIES IN MULTI-UNIT WOOD-FRAME 

RESIDENTIAL BUILDINGS 

SECTION 1. GENERAL 

1.1 Intent. The intent of this chapter is to promote public welfare and safety 

through earthquake risk reduction measures in certain buildings. The 

provisions provide a means for identifying and quantifying weak-story 

conditions that represent an unacceptable risk of collapse. The provisions 

also provide a means for quantifying the strength of retrofit elements 

installed only within the first story. 

C1.1. These model provisions are based on FEMA P-807, 

Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame 

Buildings With Weak First Stories, referred to here as the 

Guidelines. The provisions are technical; they do not 

include administrative provisions that are generally 

necessary to establish reporting requirements (other than 

construction documents), compliance schedules, fees and 

fines, or appeals processes. As discussed in Guidelines 

Appendix B, a mitigation program can be customized in 

terms of its phasing. The provisions support an evaluation 

phase and a retrofit phase but do not specify requirements 

or options for implementing or skipping phases. See also 

Section 1.3. 

1.2 Performance Objective. 

C1.2. This section includes four blanks to be filled in by the 

implementing jurisdiction. See Guidelines Sections 1.4.2 

and Appendix B for discussion of effective performance 

objectives. 

1.2.1 Hazard level. The spectral demand shall be the site-adjusted shortperiod spectral acceleration corresponding to the site-specific ___________ 

hazard level. 

C1.2.1 The implementing jurisdiction should complete or 

edit Section 1.2.1 as needed to describe the selected 

earthquake hazard level. Any hazard level may be specified. 

Possibilities include the Maximum Considered Earthquake 

(MCE), which is the theoretical basis for code-based design 

of new buildings, some fraction of the MCE, such as the 
B-10 B: Model Provisions for Mitigation Programs FEMA P-807 

2/3*MCE value used by various engineering criteria, or 

probabilistically-defined events such as those used by ASCE 

41-13. “Site-adjusted” refers to techniques that account for 

site class or soil profile type, such as building code 

provisions that modify mapped acceleration values. 

1.2.2 Performance level. Acceptable performance shall be based on drifts 

corresponding to the onset of strength loss in the seismic force-resisting 

wood-frame elements. 

C1.2.2. Criteria for “onset of strength loss” are embedded 

in the criteria provided here. See Guidelines Section 1.4 

and Chapter 7 for discussion of alternate performance 

levels. 

1.2.3 Desired drift limit probability of exceedance. The drift limit POE for 

evaluation shall be ____ percent. The drift limit POE for retrofit design shall 

be ____ percent. 

1.2.4 Acceptable drift limit probability of exceedance for optimized 

retrofit. The maximum acceptable probability of exceedance for optimized 

first-story retrofit designs shall be ____ percent. 

C1.2.4. See Guidelines Section 6.2.2 for additional 

discussion. 

1.3 Required scope of work. Compliance with the provisions of this 

chapter requires either:

1. Demonstration of an acceptable existing condition per Section 6, 

including correction of all aspects of eligibility or building survey 

non-compliance. 

2. Design and execution of a retrofit in accordance with Sections 7 and 

8 and with other applicable codes and regulations, including 

correction of all aspects of eligibility or building survey noncompliance. 

C1.3. Guidelines Appendix B discusses options for a phased 

mitigation program. These model provisions support an 

evaluation phase and a retrofit phase. (They do not support 

a screening phase per se, though one could be implemented 

by appropriate selection of the evaluation drift limit POE.) 

Programs that would give options to skip certain phases 

might need additional administrative provisions. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-11 

1.4 Limitations. These evaluation and retrofit provisions are related to the 

onset of strength loss in wood-frame elements of the seismic force-resisting 

system, a condition that indicates a substantially increased potential for 

structural collapse. As such, they might not be adequate for predicting the 

likelihood of other damage states. The retrofit provisions are premised on 

the assumption that work will be constrained to the first story and the 

second-floor diaphragm. As such, they do not necessarily provide a 

comprehensive retrofit to a stated performance objective. When followed, 

the retrofit provisions will improve performance, but they will not 

necessarily prevent damage or mitigate failure modes other than those 

related to weak-story conditions and associated torsion. 

1.5 Coordination with other codes and standards. Compliance with these 

provisions does not necessarily satisfy the requirements of International 

Building Code Chapter 34 or the International Existing Building Code as 

they apply to certain additions, alterations, repairs, or changes of occupancy. 

Compliance with these provisions does not necessarily meet any 

performance level of ASCE/SEI 31-03, or any retrofit objective of 

ASCE/SEI 41-06, or ASCE/SEI 41-13 (in preparation). 

SECTION 2. DEFINITIONS 

2.1 Terminology. Terms used in these provisions shall have the meanings 

provided in this section. Terms not defined in this section shall have the 

meanings provided in the building code. 

C2.1. In some instances, the notation and terminology differ 

slightly from those in the Guidelines. 

CENTER OF STRENGTH. At each story, the location in plan that 

represents the weighted average location of the load in all wall lines, at the 

drift associated with the story strength. 

DRIFT. For a given story, the calculated or postulated lateral deflection 

within that story divided by the story height, normally expressed as a 

percentage. 

FIRST STORY. The story of interest with respect to weak-story evaluation 

or retrofit, spanning vertically between the first floor and the second floor. 

LOAD-DRIFT CURVE. For a wall assembly, wall line, or story, the 

relationship characterizing the variation of shear resistance versus drift, for 

the full range of relevant drifts. For a wall assembly, the load value is given 

in units of force per unit length. For wall lines and stories, the load value is 

given in units of force. 
B-12 B: Model Provisions for Mitigation Programs FEMA P-807 

LOAD-ROTATION CURVE. For a story, the relationship characterizing 

the variation of torsional resistance versus story rotation, for the full range 

of relevant rotations, given in units of torque as a function of rotation angle. 

PROBABILITY OF EXCEEDANCE (POE). The desired or calculated 

probability that the structure will respond beyond the drift limits 

representing the desired performance level, in at least one direction, when 

subjected to a specified hazard level. 

QUALIFYING WALL LINE. For purposes of checking eligibility of floor 

or roof diaphragms, a wall line that contributes to the peak story strength at 

least one third as much strength as the strongest parallel wall line in the 

same story and has an adequate load path to the diaphragms it affects. 

C2.1, continued. See Guidelines Section 2.6.4 for 

discussion of rules for “qualifying” wall lines. The “one 

third” criterion is subject to judgment. 

SPECTRAL CAPACITY. For a given drift limit probability of 

exceedance, the highest level of spectral acceleration a structure can sustain 

without responding beyond the drift limits representing the desired 

performance level, given as a multiple of the acceleration of gravity, and 

calculated separately in each principal direction. 

SPECTRAL DEMAND. The site-adjusted short-period spectral 

acceleration corresponding to the specified earthquake hazard level, given 

as a multiple of the acceleration of gravity. 

STORY STRENGTH. The maximum load value from the story load-drift 

curve, calculated separately in each principal direction. 

STORY STRENGTH, BASE-NORMALIZED. The story strength 

divided by the total seismic weight of the building. 

STORY STRENGTH, STORY-NORMALIZED. The story strength 

divided by the sum of the tributary floor weights of all the floors above the 

story in question. 

STORY TORSIONAL STRENGTH. The maximum torsional resistance 

value from the story load-rotation curve. 

STRENGTH DEGRADATION RATIO. In each direction, a value 

between 0.0 and 1.0 calculated as the first-story strength divided by the load 

corresponding to a drift of 3 percent from the first-story load-drift curve. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-13 

TORSION COEFFICIENT. A value that need not be taken greater than 

1.4, calculated as the first-story torsional demand divided by the first-story 

torsional strength. 

TORSIONAL ECCENTRICITY. The absolute value of the plan distance, 

in x and y components, between the second-story center of strength and the 

first-story center of strength. 

TRIBUTARY FLOOR WEIGHT. The total seismically active weight 

tributary to a single floor level comprising dead load and applicable live 

load, snow weight, and other loads as required by the building code. 

UPPER STORY. Any story above the first story. 

WALL ASSEMBLY. A unique combination of sheathing materials over 

wood-stud framing. 

WALL LINE. A collection of full-height and partial-height wall segments 

or frames within a single story that satisfies the rules in Section 5.1.2 and 

which is assumed to contribute strength only in the direction parallel to its 

length. 

WALL SEGMENT. A portion of wood-frame wall made from a single 

wall assembly. For purposes of this definition, any sheathed run of woodstud framing that could contribute to a story’s lateral strength or stiffness 

shall be considered a potential wall segment, whether or not the framing and 

sheathing were intentionally designed, detailed, sized, or located to 

contribute that strength or stiffness. 

2.2 Notation. 

C2.2. In some instances, the notation and terminology differ 

slightly from those in the Guidelines.

AU The base-normalized upper-story strength, calculated separately for 

each direction. 

AW The weak-story ratio, calculated separately for each direction. 

CD The strength degradation ratio, calculated separately for each 

direction. 

CT The torsion coefficient. 

CU The minimum of the story-normalized story strengths of any of the 

upper stories, calculated separately for each direction. 
B-14 B: Model Provisions for Mitigation Programs FEMA P-807 

COSi The plan location, in x and y coordinates, of the center of strength of 

story i. 

ex, ey The x and y components, respectively, of the torsional eccentricity. 

fw The load-drift curve for wall line w. 

Fi The load-drift curve for story i, calculated separately for each 

direction. 

hw The floor-to-ceiling height of wall line w. 

H1 The floor-to-ceiling height of the tallest first-story wall line, 

determined separately in each direction. 

i A subscript index indicating floor or story. Story i is between floor i

and floor i+1. 

Lw The length of wall line w, taken as the longest possible length of 

wall that satisfies the rules in Section 5.1.2, including the length of 

any openings within it. 

Lx The overall building dimension in the x direction. 

Ly The overall building dimension in the y direction. 

POE Probability of Exceedance, as used extensively in the phrase, “drift 

limit POE” (i.e., drift limit Probability of Exceedance) 

Qopen The adjustment factor for openings in a wall line. 

Qot The adjustment factor for overturning of a wall line. 

Qs The story height factor for the first story, calculated separately for 

each principal direction. 

Sc The spectral capacity, calculated separately for each direction. 

Sd The spectral demand.

ti The load-rotation curve for story i. 

Ti The story torsional strength of story i. 

V1r The story strength of the retrofitted first story, calculated separately 

for each direction. 

Vi The story strength of story i, calculated separately for each 

direction. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-15 

VU The story strength of the upper story that determines the value of 

CU. 

w A subscript index indicating a single wall line. 

W The total seismic weight of the building, equal to the sum of all the 

tributary floor weights. 

Wi The tributary floor weight of floor i. 

WSP Wood structural panel 

x A subscript index indicating one of two principal directions. 

POE,0 The drift limit probability of exceedance (POE) adjustment factor 

for a CD value of 0.0. 

POE,1 The drift limit probability of exceedance (POE) adjustment factor 

for a CD value of 1.0. 

i In each direction, the drift at which the story strength of story i

occurs. 

1 The first-story torsional demand. 

SECTION 3. ELIGIBILITY 

3.1 General. Buildings that do not comply with the requirements of this 

section are not eligible for the procedures in this chapter. 

Exception: Buildings in which all aspects of non-compliance with the 

requirements of this section will be eliminated through alteration or 

retrofit are eligible for the procedures in this chapter. 

3.1.1 Massing.

1. The building is no taller than four stories above grade at any point 

around its perimeter. 

2. The building’s wood-framed stories are not supported by an abovegrade podium structure. 

3.1.2 Upper stories. 

1. The upper-story seismic force-resisting systems are bearing wall or 

building frame systems of wood-frame walls with shear panels. 

2. The upper-story floor-to-floor heights are between 8 feet and 12 feet 

and are constant within each story. 
B-16 B: Model Provisions for Mitigation Programs FEMA P-807 

3. In each upper story, in each principal direction, the distance from 

the center of strength to the center of mass of the floor below it is no 

more than 25 percent of the corresponding building dimension. 

C3.1.2 The intent of this approximate rule is to ensure that 

no upper story is prone to significant torsion, and that 

inertial forces from upper stories should transfer to the first 

story near the geometric center of the second floor. See 

Guidelines Section 2.6.2. 

4. No upper story or floor above an upper story has a weight 

irregularity as defined by ASCE/SEI 7-05 Table 12.3-2, Type 2. 

5. No upper story has a vertical geometric irregularity as defined by 

ASCE/SEI 7-05 Table 12.3-2, Type 3. 

3.1.3 First story, basement and foundation. 

1. The first-story height may vary, but the maximum first-story height, 

from top of foundation to top of second-floor framing is between 8 

feet and 15 feet. 

2. The first-story seismic force-resisting systems are bearing wall or 

building frame systems of wood-frame walls with shear panels or 

combine such systems with steel moment-resisting frame systems or 

steel buckling-restrained braced frame systems. 

C3.1.3. Ordinary or special concentrically braced frames, 

concrete shear walls, and reinforced masonry shear walls 

are not suitable retrofit elements under the Guidelines. See 

Guidelines Section 6.5. 

3. The first story includes no full-height concrete or masonry walls. 

4. The first-story walls and frames have continuous concrete footings 

or concrete slab-on-grade foundations. If some or all of the first 

floor is raised over a crawl space, the crawl space has concrete stem 

walls to the underside of the first-floor framing. 

C3.1.3, continued. Concrete stem walls are considered to 

provide a base similar to a concrete foundation. Woodframed cripple walls, whether braced or unbraced by 

sheathing of any type, are not adequate to meet this 

provision.. 

5. First-story walls and frames may be partial height over a concrete or 

reinforced masonry retaining wall or foundation stem wall, but any 
FEMA P-807 B: Model Provisions for Mitigation Programs B-17 

partial-height wall or frame is at least four feet tall from top of stem 

wall to underside of second-floor framing. 

6. If the building has a basement, the basement walls and the floor 

diaphragm just above them are capable of transferring seismic 

forces between the foundation and the first story, and the basement 

story is laterally stronger than the first story above it. 

3.1.4 Floor and roof diaphragms. 

C3.1.4. The intent of these approximate rules for 

diaphragms is to ensure that the structure does not develop 

a premature mechanism or failure mode. See Guidelines 

Section 2.6.4 for additional explanation and guidance. 

1. No portion of the second-floor diaphragm between qualifying wall 

lines has an aspect ratio greater than 2:1. 

2. The second-floor diaphragm does not cantilever more than 25 feet 

from a qualifying wall line. 

3. If the second-floor diaphragm cantilevers more than 10 feet from a 

qualifying wall line, diaphragm chords are adequate to develop the 

lesser of the strength of the diaphragm or the diaphragm forces 

associated with the peak strength of the qualifying wall line. 

4. No floor or roof diaphragm has a reentrant corner irregularity in 

which either projecting leg of the diaphragm beyond the reentrant 

corner is longer than 15 percent of the corresponding plan 

dimension of the building, unless each leg of the diaphragm 

satisfies the aspect ratio and cantilever rules of this subsection. 

C3.1.4, continued. This provision differs from the 

irregularity defined in ASCE/SEI 31-03 or as Type 2 in 

ASCE/SEI 7-05 Table 12.3-1 in order to limit diaphragm 

demands. See Guidelines Section 2.6.4. 

5. No floor or roof diaphragm has a vertical offset unless load path 

components are present and adequate to develop the diaphragm 

strength across the offset. 

6. No floor or roof diaphragm has cutouts or openings within it such 

that, along any line across the diaphragm, the sum of the opening 

widths along that line is more than 25 percent of the overall 

diaphragm dimension along that line. 
B-18 B: Model Provisions for Mitigation Programs FEMA P-807 

Exception: Diaphragms shown to have no deficiencies or irregularities that 

would prevent development of the strength of any seismic force-resisting 

wall or frame or would otherwise control the overall seismic response of the 

structure need not satisfy the eligibility requirements in this subsection. 

SECTION 4. BUILDING SURVEY 

4.1 General. Structural components shall be investigated in accordance 

with this section, as needed to confirm eligibility per Section 3 and to 

support structure characterization per Section 5, evaluation per Section 6, 

and retrofit design per Section 7. 

4.2 Building investigation and documentation. The owner shall conduct 

or cause to be conducted an investigation of the existing building. The 

engineer of record shall prepare a written report documenting procedures, 

findings, and relevant conclusions of the investigation. The report shall 

reference calculations or other documents submitted to demonstrate 

compliance with this chapter. The code official is authorized to require 

additional investigation as needed to fulfill the purpose of the report and the 

intent of this chapter. 

With respect to evaluation, the primary purpose of the investigation is to 

identify or confirm the nature of the existing construction as needed to 

justify load drift curves and tributary floor weights. A secondary purpose is 

to provide condition assessment sufficient to rule out deterioration or 

construction defects significant enough to affect earthquake performance of 

the structure as a whole. 

With respect to retrofit design, the primary purpose of the investigation is to 

confirm design assumptions regarding the adequacy of existing seismic load 

path components within the context of the retrofitted structure. With the 

approval of the code official, field verification of assumed conditions may 

be performed during the construction phase. 

4.2.1 Sources of information. The investigation shall be based on a 

combination of non-destructive testing or inspection, destructive testing or 

inspection, and reference to record documents. Where record documents are 

used to reduce the scope of testing or other on-site work, appropriate field 

verification is required. 

4.2.2 Wall framing and sheathing. The investigation shall determine the 

length and location in plan of all wall segments and wall lines in all stories 

as needed to calculate load-drift curves. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-19 

The investigation shall determine the size and location of openings in each 

wall line as needed to calculate adjustment factors for openings and 

adjustment factors for overturning. 

The investigation shall determine all unique frames or wall assemblies in 

the first story and representative wall assemblies in the upper stories. Where 

sheathing includes wood structural panel or where sheathing load-drift data 

is a function of nailing, the investigation shall also determine the nail size 

and edge nail spacing. 

4.2.3 Floor and roof framing and diaphragm. The investigation shall 

determine the construction of floor and roof framing and diaphragm 

sheathing, including the direction of framing and the mechanism of gravity 

load transfer, as needed for calculation of adjustment factors for 

overturning. The second floor shall be investigated. Subject to approval of 

the code official, the roof and upper floors need not be investigated in detail 

where there is evidence that their relevant attributes are similar to those of 

the second floor. 

4.2.4 Load path components. The investigation shall determine the nature 

of the load-path components and connections for transfer of forces between 

the second-floor diaphragm and first-story walls and frames as needed to 

confirm that the wall line will participate in resisting drift. 

C4.2.4. For non-WSP sheathing, the intent is to confirm 

that fastening reasonably conforms to conventional 

construction requirements. For existing WSP shear walls 

with nail spacing closer than six inches, it should be 

confirmed at representative locations that shear wall top 

and bottom connection capacity is reasonably in balance 

with the sheathing capacity. 

The investigation shall determine the presence or absence of hold-down 

hardware at the base of all first-story walls, as well as the adequacy of 

installation of representative types at representative locations. 

The investigation shall confirm that anchor bolts are provided at the base of 

the first-story walls. 

4.2.5 Condition assessment. The investigation shall seek evidence of 

damage, deterioration, or defective construction sufficient to affect 

significantly the performance of the seismic force-resisting system. All 

investigations performed in this regard shall be documented. 
B-20 B: Model Provisions for Mitigation Programs FEMA P-807 

SECTION 5. STRUCTURE CHARACTERIZATION 

5.1 Story strength. 

5.1.1 Wall assemblies. For each wall assembly present, a load-drift curve 

shall be computed by summing contributions from Table 5.1.1 at each drift 

level for each layer of sheathing. With approval of the code official, test 

results specific to the wall assembly or its components may be used in place 

of Table 5.1.1. Sheathing layers or wall assemblies considered to have 

significant damage, deterioration, or construction defects shall have their 

load-drift strength values reduced. 

C5.1.1 See Guidelines Section 4.4 and Appendix F 

regarding the development of Table 5.1.1 and the use of 

alternate test data. 

Table 5.1.1. Load-Drift Curve Data [plf] 

Sheathing Material 1 

Drift, j [%] 

0.5 0.7 1.0 1.5 2.0 2.5 3.0 4.0 5.0 

Stucco 333 320 262 0 -- -- -- -- --

Horizontal wood 

sheathing or wood siding 85 96 110 132 145 157 171 0 --

Diagonal wood sheathing 429 540 686 913 0 -- -- -- --

Plaster on wood lath 440 538 414 391 0 -- -- -- --

Plywood panel siding 354 420 496 549 565 505 449 0 --

Gypsum wallboard 202 213 204 185 172 151 145 107 0

Plaster on gypsum lath 402 347 304 0 -- -- -- -- --

WSP, 8d@6 521 621 732 812 836 745 686 0 --

WSP, 8d@4 513 684 826 943 1,018 1,080 1,112 798 0

WSP, 8d@3 1,072 1,195 1,318 1,482 1,612 1,664 1,686 1,638 0

WSP, 8d@2 1,393 1,553 1,713 1,926 2,096 2,163 2,192 2,130 0

WSP, 10d@6 548 767 946 1,023 1,038 1,055 1,065 843 0

WSP, 10d@4 707 990 1,275 1,420 1,466 1,496 1,496 1,185 0

WSP, 10d@3 940 1,316 1,696 1,889 1,949 1,990 1,990 1,576 0

WSP, 10d@2 1,120 1,568 1,999 2,248 2,405 2,512 2,512 2,231 0

1

 WSP = wood structural panel sheathing 
FEMA P-807 B: Model Provisions for Mitigation Programs B-21 

5.1.1.1 Wall assemblies without wood structural panel sheathing. The 

assembly load drift curve is the sum of the load drift curves for each of the 

sheathing layers. 

5.1.1.1 Wall assemblies with wood structural panel sheathing. The 

assembly load drift curve is whichever of the following two load-drift 

curves has the larger peak strength: 

1. The assembly load-drift curve using 50 percent of the strength of 

the wood structural panel layers and 100 percent of the strength of 

the other sheathing materials. 

2. The assembly load-drift curve using 100 percent of the strength of 

the wood structural panel layers and 50 percent of the strength of 

the other sheathing materials. 

5.1.2 Wall line assignment. Each segment of sheathed wall framing within 

a story shall be assigned to a wall line. Wall lines shall satisfy the following 

rules: 

1. Full-height wall segments separated by window or door openings 

but connected by sheathed segments and continuous framing above 

or below the opening shall be assigned to the same wall line, unless 

other rules require them to be treated separately. 

2. Wall segments assigned to the same wall line shall not be offset outof-plane from adjacent segments by more than four feet. 

3. At bay windows, the wall segments within the common plane shall 

be assigned to the same wall line if they satisfy the other rules, but 

the wall segments within the cantilevered portions of the bay shall 

not be counted toward the wall-line strength. 

4. Wall segments of different heights, including wall segments along a 

stepped foundation, shall be assigned to separate wall lines. 

5. A wall segment of varying height due to a sloped foundation shall 

be assigned to a separate wall line, and its height shall be taken as 

the average height of the segment. 

6. Wall segments of different wall assemblies shall be assigned to 

separate wall lines. 

7. Where hold-downs exist at each end of a wall segment, that 

segment may be considered a separate wall line. 

8. Wall segments less than one foot long shall be treated as openings. 
B-22 B: Model Provisions for Mitigation Programs FEMA P-807 

9. Wall segments between openings with height-to-length ratios 

greater than 8:1 shall be treated as openings. 

10. Steel moment frames shall be assigned to separate wall lines. 

11. Wall segments or frames considered to have significant damage, 

deterioration, or construction defects may be counted toward a wall 

line’s strength but shall have their load-drift strength values 

reduced. 

5.1.3 Wall line load-drift curve. For each wall line, a load-drift curve shall 

be computed by multiplying the applicable wall assembly load-drift curve 

by the wall line’s length and by applicable adjustment factors per Equation 

5.1.3-1. 

fw = (vw)(Lw)(Qopen)(Qot) (Equation 5.1.3-1) 

where: 

fw is the load-drift curve of wall line w, expressed as a function of drift. 

vw is the load-drift curve of the wall assembly associated with wall line w, as 

derived per Section 5.1.1 and adjusted for height variation per Section 

5.1.3.1. 

5.1.3.1 Adjustment for height variation. Where first-story wall lines in a 

given direction are of different heights, the load-drift curve of the wall 

assembly of each wood-frame wall line shall be adjusted to account for 

increased drift demands in all but the tallest first-story wall line. This may 

be done by shifting the assembly load-drift curve from the standard set of 

drifts given in Table 5.1.1 to an adjusted set of drifts for each wall line, 

given by Equation 5.1.3.1-1. 

jh = (j)(hw/H1)

0.7 (Equation 5.1.3.1-1) 

5.1.3.2 Adjustment for openings. Each wall line load-drift curve shall 

account for the effects of openings within it. This may be done by applying 

the adjustment factor for openings, given by Equation 5.1.3.2-1 and 

Equation 5.1.3.2-2. 

Qopen = 0.92a – 0.72a2

 + 0.80a3 (Equation 5.1.3.2-1) 

a  1

1

Ao

hwLf











 (Equation 5.1.3.2-2)
FEMA P-807 B: Model Provisions for Mitigation Programs B-23 

where: 

Ao = sum of the areas of the openings within the wall line 

Lf = sum of the lengths of the full-height wall segments within the wall 

line 

5.1.3.3 Adjustment for overturning. Each wall line load-drift curve shall 

account for the effects of overturning demand and resistance. This may be 

done by applying the adjustment factor for overturning, given by Equation 

5.1.3.3-1 or, for existing upper-story wall lines only, by Table 5.1.3.3. 

Qot  0.4 11.5 Mr

Mot



 1.0 (Equation 5.1.3.3-1) 

where Mot is the overturning demand on the wall line due to the peak 

strengths of wall lines in the stories above, adjusted themselves for openings 

and overturning, and Mr is the resisting moment due to all available dead 

loads tributary to the wall line plus the effects of any tie-down hardware. 

C5.1.3.3. See Guidelines Section 4.5.3.2 for guidance on 

calculating Qot. 

Table 5.1.3.3. Default Adjustment Factor for Overturning, Qot , for Existing 

Upper-story Wall Lines 

Number of Stories Above Perpendicular to 

Framing 

Parallel to 

Framing 

Unknown or 

Mixed 

Two or more 0.95 0.85 0.85 

One 0.85 0.80 0.80 

None (Top story) 0.75 0.75 0.75 

5.1.4 Story load-drift curves. For each story, in each direction, a load-drift 

curve shall be computed by adding the load-drift curves of all the walls in 

that story and aligned in that direction.

C5.1.4. Where all the wall line load-drift curves are 

mapped to the same set of drifts, the summation is 

straightforward. Where some first-story wall lines have 

load-drift curves mapped to a height-adjusted set of drifts, 

load values at the standard drift values should be 

determined by linear interpolation. Once interpolated 

values are calculated, the various load-drift curves can 

again be added in a straightforward way based on the 
B-24 B: Model Provisions for Mitigation Programs FEMA P-807 

standard drift values. See Guidelines Section 4.6 for 

additional discussion. 

5.2 First-story torsion. 

5.2.1 Center of strength. The center of strength for the first and second 

stories shall be determined based on the wall line loads at the drift at which 

the story strength in the corresponding story and direction occurs. 

C5.2.1. Guidelines Section 4.6.4 illustrates the calculation 

of the center of strength. 

5.2.2 First-story torsional demand. The first-story torsional demand 

represents the effect of the first-story strength acting at the torsional 

eccentricity, given by Equation 5.2.2-1. 

1 = exV1y + eyV1x (Equation 5.2.2-1) 

5.2.3 First-story load-rotation curve. For the first story, a load-rotation 

curve shall be derived, relating torsion about the story center of strength to 

the resulting rotation of the story, assuming a rigid second-floor diaphragm 

and accounting for the load-drift behavior of each first-story wall line. The 

load-rotation curve shall consider rotation angles up to at least the rotation 

associated with 5 percent in-plane drift in at least one first-story wall line. 

C5.2.3. Guidelines Section 4.6.6 illustrates the calculation 

of the load-rotation curve, dividing the rotation range of 

interest into ten even increments.

5.3 Characteristic coefficients. 

5.3.1 Base-normalized upper-story strength. The base-normalized upperstory strength shall be calculated for each principal direction per Equation 

5.3.1-1. 

AU  VU

W (Equation 5.3.1-1) 

C5.3.1. In typical regular buildings, the story strengths are 

roughly the same in all the upper stories, and the seismic 

weight is greater toward the lower stories, so VU is usually 

the second-story strength. 

5.3.2 Weak-story ratio. The weak-story ratio shall be calculated for each 

principal direction per Equation 5.3.2-1. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-25 

AW  V1

VU

 (Equation 5.3.2-1) 

C5.3.2. In typical regular buildings, the story strengths are 

roughly the same in all the upper stories, and the seismic 

weight is greater toward the lower stories, so VU is usually 

the second-story strength. 

5.3.3 Strength degradation ratio. The strength degradation ratio, CD, shall 

be calculated for each principal direction based on the first-story load-drift 

curves. 

C5.3.3. Guidelines Section 4.7.4 illustrates the calculation 

of the strength degradation ratio. 

5.3.4 Torsion coefficient. The torsion coefficient, given by Equation 5.3.4-

1, need not be taken greater than 1.4. 

CT  1

T1

 (Equation 5.3.4-1) 

5.3.5 Story height factor. The story height factor shall be calculated for 

each principal direction per Equation 5.3.5-1, where H1 is given in inches. 

Qs = 0.55 + 0.0047 H1 (Equation 5.3.5-1) 

SECTION 6. EVALUATION 

6.1 Evaluation relative to the performance objective. Subject to the 

additional requirements of Section 1.3, any eligible structure shall be 

deemed to comply with the requirements of this Chapter if its spectral 

capacity in each principal direction exceeds the spectral demand. 

6.1.1 Spectral capacity. Spectral capacity in each direction shall be 

calculated from Equations 6.1.1-1 through 6.1.1-5, using drift limit POE

adjustment factors given in Table 6.1.1 for the drift limit POE specified in 

Section 1.2. Drift limit POE adjustment factors for intermediate values of 

drift limit POE shall be calculated by linear interpolation. 

Sc  CD

3

Sc1  1 CD

3  Sc0 (Equation 6.1.1-1) 

Sc1  POE,1S1 (Equation 6.1.1-2) 

Sc0  POE,0S0 (Equation 6.1.1-3) 

S1    0.525  2.24AW 1 0.5CT QsAU

0.48 (Equation 6.1.1-4) 
B-26 B: Model Provisions for Mitigation Programs FEMA P-807 

S0    0.122 1.59AW 1 0.5CT QsAU

0.60 (Equation 6.1.1-5) 

Table 6.1.1. Drift Limit Probability of Exceedance Adjustment Factors. 

POE POE,1 POE,0

2% 0.36 0.29 

5% 0.44 0.37 

10% 0.53 0.46 

20% 0.66 0.60 

50% 1.00 1.00 

60% 1.14 1.16 

70% 1.30 1.37 

80% 1.52 1.66 

6.2 Calculated drift limit POE. Given a spectral demand, the drift limit 

POE of a structure, where required, shall be calculated for each principal 

direction using Equations 6.2-1 and 6.2-2. For intermediate values of CD, 

the value of the drift limit POE shall be estimated by linear interpolation 

between the two calculated values. The drift limit POE shall be calculated 

for each principal direction, and the smaller value shall be taken as the drift 

limit POE value for the structure. 

POE1  84.0 Sd

S

 0.41









 for CD = 1.0

 Equation 6.2-1) 

POE0  75.2 Sd

S

 0.33









 for CD = 0.0

 (Equation 6.2-2) 

where S is calculated by interpolating between the values given by 

Equations 6.1.1-4 and 6.1.1-5 for the actual value of CD. 

C6.2. Equations 6.2-1 and 6.2-2 are linear approximations 

that are valid when they give drift limit POE values 

between about 5 percent and 70 percent. See Guidelines 

Section 5.4.2, Chapter 7, and Appendix F when these 

equations indicate more extreme values of drift limit POE. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-27 

SECTION 7. RETROFIT 

7.1 Retrofit requirements. Where required, retrofit designs shall meet the 

performance requirements of either Section 7.2 or Section 7.3, as well as the 

general compliance requirements of Section 1.3. If the requirements of 

neither Section 7.2 nor Section 7.3 can be met, the building shall be 

considered ineligible to use the provisions of this Chapter. 

7.1.1 Retrofitted first-story strength. The first-story strength of the 

retrofitted structure shall account for all existing unaltered elements, 

existing altered elements, new elements provided to increase story strength, 

and new elements provided in accordance with Section 1.3 to correct 

aspects of eligibility or building survey non-compliance. 

7.2 Retrofit to meet the performance objective. Any eligible retrofitted 

structure shall be deemed to comply with the performance requirements of 

this Chapter if both of the following conditions are true: 

1. The retrofitted structure’s spectral capacity in each principal 

direction exceeds the spectral demand. 

2. The first-story strength of the retrofitted structure in each direction 

satisfies Equation 7.2-1. 

V1r 1.1VU 0.11AU 1.22 (Equation 7.2-1) 

C7.2. Guidelines Section 6.2.1 provides formulas for 

estimating the strength of the retrofitted first story needed 

to reach the required spectral capacity. Guidelines Sections 

6.2.2 and 6.2.3 discuss the derivation and meaning of 

Equation 7.2-1. 

7.3 Alternative retrofit to optimize first-story strength. Any eligible 

retrofitted structure shall be deemed to comply with the performance 

requirements of this Chapter if all of the following conditions are true: 

1. The first-story strength of the retrofitted structure in each direction 

satisfies Equation 7.3-1. 

2. The retrofit design satisfies the requirements of Section 7.3.1. 

3. The retrofit design satisfies the requirements of Section 7.3.2. 

0.9VU   0.11AU 1.22  V1r 1.1VU 0.11AU 1.22 (Equation 7.3-1) 

7.3.1 Maximum acceptable drift limit POE. The drift limit POE of the 

retrofitted structure in each direction, calculated in accordance with Section 
B-28 B: Model Provisions for Mitigation Programs FEMA P-807 

6.2, shall be less than the maximum acceptable drift limit POE stipulated in 

Section 1.2.4. 

C7.3.1. See Guidelines Section 6.4.2 for discussion of the 

maximum acceptable POE for optimized first-story retrofits. 

7.3.2 Minimized torsional eccentricity. Retrofit elements shall be located 

along perimeter wall lines so as to minimize the torsional eccentricity of the 

retrofitted structure, or so as to satisfy equations 7.3.2-1 and 7.3.2-2. This 

requirement may be waived with the approval of the code official to 

accommodate other building or planning code requirements or to avoid 

disproportionate construction costs. 

ex  0.10Lx (Equation 7.3.2-1) 

0.10 y y e L  (Equation 7.3.2-2) 

C7.3.2. Guidelines Section 6.3.1 discusses the need to 

locate retrofit elements so as to minimize torsion. 

7.4 Design criteria for retrofit elements. Retrofit elements shall conform 

to the following requirements. 

C7.4. Consistent with the eligibility rules in Section 3.1.3, 

Ordinary or Special Concentrically Braced Frames, 

concrete shear walls, and reinforced masonry shear walls 

are not suitable retrofit elements under the Guidelines. See 

Guidelines Section 6.5. 

1. Where wood-frame walls or steel frames are sized based on unit 

strengths from codes or standards, the full expected capacity, 

without strength reductions or resistance factors, shall be used. 

2. The load-drift curve of each retrofit element type shall be based on 

expected material properties, including overstrength. The full 

expected capacity, without strength reduction or resistance factors, 

shall be used to calculate load-drift curves and peak strengths. 

3. Each retrofit element shall be such that a load-drift curve based on 

similar elements alone would have a strength degradation ratio, CD, 

greater than or equal to 0.8. 

4. The load-drift curve of each retrofit element type shall be defined 

up to 5-percent interstory drift or as needed to fully characterize the 

retrofit design per Section 5. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-29 

5. Materials and systems for all retrofit elements shall be consistent 

with provisions of the building code for new construction. Detailing 

of retrofit wall and frame elements shall be consistent with that 

applied to special seismic force-resisting systems used in new 

construction for the corresponding occupancy and risk category. 

C7.4, continued. While codes for existing buildings 

typically allow “like materials” for repairs and alterations 

(for example, see 2012 IBC Section 3401.4.2), the 

Guidelines presume that retrofit elements will be reliably 

ductile, so detailing is important. This is consistent with 

code provisions for voluntary seismic upgrade (for 

example, see 2012 IBC Section 3404.5 or 2012 IEBC 

Section 807.6). 

6. Design criteria for load-path components and connections shall be 

appropriate to the performance objective and shall be based on the 

building code for new construction, ASCE/SEI 41-13, or principles 

of capacity design. 

7.4.1 Wood structural panel shear walls. Load-drift curves for wood 

structural panel retrofit elements shall be calculated in accordance with 

Section 5. Existing shear walls modified by replacing sheathing materials or 

by adding supplemental wood structural panels shall be considered retrofit 

elements. 

7.4.2 Steel moment frames. Steel retrofit elements that conform to the 

requirements of AISC 341-05 for Special Moment Frames or AISC 341-10 

for Special Cantilevered Column systems shall be deemed to comply with 

the provision requiring a CD value greater than or equal to 0.8.

C7.4.2. Guidelines Section 6.5.4 offers further guidance on 

characterizing and designing these elements. 

7.4.3 Steel braced frames. Steel retrofit elements that conform to the 

requirements of AISC 341-05 for buckling-restrained braced frames should 

be deemed to comply with the provision requiring a CD value greater than or 

equal to 0.8.

C7.4.3. Guidelines Section 6.5.5 offers further guidance on 

characterizing and designing these elements. 

7.5 Design criteria for load path elements and components. The retrofit 

design shall confirm or provide a load path from the second-floor 

diaphragm through the first-story seismic force-resisting elements and their 
B-30 B: Model Provisions for Mitigation Programs FEMA P-807 

foundations, to the supporting soils. The ultimate strength of load-path 

components shall be reduced with strength reduction factors as needed to 

ensure that the load-path elements are able to develop the strength and the 

intended mechanism of first-story wall and frame elements. Specific design 

criteria may be derived from principles of capacity design, from ASCE/SEI 

41-13, or from building code provisions involving the overstrength factor, 

0. 

7.5.1 Foundations and overturning. New foundation elements shall be 

provided as needed to resist bearing, sliding, and overturning forces 

associated with the retrofit elements acting at their strength. Connections 

and load-path components related to wall or frame overturning shall not 

assume any acting dead load except for the self-weight of the retrofit 

element unless the retrofit element incorporates existing gravity-loadcarrying framing or unless the design and construction explicitly transfer 

existing dead load to the retrofit element. The weight of foundation 

elements may be considered if adequately connected. 

7.5.2 Second-floor diaphragm. The second-floor diaphragm shall be 

strengthened as needed to ensure that expected forces can be transferred 

between the diaphragm and the first-story elements.

SECTION 8. QUALITY ASSURANCE 

8.1 Construction documents. Construction documents shall show all 

information necessary for compliance review and shall accurately reflect the 

results of the engineering investigation and design. The documents shall 

include: 

1. A statement that the retrofit was designed in compliance with this 

Chapter and in compliance with administrative requirements of the 

mitigation program. 

2. A statement of the performance objective stipulated in Section 1.2, 

including the hazard level, the performance level, the desired drift 

limit POE, and, where calculated, the actual drift limit POE. 

3. Where applicable, a statement regarding the compliance of the 

retrofit work with other applicable building or planning codes, 

including structural provisions of the building code for certain 

alteration projects. 

4. Documentation of existing construction, including depictions of the 

second-floor diaphragm and framing, first-story walls and frames 

and their foundations, and any basement or crawlspace conditions. 
FEMA P-807 B: Model Provisions for Mitigation Programs B-31 

5. A foundation plan, including proposed new elements and 

connections to existing elements. 

6. A first-floor retrofit plan, showing the types and locations of shear 

walls or steel frames proposed to be altered or added as retrofit 

elements. 

7. Where applicable, plans and details for strengthening the secondfloor diaphragm. 

8. A retrofit schedule, notes, and details specifying all wood-frame 

materials and their construction, including sheathing type and 

thickness; fastener type and spacing, including edge distance; holddowns and anchor bolts; alteration or supplement of studs, sill 

plates, and other framing; and quality control measures such as 

flush nailing at the wood surface and limits on notching or 

penetrations. 

9. A retrofit schedule, notes, and details specifying all steel materials 

and their construction, including bolts; shop and field welds; base 

plates and anchor bolts; and erection procedures and sequences. 

10. Load path, collector, and other details as needed for construction of 

the intended seismic force-resisting system. 

11. Scope of required field verification, structural observation, testing, 

and inspection. 

12. Other work as required for compliance with applicable requirements 

for work on existing buildings. 

13. Other information as required by the code official. 

8.2 Construction quality assurance. All work shall comply with 

inspection and testing requirements of the building code as they apply to 

existing buildings and structures. 

FEMA P-807 C: Example Calculations C-1 

Appendix C 

 Example Calculations 

This appendix illustrates the application of Guidelines Chapters 3 through 6. 

The topics illustrated are: 

 C.1: Simplified Evaluation (Chapter 3) 

 C.2: Structure Characterization and Evaluation (Chapters 4 and 5) 

 C.3: Retrofit (Chapter 6) 

 C.4: Torsion calculations (Chapters 3 and 4) 

In general, the intention of these examples is to illustrate the Guidelines’ new 

concepts and key points, not to show complete step-by-step calculations. The 

examples presume familiarity with certain provisions of ASCE/SEI 7-05 and 

the 2009 International Building Code (IBC). 

Example Building. All of the examples reference the four-story apartment 

building shown in Figure C-1. The example building is typical of multi-unit 

buildings erected in San Francisco in the 1920s. For these examples, its 

properties are loosely based on Index Building 3 from San Francisco's 

Community Action Plan for Seismic Safety (ATC, 2009b). 

Basic information for the four-story building is given in Table C-1. For 

purposes of these examples, some of the information is simplified relative to 

that of an actual building. Additional details are provided in the examples as 

needed. 

 

Figure C-1 Street elevation of example building. 
C-2 C: Example Calculations FEMA P-807 

Table C-1 Example Building Properties 

Location San Francisco, near Geary and Arguello 

Soil type Site Class D (not near liquefiable soil) 

First floor uses Parking (garage), lobby/entryway, utility, storage 

Upper floor uses Two residential units per floor 

Approximate plan area 2270 square feet, each floor

Overall depth of building 86.5 ft (long or x direction)

Overall width of building 30 ft (short or y direction)

Perimeter wall types Plaster on wood lath, both sides, all stories

Interior wall types Plaster on wood lath, both sides, all stories

Wall clear height 8 ft, all stories 

Floor to floor height 9 ft, all stories 

Diaphragm construction Diagonal 1x sheathing, wood finish floor, plaster and 

wood lath ceiling below (no ceiling above parking area 

at underside of second floor) 

Eligibility (Section 2.6). The example building is presumed to satisfy all of 

the limitations and eligibility requirements in Section 2.6, with the following 

proviso: Guidelines Section 2.6.4 requires an overall second-floor diaphragm 

aspect ratio no greater than 2:1. The building’s overall dimensions (86.5 ft by 

30 ft) do not meet this restriction. However, per Section 2.6, the building 

may be deemed eligible for Guidelines procedures if modified or retrofitted 

to meet the eligibility rules. Therefore, these examples assume that 

qualifying walls will be confirmed or added on lines B, C, D, and/or E (see 

Figure C-2) as needed to allow the second floor to qualify. See Section C.4 

for additional discussion. 

This suggests an evaluation strategy for buildings with irregular or ineligible 

conditions: Skip the evaluation of the existing building, size and locate 

potential retrofit elements as needed to make the structure eligible, and 

evaluate the modified structure instead. While rational, for purposes of 

illustrating the Guidelines’ provisions as written, these examples evaluate the 

existing condition unmodified. 

Performance Objective (Section 2.3.2). Unless noted otherwise, all of the 

examples use the Guidelines’ default performance objective with a 20 

percent drift limit probability of exceedance (POE), as described in 

Guidelines Section 2.3. The objective is stated as: “80 percent confidence of 

not exceeding the drift limits associated with onset of strength loss, in a 

Maximum Considered Earthquake.”
FEMA P-807 C: Example Calculations C-3 

C.1 Simplified Evaluation (Chapter 3) 

Drift Limit POE Adjustment Factor (Section 3.2). The drift limit POE

adjustment factor is taken from Table 3-1 based on the stated performance 

objective. For simplified evaluation, only POE,0 is used. For the 20 percent 

drift limit POE used in these examples, the adjustment factor is 0.60. 

Building Survey (Section 3.3). Guidelines Chapter 3 calls for a detailed 

survey of the first story and a limited survey of the upper stories. The first 

floor plan of the example building is shown in Figure C-2. Since it is 

assumed that no drawings are available, dimensions are based on field 

measurements. 

Figure C-2 Example building first-floor plan. 

Figure C-2 shows all the walls conforming to Guidelines Section 3.3.1—

those that are full height within the story, longer than two feet, not 

excessively narrow, structurally connected, and not deteriorated. As noted in 

Table C-1, all the walls are assumed (for the simplicity of this example) to be 

of the same construction, sheathed with wood lath and plaster on both sides. 

For the upper stories, Section 3.3.2 does not require detailed wall 

measurements or characterization. Survey data are needed only to calculate 

the weight and to estimate the center of strength. From visual observation, 

the many upper-story walls are well distributed and roughly symmetrical in 

both directions, so the center of strength is assumed to be at about the 

geometric center of the second floor. 

Though it does not affect the evaluation, it is worth noting that the upper 

story interior walls generally do not align in plan with the first-story walls. In 

fact, the first story has far fewer walls in the short direction than the upper 
C-4 C: Example Calculations FEMA P-807 

story, already suggesting the presence of a weak story in the short direction. 

(See example C.2 for more details of the upper story walls.) 

Total Building Weight (Section 3.4.1). The simplified evaluation requires 

an estimate of the seismically active weight, W, based on conventional 

assumptions. Appropriate unit weights are not addressed by the Guidelines

and are normally established through convention, experience, and judgment, 

if not stipulated by local regulations. For this building example, the total 

weight tributary to each floor level is shown in Table C-2. 

Table C-2 Example Building Weights 

Level 

Area 

(Sq.ft.)

Long Dir’n 

Wall Length 

(ft) 

Short Dir’n 

Wall Length 

(ft) 

W 

(kips) 

∑W above 

(kips) 

Roof ~227

0 

~280 ~150 below 83 

4th Floor ~227

0 

~280 ~150 122 83 

3rd Floor ~227

0 

~280 ~150 122 205 

2nd Floor ~230

0 

~280 ~150 above, 

~55 below 

111 327 

Total 438 438 

Shear Strength of First-Story Walls (Section 3.4.2). For simplified 

evaluation, the unit strength of each first-story wall assembly is calculated 

(per Equation 3-1) as the sum of the peak strengths of its sheathing layers. 

For this example, only one wall assembly is considered (see Table C-1). 

From Table 3-2, “plaster on wood lath” has a strength of 540 plf. Thus, with 

sheathing on both sides, the unit strength of the wall assembly is: 

va,w = 2 x 540 plf = 1080 plf 

Guidelines Chapter 4 accounts for openings within a wall line. The 

simplified evaluation of Chapter 3, however, considers only the full-height 

wall segments. The total shear strength of each full-height wall segment (per 

Equation 3-2) is simply its length multiplied by its unit strength. (Typically, 

this calculation involves a tabulation of dimensions and unit strengths for 

each wall segment. For this example, however, because only a single wall 

type is used, the calculation is trivial and not shown.) 

Shear Strength of First Story (Section 3.4.3). The first-story strength in 

each direction (per Equation 3-3), is the sum of the strengths of all the wall 

segments in that direction. For this example, because only a single wall type 
FEMA P-807 C: Example Calculations C-5 

is used, the strength may be calculated as the total wall length multiplied by 

the unit strength of 1080 plf: 

V1,x = 280 ft x 1080 plf = 302 k, in the long or x direction. 

V1,y = 55 ft x 1080 plf = 59 k, in the short or y direction. 

Centers of Strength and Torsion (Sections 3.4.4 through 3.4.7). The 

simplified evaluation accounts for potential torsion in the first story. While 

the calculation is not difficult, it does involve some tedious bookkeeping 

(especially where many wall segments and wall assemblies are involved), so 

an initial check ignoring torsional effects is often practical. 

Ignoring torsional effects means assuming the first-story center of strength is 

directly below the upper-story center of strength, so that the eccentricities 

(Equation 3-5) and the simplified torsion coefficient (Equation 3-6) are all 

zero. 

This, of course, is an unconservative assumption, but it offers a useful 

shortcut. If the building fails the simplified evaluation under this assumption, 

then it would certainly have failed the simplified evaluation with non-zero 

torsion. Where this is the case, a full accounting for torsion is moot and need 

not be done. Nevertheless, the Guidelines’ torsion provisions are illustrated 

and discussed in Section C.4 of this appendix. 

Site-specific Spectral Acceleration Demand (Section 3.5.1). The 

performance objective for this example sets the demand as the Maximum 

Considered Earthquake (MCE), defined in ASCE/SEI 7-05. Per Guidelines

Sections 3.5.1 and 5.4.1, the short-period spectral acceleration is used to 

represent demand. For the MCE, the demand is thus given by the ASCE/SEI 

7-05 term SMS. 

Following the provisions of ASCE/SEI 7-05, SMS for the example site and 

soil profile (see Table C-1) is 1.53g. 

Story Height Factor (Section 3.5.2). The story height factor, explained in 

Section 4.7.6, normalizes the first-story strength to that associated with an 8-

ft first story. In this example, the first-story height is 8 ft, or 96 in, so the 

factor calculates (per Equation 3-7) as expected: 

Qs = 0.55 + 0.0047(96) = 1.0 

Simplified Spectral Acceleration Capacity (Section 3.5.3). The simplified 

spectral acceleration capacity is calculated for each direction with Equation 

3-8: 
C-6 C: Example Calculations FEMA P-807 

 

0.6

1,

, ,0 1.47 0.73 x

cs x POE Ts s

V

S CQ W



       

 

Substituting values derived above, 

Scs = (0.60) [1.47 – 0.73 (0, assumed)] (1.0) (V1 / 438 k)0.6 

In the long x direction, V1,x = 302 k, and Scs,x = 0.71g. 

In the short y direction, V1,y = 59 k, and Scs,y = 0.26g. 

Evaluation (Section 3.5.4). The capacity in each direction is less than the 

demand, Sms = 1.53g, so the building fails the simplified evaluation. 

For this example, the building fails the evaluation even with the initial 

unconservative assumption of zero torsion. Had the building passed, the 

evaluation would have to be redone with torsion considered. 

Remarks. Table C-3 compares the building’s capacity as calculated above 

with its capacity as calculated by a full evaluation (Section C.2). The 

calculations in Sections C.1 and C.2 both ignore torsion in order to focus on 

other points. The effects of torsion, calculated and discussed in Section C.4, 

are also shown here. 

Table C-3 Example Building Spectral Capacity Calculated in Various Ways 

Evaluation Method Torsion 

Ignored 

Torsion 

Considered 

Capacity in long x direction 

 Simplified evaluation (Sections C.1, C.4) 0.71g 0.61g 

 Full evaluation (Sections C.2, C.4) 0.80g 0.70g 

Capacity in short y direction 

 Simplified evaluation (Sections C.1, C.4) 0.26g 0.23g 

 Full evaluation (Sections C.2, C.4) 0.24g 0.21g 

Results from a single example building do not reveal a general trend. Still it 

is noteworthy that even in this midblock building, which is not expected to 

have high torsion, the Guidelines’ torsion provisions can significantly reduce 

the calculated capacity. (Also interesting is the finding that for the short 

direction, the simplified evaluation, which is supposed to be more 

conservative, results in a higher capacity than the full evaluation. This is an 

aberration, however, due to the full evaluation counting only full-height wall 

panels, not full wall lines with openings. This simplistic approach 

underestimates the story strength.) 
FEMA P-807 C: Example Calculations C-7 

C.2 Structure Characterization and Evaluation (Chapters 

4 and 5) 

This example illustrates the full evaluation procedure of Guidelines Chapters 

4 and 5, as opposed to the simplified evaluation of Chapter 3. Figure C-3 

shows the same first story wall layout as Figure C-2, with additional 

dimensions. Figure C-4 shows similar information for the typical upper 

stories. In both figures, the dimension strings show cumulative distance from 

the origin (at the top left of the figure); this information will prove useful in 

calculating eccentricities and torsional properties in example C.4. 

Figure C-3 Example building first-story wall lengths and locations. 

Figure C-4 Example building upper-story wall lengths and locations. 
C-8 C: Example Calculations FEMA P-807 

Load-Drift Curves (Section 4.4). Table 4-1 provides load drift curves for a 

variety of sheathing materials over a range of interstory drift ratios. Because 

this example uses only one wall type, the Guidelines rules for combining 

sheathing materials are not needed, and wall strength can be calculated by 

simply multiplying each wall’s length by its peak unit strength. For plaster 

over wood lath, the peak unit strength of 1076 plf (538 plf each side) occurs 

at a drift of 0.7%. 

Note also that for plaster and wood lath, the load-drift curve falls to zero at a 

drift of just 2.0%. 

Translational Story Strength and Characteristic Coefficients (Sections 

4.6 and 4.7). Guidelines Chapter 4 provides a complete set of rules for 

deriving story strengths while accounting for wall openings, overturning, 

variable wall heights, and torsion. The purpose of this example, however, is 

merely to illustrate the characteristic coefficients and the capacity equation. 

Therefore, for simplicity of presentation, adjustments for openings, 

overturning, wall height, and torsion are ignored (though the torsion 

calculations are illustrated in Section C.4). Also, since the three upper stories 

are identical, the second story is assumed to be critical; for brevity, 

calculations for the third and fourth stories are not provided here. 

In this example, the wall lengths are calculated from Figures C-3 and C-4 

with somewhat more precision than in Section C.1. 

Long x direction walls: 

Story 

Total Wall 

Length (ft) 

Peak Strength, 

at 0.7% Drift 

Seismic Weight 

Above 

Second story 299 ft 322 k 327 k 

First story 278 ft 299 k 438 k 

Base-normalized upper-story strength (Section 4.7.2): 

AU = 322 ÷ 438 = 0.73 

Weak story ratio (Section 4.7.3): AW = 299 ÷ 322 = 0.93 

Strength degradation ratio (Section 4.7.4): CD = 0.0 

Short y direction walls: 

Story 

Total Wall 

Length (ft) 

Peak Strength, 

at 0.7% Drift 

Seismic Weight 

Above 

Second story 149 ft 160 k 327 k 

First story 59 ft 63 k 438 k 
FEMA P-807 C: Example Calculations C-9 

Base-normalized upper-story strength (Section 4.7.2): 

AU = 160 ÷ 438 = 0.36 

Weak story ratio (Section 4.7.3): AW = 63 ÷ 160 = 0.39 

Strength degradation ratio (Section 4.7.4): CD = 0.0 

Median Capacity and Spectral Acceleration Capacity (Sections 5.2 and 

5.3). Because CD is zero (due to sheathing with only plaster and wood lath), 

the median capacity may be calculated directly from Equation 5-2, with no 

interpolation between Equations 5-1 and 5-2 required. 

   0.60

0, , , 0.122 1.59 1 0.5 for 0.0 x W x T s U x D S AC    Q A C  

Similarly, the spectral capacity may be calculated directly from Equation 5-4, 

with no interpolation. The drift limit POE adjustment factor is taken from 

Table 5-1 based on the stated performance objective. For the 20 percent drift 

limit POE used in these examples, the value of POE,0 is 0.60. 

Long x direction: 

Sμ = (0.122 + 1.59 * 0.93) (1 – 0.5 * 0.0) 1.0 (0.73)0.60 = 1.33g 

Sc = 0.60 * 1.33 = 0.80g 

Short y direction: 

Sμ = (0.122 + 1.59 * 0.39) (1 – 0.5 * 0.0) 1.0 (0.36)0.60 = 0.40g 

Sc = 0.60 * 0.41 = 0.24g 

Evaluation (Section 5.4). The spectral acceleration capacity in each 

direction is less than the demand, SMS = 1.53g, so the building fails the 

evaluation in both directions. 

For this example, the building fails the evaluation even with the initial 

unconservative assumptions of zero torsion and no reduction for overturning. 

Had the building passed, the evaluation would have to be redone with torsion 

and overturning considered.

C.3 Retrofit (Chapter 6) 

This example uses the evaluation results of Section C.2 to illustrate the 

Guidelines’ retrofit procedure in concept. Again, the purpose is to explain the 

new capacity equations and the concept of optimized retrofit, not to provide a 

step-by-step calculation template. As in Section C.2, torsion is ignored (that 

is, CT is taken as zero) both to simplify the presentation and because torsion 
C-10 C: Example Calculations FEMA P-807 

effects are expected to be mild in this particular building, especially after 

retrofit. (See Section C.4 for torsion calculations.) 

For the initial pass through the retrofit equations, the strength degradation 

ratio, CD, is still taken as zero, its value in the existing building. However, 

once ductile retrofit elements are added, the actual value of CD will be greater 

than zero; this will become apparent as the retrofit design is confirmed and 

finalized. For discussion of the iterative retrofit design procedure, see 

Guidelines Section 6.2.1. 

Thus, the values needed to apply the retrofit equations of Guidelines Sections 

6.2.1 and 6.2.2 are: 

Qs = 1.0 

CT = 0.0 (assumed, to be confirmed; see Section C.4) 

CD = 0.0 (to be revised upon design confirmation) 

AU, VU, and spectral demand SMS from previous examples. 

Drift limit POE adjustment factors for the stated performance objective with 

20 percent POE, from Table 5-1: αPOE,1 = 0.66 and αPOE,0 = 0.60. 

Estimated Minimum Required Strength (Section 6.2.1). The first-story 

strength required to meet the performance objective is given by Equation 6-1, 

but Equations 6-2 through 6-5 are applied first to generate the necessary 

coefficients. 

Long x direction: 

 

 

0.48

0 ,1

0.48

1 0.5

0.66 * 0.73 * 1.0 1 – 0.5 * 0.0 

0.57

X AQ C   POE U s T





 (6-2) 

1 0

2 0

2.24 1.27 and 

0.525 0.30

X X

X X

 

  (6-3) 

 

 

0.6

0 ,0

0.60

1 0.5

0.60 * 0.73 * 1.0 1 – 0.5 * 0.0 

0.50

Y AQ C    POE U s T





 (6-4) 

1 0 Y Y 1.59 = 0.79 and 2 0 Y Y  0.122 = 0.06 (6-5) 

 

 

3 3

2 2

,min 3 3

1 1

1

1

MS D D

r U

D D

S XC Y C

V V

XC Y C

     (6-1)
FEMA P-807 C: Example Calculations C-11 

   

   

3 3

, 3 3

 1.53 – 0.30 0.0 0.06 1 0.0 1.27 0.0 0.79 1 0.0 

1.47

0.79

1.86 1.86 322k

= 599k

r min U

U

U

V V

V

V

    



 

Short y direction: 

 

 

0.48

0 ,1

0.48

1 0.5 

0.66 0.36 1.0 1 – 0.5 0.0 0.40

X AQ C   POE U s T

    (6-2)

10 2 0 XX X X    2.24 0.90 and 0.525 0.21 (6-3) 

 

 

0.6

0 ,0

0.60

1 0.5

 0.60 0.36 1.0 1 – 0.5 0.0 0.33

Y AQ C   POE U s T

  

(6-4)

10 2 0 YY Y Y    1.59 0.52 and 0.122 0.04 (6-5)

 

 

3 3

2 2

,min 3 3

1 1

1

1

MS D D

r U

D D

S XC Y C

V V

XC Y C

    

 (6-1)

   

   

3 3

,min 3 3

 1.53 – 0.21 0.0 0.04 1 0.0 0.90 0.0 0.52 1 0.0

1.49 2.87 2.87 162 k 465 k 

0.52

r U

U U

V V

V V

     

   

Estimated Maximum Acceptable Strength (Section 6.2.2). The first-story 

strength limit to avoid excessive upper-story drifts is given by Equation 6-6. 

Long x direction: 

V AV r UU , max   0.11 1.22 (6-6) 

 Vr, max = (0.11 * 0.73 + 1.22) * VU = 1.30 * VU

Vr, max = 1.30 * 322 k = 419 k 

Short y direction: 

  , max 0.11 1.22 V AV r UU   (6-6) 

, max 0.11*0.36 1.22 1.26 

 1.26 162 k 204 k

V V r U   VU

 
C-12 C: Example Calculations FEMA P-807 

Estimated Range of Retrofitted Strength (Section 6.2.3). The minimum 

and maximum values calculated above are summarized in the following 

table. In both directions, the estimated minimum exceeds the estimated 

maximum, so it appears that no solution will satisfy the performance 

objective (unless the retrofit also substantially increases CD, as shown 

below). In these cases, Guidelines Section 6.2.3 provides for an optimized 

retrofit strength within 10 percent of the estimated maximum (Equation 6-7), 

subject to a maximum acceptable drift limit POE (Section 6.4.2). Ignoring 

the maximum drift limit POE for now, the recommended strength range in 

each direction is as follows: 

Existing 

Strength 

Minimum 

Required 

Strength 

Maximum 

Acceptable 

Strength 

Recommended 

Strength 

Range 

Long x direction 299 k 599 k 419 k 377 – 461 k 

Short y direction 63 k 465 k 204 k 184 – 224 k 

Selection and Initial Sizing of the Retrofit Elements. The table above 

indicates roughly how much additional strength needs to be provided. As 

shown below, however, if the existing strength and the added strength occur 

at different drift levels, the total story strength will not be their simple sum. 

New sheathing may also replace existing sheathing, so the net strength 

increase should also consider the amount of existing strength removed. 

Considerations of required strength and available locations for new elements, 

together with ample engineering experience and judgment, determine the 

retrofit element types and sizes to be considered with a trial design. Though 

outside the scope of this example, fire-safety requirements might also affect 

the types of appropriate sheathing and finishes. In addition to the primary 

retrofit elements, foundations, load path elements, and other details will need 

to be specified. 

As an initial scheme, consider wood structural panels (WSP) comprising 

plywood nailed to existing studs along first-story wall lines, primarily those 

that stack with walls above. This will require the removal of existing lath and 

plaster. 

Long x direction: 

Referring to Guidelines Table 4-1, WSP sheathing with 8d nails at 2 inches is 

good for a peak strength of 2192 plf at a drift of 3.0%. Since the existing 

plaster contributes no strength at that drift, consider the WSP acting alone. 

Per the table above, if 377 k of strength are needed, then 377 k / 2.192 klf = 

172 ft of new WSP sheathing are needed. 
FEMA P-807 C: Example Calculations C-13 

Thus, as a trial design: 

 Replace 96 linear feet of existing lath and plaster with 5/8-inch WSP 

(8d@2”) on the inside face of existing perimeter stud walls (on lines 1 

and 6), in four roughly equal segments of 24 feet each. 

 Replace 76 linear feet of existing lath and plaster with 5/8-inch WSP 

(8d@2”) on other interior first-story walls, located so that the overall 

first story resistance is symmetric and minimizes torsion. 

While the retrofit is initially sized based on strength at 3.0% drift, it is 

possible that the story’s peak strength will occur at a lower drift and will be 

based on a combination of the new WSP and the existing plaster. As the 

design is confirmed, it will be necessary to ensure that the peak strength does 

not exceed the recommended range. 

Short y direction: 

Again consider 5/8-inch WSP (8d@2”). The total length of wall needed to 

achieve strength in the range shown above would be 184 k / 2.192 klf = 84 ft. 

To locate this new sheathing on walls that align with walls above will require 

replacement of existing lath and plaster on both faces. 

Thus, as a trial design: 

 Replace 42 linear feet of existing lath and plaster with 5/8-inch WSP 

(8d@2”), each face, at existing wall locations, with the length on each 

line limited as needed to maintain symmetry and minimize torsion (see 

Section C.4). 

This scheme may require some minor relocation or extension of interior firststory walls, which would likely also involve new or extended foundation 

elements. If the retrofit walls cannot fit in the space without interfering with 

the garage area drive aisle (see Figure C-3), an alternative design could use 

single-bent steel moment frames, or a combination of steel frames and wood 

structural panels. Guidelines for selecting, sizing, and detailing a steel frame 

system are given in Sections 6.5 and 6.5.4. 

Confirmed Performance (Section 6.4). The measure of a retrofit design is 

not whether it hits the strength range estimated in Guidelines Chapter 6 but 

whether it satisfies the evaluation criteria from Chapter 5 and Section 6.4. 

Therefore, the retrofit design is re-characterized and re-evaluated. The key 

parameters are: 

Qs = 1.0 (unchanged) 
C-14 C: Example Calculations FEMA P-807 

CT = 0.0 (assumed, to be confirmed per Section 6.4.2; see Section 

C.4) 

CD no longer 0.0, to be recalculated based on retrofit load-drift 

curves. 

AU, VU, and spectral demand SMS from previous examples. 

Note that the upper story strength and base-normalized strength do not 

change with a first story-only retrofit (unless the retrofit changes the seismic 

weight of the building significantly). 

Drift limit POE adjustment factors for the stated performance objective with 

20 percent POE, unchanged: αPOE,1 = 0.66 and αPOE,0 = 0.60. 

In Section C.2, with only one wall type to evaluate, it was only necessary to 

check the peak strength at a single drift level. For the retrofit, which 

combines existing brittle elements with new relatively ductile elements, it is 

necessary to consider more of the load-drift curve in order to locate the peak 

story strength. In particular, the strength at 3.0% drift is needed to calculate 

the new value of CD. Therefore, the example calculations that follow show 

wall strengths at three drift levels. (In the two calculation tables that follow, 

existing lath and plaster, denoted “E,” is replaced for certain lengths by new 

WSP sheathing, denoted “N,” and no additional sheathing or finishes that 

would add even more strength is installed over the new WSP.) 

Long x direction: 

Story and Wall Type 

Total Wall 

Length (ft) 

Strength 

at 0.7% 

Drift 

Strength 

at 1.0% 

Drift 

Strength 

at 3.0% 

Drift 

Seismic 

Weight 

Above 

Second story (E, 2-side), 1076 plf 

peak 299 ft 322 k 248 k 0 k 327 k 

First story (E+N, 2-side), comprising: 278 ft -- -- -- 438 k 

- First story (N, 1-side), 2192 plf peak 172 ft 267 k 295 k 377 k -- 

- First story (E, 1-side), 269 plf peak* 172 ft 46.3 k 35.6 k 0 k -- 

- First story (E, 2-side), 1076 plf peak 106 ft 114 k 87.8 k 0 k -- 

First story, total load-drift curve -- 427 k 418 k 377 k -- 

* Non-WSP materials combined with WSP materials in the same wall assembly are subject to a 50% 

strength factor per Section 4.5.1, so the strength shown is 269 plf = 0.50 x 538 plf. 

Base-normalized upper-story strength (Section 4.7.2): 

AU = 322 ÷ 438 = 0.73 

Weak story ratio (Section 4.7.3): AW = 427 ÷ 322 = 1.33 
FEMA P-807 C: Example Calculations C-15 

Strength degradation ratio (Section 4.7.4): CD = 377 ÷ 427 = 0.88 

Comparing with the corresponding values from the existing structure in 

Section C.2: 

 The peak story strength still occurs at 0.7% drift, but the retrofitted story 

now has strength even beyond 3.0% drift. 

 The weak-story ratio has increased to about 1.3, due in part to the 

contributions of the remaining existing walls to the first story peak 

strength. The peak strength of 427 k is still within the recommended 

range determined above. 

 The strength degradation ratio has increased substantially, from 0.0 to 

0.88. Evaluation of the retrofit design using Guidelines Equations 5-1 

through 5-5 will now involve interpolation. 

Substituting into Equations 5-1 through 5-4: 

Sc,1 = 0.66 (0.525 + 2.24 x 1.33) (1 – 0.5 x 0) (1.0) (0.73)0.48 = 1.99g 

Sc,0 = 0.60 (0.122 + 1.59 x 1.33) (1 – 0.5 x 0) (1.0) (0.73)0.60 = 1.11g 

Interpolating per Equation 5-5: 

Sc = 0.883

(1.99g) + (1-0.883) (1.11g) = 1.36g + 0.35g = 1.71g 

The spectral acceleration capacity is now greater than the spectral 

acceleration demand of 1.53g, so this retrofit design appears to meet the 

performance objective in the long x direction. Keep in mind, however, that 

for purposes of this example, torsion has been neglected, as have the effects 

of openings within existing wall lines. The additional capacity above the 

demand might be enough to accommodate a small amount of torsion. 

Short y direction: 

Story and Wall Type 

Total Wall 

Length (ft) 

Strength 

at 0.7% 

Drift 

Strength 

at 1.0% 

Drift 

Strength 

at 3.0% 

Drift 

Seismic 

Weight 

Above 

Second story (E, 2-side), 1076 plf 

peak 149 ft 160 k 123 k 0 k 327 k 

First story (E+N, 2-side), comprising: 59 ft -- -- -- 438 k 

- First story (N, 2-side), 4384 plf peak 42 ft 130 k 144 k 184 k -- 

- First story (E, 2-side), 1076 plf peak 17 ft 18.2 k 14.0 k 0 k -- 

First story, total load-drift curve -- 148 k 158 k 184 k -- 

Base-normalized upper-story strength (Section 4.7.2): 
C-16 C: Example Calculations FEMA P-807 

AU = 160 ÷ 438 = 0.36 

Weak-story ratio (Section 4.7.3): AW = 184 ÷ 160 = 1.15 

Strength degradation ratio (Section 4.7.4): CD = 184 ÷ 184 = 1.0 

Comparing with the corresponding values from the existing structure in 

Section C.2, we see how the added elements are dominating the retrofitted 

first story more in the short direction than in the long direction, because the 

existing short direction was so much weaker: 

 The peak strength of the retrofitted first story now occurs where the 

strength of the retrofit elements is highest, at 3.0% drift. 

 The first-story strength has increased only to 184 k, which is at the low 

end of the recommended range and just satisfies Equation 6-7. The 

existing elements make no usable contribution to the first-story strength. 

 The strength degradation ratio has increased fully to 1.0. 

With the new CD equal to 1.0, the spectral capacity of the retrofit can be 

calculated without interpolation, directly from Equations 5-1 and 5-3: 

Sc,1 = 0.66 (0.525 + 2.24 x 1.15) (1 – 0.5 x 0) (1.0) (0.36)0.48 = 1.25g 

At 1.25g, the spectral acceleration capacity in the short direction is greatly 

increased from the existing value of 0.24g but is still less than the spectral 

acceleration demand of 1.53g, so this retrofit does not meet the performance 

objective, though this was expected from the estimated retrofit range. The 

actual capacity might be slightly lower due to torsion, ignored here. 

The retrofit elements were sized to hit the low end of that range, resulting in 

the minimum amount of new material and the least disruption of the existing 

walls and first-floor layout. Adding a greater length of new WSP sheathing, 

while staying within the practical range, would increase the spectral capacity, 

but it would also require more coordination to make the new elements fit 

within the existing space. 

Since the retrofit does not meet the performance objective, two additional 

checks are required (per Guidelines Section 6.4.2). Briefly: 

 The retrofit elements must be located so as to minimize torsion. The 

calculation of eccentricities and torsion is illustrated in Section C.4. 

 The drift limit POE of the retrofitted structure must be less than the 

maximum acceptable drift limit POE, if one is specified for the project. 

With CD equal 1.0, the actual drift limit POE is calculated quickly with 

Equation 5-7 as approximately 32 percent, not far off from the 20 percent 
FEMA P-807 C: Example Calculations C-17 

objective. Since no maximum acceptable value was set for this example, 

however, no conclusion as to acceptability is reached here. 

C.4 Torsion Calculations (Chapters 3 and 4) 

This example illustrates the Guidelines’ procedures to account for torsion. In 

general, this example building is not expected to undergo significant torsion, 

even in its existing state. With substantial walls along three sides and partial 

walls along the open front, the building is likely to have some eccentricity, 

but not nearly as much as a building with two fully open sides. Nevertheless, 

the torsion calculations are an important feature of the Guidelines

procedures, so they are illustrated here. 

Center of Strength Location and Eccentricity (Sections 3.4.4 through 

3.4.6 and 4.6.4 through 4.6.5). The following tables illustrate the 

bookkeeping used to calculate the center of strength (COS) at each story, 

from which eccentricities and torsion parameters are derived. The wall 

lengths and locations are from Figures C-3 and C-4. In the figures, dimension 

strings also show the cumulative distance from the origin (at the upper left of 

each figure). 

The Guidelines provide two sets of equations for determining the COS, one 

in Chapter 3 for simplified evaluation, and one in Chapter 4 for full 

evaluation. There are two significant differences between them: 

 The full evaluation considers the strength of each wall line at the drift at 

which the whole story reaches its peak strength. By contrast, the 

simplified evaluation considers each wall line at its own peak strength. 

For this example, where the existing building has only one wall type, the 

peak strength of each wall line and of the story as a whole all occur at the 

same drift level, so there will be no difference between the two COS

calculations in this regard. 

 The full evaluation considers the strength of each full wall line, 

discounted for the openings between full-height wall segments. The 

simplified evaluation considers only the full height segments (and thus 

underestimates the wall line strength). In these examples, the effects of 

openings have been ignored and only full height wall segments have 

been considered, so for this example there will be no difference between 

the two COS calculations in this regard. 

As described in previous examples, the existing walls are all sheathed with 

lath and plaster on both sides. From Guidelines Table 3-2 or 4-1, the peak 
C-18 C: Example Calculations FEMA P-807 

unit strength of each wall (which occurs at a drift of 0.7%) is therefore 2 x 

538 plf, or 1076 plf. This is the strength at which the COS is calculated. In 

the tables that follow, the wall lengths do not exactly match the 

approximations used in Sections C.2 and C.3. 

First Story, Long (x) Direction walls, Existing Building 

Grid y [ft] L [ft] 

v at 0.7% 

[plf] 

V at 0.7% 

[k] 

(V) x (y) 

[ft-k] 

1:A 0.00 21.00 1076 22.6 0 

1:D 0.00 36.00 1076 38.7 0 

2:A 3.67 28.00 1076 30.1 111 

2:D 3.67 36.00 1076 38.7 142 

3:B 6.25 21.42 1076 23.0 144 

4:A 20.08 50.00 1076 53.8 1080 

5:C 23.75 21.42 1076 23.0 547 

6:A 28.42 36.00 1076 38.7 1101 

6:E 28.42 28.00 1076 30.1 856 

Total 277.84 299.0 3982 

First Story, Short (y) Direction Walls, Existing Building 

Grid x [ft] L [ft] 

v at 0.7% 

[plf] 

V at 0.7% 

[k] 

(V) x (x) 

[ft-k] 

A:2 0.00 3.25 1076 3.5 0 

A:3.5 0.00 5.58 1076 6.0 0 

A.3:4 7.42 3.58 1076 3.9 29 

A.3:5 7.42 3.00 1076 3.2 24 

B:2 28.00 3.00 1076 3.2 90 

C:5 36.00 6.00 1076 6.5 232 

D:2 50.00 3.00 1076 3.2 161 

E:5 58.00 6.00 1076 6.5 374 

F:2 86.00 25.17 1076 27.1 2329 

Total 58.58 63.0 3240 

Thus, the first story COS is calculated (by either Equation 3-4 or Equation 4-

12) as: 

COS1 = (3240/63, 3982/299) = (51.4 ft, 13.3 ft) 
FEMA P-807 C: Example Calculations C-19 

Upper Story, Long (x) Direction Walls, Existing Building 

Grid y [ft] L [ft] 

v at 0.7% 

[plf] 

V at 0.7% 

[k] 

(V) x (y) 

[ft-k] 

1:A 0.00 28.00 1076 30.1 0 

1:E 0.00 28.00 1076 30.1 0 

3:B 6.25 29.42 1076 31.7 198 

3.5:A 14.00 12.00 1076 12.9 181 

3.7:A.5 19.00 4.00 1076 4.3 82 

3.4:A.6 10.50 11.42 1076 12.3 129 

3.5:A.6 14.00 7.42 1076 8.0 112 

3.6:A.6 17.30 7.42 1076 8.0 138 

3.5:B 14.00 29.42 1076 31.7 443 

3.4:E 10.50 11.42 1076 12.3 129 

3.5:E 14.00 11.42 1076 12.3 172 

3.6:B 17.30 3.00 1076 3.2 56 

3.6:D 17.30 5.00 1076 5.4 93 

3.6:E.2 17.30 7.42 1076 8.0 138 

3.5:E.5 14.00 12.00 1076 12.9 181 

6:A 23.75 28.00 1076 30.1 716 

5:B 28.42 29.42 1076 31.7 900 

6:E 28.42 28.00 1076 30.1 856 

Total 292.78 315.0 4523 

Upper Story, Short (y) Direction Walls, Existing Building 

Grid x [ft] L [ft] 

v at 0.7% 

[plf] 

V at 0.7% 

[k] 

(V) x (x) 

[ft-k] 

A:1 0.00 2.67 1076 2.9 0 

A:3.5 0.00 5.17 1076 5.6 0 

A:5.5 0.00 2.67 1076 2.9 0 

A.5:1 12.00 10.42 1076 11.2 135 

A.5:4 12.00 10.42 1076 11.2 135 

A.6:3.5 16.00 3.33 1076 3.6 57 

B:1 28.00 6.25 1076 6.7 188 

B:3.5 28.00 4.42 1076 4.8 133 

B:4 28.00 12.00 1076 12.9 362 

C:3 37.00 4.42 1076 4.8 176 

C:4 37.00 6.00 1076 6.5 239 

D:3 48.00 4.42 1076 4.8 228 

D:4 48.00 6.00 1076 6.5 310 

E:1 58.00 13.50 1076 14.5 843 Note: continued on next page
C-20 C: Example Calculations FEMA P-807 

Upper Story, Short (y) Direction Walls, Existing Building 

Grid x [ft] L [ft] 

v at 0.7% 

[plf] 

V at 0.7% 

[k] 

(V) x (x) 

[ft-k] 

E:4 58.00 12.00 1076 12.9 749 

E.4:3.5 70.00 3.33 1076 3.6 251 

E.4:4 70.00 9.00 1076 9.7 678 

E.5:1 74.00 10.42 1076 11.2 830 

E.5:4 74.00 10.42 1076 11.2 830 

F:1 86.00 2.67 1076 2.9 247 

F:3.5 86.00 5.17 1076 5.6 478 

F:5.5 86.00 2.67 1076 2.9 247 

Total 147.37 158.6 7114 

The COS for all upper stories is thus: 

COS2 = (7114/159, 4523/315) = (44.7 ft, 14.4 ft) 

Comparing the first story and upper story centers of strength gives the 

eccentricities (per Equation 3-5 or Equations 4-13 and 4-14): 

ex = 51.4 – 44.7 = 6.7 ft. ey = 14.4 – 13.3 = 1.1 ft 

Simplified Torsion Coefficient (Section 3.4.7). For simplified evaluation, 

the torsion coefficient is approximated by Equation 3-6: 

CTs = 4 (ex + ey) / (Lx + Ly) = 4 (6.7 + 1.1) / (86.5 + 30.0) = 0.27 

Reviewing Section C.1 shows the effect this approximation has on the 

estimated spectral capacity. When torsion was ignored, Guidelines Equation 

3-8 included a factor of 1.47. With the calculated coefficient, this factor 

becomes (1.47 – 0.73*0.27), or 1.27, a reduction of 13 percent. That is, for 

this building, the simplified capacity estimated with torsion considered is 

about 87 percent of the capacity estimated without torsion. 

Note that the greatest portion of the reduction results from the x-direction 

eccentricity of 6.7 ft. Guidelines Section 6.4.2 accepts an unavoidable 

eccentricity that is less than 10 percent of the building dimension. In this 

case, 6.7 ft is less than 10 percent of the 86.5-ft long dimension, yet it still 

has an effect on the simplified capacity estimate. 

Torsion Coefficient (Sections 4.6.6 through 4.6.8 and Section 4.7.5). For 

the full evaluation, the torsion coefficient is a function of the potential firststory torsional demand and the first-story torsional strength, considering the 

load-drift behavior of each wall line over a range of twist angles (Section 

4.6.6). At each twist angle, the corresponding drift of each wall line is 
FEMA P-807 C: Example Calculations C-21 

determined, and the in-plane force resisted by that wall line is then 

determined from its load-drift curve (derived from Guidelines Table 4-1). 

While the Guidelines prescribe a method of checking ten incremental 

rotations, the torsional strength can also be found by iteration with a 

spreadsheet. The torsional strength will generally occur when the major walls 

in one direction or the other reach their peak strength. For example, the 

following table shows the torsional strength where the short-direction end 

wall on line F, shown shaded, reaches its peak strength (1076 plf) at 0.7% 

drift. At this point, the torsion resisted by the walls is 2976 ft-k (of which 

1294 ft-k is provided by the long-direction walls and 1682 ft-k is provided by 

the short-direction walls). 

First Story, Long (x) Direction Walls, Existing Building 

Grid y [ft] L [ft] dy [ft] 

drift 

[%] v [plf] V [k] 

T = (V) x (dy) 

[ft-k] 

1:A 0.00 21.00 -13.3 0.27 474 10.0 133 

1:D 0.00 36.00 -13.3 0.27 474 17.1 227 

2:A 3.67 28.00 -9.6 0.20 344 9.6 93 

2:D 3.67 36.00 -9.6 0.20 344 12.4 119 

3:B 6.25 21.42 -7.1 0.14 252 5.4 38 

4:A 20.08 50.00 6.8 0.14 241 12.0 81 

5:C 23.75 21.42 10.4 0.21 371 8.0 83 

6:A 28.42 36.00 15.1 0.31 538 19.4 292 

6:E 28.42 28.00 15.1 0.31 538 15.1 227 

 Total: 1294 

First Story, Short (y) Direction Walls, Existing Building 

Grid x [ft] L [ft] dx [ft] 

drift 

[%] v [plf] V [k] 

T = (V) x (dx) 

[ft-k] 

A:2 0.00 3.25 -51.4 1.04 794 2.6 133 

A:3.5 0.00 5.58 -51.4 1.04 794 4.4 228 

A.3:4 7.42 3.58 -44.0 0.89 919 3.3 145 

A.3:5 7.42 3.00 -44.0 0.89 919 2.8 121 

B:2 28.00 3.00 -23.4 0.47 833 2.5 59 

C:5 36.00 6.00 -15.4 0.31 549 3.3 51 

D:2 50.00 3.00 -1.4 0.03 50 0.2 0 

E:5 58.00 6.00 6.6 0.13 235 1.4 9 

F:2 86.00 25.17 34.6 0.70 1076 27.1 937 

 Total: 1682 
C-22 C: Example Calculations FEMA P-807 

However, this condition does not yield the maximum torsional strength, 

which occurs when the substantial long-direction walls on line 6 reach their 

peak, as shown in the following table (with the line 6 walls shown shaded). 

Note that at this point, the short-direction walls on line A have already failed 

and are no longer resisting any force. Still, the total torsional resistance is 

higher: 3195 ft-k (2745 ft-k from the long-direction walls and 450 ft-k from 

the short-direction walls). 

Thus, the torsional strength, T, is 3195 ft-k. 

First Story, Long (x) Direction Walls, Existing Building 

Grid y [ft] L [ft] dy [ft] 

drift 

[%] v [plf] V [k] 

T = (V) x (dy) 

[ft-k] 

1:A 0.00 21.00 -13.3 0.62 995 20.9 278 

1:D 0.00 36.00 -13.3 0.62 995 35.8 477 

2:A 3.67 28.00 -9.6 0.45 787 22.0 213 

2:D 3.67 36.00 -9.6 0.45 787 28.3 273 

3:B 6.25 21.42 -7.1 0.33 577 12.3 87 

4:A 20.08 50.00 6.8 0.31 552 27.6 186 

5:C 23.75 21.42 10.4 0.48 851 18.2 190 

6:A 28.42 36.00 15.1 0.70 1076 38.7 585 

6:E 28.42 28.00 15.1 0.70 1076 30.1 455 

 Total: 2745 

First Story, Short (y) Direction Walls, Existing Building 

Grid x [ft] L [ft] dx [ft] 

drift 

[%] v [plf] V [k] 

T = (V) x (dx) 

[ft-k] 

A:2 0.00 3.25 -51.4 2.38 0 0.0 0 

A:3.5 0.00 5.58 -51.4 2.38 0 0.0 0 

A.3:4 7.42 3.58 -44.0 2.04 0 0.0 0 

A.3:5 7.42 3.00 -44.0 2.04 0 0.0 0 

B:2 28.00 3.00 -23.4 1.08 755 2.3 53 

C:5 36.00 6.00 -15.4 0.71 1064 6.4 98 

D:2 50.00 3.00 -1.4 0.07 115 0.3 0 

E:5 58.00 6.00 6.6 0.31 538 3.2 21 

F:2 86.00 25.17 34.6 1.60 317 8.0 276 

 Total: 450 

The first story torsional demand is calculated by Guidelines Equation 4-20: 

exV1y + eyV1x = (6.7 ft)(63 k) + (1.1 ft)(299 k) = 422 + 329 = 751 ft-k 
FEMA P-807 C: Example Calculations C-23 

Finally, the torsion coefficient is calculated from Guidelines Equation 4-26: 

CT = (751 ft-k) / (3195 ft-k) = 0.24. 

Reviewing Section C.2 shows that a CT value of 0.24 has a mild effect on the 

spectral capacity. When torsion is ignored, Guidelines Equations 5-1 and 5-2 

each include a factor of 1.0 for potential torsion. With the calculated 

coefficient, this factor becomes (1.0 – 0.50*0.24), or 0.88. That is, for this 

building, the spectral acceleration capacity with torsion considered is 88 

percent of the capacity estimated without torsion. 

Locating Retrofit Elements (Section 6.3). Any ineligible condition must be 

made eligible for the application of the Guidelines’ procedures to be valid 

(see Guidelines Section 2.6). As noted at the beginning of this appendix, the 

overall diaphragm aspect ratio exceeds the 2:1 limit unless the short existing 

walls at the ends of the light wells are adequate as qualifying walls. With the 

retrofit scope determined in Section C.3, this question becomes moot, 

assuming retrofit elements will be located so as to create eligible diaphragm 

segments between the retrofit wall lines. This is achieved by locating the 

short direction retrofit elements along lines B, C, D and/or E. 

In addition, because the optimized retrofit in the short y direction will not 

achieve the stated performance objective (see the latter portion of Section 

C.3), the proposed retrofit elements must be located so as to minimize 

torsion. This example illustrates the requirement by assuming the confirmed 

retrofit solution from Section C.3 and redoing the COS calculation in the 

short direction. 

From the example in Section C.3, the proposed short-direction retrofit 

replaces about 42 ft of existing plaster-sheathed wall (1076 plf peak strength 

at 0.7% drift) with 2-sided WSP (4384 plf peak strength at 3.0% drift), 

providing the estimated required strength of 182 k. 

From the calculation above, the x component of the existing first story COS

is 51.4 ft from the front of the building. The eccentricity (and the resulting 

torsion) will be minimized if the COS can be shifted toward the front of the 

building to match the second story COS, at x = 44.7 ft. Per Guidelines

Section 6.3, an eccentricity less than 10 percent of the building dimension—

in this case about 8.5 ft—is acceptable. The existing eccentricity of 6.7 ft is 

thus already acceptable if necessary, but the performance would be better if 

this value can be minimized by trial and error location of retrofit elements. 

Following Guidelines Section 4.6.4, the COS is calculated with wall line 

strengths at the drift corresponding to the story’s peak strength. As shown in 
C-24 C: Example Calculations FEMA P-807 

the confirmation calculation in Section C.3, the peak strength of the retrofit 

scheme is expected to occur at 3.0% drift, at which point any remaining 

plaster walls do not contribute any strength. Therefore, the retrofit COS

calculation, per the tables below, considers only the new retrofit elements at 

4384 plf. (For this example, adjustments for overturning and openings are 

again ignored for simplicity of presentation.) 

The easiest retrofit layout would simply re-sheath the existing walls at their 

current lengths (see Figure C-3). The short-wall segments on line A.3 are 

ignored, as they are not perimeter walls and might not have footings adequate 

for a WSP wall. Otherwise, if all the wall segments toward the front of the 

building are fully sheathed, and the balance of the required wall length is 

added to the wall on line F, the COS will be at x = 9531/187.8 = 50.8 ft, as 

shown by the following calculation table: 

First Story, Short (y) Direction Walls, Retrofitted Building 

Grid x [ft] L [ft] 

v at 3.0% 

[plf] 

V at 3.0% 

[k] 

(V) x (x) 

[ft-k] 

A:2 0.00 3.25 4384.0 14.3 0 

A:3.5 0.00 5.58 4384.0 24.5 0 

B:2 28.00 3.00 4384.0 13.2 368 

C:5 36.00 6.00 4384.0 26.3 947 

D:2 50.00 3.00 4384.0 13.2 658 

E:5 58.00 6.00 4384.0 26.3 1526 

F:2 86.00 16.00 4384.0 70.1 6032 

Total 42.83 187.8 9531 

This COS location reduces the eccentricity slightly and is acceptable by the 

Guidelines, but it does not minimize torsion. One alternative approach might 

lengthen the wall segment on line B and shorten the segment on line F to 

maintain the same overall length of new wall, but this might interfere with 

the use of the parking area. 

Another alternative might use a stronger WSP type at line A, and shorten the 

line F wall to maintain the same overall required strength of 182 k. The 

following table shows the results of this approach, using a peak strength of 

5024 plf along line A (Per Table 4-1, 2-sided WSP with 10d nails at 2 

inches). This puts the COS at x = 8777 / 184.6 = 47.5 ft and reduces the 

eccentricity relative to the second story to ex = 47.5 – 44.7 = 2.8 ft—still not 

zero, but significantly less than the existing condition. 
FEMA P-807 C: Example Calculations C-25 

First Story, Short (y) Direction Walls, Retrofitted Building (Alternative) 

Grid x [ft] L [ft] 

v at 3.0% 

[plf]

V at 3.0% 

[k]

(V) x (x) 

[ft-k]

A:2 0.00 3.25 5024.0 16.3 0 

A:3.5 0.00 5.58 5024.0 28.0 0 

A.3:4 7.42 0.00 0.0 0.0 0 

A.3:5 7.42 0.00 0.0 0.0 0 

B:2 28.00 3.00 4384.0 13.2 368 

C:5 36.00 6.00 4384.0 26.3 947 

D:2 50.00 3.00 4384.0 13.2 658 

E:5 58.00 6.00 4384.0 26.3 1526 

F:2 86.00 14.00 4384.0 61.4 5278 

Total 40.83 184.6 8777 

FEMA P-807 D: Characterization of Existing Materials D-1 

Appendix D 

Characterization of 

Existing Materials 

D.1 Introduction 

Buildings to be evaluated under these Guidelines have walls that are braced 

with a wide variety of sheathing and finish materials. The Guidelines’

methodology incorporates load-drift curves for each of the commonly 

anticipated materials for which information is currently available. The 

purpose of this appendix is to provide background on the provisions of 

Sections 4.3 through 4.6 of the Guidelines, which characterize existing 

material and building load-drift behavior. 

Sections D.2 through D.4 address information from which load-drift curves 

were derived. Section D.2 summarizes the available testing, organized by 

research project. Section D.3 illustrates load-drift backbone curves derived 

from the data in Section D.2 and discusses data included and adjustments 

made. Section D.4 discusses recommendations made for material property 

modeling in this Guidelines document. 

Sections D.5 through D.8 address adjustment factors used in Section 4.5 to 

modify load-drift behavior. Section D.5 summarizes available data for 

characterizing combinations of bracing materials. Section D.6 addresses 

background for the adjustment factor for openings in the wall line. Section 

D.7 provides background for the adjustment factor for overturning. Section 

D.8 provides background for the drift adjustment for first-story wall-line 

height. 

Section D.9 summarizes available research information relating observed 

damage to drift ratios. Finally, Section D.10 provides recommendations for 

research needed to allow future refinement of upper-story characterization. 

D.2 Research Addressing Wall Bracing Materials 

This section summarizes the available testing of wall bracing materials. 

Forest Products Laboratory (1956) 

The Rigidity and Strength of Frame Walls, Information Reviewed and 

Reaffirmed Report, No. 896 by G. W. Trayer, U. S. Department of 
D-2 D: Characterization of Existing Materials FEMA P-807 

Agriculture (USDA) Forest Products Laboratory, March 1956. This test 

report describes testing that was originally conducted circa 1930. The 

purpose of the testing was to assess the strength and stiffness of wall bracing 

materials for light-frame construction, including horizontal sheathing, 

diagonal sheathing, and plaster on wood lath. Walls tested included 9’-0” 

high by 14’-0” long and 7’-4” high by 12’- 5

8 1 

long assemblies. Both solid 

walls and walls with door and window openings were included. Most were 

tested using single-direction monotonic loading, while several others were 

loaded with a large number of vibration cycles. The test set-up included stiff 

overturning restraint of the panels, making the results comparable to the 

American Society for Testing and Materials (ASTM) E72 test methods. 

Schmid (1984) 

Shear Test of Existing Wood Lath and Plaster Walls Relative to Division 88, 

by Ben Schmid, 1984. In 1984, Ben Schmid tested two interior plaster and 

wood lath walls in an unreinforced masonry building in the City of Los 

Angeles. The walls started out 10-feet high by 11-to-14-feet long, and were 

cut down to 8 feet by 8 feet in order to allow attachment of the testing jacks. 

Both faces of the test walls had plaster and wood lath finishes. The bottom 

edges of the panel remained per original construction. The plaster and wood 

lath was cut vertically and left free to slide at the vertical edges. At the top 

edge, blocking was installed to restrain upward movement of the plaster and 

wood lath. The dead load of the floor above was used to resist overturning; 

however, during peak loads, uplift displacements of almost an inch were 

recorded. Testing was force-controlled and involved loading in one direction, 

release of the load, and loading in the opposite direction. The Test 1 panel 

withstood four excursions and failed on the fifth. The Test 2 panel withstood 

six excursions and failed on the seventh. Load histories, load-deflection plots 

and low-resolution photos of the testing are available. 

Forest Products Laboratory (1940)

New England Eastern White Pine as a House Framing Material by E. C. O. 

Erickson, U. S. Dept. of Agriculture (USDA) Forest Products Laboratory, 

September 1940. This test report describes testing of second growth eastern 

white pine timber framing in order to evaluate differences in strength and 

rigidity from virgin growth. Based on currently tabulated specific gravities, 

the eastern white pine stiffness would be anticipated to be slightly less than 

coastal redwood. Walls tested were 7'-4" high by 12'- 5

8 1  long assemblies, 

fully sheathed without openings. Six sheathing configurations were used, 

including horizontal and diagonal lumber sheathing alone and in combination 

with let-in braces. Testing used single-direction monotonic loading. The test 
FEMA P-807 D: Characterization of Existing Materials D-3 

set-up included stiff overturning restraint of the panels, making the results 

comparable to ASTM E72 test methods. 

Forest Products Laboratory (1958)

Adequacy of Light Frame-Wall Construction Report, No. 2137 by R. F. 

Luxford, and W. E. Bosner, USDA Forest Products Laboratory, November 

1958. The purpose of the testing was to assess methods to reduce costs 

through reduction of labor or materials. Control tests used horizontal 

sheathing of southern yellow pine. These results were compared to horizontal 

southern yellow pine sheathing with let-in braces and 1⁄4 -inch Douglas-fir 

plywood sheathing with and without let-in braces. Walls tested were 8'-0" 

high by 12'-0" long, fully sheathed. Testing used single-direction monotonic 

loading. The test set-up included stiff overturning restraint of the panels, 

making the results comparable to ASTM E72 test methods. 

Forest Products Laboratory (1951) 

Results of Racking Tests of a Few Types of House-Wall Construction, by E. 

W. Kuenzi, USDA Forest Products Laboratory, in cooperation with Housing 

and Home Finance Agency, filed 16 October 1951. This report describes 

testing of various wall bracing materials, including horizontal and diagonal 

sheathing alone and in combination with let-in bracing, as well as a type of 

cement panel. Walls tested were 8'-0" high by 8'-0" long, fully sheathed. 

Walls were tested using single-direction monotonic. The test set-up included 

stiff overturning restraint of the panels, making the results comparable to 

ASTM E72 test methods. The available copy of the report is of poor print 

quality and nearly impossible to read. Information has been included based 

on the higher quality tables and figures. 

City of Los Angeles (2001) 

Report of a Testing Program of Light-Framed Walls with Wood-Sheathed 

Shear Panels by Structural Engineers Association of Southern California, 

City of Los Angeles – University of California at Irvine (COLA-UCI) Light 

Frame Test Committee, Subcommittee of Research Committee and 

Department of Civil and Environmental Engineering, University of 

California, Irvine, December 2001. This test report describes testing of 36 

groups of shear walls sheathed with plywood, oriented strand board, stucco 

and gypsum wallboard, and includes both wood and cold-formed steel 

framing and a variety of sheathing fasteners. The testing was conducted on 8-

ft-by-8-ft shear walls. Overturning restraint was provided by 4 × 4 end posts 

and specially designed heavy-duty tie-down devices, designed to minimize 

uplift deflection; these devices were purposely chosen to be substantially 
D-4 D: Characterization of Existing Materials FEMA P-807 

stiffer than devices commonly used in construction. The test used the 

displacement controlled Technical Coordinating Committee for Masonry 

Research (TCCMAR) Sequential Phased Displacement (SPD) protocol, as 

published by the Structural Engineers Association of Southern California 

(SEAOSC) in 1997. 

Pardoen et al. (2003) 

Testing and Analysis of One-Story and Two-Story Shear Walls Under Cyclic 

Loading (California Universities for Research in Earthquake Engineering 

[CUREE] W-25 Report), by G. Pardoen, A. Waltman, R. Kazanjy, E. 

Freund, and C. Hamilton, 2003. This test report describes testing of 25 

groups of one-story shear walls and two two-story shear walls, sheathed with 

oriented strand board (OSB), stucco, gypsum wallboard, and combinations 

thereof. Objectives included correlation between component tests and shake 

table tests and investigation of walls with combinations of sheathing 

materials. The one-story walls were 8-feet tall and 16-feet long. 

Configurations included fully sheathed, one pedestrian door opening, and one 

garage door opening. The walls matched the first-story walls of a singlefamily dwelling that was tested on the University of California (UC) San 

Diego shake table (CUREE W-2 Report). Commercially available tie-downs 

were used for overturning restraint. The sheathing materials were free to slip 

relative to framing on all four sides of the shear walls. One portion of the 

loading used the CUREE protocol. Another portion used displacement time 

histories recorded during the UC San Diego shake table testing. 

McMullin and Merrick (2002) 

Seismic Performance of Gypsum Walls: Experimental Test Program

(CUREE W-15 Report), by K. McMullin and D. Merrick, 2002. This test 

report describes a series of 17 tests of gypsum wallboard sheathed walls. The 

overall wall was 8-ft high by 16-ft long. Test walls had either one door 

opening or one door and one window. Fastening used both nails at a spacing 

of eight inches on center or screws at a spacing of sixteen inches on center. 

These were chosen to replicate partition-wall construction that would not 

have been identified as structural shear walls. At the top, bottom, and ends of 

the walls, special attention was paid to develop detailing that would be 

representative of interior wall construction. At the wall ends and top, wood 

blocking was provided restricting the sheathing from sliding horizontally 

relative to the framing. At the wall base a 1/4-inch gap was provided beyond 

which a block stopped further slippage. This detailing is a significant 

departure from prior testing. The test setup used heavy tie-down rods to 

restrain wall ends against uplift, reflecting restraint that would be provided 
FEMA P-807 D: Characterization of Existing Materials D-5 

by perpendicular walls. Testing used a combination of monotonic and 

CUREE protocols. Significant data was collected correlating drift levels to 

damage descriptions. See Tables 9 and 10 of the CUREE report for more 

detail. 

American Plywood Association (1993) 

Appendix A of American Plywood Association (APA) Report 154, Wood 

Structural Panel Shear Walls, 1993, provides ultimate loads for 5/16-inch 

and 3/8-inch plywood panel siding fastened with 6d casing nails spaced at six 

inches on center. Details of testing are not provided; however, based on 

Appendix E discussion, it is likely that these values were determined using 

ASTM E72 test methods. 

Gatto and Uang (2002) 

Cyclic Response of Woodframe Shearwalls: Loading Protocol and Rate of 

Load Effects (CUREE W-13 Report) by K. Gatto and C.-M. Uang, 2002. 

This test report describes testing of plywood and stucco sheathed walls, both 

with and without gypsum wallboard and stucco finish materials. The primary 

focus of the testing was to determine the effect of various loading protocols, 

including the Sequential Phased Displacement (SPD), CUREE, and CUREE 

near-fault protocols and both quasi-static and dynamic loading rates. The 

tests were conducted on 8-ft-by-8-ft walls. Sheathing and finish materials 

were free to slip relative to the framing at all edges. Commercially available 

tie-down devices were used for overturning restraint. Several tests are 

incorporated into the recommendations in Section D.2 of the CUREE W-13 

Report. In addition, recommendations from this report for conversions of test 

results between the CUREE and SPD protocols were used. 

Schmid (2001) 

 In 2001, Ben Schmid tested shear walls with gypsum lath and plaster. The 

walls were part of a comparison to gypsum wallboard shear walls. The walls 

were 8' high by 10'-8" long, and the SEAOSC Sequential Phased 

Displacement (SPD) protocol was used in the testing. Test 3 had special 

detailing to provide continuity at all boundaries. Test 7 had special continuity 

detailing at the wall top only. 

D.3 Load-Deflection Backbone 

For each material for which information was available, mean backbone 

curves and beta values were derived from what was considered applicable 

data. This section summarizes the data that were determined to be applicable 

and the derived results. Beta is calculated using the formula: (ln (1+ (std 
D-6 D: Characterization of Existing Materials FEMA P-807 

dev/mean)2 ))0.5. The amount of data available did not justify refined 

determination of beta values for the capacity at various deflections. For this 

reason the following recommendations include betas of 0.15, 0.30 and 0.45 

based on the calculated beta included in the tables, adjusted using 

engineering judgment based on the number of available tests. 

In addition it is important to note that new load-drift curves are permitted to 

be developed for materials not described. These should use a cyclic load 

protocol (preferably the CUREE protocol, as the SPD protocol would require 

use of correction factors). The positive and negative quadrant values should 

be averaged and preferably no less than two tests would be included. 

Attention to realistic boundary conditions is of great importance in order to 

capture realistic load-drift behavior. 

D.3.1 Plaster on Wood Lath 

Table D-1 and Figure D-1 illustrate information available for quantification 

of load-drift behavior for plaster on wood lath. As can be seen, very limited 

information is available. The two sources included are the 1956 Forest 

Products Laboratory (FPL) monotonic testing with heavy overturning 

restraint and the cyclic testing with limited overturning restraint conducted 

Table D-1 Load-Drift Data for Plaster on Wood Lath 

Sheathing Shear Capacities (plf) 

Data Source / Type 

 Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Forest Products Lab. (FPL) (1956) Test 11 (a) 0 720 814 

Schmid (1984) Test 1 (b) 0 300 350 359 391 

Schmid (1984) Test 2 (b) 0 300 450 469 

Average 0 440 538 414 391 

Standard deviation 0 242 244 78 

Covariance (COV) 0 55% 45% 19% 

Average + 1 standard deviation 0 682 782 492 

Average - 1 standard deviation 0 198 294 337 

Recommended upper bound 0 720 810 

Recommended lower bound 0 300 350 360 390 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (default properties) 

0 0.3 1.4 1.4 1.5 

0 267 400 80 80 

(a) Monotonic testing. No description of post-peak behavior provided. 

(b) In-situ testing of existing walls. Limited load cycling. 
FEMA P-807 D: Characterization of Existing Materials D-7 

Figure D-1 Load-drift data for plaster on wood lath. FPL = Forest Products Laboratory. Additional 

information on testing procedures for each data source is provided in Table D-1. 

by Schmid in 1984. The results of these two tests vary considerably. Because 

neither test could be deemed significantly more representative, it is 

recommended that the average of these tests be used to estimate load 

deflection behavior. ASCE/SEI 41 Seismic Rehabilitation of Existing 

Buildings (ASCE, 2006b) default properties are shown for comparison; peak 

capacities are in reasonable agreement, given the variability. A beta of 0.45 is 

recommended based on the combinations of low number of tests and high 

variability. 

D.3.2 Horizontal Lumber Sheathing 

Table D-2 and Figure D-2 illustrate information available for quantification 

of load-drift behavior for horizontal wood sheathing. The various reports 

available from the Forest Products Laboratory (FPL) provide several tests for 

consideration. From the FPL reports, tests that were used included horizontal 

sheathing only, and not let-in braces. This is based on the authors' 

observation of let-in bracing not being prevalent in San Francisco area 

(1984)

(1984)
D-8 D: Characterization of Existing Materials FEMA P-807 

buildings with horizontal sheathing through the 1950s. All tests are 

understood to have been single-direction monotonic loading with heavy 

overturning restraint. All tests were considered equally applicable, and the 

average of the tests was recommended for use in estimating load-deflection 

behavior. ASCE/SEI 41 default properties are shown for comparison; of note 

is that all of the tests show considerably more displacement capacity than 

currently considered by ASCE/SEI 41. American Forest and Paper 

Association, Special Design Provisions for Wind and Seismic (AF&PA 

SDPWS) load and deflection at nominal capacity are also included for 

Table D-2 Load-Drift Data for Horizontal Wood Sheathing 

Sheathing Shear Capacities (plf) 

Data Source / Type 

 Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Forest Products Laboratory (FPL) 

(1956) Test 1-4 average (a) 0 96 114 131 147 162 170 186 

FPL (1940) Test 1 (b) 0 77 81 88 99 110 121 133 

FPL (1940) Test 2 (b) 0 100 107 117 134 151 168 185 

FPL (1958) Control (c) 0 100 106 114 128 142 156 170 198 225 

FPL (1951) Control (d) 0 50 70 100 150 160 170 180 200 220 

Average 0 85 96 110 132 145 157 171 

Standard deviation 0 22 19 17 20 21 21 22 

Covariance (COV) 0.00 0.25 0.20 0.15 0.15 0.15 0.13 0.13 

Average + 1 Standard deviation 0.00 106.16 114.61 126.51 151.95 166.12 177.95 192.86 

Average - Standard deviation 0.00 63.04 76.59 93.49 111.25 123.88 136.05 148.74 

Beta 0.25 0.20 0.15 0.15 0.14 0.13 0.13 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation 

of Existing Buildings (default 

properties) 

0 0.24 1.2 1.2 1.4 

0 53 80 24 24 

 Drift Ratio 

(%) 

American Forest and Paper 

Association, Special Design 

Provisions for Wind and Seismic

0 0.6 

0 100 

(a) Monotonic testing. No description of post-peak behavior provided. 

(b) Monotonic testing. Load at 1.5 inch and peak known; balance is estimated. 

(c) Monotonic testing. Eastern white pine. Load at 0.5 inch and peak load known; balance is estimated. 

(d) Monotonic testing. Load at 1.5 inch and peak known; balance is estimated. 
FEMA P-807 D: Characterization of Existing Materials D-9 

Figure D-2 Load-drift data for horizontal wood sheathing. FPL = Forest Products Laboratory. AF&PA 

SDPWS = American Forest and Paper Association, Special Design Provisions for Wind and 

Seismic. Additional information on testing procedures for each data source is provided in 

Table D-2. 

comparison; the deflection only includes the shear component and not 

overturning deflection. Like ASCE/SEI 41, SDPWS appears to noticeably 

underestimate displacement capacity. 

D.3.3 Diagonal Lumber Sheathing 

Table D-3 and Figure D-3 illustrate information available for quantification 

of load-drift behavior for diagonal wood sheathing. Again, the various 

reports available from the Forest Products Laboratory (FPL) provide several 

tests for consideration. From the FPL reports, tests that were used included 

diagonal sheathing only, and not let-in braces. This in based on the authors' 

observation of let-in bracing not being prevalent in San Francisco area 

buildings with diagonal sheathing through the 1950s. All tests are understood 

to have been single-direction monotonic loading with heavy overturning 

restraint. This test group shows more variability that the horizontal sheathing; 
D-10 D: Characterization of Existing Materials FEMA P-807 

however, all tests were considered equally applicable, and the average of the 

tests was recommended for use in estimating load deflection behavior. 

ASCE/SEI 41 default properties are shown for comparison; peak capacities 

are in reasonable agreement with the average of the available tests. American 

Forest and Paper Association, Special Design Provisions for Wind and 

Seismic (AF&PA SDPWS) load and deflection at nominal capacity are also 

included for comparison; the deflection only includes the shear component 

and not overturning deflection. The SDPWS nominal capacity appears 

somewhat conservative. A beta of 0.30 is recommended based on the 

combinations of moderate number of tests and variability. 

Table D-3 Load-Drift Data for Diagonal Lumber Sheathing 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Forest Products Laboratory (FPL) 

(1956) Test 5 (a) 0 418 491 565 658 

FPL (1956) Test 31 (a) 0 252 297 342 397 

FPL (1956) Test 9A (b) 0 709 834 959 1116 

FPL (1940) Test 3 (c) 0 338 452 623 908 

FPL (1940) Test 5 (c) 0 433 599 848 1263 

FPL (1940) Test 7 (c) 0 426 567 780 1133

Average 0 429 540 686 913 

Standard deviation 0 154 179 222 330 

Covariance (COV) 0 36% 33% 32% 36% 

Average + 1 standard deviation 0 583 719 908 1242 

Average - 1 standard deviation 0 276 361 464 583 

Beta 0.35 0.32 0.32 0.35 

Recommended Beta 0.30 0.30 0.30 0.30 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic 

Rehabilitation of Existing Buildings 

(default properties) 

0 0.5 1.6 1.6 2 

0 467 700 140 140 

 Drift Ratio 

(%) 

American Forest and Paper 

Association, Special Design 

Provisions for Wind and Seismic

0 0.9 

0 600 

(a) Monotonic testing; diagonals in tension. No description of load-deflection behavior beyond 1.5 inches was provided. 

(b) Monotonic testing; diagonals in compression. No description of load-deflection behavior beyond 1.5 inches was provided. 

(c) Monotonic testing; diagonals in tension. Capacity at 0.5 inch and peak given, balance estimated. 
FEMA P-807 D: Characterization of Existing Materials D-11 

Figure D-3 Load-drift data for diagonal lumber sheathing. FPL = Forest Products Laboratory. AF&PA SDPWS 

= American Forest and Paper Association, Special Design Provisions for Wind and Seismic. 

Additional information on testing procedures for each data source is provided in Table D-3.

D.3.4 Stucco 

Table D-4 and Figure D-4 illustrate information available for quantification 

of load-drift behavior for stucco (portland cement plaster). Available data 

includes four City of Los Angeles (CoLA) tests using SPD protocol and 

heavy tie-down restraint, and two Pardoen et al. (2003) tests with CUREE 

protocol and free boundaries at all edges. Also included due to their 

similarity are two Ben Schmid (2001) tests of plaster and gypsum lath. The 

Figure D-4 plot illustrates that the capacity and drift of the Pardoen et al. 

tests are significantly higher than other tests. The Pardoen et al. tests are not 

considered representative because of the boundary conditions with the stucco 

free to slip relative to framing; this resulted in a test of the reasonably ductile 

staples fastening the stucco rather than the more brittle stucco material. 

Similarly Schmid (2001) Test 3 shows peak capacity higher than the other 

tests. Both the Pardoen et al. (2003) tests and the Schmid (2001) Test 3 were 

removed from the group averaged in order to determine estimated load-
D-12 D: Characterization of Existing Materials FEMA P-807 

deflection behavior. The red line on the chart (Figure D-4) shows the average 

of the remaining group. Additional testing with appropriate boundary 

conditions is recommended. ASCE/SEI 41 default properties are shown for 

comparison and are reasonably comparable. A beta of 0.45 is recommended 

based on the combinations of low number of tests and high variability. 

Table D-4 Load-Drift Data for Stucco 

Sheathing Shear Capacities (plf) 

Data Source / Type 

 Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

City of Los Angeles (CoLA) (2001)Test 20A (a) 0 344 332 219 

CoLA (2001)Test 20B (a) 0 379 379 278 

CoLA (2001)Test 21A (b) 0 325 325 262 

CoLA (2001)Test 21B (b) 0 325 312 289 

Schmid (2001) Panel 7B (c) 0 292 250 

Schmid (2001) Panel 3 (d) 0 512 443 304 

Pardoen et al. (2003) Test 16A (e) 0 375 582 621 655 695 745 745 745 745 

Pardoen et al. (2003) Test 17A (f) 0 545 545 560 600 640 600 560 492 

Average 0 333 320 262 

Standard deviation 0 32 46 31 

Covariance (COV) 0 10% 15% 12% 

Average + 1 standard deviation 0 365 366 293 

Average - 1 standard deviation 0 301 273 231 

 0.10 0.14 0.12 

Recommended Beta 0.45 0.45 0.45 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of Existing 

Buildings (default properties) 

0 0.13 0.47 0.47 0.52 

0 233 350 70 70 

(a) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No confinement at boundaries. Furring nails at 6". 

(b) Cyclic testing, SPD protocol. No confinement at boundaries. Staples at 6". 

(c) Cyclic testing, SPD protocol. Confined at wall top only. 

(d) Cyclic testing, SPD protocol. Confined at all boundaries. 

(e) Cyclic testing, CUREE protocol. No confinement at boundaries. Wall with garage door. 

(f) Cyclic testing, CUREE protocol. No confinement at boundaries. Wall with pedestrian door. 

Gray cells not included in average, beta 
FEMA P-807 D: Characterization of Existing Materials D-13 

Figure D-4 Load-drift data for stucco. CoLA = City of Los Angeles. Additional information on testing 

procedures for each data source is provided in Table D-4. 

D.3.5 Gypsum Wallboard 

Table D-5 and Figure D-5 illustrate information available for quantification 

of load-drift behavior for gypsum wallboard. Included are four tests by 

McMullin and Merrick, two tests by Pardoen et al., two City of Los Angeles 

(CoLA) tests and one Schmid (2001) test. Overall the trend of loaddeflection behavior is very similar among the tests, but the variation in 

capacity is large. Because of the construction of realistic boundary conditions 

in the McMullin and Merrick tests, these are felt to be more representative of 

expected properties than the other tests. For this reason the recommended 

estimate of average load-deflection behavior used the four McMullin and 

Merrick tests only. ASCE/SEI 41 default properties are shown for 

comparison; the ASCE/SEI 41 properties are significantly outside of the 

entire range of tests. American Forest and Paper Association, Special Design 

Provisions for Wind and Seismic (AF&PA SDPWS) are also significantly 

outside of the test data. A beta of 0.30 is recommended based on the 

combinations of moderate number of tests and higher variability. 
D-14 D: Characterization of Existing Materials FEMA P-807 

Table D-5 Load-Drift Data for Gypsum Wallboard 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

McMullin and Merrick (2002) Test 1 (a) 0 235 225 205 176 149 138 

McMullin and Merrick (2002) Test 6 (b) 0 190 202 210 209 197 153 141 115 

McMullin and Merrick (2002) Test 7 (b) 0 159 169 174 151 146 128 123 77 

McMullin and Merrick (2002) Test 11 (c) 0 225 254 225 205 197 186 170 128 

Pardoen et al. (2003) Test 19A (d) 0 131 125 115 102 92 77 73 69 

Pardoen et al. (2003) Test 19B (d) 0 121 115 102 88 86 83 78 71 

City of Los Angeles (2001) Test 8A (e) 0 198 175 139 125 109 

City of Los Angeles (2001) Test 8B (e) 0 165 131 108 101 

Schmid (2001) Panel 6B (f) 0 230 271 271 

Average 0 202 213 204 185 172 151 145 107 

Standard deviation 0 35 36 21 27 29 25 24 27 

Covariance (COV) 0 17% 17% 11% 15% 17% 17% 16% 25% 

Average + 1 standard deviation 0 237 248 225 212 201 177 168 133 

Average - 1 standard deviation 0 168 177 182 158 144 126 121 80 

Beta 0.17 0.17 0.10 0.15 0.16 0.17 0.16 0.24 

Recommended Beta 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of Existing 

Buildings (default properties) 

0 0.07 0.4 0.4 0.44 

0 67 100 20 20 

 Drift Ratio (%) 

American Forest and Paper Association, Special 

Design Provisions for Wind and Seismic

0 0.14 0.22

0 60 96 

(a) Cyclic testing, CUREE protocol. Fastened with nails at 8". Door opening. 

(b) Cyclic testing, CUREE protocol. Fastened with screws at 16 inches on center. Average positive and negative quadrant. Door 

opening. 

(c) Cyclic testing, CUREE protocol. Fastened with screws at 16". Door and window opening. 

(d) Cyclic testing, CUREE protocol. Fastened with #6 screw at 6". Door opening. 

(e) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No openings. 

(f) Cyclic testing, SPD protocol. Fastened with nails at 7". No openings. 

Gray cells not included in average, beta 
FEMA P-807 D: Characterization of Existing Materials D-15 

Figure D-5 Load-drift data for gypsum wallboard. CoLA = City of Los Angeles. AF&PA SDPWS = 

American Forest and Paper Association, Special Design Provisions for Wind and Seismic. 

Additional information on testing procedures for each data source is provided in Table D-5.

D.3.6 Plaster on Gypsum Lath 

Table D-6 and Figure D-6 illustrate information available for quantification 

of load-drift behavior for plaster on gypsum lath. As previously described 

two tests by Schmid (2001) are available. The tests have varying boundary 

conditions, resulting in widely varying capacities. Both tests were considered 

equally applicable, and the average of the tests was recommended for use in 

estimating load-deflection behavior. ASCE/SEI 41 default properties are 

shown for comparison; the ASCE/SEI 41 properties are significantly outside 

of the entire range of tests. A beta of 0.45 is recommended based on the 

combinations of low number of tests and high variability.
D-16 D: Characterization of Existing Materials FEMA P-807 

Table D-6 Load-Drift Data for Plaster on Gypsum Lath 

Sheathing Shear Capacities (plf) 

Data Source / Type 

 Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Schmid (2001) Panel 3 (a) 0 512 443 304 

Schmid (2001) Panel 7B (b) 0 292 250 

Average 0 402 347 304 

Standard deviation 0 156 136 

Covariance (COV) 0 39% 39% 

Average + 1 Standard deviation 0 558 483 

Average - Standard deviation 0 246 210 

Beta 0.37 0.38 

Recommended Beta 0.45 0.45 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (default properties) 

0 0.04 0.2 0.2 0.24 

0 53 80 16 16 

(a) Cyclic testing, Sequential Phased Displacement (SPD) protocol. Confined at all boundaries. 

(b) Cyclic testing, SPD protocol. Confined at wall top only. 

Figure D-6 Load-drift data for plaster on gypsum lath. Additional information on testing 

procedures for each data source is provided in Table D-6. 
FEMA P-807 D: Characterization of Existing Materials D-17 

D.3.7 Wood Structural Panel Siding 

Table D-7 and Figure D-7 illustrate information available for quantification 

of load-drift behavior for wood structural panel siding. Available information 

was limited to peak capacities reported by American Plywood Association 

(APA) from one test with 5/16′′ panel and one with a 3/8′′ panel. The shape 

of the load-deflection curve shown was taken from the wood structural panel 

testing with 8d@6 inches on center nailing discussed below and adjusted for 

the APA reported peak capacities for wood structural panel siding and 6d@6 

nailing. A beta of 0.15 has been recommended for the entire range of wood 

Table D-7 Load-Drift Data for Wood Structural Panel Siding 

Sheathing Shear Capacities (plf) 

Data Source / Type 

 Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

APA (1993) 5/16′′ panel

WSP Siding 6d@6 (a) 0 452 496 588 639 650 580 517 

APA (1993) 3/8′′ panel

WSP Siding 6d@6 (a) 0 256 345 404 460 480 429 381 

Average 0 354 420 496 549 565 505 449 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

(a) APA testing with casing nails. Peak capacity known (650 plf at 2% drift); balanced proportioned from 8d@6. 

Figure D-7 Load-drift data for wood structural panel siding (5/16′′ and 3/8′′

thickness). Additional information on testing procedures for each data 

source is provided in Table D-7. 
D-18 D: Characterization of Existing Materials FEMA P-807 

structural panel sheathed shear walls based on our better knowledge of this 

shear-wall group. 

D.3.8 Wood Structural Panel Sheathing 

Tables D-8 through D-12 and Figures D-8 through D-12 illustrate information 

available for quantification of load-drift behavior for wood structural panel 

shear walls with varying nailing. Available information includes four tests 

using the CUREE protocol and Sequential Phased Displacement (SPD) 

protocols, a combination of rated sheathing and Structural I sheathing, and a 

combination of box nails and common nails. CUREE testing suggested that 

the sheathing (Structural versus rated sheathing) and nail type (common 

versus box) differences have only minor impact on the peak capacity and 

deflection at peak capacity of the walls, with Structural I sheathing providing 

slightly higher capacities that rated sheathing, and box nails providing slightly 

lower capacity than common nails. The differences in capacities were small 

enough that differentiation of load-drift behavior is not recommended. The 

SPD protocol was demonstrated by Gatto and Uang to significantly impact 

capacity and deflection of wood structural panel shear walls. For this reason, 

City of Los Angeles (CoLA) tests are converted using conversion factors 

derived by Gatto and Uang. ASCE/SEI 41 default properties are shown for 

comparison; of note is that for a number of materials the tests show 

considerably more displacement capacity than currently considered by 

ASCE/SEI 41. A beta of 0.15 has been recommended for the entire range of 

wood structural panel sheathed shear walls based on calculated betas and our 

better knowledge of this shear wall group. 

Following the 1994 Northridge earthquake, building code requirements for 

3x studs at abutting wood structural panel sheathing edges and 3x foundation 

sill plates were added for moderate- to high-capacity shear walls, as were 

requirements for steel-plate washers on anchor bolts. The requirements for 3x 

foundation sill plates have since been removed from the code. In general, it is 

intended that recommended shear-wall load-drift behavior can be modeled 

without consideration of whether this detailing is provided. Two exceptions 

are recommended for wood structural panel sheathed shear walls. First, 

where 2x studs are used at abutting panel edges in combination with 8d or 

10d nails spaced three inches on center or closer, it is recommended that the 

peak drift capacity of the shear wall be reduced to approximately two inches, 

as stud splitting has been seen to occur at higher drift levels. In addition, 

where significant overturning uplift is anticipated to occur in wood structural 

panel shear walls and steel-plate washers are not used, consideration should 

be given to adjustment of wall peak capacity based on possible foundation 

sill plate splitting at anchor bolts. Refer to Mahaney and Kehoe (2002) for 
FEMA P-807 D: Characterization of Existing Materials D-19 

further information on both exceptions. Where retrofitting or addition of 

shear walls is to occur, it is intended that such retrofitted or added shear walls 

conform to all detailing requirements of the applicable building code or 

standard. 

Wood Structural Panel 8d@6 

Table D-8 and Figure D-8 illustrate information available for quantification 

of load-drift behavior for wood structural panel shear walls with 8d@6” 

Table D-8 Load-Drift Data for Wood Structural Panel 8d@6 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Pardoen et al. (2003) Test 4A (a) 0 430 508 595 693 722 722 722 

Pardoen et al. (2003) Test 4B (a) 0 517 592 670 762 762 739 716 

Pardoen et al. (2003) Test 6A (b) 0 769 778 901 949 974 613 589 

Pardoen et al. (2003) Test 6B (b) 0 517 595 673 745 805 723 641 589 

City of Los Angeles (COLA) (2001) 

Test 1A (c) 0 551 625 706 706 544 

CoLA (2001) Test 1B (c) 0 485 544 589 610 544 

CoLA (2001) Test 1A converted (d) 0 476 666 831 939 939 886 724 

CoLA (2001) Test 1B converted (d) 0 419 586 724 783 811 790 724 

Average (w/converted) 0 521 621 732 812 836 745 686 

Standard deviation 0 128 92 114 107 100 90 57 

Covariance (COV) 0 25% 15% 16% 13% 12% 12% 8% 

Average + 1 std dev 0 650 713 846 919 935 835 743 

Average - 1 std dev 0 393 529 619 705 736 656 628 

Beta 0.24 0.15 0.15 0.13 0.12 0.12 0.08 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (default properties) 

0 0.2 0.9 0.9 1.1 

0 320 480 144 144 

Drift Ratio (%) 

CoLA (2001) Testing Converted: 0 0.77 1.078 1.54 2.31 3.08 3.85 4.62 6.16 7.7 

CoLA (2001) Test 1A 0 732.83 831.25 938.98 938.98 723.52 0 0 0 0 

CoLA (2001) Test 1B 0 645.05 723.52 783.37 811.3 723.52 0 0 0 0 

(a) Cyclic testing, CUREE protocol. No openings. 8db (box nails) at 6". 

(b) Cyclic testing, CUREE protocol. Pedestrian door opening. 8db at 6". 

(c) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No openings. 8dc (common nails) at 6" 

(d) Cyclic testing, SPD protocol adjusted to CUREE (see row labeled “CoLA Testing Converted”). No openings. 8dc at 6" 

Gray cells not included in average, beta 
D-20 D: Characterization of Existing Materials FEMA P-807 

Figure D-8 Load-drift data for wood structural panel 8d@6. CoLA = City of Los Angeles. Additional 

information on testing procedures for each data source is provided in Table D-8. 

nailing. Available information includes four tests by Pardoen et al. (2003) 

using the CUREE protocol and two tests by the City of Los Angeles (CoLA) 

using the SPD protocol. CoLA tests are converted using the protocol 

conversion factors derived by Gatto and Uang. The Pardoen et al. (2003) 

tests and converted CoLA tests were considered equally applicable, and the 

average of the tests was used in estimating load-deflection behavior. 

Wood Structural Panel 8d@4 

Table D-9 and Figure D-9 illustrate information available for quantification 

of load-drift behavior for wood structural panel walls with 8d@4 nailing. 

Available information includes two tests by Gatto and Uang using the 

CUREE protocol and two tests by the City of Los Angeles (CoLA) using the 

Sequential Phased Displacement (SPD) protocol. CoLA tests are converted 

using conversion factors derived by Gatto and Uang. The Gatto & Uang tests 

and converted CoLA tests were considered equally applicable, and the 

average of the tests was recommended for use in estimating load deflection 

behavior. 
FEMA P-807 D: Characterization of Existing Materials D-21 

Table D-9 Load-Drift Data for Wood Structural Panel 8d@4 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Gatto & Uang (2002) Test 2 (a) 0 432 514 616 756 885 958 1009 870 

Gatto & Uang (2002) Test 6 (b) 0 456 592 682 785 886 993 1031 1051 983

City of Los Angeles (CoLA) (2001) Test 2A 

(c) 0 678 759 859 914 927 475 

CoLA (2001) Test 2B (c) 0 669 750 818 851 885 481 

CoLA (2001) Test 2A converted (d) 0 586 820 1009 1142 1186 1222 1233 632 

CoLA (2001) Test 2B converted (d) 0 578 809 998 1088 1114 1149 1177 640 

Average (w/converted) 0 513 684 826 943 1018 1080 1112 798 

Standard deviation 0 80 154 206 201 156 126 110 201 

Covariance (COV) 0 16% 23% 25% 21% 15% 12% 10% 25% 

Average + 1 standard deviation 0 593 838 1033 1143 1173 1206 1222 1000 

Average - 1 standard deviation 0 433 529 620 742 862 955 1003 597 

Beta 0.16 0.22 0.25 0.21 0.15 0.12 0.10 0.25 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (default properties) 

0 0.2 0.9 0.9 1.1 

0 467 700 210 210 

Drift Ratio (%) 

CoLA (2001) Testing Converted: 2.5 0.77 1.078 1.54 2.31 3.08 3.85 4.62 6.16 7.7 

CoLA (2001) Test 2A converted (d) 0 902 1009 1142 1216 1233 632 0 0 0 

CoLA (2001) Test 2B converted (d) 0 890 998 1088 1132 1177 640 0 0 0 

(a) Cyclic testing, CUREE protocol. No openings. Plywood 8db (box nails) at 4". Average positive and negative quadrant. 

(b) Cyclic testing, CUREE protocol. No openings. OSB 8db at 4". Average positive and negative quadrant. 

(c) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No openings. Str-I plywood 8dc (common nails) at 4". 

(d) Cyclic testing, SPD protocol converted to CUREE). No openings. Str I plywood 8dc at 4". 

Gray cells not included in average 
D-22 D: Characterization of Existing Materials FEMA P-807 

Figure D-9 Load-drift data for wood structural panel 8d@4. CoLA = City of Los Angeles. 

Additional information on testing procedures for each data source is provided 

in Table D-9. 

Wood Structural Panel 8d@3 

Table D-10 and Figure D-10 illustrate information available for 

quantification of load-drift behavior for wood structural panel walls with 

8d@3 nailing. Available information includes four tests by Pardoen et al. 

(2003) using the CUREE protocol. The Pardoen et al. (2003) tests used 16-ftlong walls with a 10-ft garage opening, resulting in two 3-ft wall piers. As 

seen in Figure D-10, this resulted in the shear walls having a higher 

deflection at peak capacity than other comparable walls. Current design 

standards would require adjustments of allowable unit shears for deformation 

compatibility for these walls based on the high aspect ratio. For this reason, 

the Pardoen et al. (2003) tests were converted using aspect ratio conversion 

factors specified in the International Building Code (IBC) and American 

Forest and Paper Association, Special Design Provisions for Wind and 

Seismic (AF&PA SDPWS), as shown at the bottom of Table D-10. This 

brought the drift at peak capacity down to three inches. The four converted 

Pardoen et al. (2003) tests were considered equally applicable, and the 

average of the tests was used in estimating load deflection behavior. 
FEMA P-807 D: Characterization of Existing Materials D-23 

Table D-10 Load-Drift Data for Wood Structural Panel 8d@3 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Pardoen et al. (2003) Test 8A (a) 0 833 1028 1158 1288 1420 1523 1588 1666 1693

Pardoen et al. (2003) Test 8B (a) 0 833 1003 1185 1342 1458 1588 1640 1667 1563

Pardoen et al. (2003) Test 10A (b) 0 1055 1212 1315 1472 1563 1667 1718 1718 1667

Pardoen et al. (2003) Test 10B (b) 0 990 1158 1215 1367 1485 1588 1667 1693 1630

Pardoen et al. (2003) Test 8A adjusted 

for aspect ratio (c) 0 996 1132 1245 1420 1545 1614 1666 1693

Pardoen et al. (2003) Test 8B adjusted 

for aspect ratio (c) 0 975 1149 1290 1458 1605 1649 1667 1563

Pardoen et al. (2003) Test 10A adjusted 

for aspect ratio (d) 0 1186 1294 1420 1563 1684 1718 1718 1667

Pardoen et al. (2003) Test 10B adjusted 

for aspect ratio (d) 0 1130 1204 1316 1485 1614 1676 1693 1630

Average 0 1072 1195 1318 1482 1612 1664 1686 1638 

Standard deviation 0 103 73 74 61 57 44 25 56 

Covariance (COV) 0 10% 6% 6% 4% 4% 3% 1% 3% 

Average + 1 standard deviation 0 1174 1268 1392 1542 1669 1708 1711 1695 

Average - 1 standard deviation 0 969 1121 1243 1421 1555 1620 1661 1582 

Beta 0.10 0.06 0.06 0.04 0.04 0.03 0.01 0.03 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (default properties) 

0 0.21 1 1 1.2 

0 600 900 270 270 

Drift Ratio (%) 

Aspect Ratio Adjustments: 0 0.375 0.525 0.75 1.125 1.5 1.875 2.25 3 3.75

Pardoen et al. (2003) Test 8A adjusted 

for aspect ratio 0 833 1028 1158 1288 1420 1523 1588 1666 1693

Pardoen et al. (2003) Test 8B adjusted 

for aspect 0 833 1003 1185 1342 1458 1588 1640 1667 1563

Pardoen et al. (2003) Test 10A adjusted 

for aspect 0 1055 1212 1315 1472 1563 1667 1718 1718 1667

Pardoen et al. (2003) Test 10B adjusted 

for aspect 0 990 1158 1215 1367 1485 1588 1667 1693 1630

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Pardoen et al. (2003) Test 8A adjusted 

for aspect ratio 0 996 1132 1245 1420 1545 1614 1666 1693

Pardoen et al. (2003) Test 8B adjusted 

for aspect 0 975 1149 1290 1458 1605 1649 1667 1563

Pardoen et al. (2003) Test 10A adjusted 

for aspect 0 1186 1294 1420 1563 1684 1718 1718 1667

Pardoen et al. (2003) Test 10B adjusted 

for aspect 0 1130 1204 1316 1485 1614 1676 1693 1630

(a) Cyclic testing, CUREE protocol. Garage door opening. OSB 8d box at 3". 

(b) Cyclic testing, CUREE protocol. Garage door opening. OSB 8d common at 3". 

(c) Cyclic testing, CUREE protocol. Garage door opening. OSB 8d box at 3", adjusted for aspect ratio. 

(d) Cyclic testing, CUREE protocol. Garage door opening. OSB 8d common at 3", adjusted for aspect ratio. 

Gray cells not used in average, beta 
D-24 D: Characterization of Existing Materials FEMA P-807 

Figure D-10 Load-drift data for wood structural panel 8d@3. Additional information on testing procedures 

for each data source is provided in Table D-10. 

Wood Structural Panel 10d@6 

Table D-11 and Figure D-11 illustrate information available for 

quantification of load-drift behavior for wood structural panel walls with 

10d@6 nailing. Available information includes two tests by the City of Los 

Angeles (CoLA) using the Sequential Phased Displacement (SPD) protocol. 

CoLA tests are converted using conversion factors derived by Gatto and 

Uang. The converted CoLA tests were considered equally applicable, and the 

average of the tests was recommended for use in estimating load deflection 

behavior. 

 
FEMA P-807 D: Characterization of Existing Materials D-25 

Table D-11 Load-Drift Data for Wood Structural Panel 10d@6 

Sheathing Shear Capacities (plf) 

Data Source / Type 

 Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

City of Los Angeles (CoLA) (2001) Test 3A (a) 0 636 709 773 795 819 636 

CoLA (2001) Test 3B (a) 0 632 714 765 782 782 632 

CoLA (2001) Test 3A converted (b) 0 549 769 943 1028 1045 1069 1089 846 

CoLA (2001) Test 3B converted (b) 0 546 764 950 1017 1031 1040 1040 841 

Average (w/converted) 0 548 767 946 1023 1038 1055 1065 843 

Standard deviation 0 2 3 5 8 10 21 35 

Covariance (COV) 0 0% 0% 0% 1% 1% 2% 3% 

Average + 1 standard deviation 0 550 770 951 1030 1048 1075 1099 

Average - 1 standard deviation 0 545 763 942 1015 1028 1034 1030 

Beta 0.00 0.00 0.00 0.01 0.01 0.02 0.03 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of Existing 

Buildings (default properties) 

0 0.31 1.4 1.4 1.7 

0 413 620 186 186 

Drift Ratio (%) 

CoLA (2001) Testing Converted: 0 0.77 1.078 1.54 2.31 3.08 3.85 4.62 6.16 7.7

CoLA (2001) Test 3A converted (b) 0 846 943 1028 1057 1089 846 

CoLA (2001) Test 3B converted (b) 0 841 950 1017 1040 1040 841 

(a) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No openings. Str-I plywood 8dc (common nails) at 4". 

(b) Converted to CUREE protocol. 

Gray cells not included in average 

Figure D-11 Load-drift data for wood structural panel 10d@6. CoLA = City of Los Angeles. Additional 

information on testing procedures for each data source is provided in Table D-11. 
D-26 D: Characterization of Existing Materials FEMA P-807 

Wood Structural Panel 10d@4 

Table D-12 and Figure D-12 illustrate information available for 

quantification of load-drift behavior for wood structural panel walls with 

10d@4 nailing. Available information includes two tests by the City of Los 

Angeles (CoLA) using the Sequential Phased Displacement (SPD) protocol. 

CoLA tests are converted using conversion factors derived by Gatto and 

Uang. The converted CoLA tests were considered equally applicable, and the 

average of the tests was used in estimating load deflection behavior. 

Table D-12 Load-Drift Data for Wood Structural Panel 10d@4 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

City of Los Angeles (CoLA) (2001) 

Test 4A (a) 0 732 884 1025 1116 1216 1116 

CoLA (2001) Test 4B (a) 0 905 1034 1111 1134 1034 666 

CoLA (2001) Test 4A converted (b) 0 632 885 1176 1363 1436 1534 1617 1484 

CoLA (2001) Test 4B converted (b) 0 782 1094 1375 1478 1496 1458 1375 886 

Average (w/converted) 0 707 990 1275 1420 1466 1496 1496 1185 

Standard deviation 0 106 148 141 81 43 54 171 

Covariance (COV) 0 15% 15% 11% 6% 3% 4% 11% 

Average + 1 standard deviation 0 813 1138 1417 1501 1508 1550 1667 

Average - 1 standard deviation 0 601 842 1134 1340 1423 1442 1325 

Beta 0.15 0.15 0.11 0.06 0.03 0.04 0.11 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings (default properties) 

0 0.39 1.7 1.7 2 

0 647 970 290 290 

Drift Ratio (%) 

CoLA Testing Converted: 0 0.77 1.078 1.54 2.31 3.08 3.85 4.62 6.16 7.7 

CoLA (2001) Test 4A converted (b) 0 974 1176 1363 1484 1617 1484 

CoLA (2001) Test 4B converted (b) 0 1204 1375 1478 1508 1375 886 

(a) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No openings. Str-I plywood 8dc (common nails) at 4". 

(b) Converted to CUREE protocol. 

Gray cells not included in average 
FEMA P-807 D: Characterization of Existing Materials D-27 

Figure D-12 Load-drift data for wood structural panel 10d@4. CoLA = City of Los Angeles. Additional 

information on testing procedures for each data source is provided in Table D-12. 

Wood Structural Panel 10d@2 

Table D-13 and Figure D-13 illustrate information available for 

quantification of load-drift behavior for wood structural panel walls with 

10d@2 nailing. Available information includes four tests by the City of Los 

Angeles (CoLA) using the Sequential Phased Displacement (SPD) protocol. 

CoLA tests are converted using conversion factors derived by Gatto and 

Uang. The converted CoLA tests were considered equally applicable, and the 

average of the tests was used in estimating load deflection behavior. 
D-28 D: Characterization of Existing Materials FEMA P-807 

Table D-13 Load-Drift Data for Wood Structural Panel 10d@2 

Sheathing Shear Capacities (plf) 

Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

City of Los Angeles (CoLA) (2001) 

Test 9A (a) 0 1197 1436 1655 1859 1863 1683 1258 

CoLA (2001) Test 9C (a) 0 1197 1436 1585 1859 1907 1834 1430 

CoLA (2001) Test 13B (a) 0 1397 1552 1726 1878 1840 954 

CoLA (2001) Test 13C (a) 0 1397 1587 1795 1958 1946 1640 

CoLA (2001) Test 9A converted (b) 0 1033 1447 1910 2201 2363 2474 2477 2128 

CoLA (2001) Test 9C converted (b) 0 1033 1447 1910 2108 2325 2496 2536 2334 

CoLA (2001) Test 13B converted (b) 0 1207 1690 2064 2295 2416 2478 2447 

CoLA (2001) Test 13C converted (b) 0 1207 1690 2110 2388 2517 2598 2588 

Average (w/converted) 0 1120 1568 1999 2248 2405 2512 2512 2231 

Standard deviation 0 100 140 104 120 83 58 63 

Covariance (COV) 0 9% 9% 5% 5% 3% 2% 2% 

Average + 1 standard deviation 0 1220 1708 2103 2368 2489 2570 2575 

Average - 1 standard deviation 0 1020 1428 1895 2127 2322 2453 2449 

Beta 0.09 0.09 0.05 0.05 0.03 0.02 0.02 

Recommended Beta 0.15 0.15 0.15 0.15 0.15 0.15 0.15 

 Drift Ratio (%) 

ASCE/SEI 41, Seismic Rehabilitation of 

Existing Buildings - Plywood (default 

properties) 

0 0.36 1.6 1.6 2 

0 1030 1540 462 462 

ASCE/SEI 41 - OSB (default properties) 

0 0.16 0.7 0.7 0.9 

0 1030 1540 462 462 

Drift Ratio 

CoLA (2001) Testing Converted:- 0 0.77 1.078 1.54 2.31 3.08 3.85 4.62 6.16 7.7 

CoLA (2001) Test 9A converted (b) 0 1592 1910 2201 2472 2477 2238 1674 

CoLA (2001) Test 9C converted (b) 0 1592 1910 2108 2472 2536 2439 1902 

CoLA (2001) Test 13B converted (b) 0 1859 2064 2295 2498 2447 1268 0 

CoLA (2001) Test 13C converted (b) 0 1859 2110 2388 2605 2588 2181 0 

(a) Cyclic testing, Sequential Phased Displacement (SPD) protocol. No openings. Str-I plywood, OSB 8dc at 2". 

(b) Converted to CUREE protocol. 

Gray cells not included in average 
FEMA P-807 D: Characterization of Existing Materials D-29 

Figure D-13 Load-drift data for wood structural panel 10d@2. CoLA = City of Los Angeles. Additional 

information on testing procedures for each data source is provided in Table D-13. 

D.4 Recommended Descriptions of Wall Bracing 

Materials 

This section presents recommendations that were made for describing wall 

bracing material load-deflection behavior for this Guidelines document. The 

recommendations are based on Section D.3 data, Table D-14 provides 

estimated mean capacities at specified drift levels ranging between 0.5 and 4 

percent of the wall height. Also tabulated are recommended beta values for 

the variability of the capacity. The beta values are intended to apply at all 

drift levels. See other sections of these Guidelines for a description of how 

this information was used in developing the retrofit solutions. 
D-30 D: Characterization of Existing Materials FEMA P-807 

Table D-14 Recommended Values for Estimated Capacity and Variability 

Material Beta Estimated Mean Capacity (plf) at Specified Drift Level (% height) 

0.5 0.7 1 1.5 2 2.5 3 4 

Stucco 0.45 333 320 262 

Horizontal Lumber 

Sheathing 0.15 85 96 110 132 145 157 171 

Diagonal Lumber 

Sheathing 0.30 429 540 686 913 

Plaster on Wood 

Lath 0.45 440 538 414 391 

Plywood Panel 

Siding 0.15 354 420 496 549 565 505 449 

Gypsum Wallboard 0.30 202 213 204 185 172 151 145 107 

Plaster on Gypsum 

Lath 0.45 402 347 304 

Wood Structural 

Panel 8d@6 0.15 521 621 732 812 836 745 686 

Wood Structural 

Panel 8d@4 0.15 513 684 826 943 1018 1080 1112 798 

Wood Structural 

Panel 8d@3 0.15 1072 1195 1318 1482 1612 1664 1686 1638 

Wood structural 

Panel 10d@6 0.15 548 767 946 1023 1038 1055 1065

Wood Structural 

Panel 10d@4 0.15 707 990 1275 1420 1466 1496 1496 1185 

Wood Structural 

Panel 10d@2 0.15 1120 1568 1999 2248 2405 2512 2512 2231 

D.5 Adjustment Factor for Combinations of Bracing 

Materials 

Where more than one material with differing load-drift behavior is applied to 

the same section of bracing wall, the load-deflection behavior for the 

combination of materials must be determined. This section presents the 

available data used in Section 4.4 of the Guidelines. 

At time of writing, only limited research data were available in which 

bracing materials were tested individually and then in combination. 

Testing by Pardoen et al. (2003), presented earlier, had the evaluation of 

individual and combined materials as one of its goals. From this testing, 

individual test walls were evaluated with wood structural panel sheathing, 

gypsum wall board, and stucco. In addition, a wall was tested with all three 

materials applied. The results of this testing are shown in Table D-15 and 

Figure D-14. The figure clearly illustrates that even when individual wall 
FEMA P-807 D: Characterization of Existing Materials D-31 

Table D-15 Data for Combined Materials 

Sheathing Shear Capacities (lb) 

Material / Data Source / Type Drift Ratio (%) 

0 0.5 0.7 1 1.5 2 2.5 3 4 5 

Combined test - Pardoen et al. 

(2003) Test 13A (a) 0 10880 12910 14250 15160 14470 11460 8360 7170 

OSB - Pardoen et al. (2003) Test 

6A 0 8220 9080 10060 10780 11190 8980 7050 6520 

Stucco - Pardoen et al. (2003) 

Test 17A 0 6970 7230 7230 7580 8110 7690 7230 6460 

Gypsum wallboard - Pardoen et 

al. (2003) Test 19A 0 1500 1470 1330 1220 1130 1140 1150 990 

Summed - Pardoen et al. (2003) 

Test 6A+17A+19A 0 16690 17780 18620 19580 20430 17810 15430 13970 

Alt Stucco - 0 4930 4930 3610 

Combined with Alt Stucco 0 14650 15480 15000 12000 12320 10120 8200 7510 

Wood plus 50% other 12455 13430 14340 15180 15810 13395 11240 10245 

Other plus 50% wood 12580 13240 13590 14190 14835 13320 11905 10710 

capacities are summed for each drift ratio, the sum implied by the individual 

test is greater than justified by the test with all three materials. Also shown in 

Figure D-14 are two recommended approaches for summing materials. One 

adds the full capacity of the materials that peak at low drift ratios (stucco and 

gypsum wallboard) to half of the capacity of the wood structural panel wall 

that peaks at higher drift ratios. The second adds half of the low drift ratio 

materials to the full capacity of the wood structural panel walls. Both appear 

to give a reasonable prediction of the test with combined materials. 

A second data source to be considered for combining materials comes from 

testing by Forintek (Karacabeyli, 1997). Average peak capacities are reported 

for shear wall testing with oriented strand board (OSB) alone (2.21 k), 

gypsum wallboard only (0.84 k) and the two tested in combination (2.77 k). 

This would support adding all of the OSB peak capacity to half of the 

gypsum wallboard capacity. 

A third data source is testing is Toothman (2003) who performed cyclic 

testing of 4-ft-by-8-ft walls with gypsum wallboard alone, OSB alone, and 

gypsum wallboard plus OSB combined. Data indicate that the peak capacity 

of the combined gypsum wallboard and OSB is equal to 100% of the OSB 

peak capacity plus approximately 60% of the gypsum wallboard peak 

capacity. 
D-32 D: Characterization of Existing Materials FEMA P-807 

Figure D-14 Plotted load-deflection curves for combined materials. 

These are only three points of data in a wide range of potential material 

combinations. While they have provided a general direction for the 

Guidelines document, much more research in this area is needed to properly 

characterize building behavior. 

D.6 Adjustment Factor for Openings in the Wall Line 

This section presents background information on the adjustment factor for 

openings in wall lines, presented in Section 4.5.2 of the Guidelines. 

This adjustment has its basis in research used for the perforated shear-wall 

design methodology, currently included in the American Forest and Paper 

Association, Special Design Provisions for Wind and Seismic (AF&PA 

SDPWS, 2008), as well as other publications. Perforated shear walls 

typically have overturning restraint only at the extreme ends of the wall line, 

and use reduction factors to recognize the lower strength and stiffness 

inherent in the wall as a result of door and window openings. References for 

the perforated shear wall method include Sugiyama, 1981; Dolan and 

Johnson, 1997a, 1997b; and APA, 2005. 

The use of this concept in Section 4.5.2 has several important distinctions 

from the SDPWS rules of application. First, the formula for the adjustment 

factor is applied to the out-to-out length of the wall line, Lw, whereas the 

perforated shear wall method uses the sum of full-height segments. The 
FEMA P-807 D: Characterization of Existing Materials D-33 

alternate formulation using Lw is derived from research by Johnson (1997). 

This formulation was incorporated into the Guidelines based on the 

conclusions in the Johnson report that the SDPWS formulations of the 

adjustment factor were conservative. For purposes of the Guidelines, the 

intent is to use the most precise formulation possible. The second distinction 

is that, for purposes of the Guidelines, it is intended that the adjustment 

factor for overturning, in accordance with Section 4.5.3, be applied in 

addition to the adjustment factor for openings. 

D.7 Adjustment Factor for Overturning 

This section presents background on the adjustment factor for overturning, 

presented in Section 4.5.3 of the Guidelines. The wall component testing data 

used to develop Table 4-1 load-drift curves included sufficient overturning 

restraint to develop the shear capacity of the wall bracing. In actual building 

configurations, adequate overturning restrain may not always be available. 

Section 4.5.3.1 presents a simplified approach to the adjustment for 

overturning restraint based on a detailed analytical study of a multi-story 

wood-frame building that is further discussed in Appendix E. The intent of 

the model was to demonstrate that deformation and loading of the bracing 

walls that are required to mobilize dead load resistance can occur without 

significant loss of strength to the bracing elements. The factors tabulated in 

Table 4-2 are an indication of what strength loss is thought to occur as dead 

load resistance is mobilized. 

Section 4.5.3.2 presents a calculated method for determining the overturning 

adjustment factor. It is intended that this method follow typical design 

practice in quantifying resisting moments due to uniform and concentrated 

dead loads. The overturning moment to be used is based on the peak capacity 

of the wall line, including use of the procedures for combining load-drift 

curves for sheathing materials and the adjustment factors for openings. 

The calculated method is permitted to be used considering only the 

overturning and resisting moments from the single story. This assumes that 

overturning and revisiting moments are balanced in the story above. This is 

particularly helpful for first-story walls that do not stack with walls in the 

stories above. The calculated method is also permitted to be used considering 

the overturning and resisting moments from the story under consideration 

and stories above, as is current design practice. This is more realistic for 

exterior walls that stack with stories above and therefore have a good deal of 

inherent continuity. 
D-34 D: Characterization of Existing Materials FEMA P-807 

Equation 4-5 calculates the adjustment factor, Qot, considering the 

overturning and resisting moments. The equation defaults to 0.4 when the 

resisting moment is zero, based on the judgment of the Guidelines’ writers. 

Although the detailed analytical overturning study included modeling of the 

first story and factors were derived for the first story, the Guidelines require 

that the first story use the Section 4.5.3.2 calculated method of determining 

the overturning factor. A number of factors affected this decision including: 

 The first-story capacity is critical to the behavior of weak-story 

buildings. This one detailed analytical study does not provide a level of 

comfort adequate to set aside current design practice for overturning 

restraint of these walls. 

 Two of the case study buildings documented in Woodframe Project Case 

Studies (Schierle, 2001) were weak-story buildings constructed circa 

1971. Both were proportioned for shear but lacked overturning restraint, 

and both suffered substantial collapse. Although the lack of overturning 

restraint was not the only possible source of weakness, these case studies 

point to needing a better understanding prior to allowing the use of Table 

4-2 adjustment factors in the first story. 

D.8 Drift Adjustment for First-Story Wall-Line Height 

Section 4.5.4 specifies an adjustment of the drift ratios used to define the 

load-drift curve. It is applied to first-story wall lines with a height of less than 

eight feet, and recognizes that the drift at peak capacity is reduced for a 

shorter wall height. Based on cripple wall testing from the CUREE project 

(Chai et al., 2002), however, the reduction in drift at peak capacity is less 

severe than a linear reduction based on wall height. Cripple walls with a 

height of two feet (specimens 4 and 5 in the Chai et al. study) and sheathed 

with wood structural panel and stucco were seen to have a drift at peak 

capacity of approximately 1”. Similar cripple walls with a height of four feet 

(specimens 7 and 8) were seen to have a drift at peak capacity of 11⁄2 to 2′′. 

These can be compared to drifts at peak capacity of 21⁄2 to 3′′ for 8-ft walls. A 

reduction based on the ratio of heights to the 0.7 power is used to 

approximate this behavior. 

In order for wall lines of different heights to be combined, a common set of 

drift ratios will need to be used. Straight-line interpolation is recommended 

for adjusting back to the typical drift ratios. 
FEMA P-807 D: Characterization of Existing Materials D-35 

D.9 Descriptions of Damage versus Drift 

In order to relate observed damage to drift demand, it is desirable to have 

descriptions of damage to bracing materials as a function of the story drift 

imposed during testing. This section summarizes available information from 

three testing programs. The reader is cautioned that these must be considered 

general indications of damage only, as it is anticipated that damage observed 

can vary widely. 

Arnold, Uang and Filiatrault (2003) 

Two configurations of walls were tested to failure. Wall 1 was 8 ft by 16 ft 

with two window openings. Wall 2 was 8 ft by 16 ft with one door and one 

window opening. Displacement controlled testing using the CUREE protocol 

was used. Each wall was sheathed with stucco on one side and gypsum 

wallboard on the other. The report provides written descriptions of visual 

damage at drift ratios of 0.2%, 0.5%, 0.7% and “failure” (defined as 

reduction to below 80% of peak capacity). The report also provides crack 

maps at these drift intervals, and numerous photos of damage examples. Note 

that these panels reached peak capacity at about 1% drift and “failure” 

between 1.7% and 2%. These drifts are higher than described earlier in this 

report for the individual materials tested separately. While this complicates 

interpretation, it is the best available information. It is suggested that the 

descriptions of damage be considered applicable at the stated drifts rather 

than conversion of drifts being made. 

Figures D-15 through D-30 are excerpted from the Arnold et al. (2003) 

report, including paraphrasing of damage descriptions. See the full report for 

more detail. Crack widths indicated are at zero applied load, following 

loading to the noted drift. 
D-36 D: Characterization of Existing Materials FEMA P-807 

 

Figure D-15 Crack maps for stucco sheathing at 0.2% drift for (top) Wall 1 

and (bottom) Wall 2. Minor cracking of finish started at opening 

corners and propagated diagonally. No deterioration of 

behavior occurred during trailing cycles. CL indicates a crack 

that closed during unloading. HC denotes hairline crack of 

width less that 0.002 inches (from Arnold, Uang and Filiatrault, 

2003). 

 
FEMA P-807 D: Characterization of Existing Materials D-37 

 

Figure D-16 Crack maps for stucco sheathing at 0.4% drift for (top) Wall 1 

and (bottom) Wall 2. Stucco cracks from 0.2% drift increased in 

length and width. New cracks branched from the existing cracks 

and at some locations cracks propagated to the stucco 

boundaries. CL indicates a crack that closed during unloading. 

HC denotes hairline crack of width less that 0.002 inches (from 

Arnold, Uang and Filiatrault, 2003). 
D-38 D: Characterization of Existing Materials FEMA P-807 

 

 

Figure D-17 Crack maps for stucco sheathing at 0.7% drift for (top) Wall 1 

and (bottom) Wall 2. Most cracks that originated at opening 

corners propagated to the stucco boundaries. More cracks 

initiated at the stucco boundaries and at wall pier edges. All 

existing cracks increased in length and width. HC denotes 

hairline crack of width less that 0.002 inches. SP indicates 

locations where the stucco finish coat spalled, such that it was 

not possible to measure a crack width (from Arnold, Uang and 

Filiatrault, 2003). 

 
FEMA P-807 D: Characterization of Existing Materials D-39 

 

Figure D-18 Crack maps for stucco sheathing at failure for (top) Wall 1 and 

(bottom) Wall 2. In addition to stucco cracking shown, damage 

included spalling of the stucco, rotation of j-molds at the wall 

top, and twisted studs at wall ends (from Arnold, Uang and 

Filiatrault, 2003). 
D-40 D: Characterization of Existing Materials FEMA P-807 

Figure D-19 Photos of characteristic cracking at 0.4% drift. Red dot indicates location of photograph 

(from Arnold, Uang and Filiatrault, 2003).

 
FEMA P-807 D: Characterization of Existing Materials D-41 

Figure D-20 Photos of characteristic cracking at 1.5% drift (from Arnold, 

Uang and Filiatrault, 2003). 

 
D-42 D: Characterization of Existing Materials FEMA P-807 

Figure D-21 Photos of characteristic cracking at failure (from Arnold, Uang and 

Filiatrault, 2003). 
FEMA P-807 D: Characterization of Existing Materials D-43 

 

Figure D-22 Crack maps for gypsum wallboard sheathing at 0.2% drift for 

(top) Wall 1 and (bottom) Wall 2. Small hairline cracks formed 

near corners of the windows and along the edges of corner 

beads (from Arnold, Uang and Filiatrault, 2003). 

 
D-44 D: Characterization of Existing Materials FEMA P-807 

Figure D-23 Crack maps for gypsum wallboard sheathing at 0.4% drift for 

(top) Wall 1 and (bottom) Wall 2. Cracking at corners and edges 

of windows increased. Joint tape bubbling and nail popping 

started to occur (from Arnold, Uang and Filiatrault, 2003). 
FEMA P-807 D: Characterization of Existing Materials D-45 

 

Figure D-24 Crack maps for gypsum wallboard sheathing at 0.7% drift for 

(top) Wall 1 and (bottom) Wall 2. Crack width and length 

increased. Nail pops increased. Crushing of the gypsum core 

occurred at window corners in compression. Tearing of the joint 

tape occurred, leading to wall board panels rotating individually 

(from Arnold, Uang and Filiatrault, 2003). 
D-46 D: Characterization of Existing Materials FEMA P-807 

Figure D-25 Crack maps for gypsum wallboard sheathing at failure for (top) 

Wall 1 and (bottom) Wall 2. Most of the wallboard joints were 

significantly damaged, and wallboard piers rotated relative to 

each other. Large crack widths and lengths were observed at all 

opening corners. “Ridging” at the wallboard joints was observed 

following large displacements. Nail popping became more 

obvious. Gypsum wallboard movement relative to the framing 

was obvious at the door opening (from Arnold, Uang and 

Filiatrault, 2003). 

 
FEMA P-807 D: Characterization of Existing Materials D-47 

Figure D-26 Photos of characteristic cracking at 0.4% drift (from Arnold, 

Uang and Filiatrault, 2003). 

 
D-48 D: Characterization of Existing Materials FEMA P-807 

Figure D-27 Photos of characteristic cracking at 0.7% drift (from Arnold, 

Uang and Filiatrault, 2003). 

 
FEMA P-807 D: Characterization of Existing Materials D-49 

Figure D-28 Photos of characteristic cracking at 1.5% drift (from Arnold, 

Uang and Filiatrault, 2003). 

 
D-50 D: Characterization of Existing Materials FEMA P-807 

Figure D-29 Detailed photos of characteristic wall cracking at 1.5% drift (from Arnold, 

Uang and Filiatrault, 2003). 

 
FEMA P-807 D: Characterization of Existing Materials D-51 

Figure D-30 Photos of characteristic cracking at 1.5% drift showing 

wallboard fastener popping (from Arnold, Uang and Filiatrault, 

2003). 

 
D-52 D: Characterization of Existing Materials FEMA P-807 

Table D-16 Descriptions of Damage States and Drifts (from McMullin and Merrick, 2002). 

Wall Drift (inches)1

Damage State Test 6 

Front 

Test 6 

Back 

Test 7 

Front 

Test 7 

Back 

Test 11 

Front 

Test 11 

Back 

Cracking of Paint over Fastener Head 0.34 

034 

(-25) 

0.18 

0.24 

(-23) 

0.250 

0.250 

(+25) 

0.250 

0.250 

(+25) 

0.524 

0.524 

(+32) 

0.472 

0.472 

(+29) 

Cracking of Wallboard at Wall Penetration 0.24 

0.24 

(+21) 

0.24 

0.24 

(+21) 

0.090 

0.120 

(+17) 

0.090 

0.120 

(+17) 

0.121 

0.121 

(-14) 

0.258 

0.258 

(+21) 

Crushing of Wallboard at Perimeter 2.00 

2.00 

(+41) 

1.25 

1.25 

(+38) 

0.777 

0.777 

(+32) 

NR 2.376 

2.376 

(+41) 

N/A 

Cracking of Vertical Butt Joint N/A 0.75 

0.75 

(+32) 

0.301 

0.419 

(+27) 

0.301 

0.419 

(+27) 

0.357 

0.472 

(+31) 

0.268 

0.394 

(-28) 

Cracking of Horizontal Wall Joint N/A N/A N/A N/A 0.660 

0.660 

(-32) 

N/A 

Cracking of Vertical out-of-Plane Joint 0.25 

0.36 

(+29) 

0.25 

0.25 

(-25) 

0.301 

0.419 

(+27) 

0.359 

0.359 

(-25) 

0.785 

0.785 

(+32) 

N/A 

Local Buckling of Panel at Wall Penetration 0.75 

0.75 

(-32) 

Note A 0.419 

0.419 

(+25) 

0.359 

0.359 

(-25) 

0.130 

0.130 

(+14) 

0.258 

0.258 

(+21) 

Global Buckling of Panel 1.94 

1.94 

(+41) 

4.17 

4.17 

(+50) 

N/A 1.710 

1.710 

(+38) 

N/A N/A 

Notes: 

1: First row of data in each data set is the drift at which the damage threshold was observed; second row of data is the 

maximum drift in the same direction that the wall had sustained when the damage threshold was identified; the third row of 

data is the loading excursion number when the damage threshold was observed. 

A: Local buckling was not seen as a distinct damage state; instead, all re-entrant corners at wall openings showed initial cracking 

at low levels of drift. 

N/A: not applicable. 

NR: not recorded (assumed meaning, as meaning not provided in reference) 

McMullin and Merrick (2002) 

A series of damage states and associated drifts for the cyclic tests conducted 

by McMullin and Merrick (2002), as documented in Table 10 of their report, 

is provided in Table D-16. The three test specimens described were gypsum 

wallboard with screws at 16 inches on center, tested cyclically. The walls 

reached peak capacity between 0.7% and 1% drift. Note that between test 

walls there was significant variability in the drift at which damage states 

occurred. 
FEMA P-807 D: Characterization of Existing Materials D-53 

Forest Products Laboratory (1956) 

Figure D-31 provides illustrations of the damage condition of two tested 

walls with plaster and wood lath. The photos are assumed to have been taken 

Figure D-31 Photos of characteristic cracking at completion of Forest 

Products Lab testing (from Trayer, 1956). 
D-54 D: Characterization of Existing Materials FEMA P-807 

at the conclusion of testing. Based on limited notes provided in the test 

report, it is estimated that cracking on the upper panel initiated at 

approximately 0.5% drift, and the photo was taken after testing to 0.7% drift. 

Similarly it is estimated for the bottom panel that cracking initiated at 0.1% 

drift and the photo was taken after testing to 0.9% drift. These panels were 

loaded monotonically, and post-peak capacity behavior was not investigated.

Discussion of Research Results 

Based on the combination of the descriptions and photos provided by 

Merrick and McMullin (2002) and Arnold, Uang and Filiatrault (2003), for 

gypsum wallboard, it appears that breaking down of the taped joints, 

resulting in panels being able to rotate individually, are key behaviors 

relating to declining strength of gypsum wallboard sheathing. Regardless of 

this performance similarity, photos appear to indicate that visible damage in 

the Arnold, Uang and Filiatrault (2003) testing was primarily at taped joints 

and window and door openings, while prominent visible damage in the 

McMullin and Merrick (2002) testing was cracking initiating at opening 

corners. 

D.10 Recommended Future Research 

Efforts to characterize upper-story strength and stiffness for these Guidelines

pointed out a number of areas in which additional information would help 

provide more reliable predictions, allowing better optimization of retrofit 

designs. The steps selected for characterization for these Guidelines involved 

identifying material load-deflection behavior, combining material behavior, 

establishing wall lines for analysis, adjusting wall line capacity for wall 

openings and overturning restraint, and combining wall lines to describe 

story behavior. At each step, limitations were encountered due to lack of 

substantial relevant data and lack of quantified full building behavior to 

provide validation of modeling. Future research is needed to better quantify 

the characteristics of upper-story bracing, whether using this same step by 

step process or a more integrated approach. Adequate characterization of the 

upper stories is critical to providing the widest range of optimized retrofit 

designs and better understanding of the performance of the retrofitted 

building. 

As a minimum the following are recommended as high priority for future 

research: 
FEMA P-807 D: Characterization of Existing Materials D-55 

 Component testing with archaic materials to better establish the range of 

anticipated material behavior. Significant attention is needed to 

establishing realistic boundary conditions for the testing. 

 Evaluation and incorporation of data from in-plane testing of brick 

veneer. 

 Component testing for individual materials and differing materials used 

in combination, to better establish how common combinations of 

materials perform. 

 Analysis and data sets for validation of models converting individual 

wall pier behaviors to full building behavior, accounting for openings 

and overturning restraint. 

 Additional testing correlating visual damage to peak sustained drifts and 

anticipated load-deflection properties. 

As additional testing is conducted, the following are important: 

 Use of a consistent loading protocol or additional data to allow 

conversion between protocols. 

 Testing to drift levels that result in collapse mechanisms. 

 Realistic bracing material boundary conditions. 

 Attention to loading beam stiffness and interaction with components 

being tested. 

FEMA P-807 E: Detailed Analytical Background E-1 

Appendix E 

Detailed Analytical Background 

E.1 Purpose 

The purpose of this appendix is to provide a link between the 

recommendations in Chapters 3 through 7 and the underlying analytical 

work. 

E.2 General 

E.2.1 Overview and Limitations 

The main goals of the analysis work done to support the Guidelines are as 

follows: 

 Estimate the seismic performance of existing structures with weak-story 

vulnerabilities; 

 Explore the applicability of the first-story retrofit and validate its 

effectiveness; 

 Quantify the first-story retrofit strength that optimizes seismic 

performance for a stipulated set performance criteria; and 

 Take into account the effect of torsion. 

The focus of the Guidelines is wood-framed structures between two and four 

stories with lateral resistance from stud walls with various sheathing 

materials. Buildings with varied weak-story vulnerabilities were analyzed. 

E.2.2 Building Characterization 

The approach to understand the seismic performance of both the existing and 

retrofitted structures relies on a large breadth of nonlinear response-history 

analyses performed on simplified building models. There are three main 

characteristics that vary among the many permutations of model buildings, 

and each has a corresponding parameter in the Guidelines: 

 Residual strength, parameterized by the strength degradation ratio, CD, 

 Base-normalized, upper-story strength, parameterized by AU, 

 Ratio of first-to-upper-story strength (i.e., weak-story ratio), 

parameterized by, AW. 
E-2 E: Detailed Analytical Background FEMA P-807 

The suite of analyses covers a large range of variations among these three 

parameters to form a reliable basis for recommendations. 

E.2.3 IDA Approach 

The Guidelines accommodate a range of building configurations and seismic 

hazards. This is achieved in the analysis by running a range of increasing 

seismic intensities on every building model permutation. This Incremental 

Dynamic Analysis (IDA) approach (Vamratsikos and Cornell, 2002) is useful 

in part because it lends itself to a probabilistic treatment of both seismic 

hazard and seismic performance. Thus, all results really boil down to 

probabilistic statements, e.g., the probability of exceeding a particular drift 

ratio, D, is P for a given seismic hazard, H, which is, in turn, defined by the 

probability of that hazard being exceeded in Y years. 

The results of the IDA can be analyzed by counting the number of responsehistory records in which a specified set of performance (e.g., interstory drift) 

criteria were exceeded for each earthquake intensity. The probability of 

exceedance at each intensity is computed by dividing the number of timehistories causing exceedance by the total number of time-histories. 

Generally, as the earthquake intensity increases, so does the probability of 

exceedance, and the data may be fit with good agreement using a log-normal 

cumulative density function (CDF). The log-normal CDF is defined by two 

parameters: the mean and the log-normal standard deviation, . These curves 

are commonly referred to as fragility curves. 

Quantifying seismic performance from IDA results requires two input 

parameters. The general problem statement may be framed as follows: given, 

 A building model, 

 Seismic performance (e.g., interstory drift) criteria, and 

 Seismic intensity (corresponding to some site-specific hazard), 

What is the probability that the performance criteria will be exceeded? See 

Figure E-1. 

Conversely the problem statement could flow in the opposite direction: 

instead of specifying the seismic intensity and asking for the probability of 

exceedance, one could specify the probability and find the corresponding 

seismic intensity. 
FEMA P-807 E: Detailed Analytical Background E-3 

E.2.4 Material Characterization 

The Guidelines document load-drift data for sixteen different sheathing 

material types; about one-quarter of those are archaic sheathing materials: 

lath and plaster, horizontal and diagonal wood sheathing. Among the other 

materials commonly used today, several are finish materials not often 

considered to provide lateral bracing in design of new buildings in areas of 

high seismicity. It is recognized that all sheathing materials provide lateral 

bracing strength and stiffness, but quantifying that, especially for archaic 

materials is not trivial. There are two basic hurdles that the Guidelines

attempt to overcome: 

 Quantifying load-drift behavior of a large set of materials, and 

 Addressing the fact that these sheathing materials may be combined into 

a large number of different assemblies. 

In order to provide a more accurate evaluation and a better optimized retrofit, 

it was deemed appropriate to consider each material and its unique load-drift 

curve. As a simplification, if one assumes that a story level translates without 

twisting, then all sheathing materials would react to the movement according 

to their load-drift (backbone) curves. Extending this idea, the Guidelines

consider that the load-drift curves for sheathing layers on the same wall may 

be added with some reduction based on limited test evidence. 

Figure E-1 Illustration of solution flow for Incremental Dynamic Analysis results. 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Seismic Intensity

Cumulative Probability

Site-specific seismic intensity

Probabilty of exceeding 

performance (drift) criteria Data

Log-normal fit
E-4 E: Detailed Analytical Background FEMA P-807 

Median unit load-drift curves were compiled from available test data and are 

summarized in detail in Appendix D. Where data was limited, gaps were 

filled for expected values based on extrapolation and judgment. These 

materials have been organized for convenience into two general categories: 

low-displacement capacity (Figure E-2) or relatively high-displacement 

capacity (Figure E-3). The criterion distinguishing the two material types is 

the story drift ratio at which the material exhibits no residual strength. The 

low-displacement capacity (Ld) materials have no residual strength at less 

than 3% interstory drift, the high-displacement capacity (Hd) materials have 

residual strength that go beyond 3% to about 4% or 5%. 

It should be noted here that, given the limited testing for the lowdisplacement capacity (Ld) materials, there may be more actual displacement 

capacity than that considered in these analyses. It is difficult to imagine that a 

structure with these types of materials would become laterally unstable at a 

drift ratio of around 2%, corresponding to perhaps 2.5 inches of lateral 

displacement, despite the loss of strength demonstrated in tests. More testing 

of these materials is needed to improve expectations for the seismic 

performance of these structures. 

Figure E-2 Unit load-drift curves for materials with low-displacement capacity. 

0

100

200

300

400

500

600

700

800

900

1,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Unit Force, plf

Stucco

Diagonal wood sheathing

Plaster on wood lath

Plywood panel siding

Plaster on gypsum lath
FEMA P-807 E: Detailed Analytical Background E-5 

To achieve the analysis objective of modeling a large breadth of buildings, 

these two categories of materials were simplified into two archetypical forms 

that were actually modeled (see Figure E-4). These forms, termed lowdisplacement capacity and high-displacement capacity, are composites of 

typical assemblies that might be present in the existing buildings of interest. 

The low-displacement capacity archetype approximately corresponds to a 

story with a strength degradation ratio, CD, of 0.0. The high-displacement 

capacity archetype approximately corresponds to a story with a strength 

degradation ratio , CD, of 0.0. Note that low-displacement capacity can be 

characterized as similar to one layer of stucco and one layer of lath and 

plaster, and that high-displacement capacity can be characterized as plywood 

structural panels with edge nailing 8d at 4” on center finished with stucco. 

E.2.5 Performance Criteria 

To draw useful conclusions from the IDA results, one must specify a set of 

performance criteria against which a building model will be tested for each 

response-history, at each intensity increment. One widely used measure of 

seismic performance is interstory drift ratio. The Guidelines optimize 

performance against collapse by limiting drift on the basis of material 

Figure E-3 Unit load-drift curves for materials with high-displacement capacity. Wall panel nailing 

notation: nail size (e.g., 8d) @ distance between center of nails in inches. 

0

500

1,000

1,500

2,000

2,500

3,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Drift Ratio, %

Unit Force, plf

Horizontal wood sheathing

Gypsum wall board

Wood structural panel 8d@6

Wood structural panel 8d@4

Wood structural panel 8d@3

Wood structural panel 8d@2

Wood structural panel 10d@6

Wood structural panel 10d@4

Wood structural panel 10d@3

Wood structural panel 10d@2
E-6 E: Detailed Analytical Background FEMA P-807 

displacement capacity. For this reason, the Onset of Strength Loss (OSL) was 

selected for the drift criteria for each material form. These terms are 

indicative of the expected state of the wall elements at each level. At Onset of 

Strength Loss, the sheathing material is on the verge of losing capacity to 

resist lateral forces. 

Figure E-4 Load-drift curves for archetypical material forms. 

The interstory drift criteria used in quantifying seismic performance are 

tabulated in Table E-1. For the un-retrofitted archetype building that has 

high-displacement capacity the OSL drift limits are 4% for both the upper 

structure and the first story. Retrofitting the first story with frames or walls 

with high-displacement capacity does not change these limits. For the unretrofitted archetype building that has low-displacement capacity the OSL

drift limits are 1.25% for both the upper stories and the first story. 

Retrofitting the first story with frames or walls with high-displacement 

capacity has the effect of improving the displacement capacity of the entire 

story. For this reason, the retrofitted first story is given a displacement limit 

of 4%. The drift limit for the unimproved upper stories remains at 1.25% 

after retrofit. This is the set of conditions illustrated in Figure E-4. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 1.0 2.0 3.0 4.0 5.0

Interstory Drift, %

Shear Ratio

High-displacement

Low-displacement capacity

capacity
FEMA P-807 E: Detailed Analytical Background E-7 

Table E-1 Drift Criteria, Interstory Drift Ratios in Percent 

Name 

High-Displacement 

Capacity (Hd) 

Low-Displacement Capacity 

(Ld) 

First Story 

Upper 

Stories First Story 

Upper 

Stories 

Onset of Strength Loss, 

Original Condition 4.0 4.0 1.25 1.25 

Onset of Strength Loss, 

Retrofitted 4.0 4.0 4.0 1.25 

E.3 Modeling Details 

E.3.1 Software 

Perform 3D (Version 4, CSI, 2006), a software package suited for nonlinear 

response-history analysis was used for the majority of the analysis work. It 

has an extensive library of nonlinear capabilities mostly built upon the 

concept of piece-wise linear backbone curves and event-to-event analysis. 

Perform 3D does not have elements in its library ready-made to model the 

types of walls under consideration. The approach taken was to use bar 

elements (axial load/deformation only) forming cross-struts from floor to 

floor. These bar elements were assigned material properties calibrated as 

illustrated in Figure E-5 to achieve the desired hysteretic behavior. 

Early in the study, only one pair of compression strut elements were used as 

illustrated in Figure E-5. Because the elements in Perform 3D are trilinear, 

there is an elastic portion of the load-drift curve over which no energy would 

be dissipated. The analysis was refined to account for hysteretic damping at 

low-drift ratios. This was done by adding another pair of cross-struts to each 

story making four per story. The yield deflections for each pair of cross-struts 

are staggered so one pair yields at low levels of drift, the other at larger drift. 

The composite effect is hysteretic damping at low levels of drift (see Section 

E.3.3 for additional information on hysteretic damping). 

E.3.2 Typical Building Model 

The typical building model had four levels at which the cross-struts were 

vertically restrained. For the translation models, all degrees of freedom 

except translation were restrained at each floor. The base was fixed. See 

Figure E-6. The width of each building model was 50 in. and the floor-tofloor was 100 in. At each level, there was one-quarter of the weight, 0.25 

kips, so that the total building weight was 1 kip. Thus, the material properties 

for each strut were normalized to the unit weight of the building. 
E-8 E: Detailed Analytical Background FEMA P-807 

Figure E-5 Schematics illustrating simplified building model bar elements. 

To model the first-story retrofit with ductility characteristics of a steel 

moment frame, a diagonal inelastic bar element was added. This element was 

calibrated so that the yield drift corresponds to that expected in a typical 

moment frame used for this type of application. Plywood retrofit options 

were also modeled. The plywood retrofit options had slightly better 

performance than those with moment frames. Because the difference in 

performance was small, both options were treated equally. This study is 

described in Section E.5.5 
FEMA P-807 E: Detailed Analytical Background E-9 

E.3.3 Hysteretic Damping 

The building models were capable of modeling energy dissipation by 

inelastic hysteresis. The true hysteretic behavior of these walls was not 

adequately characterized by full hysteresis loops characteristic of highdisplacement capacity steel hysteresis. Rather, the bottom-right and top-left 

quadrants of the hysteresis loops were relatively vacant, as illustrated in 

Figure E-7 and Figure E-8. 

Figure E-6 Screen-shot of typical four-story simplified building model in 

Perform 3D. Typically, twelve simplified buildings were 

analyzed simultaneously in one model file. The support 

conditions are shown at each node. The four-level vertical 

element on the right of each model is the leaning column used 

to capture P-delta effects. 
E-10 E: Detailed Analytical Background FEMA P-807 

Figure E-7 Plot showing hysteretic behavior of simplified structure models constrained by the backbone 

curve for the high-displacement capacity material form. 

Figure E-8 Plot showing hysteretic behavior of simplified structure models constrained by the backbone 

curve for the low-displacement capacity material form. 

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Force

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Force
FEMA P-807 E: Detailed Analytical Background E-11 

E.3.4 Viscous Damping 

All models implemented modal viscous damping of 2% for each mode. This 

value was deemed to be reasonable when considering large-displacement 

actions near collapse. It may be somewhat large for estimating smalldisplacement performance, as hysteretic damping at small displacements was 

modeled directly. 

E.3.5 P-Delta 

P-delta effects were modeled in the translational models by adding to each 

building a “leaning” column loaded axially with 0.25 kips per floor (see 

Figure E-6). In the torsional models, two “leaning” columns were added, one 

in each opposing corner, each loaded axially with 0.1 kips at each floor. 

Perform 3D calculates the P-delta lateral force during the response-history 

analyses. 

Early in the study, the modeling did not take P-delta effects into account. It 

was determined that P-delta should be addressed, so the models of retrofits 

were modified to include the P-delta effect. The translational models used to 

determine the magnitude of retrofit strength needed to optimize seismic 

performance did not include the P-delta effect. However, once the optimal 

retrofit strength was determined, the optimally retrofitted models were reanalyzed considering P-delta so that the performance reported in the 

Guidelines takes the effect into account. There is not much variation in the 

strength of the optimal retrofit, so it is assumed that a model optimally 

retrofitted not considering P-delta will still be optimally retrofitted if P-delta 

is considered. Thus, re-analyzing the whole set of models was assumed to be 

unnecessary. 

E.3.6 Accounting for Overturning Effects 

The resistance to overturning in the upper stories is complex and difficult to 

account for on a wall-by-wall basis. Overturning resistance is from deadload, coupling benefits at perforations, and the so-called “shell effects” due 

to the interaction between perpendicular walls and floors. To quantify the 

overall effect, a Perform 3D model was created for a structure similar to the 

example structure with tuck-under parking shown in Chapter 1, Figure 1-2. 

The model was modified to have four stories. The model included dead-load 

effects and all interconnected walls, headers and sills at openings and floor 

framing. The walls were modeled with fiber elements capable of both shear 

deformations and overturning. No discrete elements such as straps or hold 

downs were included. When the overturning resistance, such as from dead 

load is present, the wall segments roughly follow the load deformation 
E-12 E: Detailed Analytical Background FEMA P-807 

pattern of a shear model as shown at the lower right of Figure E-9. When 

overturning restraint is limited, the tension ends of the walls uplift. This 

reduces the capacity and roughly follows the load-deformation pattern of the 

fiber model as shown in the upper right of Figure E-9. 

The overturning adjustment factor, Qot, was determined by isolating each 

story and creating a load-drift curve from a pushover. For the baseline cases, 

the model was constrained to resist overturning by imposing vertical 

constraints at the ends of the walls. These constrained models were compared 

to models free to uplift at the ends of walls. For each pushover, the floor 

below the story under consideration was laterally fixed. Thus, fixing the 

second floor tests the second story in shear. The models were tested in both 

the transverse and longitudinal directions. Results that compare story shear 

strength for the longitudinal direction are shown in Figure E-10. The 

reduction for the lack of overturning restraint decreases for lower stories due 

to the increased dead load. The reduction is also lower when the direction 

under consideration is perpendicular to the floor or roof framing. Table 4-2 

captures these effects. When the floor framing is unknown or mixed, the 

greater reduction is recommended. 

Figure E-9 Schematic of fiber model showing how wall elements were modeled to capture 

overturning restraint and allow uplift. 
FEMA P-807 E: Detailed Analytical Background E-13 

 

a. Pushover fixed at ground level. 

 

b. Pushover fixed at second level. 

 

c. Pushover fixed at third level. 

 

d. Pushover fixed at fourth level. 

Figure E-10 Schematic of building displaced shapes and related pushover curves used in study to 

determine overturning adjustment factor, Qot. 

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%

Story Shear, kips

Second story fixed

Second story with uplift

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%

Story Shear, kips

Third story fixed

Third story with

uplift

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%

Interstory Drift Ratio

Story Shear, kips

Fourth story fixed

Fourth story with uplift

0

50

100

150

200

250

300

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0%

Story Shear, kips

First story fixed

First story with uplift
E-14 E: Detailed Analytical Background FEMA P-807 

E.4 Ground Acceleration Records 

A suite of 22 ground acceleration records used in the development of the 

FEMA P-695 Report, Quantification of Building Seismic Performance 

Factors (FEMA, 2009), were selected for these analyses. Each record has 

two horizontal components that were considered independently for the 

translational analyses, making 44 records total. All were strong-motion 

records without near-field effects. They were first scaled so that the geomean 

of the spectral acceleration of the 44 records equaled 1g at a period of 0.3 

seconds. This period was selected as the target, consistent with (1) the period 

expected for four-story structures and (2) values computed by simplified 

estimates in common evaluation codes. For the IDA, the set of records were 

then re-scaled consistently to values ranging from 0.1g to 3.5g, 35 scale 

factors total (see Figure E-11). 

E.5 Translational Analyses 

E.5.1 Analysis Flow 

The main set of analyses was translational, done with 2-dimensional building 

models as illustrated in Figure E-6. In this set of analyses, a range of values 

were assigned to the three parameters of interest (see Section E.2.2) and 

many combinations were considered. 

The objective was both to quantify the response of a range of existing 

buildings and also to find the first-story retrofit that optimizes seismic 

Figure E-11 Plots of acceleration spectra for selected response-history records. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Period, sec.

Spectral Acceleration, g

Mean Median Geomean
FEMA P-807 E: Detailed Analytical Background E-15 

performance. This implied that many existing building archetypes needed to 

be analyzed to develop a good understanding of the trends of seismic 

performance for this class of buildings. It also implied that many potential 

retrofit strengths needed to be considered to find which retrofit strength 

optimizes seismic performance for each building form. 

Figure E-12 illustrates the analysis tree for the translational analyses. The 

two main branches from which all the building permutations flow were the 

two material forms. For each material form, there were four base-normalized 

upper-story strengths considered relative to the total building. For each basenormalized upper-story strength, six weak-story ratios (defined as first-story 

strength divided by upper-story strength) were considered. For each weakstory ratio, the existing condition was analyzed. A high-displacement 

capacity first-story retrofit was then added with strength increasing so that 

the ratio of total retrofitted first-story strength divided by the upper-story 

strength ranged from the existing weak-story ratio (zero retrofit) to 1.6, a 

total of (51) building models per base-normalized upper-story strength. 

E.5.2 Median Performance 

Peak drift values were recovered from the IDA results for all of the building 

models, each of which is defined by material form, base-normalized upperstory strength, and weak-story ratio. Given a set of drift criteria for the first 

and upper stories, the IDA drift results were analyzed probabilistically, 

assuming a lognormal distribution. The median earthquake spectral 

acceleration response and lognormal standard deviation were computed so 

that the lognormal Cumulative Distribution Function (CDF) minimizes the 

error relative to the results under a given set of drift criteria. This median 

represents the value at which the probability of exceedance of the drift 

criteria is 50%. Because the ground acceleration records were scaled to a 

spectral acceleration response of 1g at a period of 0.3 seconds, this median 

earthquake spectral acceleration was taken to be the median “spectral 

acceleration capacity,” S of the structure for the drift criteria under 

consideration. Thus, at the median spectral acceleration capacity, S, the 

probability of exceedance of the specified drift criteria is 50%. 

In Chapter 5 of the Guidelines a set of drift criteria is defined to represent the 

onset of significant strength loss. Using these criteria, the median spectral 

acceleration capacities of all the building models were computed and curvefitted as illustrated in Figure E-13 and Figure E-14. Linear curve-fitting was 

considered inadequate in terms of accuracy at fitting the data. Given the basic 

form of the curve, 

  , U

U W Wx U S AA     (E-1) 
E-16 E: Detailed Analytical Background FEMA P-807 

Figure E-12 Flow chart used in translational analyses to optimize retrofit. Ductile materials 

are those with high-displacement capacity; brittle materials are those with lowdisplacement capacity. CDF = Cumulative Distribution Function. Sa = spectral 

acceleration. T = period of oscillation. P = probability of not being exceeded. 

Ductile 

Base-normalized upper-story 

strength, Au: 

(4) per mat'l form

Material forms:

(2) total

0.1 0.2 0.4

Weak-story ratios, Aw:

0.6 to 1.1 by 0.1

(6) per upper-story strength

Retrofit strengths:

Aw to 1.6

(51) per base-normalized upper-story strength 

TOTAL NUMBER OF

BUILDINGS:

2 x 4 x 51 = 408

Response-history 

seed records:

(22) Bi-directional records = (44) individual

Scaled so that median Sa( T = 0.3 sec ) = 1.0g

0.6

Brittle 

0.1 0.2 0.4 0.6

(35) intensities per seed

record varying from 0.1

to 3.5 by 0.1

Given drift criteria, fit

log-normal CDF

Recover peak interstory

drift ratios for each

analysis

Mean Spectral Acceleration at T = 0.33 sec

0 1.0 (Sa = 1g) 3.5

0

1.0

0.5
FEMA P-807 E: Detailed Analytical Background E-17 

Figure E-13 Curve fits for IDA results relating median spectral acceleration capacity 

(considering Onset of Strength Loss drift criteria) to base-normalized 

upper-story strength, AU for various weak-story ratios AW. Strength 

degradation ratio, CD = 1.0, and torsion coefficient CT = 0.0. 

Figure E-14 Curve fits for IDA results relating median spectral acceleration capacity 

(considering Onset of Strength Loss drift criteria) to base-normalized 

upper-story strength, AU for various weak-story ratios AW. Strength 

degradation ratio, CD = 0.0, and torsion coefficient, CT = 0.0. 

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Median Spectral Capacity, S

  60.0 S  0  0 .  1 122 .59 A AUW

Base-Normalized Upper-Story Strength, AU

Aw = 0.6

Aw = 0.7

Aw = 0.8

Aw = 0.9

Aw = 1

Aw = 1.1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Median Spectral Capacity, 

S

  48.0 S  1  0 .  2 525 . 24 A AUW

Base-Normalized Upper-Story Strength, AU
E-18 E: Detailed Analytical Background FEMA P-807 

the coefficients U, W, and U were computed to minimize the error relative 

to the entire field of the analysis results. Thus, the curve may fit certain 

values of AW better than others or certain ranges of AU better than others, but 

the error on the whole was minimized. There exist many other choices for the 

basic form of the curve, but given all of the uncertainties inherent in the 

problem under consideration and the mandate for Guidelines that are simple 

yet effective, the chosen form was deemed to be an adequate balance. 

E.5.3 Interpolation for Intermediate Values of CD

As is discussed in the following sections, the first-story strength was varied 

to represent adding new retrofit strength. If the unretrofitted condition 

initially has a strength degradation ratio, CD of zero, adding retrofit elements 

with a CD of one causes the CD value of the retrofitted condition to be 

between zero and one. The spectral acceleration capacity of these models 

provides the basis for interpolating between CD values of zero and one. 

Initially, it was assumed that linear interpolation on CD would be adequate. 

However, that assumption proved overly unconservative when the curve fit 

was plotted against the analytical results, as illustrated in Figure E-15. The 

results in the graph are from buildings with initial CD ratios of zero and AW

ratios varying from 0.6 to 1.1. The retrofitted AW ratio is approximately 1.3 

Figure E-15 Curve fits for IDA results using linear interpolation model for CD relating 

median spectral acceleration capacity (considering Onset of Strength Loss

drift criteria) to base-normalized upper-story strength, AU for various 

values of strength degradation ratio, CD, and torsion coefficient, CT = 0.0. 

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Base-Normalized Upper-Story Strength, A U

Median Spectral Capacity, 

S

CD = 0.53

CD = 0.46

CD = 0.38

CD = 0.30

CD = 0.22

CD = 0.14

  1 0 S  C D S  1 C D S    
FEMA P-807 E: Detailed Analytical Background E-19 

for reasons discussed in the following sections that explore the optimal 

retrofitted first-story strength. Figure E-15 shows that, for the intermediate 

values of CD studied, the median spectral acceleration capacity predicted 

using linear interpolation was consistently larger, and often significantly 

larger than the analytical results would indicate. Physically, this means that 

starting with a structure with a low CD ratio and increasing it by some 

amount does not lead to a performance enhancement proportional to the 

change in CD. A different model for interpolation was clearly needed. 

The interpolation on CD was assumed to be of the form: 

1 0 1  x x

D D S CS C S      (E-2) 

where Sμ and Sμ0 are the two extreme values of spectral acceleration capacity 

for CD = 1 and CD = 0, respectively. 

Choosing the value for the exponent, x = 3 adequately reduced the error over 

the field of data (see Figure E-16). For simplicity, a more precise number 

was not used. Figure E-17 illustrates the error between the analytical results 

and the linear and cubic interpolation assumptions. For each assumption, the 

Figure E-16 Curve fit for IDA results using cubic interpolation model for CD relating 

median spectral acceleration capacity (considering Onset of Strength Loss

drift criteria) to base-normalized upper-story strength, AU, for various 

values of strength degradation ratio, CD, and torsion coefficient, CT = 0.0. 

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Base-Normalized Upper-Story Strength, AU

Median Spectral Capacity,

S

CD = 0.53

CD = 0.46

CD = 0.38

CD = 0.30

CD = 0.22

CD = 0.14

  0

3

1

3 1    S C S C S D D 
E-20 E: Detailed Analytical Background FEMA P-807 

Figure E-17 Plots of error data, as a function of strength degradation radio, CD, and 

base-normalized upper-story strength, AU, for linear and cubic 

interpolation models for estimating median spectral acceleration 

capacity, Sμ. 

percent difference is plotted (vertical axis) against the strength degradation 

ratio, CD (horizontal axis). Whereas linear interpolation shows error that is 

generally large (between 10% and 50%) and always positive (i.e. overpredicting spectral capacity), the cubic assumption shows error less than 10% 

and has some balance between positive and negative error. 

E.5.4 Adjustment for Uncertainty 

Given a particular building model and set of drift criteria, the number of 

response-history records that cause exceedance generally increases as the 

earthquake ground shaking increases. The probability distribution will center 

about the median earthquake spectral acceleration response found by 

performing a log-normal curve fit. The dispersion around the median spectral 

acceleration response is characterized by the log-normal standard deviation 

of the curve-fit, quantifying uncertainty in the structural response due to the 

variability of the ground-motion time-histories. There are other uncertainties 

that exist and may be taken into account by adjusting the standard deviation. 

For this study, three parameters of uncertainty were considered: 

 Initial stiffness, K,

 Peak strength, FU, and 

 Drift ratio at strength loss, DL. 

-20%

-10%

0%

10%

20%

30%

40%

50%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Degradation Ratio, C D

% Difference btwn. Data and Curve Fit

Au = 0.1

Au = 0.2

Au = 0.4

Au = 0.6

Curve-fit using cubic 

interpolation on C D

Curve-fit using linear 

interpolation on C D

  0

3

1

3

 D  1 D SCSCS 

    D 1 1 D SCSCS  0

Not interpolated, C D =1.0

Not interpolated, C D =0.0

Strength Degradation Ratio, CD
FEMA P-807 E: Detailed Analytical Background E-21 

By varying each parameter independently and running the IDA on the 

variations, partial derivatives (or gradients) were computed relating the 

change in the natural logarithm of the median spectral acceleration response, 

, to the change in the natural logarithm of the parameter. This was done for 

building models with several uniform strength ratios (0.1, 0.2, 0.4) for each 

material form. The variations are illustrated in Figure E-18, Figure E-19, and 

Figure E-20. 

Using the gradients, one can compute a new value for the log-normal 

standard deviation, total, adjusted to account for material uncertainties in the 

parameters of interest. This is given by: 

3 3

2

1 1

ln( ) ln( )

ln( ) ln( ) total ij i j TH

i j X X i j

     

 

   

   

     (E-3) 

where: 

 total = Log-normal standard deviation adjusted to account for material 

uncertainties, 

Xi = Parameter, i, either K, FU, or DL,

 = Median earthquake spectral acceleration response satisfying lognormal curve-fit, 

ij = Correlation coefficient of ln(Xi) and ln(Xj) from material testing, 

i = Standard deviation of natural logarithm parameter Xi from 

material testing, and 

 TH = Log-normal standard deviation resulting from curve fit to IDA 

results using median material properties. 

The material statistics tabulated in Table E-2 were computed from the tests 

considered for these Guidelines as documented in Appendix D. Little 

experimental data of sheathing materials exists that was useful in the current 

context. The data set from which the statistics were computed is small, 

especially for materials like stucco and lath and plaster. Thus, the statistics 

for the expected behavior of these materials may not be very accurate. 

Further research and testing to more thoroughly understand the median 

behavior and variability of the finish materials is therefore warranted. 

Adjustments were made to convert the wood structural panel test data from 

multiple sources onto a basis consistent with the current context, as 

documented in Appendix D. These adjustments may have artificially 

decreased the variability of the backbone. In addition, it is noteworthy that 

the sizes of the data sets were not very large: four or more for the various 8d 

nailing configurations and two for the 10d nailing configurations. 
E-22 E: Detailed Analytical Background FEMA P-807 

Figure E-18 Plots showing stiffness variations in high-displacement capacity materials (left) and lowdisplacement capacity materials (right) as a function of normalized force (acceleration 

response) and drift ratio. 

Figure E-19 Plots showing strength variations in high-displacement capacity materials (left) and lowdisplacement capacity materials (right) as a function of normalized force (acceleration 

response) and drift ratio. 

Figure E-20 Plots showing variations in drift at loss of strength in high-displacement capacity materials (left)

and low-displacement capacity materials (right) as a function of normalized force (acceleration

response) and drift ratio. 

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 1.00 2.00 3.00 4.00 5.00

Drift, %

Normalized Force

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 1.00 2.00 3.00 4.00 5.00

Drift, %

Normalized Force

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Drift, %

Normalized Force

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 0.50 1.00 1.50 2.00 2.50

Drift, %

Normalized Force

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Drift, %

Normalized Force

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 1.00 2.00 3.00 4.00 5.00

Drift, %

Normalized Force
FEMA P-807 E: Detailed Analytical Background E-23 

Table E-2 Computed Material Statistics: x = Log-Normal Standard 

Deviation of Variable x, and xy = Correlation Coefficient of the 

Natural Logarithm of Variable x and y. K = Initial Stiffness; FU = 

Peak Strength, and DL = Drift Ratio at Strength Loss 

Low-Displacement Capacity High-Displacement Capacity 

K 0.260 0.158 

FU 0.214 0.075 

DL 0.259 0.076 

K,FU 0.975 0.823 

K,DL -0.234 -0.306 

FU, DL -0.180 0.050 

Gradients plots showing changes in initial stiffness, K, peak strength, FU, and 

drift ratio at strength loss, DL, for different materials, as a function of 

earthquake shaking intensity, are plotted for the onset of strength loss set of 

drift criteria in Figure E-21, Figure E-22, and Figure E-23, respectively. 

Similar gradients were computed for the other drift criteria but are not shown 

here. Clearly from these figures, the parameter with the largest gradient is 

peak strength. 

Curve-fitting the IDA results, the value of TH varies from 0.32 to 0.45 for 

the models with the low-displacement capacity (Ld) material and 0.32 to 0.40 

for the high-displacement capacity (Hd). The first term in Equation E-3 is the 

contribution of the material to the total uncertainty, defined as M

2

. 

Combining the material statistics in Table E-2 with the gradients shown in 

Figure E-21, Figure E-22, and Figure E-23, the adjustment for material 

uncertainty, M

2

, is computed to be only 0.0196 for the models with the lowdisplacement capacity (Ld) material and 0.0009 for the high-displacement 

capacity (Hd). This causes the range of total to become 0.35 to 0.47 for the 

models with the low-displacement capacity (Ld) material and 0.32 to 0.41 for 

the high-displacement capacity (Hd), a nearly negligible change. 

It was considered that the low  values in the material statistics might be 

inaccurate, so the material statistics were modified as tabulated in Table E-3. 

This caused computed M

2

 to become 0.04 for the models with the lowdisplacement capacity (Ld) material and 0.0144 for the high-displacement 

capacity (Hd). This had a very minor effect on total, causing the range to 

become 0.38 to 0.49 for the models with the low-displacement capacity (Ld) 

material and 0.34 to 0.42 for the high-displacement capacity (Hd), still a very 

small change. 
E-24 E: Detailed Analytical Background FEMA P-807 

Figure E-21 Plot showing effect of variation in stiffness, K, on median spectral capacity, S, for 

various configurations of material form and upper-story strength ratio, AU. The 

median spectral capacity is determined using the Onset of Strength Loss (OSL) set 

of drift criteria. Ductile materials are those with high-displacement capacity 

(CD=1.0). Brittle materials are those with low-displacement capacity (CD=0.0). 

The value, g, is the gradient (slope) quantifying the effect of the variation. 

Table E-3 Modified Material Statistics: x = Log-Normal Standard 

Deviation of Variable x, and xy = Correlation Coefficient of the 

Natural Logarithm of Variable x and y. K = Initial Stiffness; FU = 

Peak Strength, and DL = Drift Ratio at Strength Loss 

 Low-Displacement Capacity High-Displacement Capacity 

K 0.4 0.4 

FU 0.4 0.4 

DL 0.4 0.4 

K,FU 0.5 0.5 

K,DL -0.5 -0.5 

FU, DL -0.5 -0.5 

Regardless of the uncertainty in the material properties, the gradients in the 

seismic response relative to material variations are not large enough to cause 

significantly more overall uncertainty. Other sources of uncertainty and 

important issues not evident from the tests include: 

g=0.013 Ductile, Au=0.1

g=0.067

Brittle, Au=0.1

g=0.071

Ductile, Au=0.2

g=0.143

Brittle, Au=0.2

g=0.030

Ductile, Au=0.4

g=0.192

Brittle, Au=0.4

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Natural Logarithm of Stiffness, Ln(K )

Natural Logarithm of Median Spectral 

Capacity, Ln(

S )
FEMA P-807 E: Detailed Analytical Background E-25 

Figure E-22 Plot showing effect of variation in peak strength, FU, on median spectral capacity, 

S, for various configurations of material form and upper-story strength ratio, AU. 

The median spectral capacity is determined using the Onset of Strength Loss 

(OSL) set of drift criteria. Ductile materials are those with high-displacement 

capacity (CD=1.0). Brittle materials are those with low-displacement capacity 

(CD=0.0). The value, g, is the gradient (slope) quantifying the effect of the 

variation. 

 Inherent uncertainties in the process of surveying the existing building 

like measurements and identification of sheathing materials; 

 Workmanship in test specimens, which is likely to be better quality and 

uniformity than that found in the field; and 

 There may be damage potential that cannot be identified by selectively 

surveying material properties. 

Table E-4 summarizes the conclusions regarding the treatment of 

uncertainty. Because of the factors identified above, the values for total, 

which are denoted as , were artificially inflated to 0.6 for low-displacement 

capacity materials and 0.5 for high-displacement capacity materials. All 

results dependent on  are based on these values unless noted otherwise. 

Variations in  do not affect the median response (Probability = 0.5), by 

definition, of the log-normal CDF. Figure E-24 illustrates the effect of 

increasing  from 0.4 to 0.5 and 0.6. The effect becomes more pronounced 

further from the median and for higher values of spectral acceleration 

response. 

g=0.242

Ductile, Au=0.1

g=0.405

Brittle, Au=0.1

g=0.413

Ductile, Au=0.2

g=0.385

Brittle, Au=0.2

g=0.328

Ductile, Au=0.4

g=0.726

Brittle, Au=0.4

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

Natural Logarithm of Peak Strength, Ln(F U )

Natural Logarithm of Median Spectral 

Capacity, Ln(

S )
E-26 E: Detailed Analytical Background FEMA P-807 

Figure E-23 Plot showing effect of variation in drift at strength loss, DL, on median spectral 

capacity, S, for various configurations of material form and upper-story 

strength ratio, AU. The median spectral capacity is determined using the Onset 

of Strength Loss (OSL) set of drift criteria. Ductile materials are those with 

high-displacement capacity (CD=1.0). Brittle materials are those with lowdisplacement capacity (CD=0.0). The value, g, is the gradient (slope) 

quantifying the effect of the variation. 

Table E-4 Summary of Composite Log-Normal Standard Deviation, total 

(also known as ) 

Low-Displacement Capacity High-Displacement Capacity 

From Time-Histories without 

adjustment for material 

uncertainties 

0.32 to 0.45 0.32 to 0.45 

Based on material statistics 0.35 to 0.47 0.32 to 0.40 

Based on modified material 

statistics 0.38 to 0.49 0.34 to 0.42 

Selected for Guidelines 0.6 0.5 

E.5.5 Assessment and Probability of Exceedance 

Given the median spectral acceleration capacity, S, and dispersion, , the 

spectral capacity, Sc, at any desired drift-limit probability of exceedance, 

POE, may be recovered from the log-normal Cumulative Distribution 

Function (CDF). As discussed in the previous section, it is deemed 

g=0.145 Ductile, Au=0.1

g=0.315

Brittle, Au=0.1

g=0.178

Ductile, Au=0.2

g=0.137 Brittle, Au=0.2

g=0.222

Ductile, Au=0.4

g=0.203 Brittle, Au=0.4

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

-5.5 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5

Natural Logarithm of Drift at Strength Loss, Ln(D L )

Natural Logarithm of Median Spectral 

Capacity, Ln(

S )
FEMA P-807 E: Detailed Analytical Background E-27 

appropriate to simplify the dispersion to just two values depending on the 

strength degradation ratio, CD. For a given value of , the log-normal 

distribution has the property that the ratio, Sc / S for a specified drift limit 

POE is constant with respect to varying values of S as illustrated in Figure 

E-25. In order words, for a drift limit POE = 0.2 and  = 0.5, the ratio of Sc / 

S is 0.66 for any value of S. This implies that for a specified drift limit 

POE, an adjustment factor can be identified to convert the median spectral 

acceleration capacity to the spectral acceleration capacity with the specified 

drift limit POE. Taking advantage of this property of the log-normal 

distribution, the evaluation equations in Chapter 5 and the retrofit equations 

in Chapter 6 can accommodate any drift limit POE through the drift limit 

POE modification factors,  POE,0 and  POE,1 . 

It is presumed that most practicing engineers do not have a working 

knowledge of the log-normal distribution, and it is not a closed-form 

equation that can be manipulated with a hand calculator. For a given median 

spectral acceleration capacity, S and dispersion, , Microsoft Excel has a 

function for computing the drift limit POE at a specified value of Sc: 

POE LognormDist S S   c ,ln( ),    (E-4) 

Figure E-24 Cumulative Distribution Function plots showing effect of increasing log-normal 

standard deviation, , as a function of spectral acceleration response. 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Seismic Intensity

Cumulative Probability

 = 1.5  = 0.4

 = 0.6

 = 0.5

 = 0.5  = 0.4

 = 0.6

 = 0.5

Spectral Acceleration Response
E-28 E: Detailed Analytical Background FEMA P-807 

and conversely the value Sc at a specified drift limit POE, given the median 

and dispersion: 

S LogInv POE S c   ,ln( ),    (E-5) 

The Guidelines could define the drift limit POE modification factor, , POE in 

terms of these black-box functions, but this complicates the Guidelines

somewhat and could lead to confusion and user error. It was deemed to be an 

adequate and reasonable compromise to linearize the log-normal distribution 

focusing on a limited range of probabilities and the two selected values for 

the dispersion, : 

,1 0.0119 0.4102 POE  POE , for CD = 1.0 (E-6) 

,0 0.0133 0.3298 POE  POE , for CD = 0.0 (E-7) 

where: 

POE = probability of exceedance represented as a percentage. For 

example, for a 20% probability of exceedance, the drift limit 

POE = 20. 

As illustrated in Figure E-26, the error relative to the linear approximation is 

less than 10% over the range of probabilities of exceedance from 5% to 70% 

and is less than 5% over a range of probabilities from 6% to 65%. This range 

of probabilities encompasses the range of interest in the Guidelines, so the 

simplification comes with no cost in terms of the applicability of the 

evaluation and retrofit methods. 

Figure E-25 Plots of ratio of spectral acceleration capacity, Sc, at varying values of 

drift limit POE to median spectral capacity. 

0

10

20

30

40

50

60

70

80

90

100

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Ratio of Spectral Capacity to Median Capacity (Sc /S )

Probability of Exceedance, %

 = 0.6 (C D = 0.0)

= 0.5 (C D = 1.0)
FEMA P-807 E: Detailed Analytical Background E-29 

E.5.6 Retrofit Analyses 

For the building models representing the range of potential existing weakstory buildings under consideration, new elements were modeled to represent 

adding new strength to the first story as retrofitted. As discussed in the 

following section, the retrofit strength was varied in discreet increments to 

discover the right amount of strength to add given the characteristics (AU, AW, 

and CD) of the existing structure. For each retrofit strength increment, the 

form of the backbone curve for the new elements was set with constant yield 

and ultimate drift values of 1% and 5%, respectively, and constant ratio of 

yield-to-ultimate strength of 1.33. The backbone curve is illustrated in Figure 

E-27 for various strength increments relative to the upper-story shear 

strength, VU. The hysteretic behavior of the retrofit elements is full-loop as 

illustrated in Figure E-28. This backbone curve form is deemed to represent 

retrofits comprising ductile steel moment resisting frames that may be 

commonly used in the structures considered. Retrofits comprising structural 

wood panels are also considered, as described in Section E.5.9, and the form 

and hysteretic backbone curve for those analyses is based on the wood 

structural panel backbone curves in the table of commonly used sheathing 

materials. 

Figure E-26 Lognormal distribution for standard deviations,  = 0.5 and 0.6, for ratio of spectral 

acceleration demand to mean spectral acceleration capacity, over range of probabilities of 

exceedance, with linear fit (left) and the error (% difference) relative to the linear fit (right). 

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Ratio of Spectral Acceleration Demand to Median Capacity (S MS /S)

Probability of Exceedance, %

 = 0.6 (C D = 0.0)

= 0.5 (C D = 1.0)

-10% 0% 10%

Error

 = 0.6 (CD = 0.0)

= 0.5 (CD = 1.0)
E-30 E: Detailed Analytical Background FEMA P-807 

Figure E-27 Retrofit backbone curves for various strength increments relative to the 

upper-story shear strength, VU. 

Figure E-28 Plot illustrating hysteretic behavior of moment frame retrofit elements. 

0.75 Vu

1.0 Vu

0.15 Vu

0.2 Vu

0.30 Vu

0.45 Vu 0.4 Vu

0.6 Vu

0.60 Vu

0.8 Vu

1.2 Vu

0.90 Vu

0

0.2

0.4

0.6

0.8

1

1.2

0123456

Interstory Drift Ratio, %

Force in Terms of Building Weight, 

W

-400

-300

-200

-100

0

100

200

300

400

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

Deflection, in.

Force, kips
FEMA P-807 E: Detailed Analytical Background E-31 

E.5.7 Effect of First-Story Retrofit 

Adding some retrofit strength in the first story of a building with significant 

weak-story deficiency generally improves expected seismic performance. 

The improvement attained by adding first-story strength can be quantified in 

terms of spectral acceleration capacity relative to a set of drift criteria as 

illustrated in Figure E-29 and Figure E-30, which show that increasing firststory retrofit strength increases spectral capacity to a point. Thus, flowing 

from the constraint of retrofitting only the first story is a limit on the best 

achievable or optimal seismic performance. The plots in figures E-29 and E30 show four levels of strength (AU), each with three initial weak-story ratios 

(AW). Figure E-29 is for buildings with original construction capable of high 

displacement (CD = 1.0) and Figure E-30 is for buildings with original 

construction only capable of low displacement (CD = 0.0). It is noteworthy 

that, with little regard for the value of AU and unretrofitted value of AW, the 

value of AW after retrofit (i.e., along the horizontal axis) that leads to the 

largest spectral capacity occurs consistently between 1.2 and 1.3. 

Figure E-29 Plots of spectral acceleration capacity (spectral capacity) as a function of total 

first-story retrofitted strength, Vr, divided by upper-story strength, VU, for four 

levels of base-normalized upper-story strength, AU, varying initial pre-retrofit 

weak-story ratios, AW, original construction having high-displacement capacity 

(CD = 1.0), and Onset of Strength set of drift limits. 

Aw=0.6

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

0.7

1.2

1.7

2.2

2.7

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Total Ground Floor Strength/Upper Floor Strength, V r /V U

Spectral Capacity, 

Sc

Au = 0.4

Au = 0.6

Au = 0.2

Au = 0.1

Total First-Story Retrofitted Strength/Upper-Story Strength, Vr/VU

Spectral Capacity, 

Sμ
E-32 E: Detailed Analytical Background FEMA P-807 

Figure E-30 Plots of spectral acceleration capacity (spectral capacity) as a function of total 

first-story retrofitted strength, Vr, divided by upper-story strength, VU, for four 

levels of base-normalized upper-story strength, AU, varying initial pre-retrofit 

weak-story ratios, AW, original construction having low-displacement capacity 

(CD = 0.0), and Onset of Strength set of drift limits. 

The performance-optimal strength of the retrofitted first-story to upper-story 

strength ratio (termed weak-story ratio) was either 1.2 or 1.3 for 16 of 18 

conditions examined. Thus, it seems reasonable to create a nearly-constant 

linear approximation of the optimal retrofit strength that is close to 1.25 

irrespective of weak-story ratio. Plots of the analytical results and linear fit 

approximation (an equation used in Chapter 6) are shown in Figure E-31. 

The retrofit strength equations in Chapter 6 allow for the range of retrofit 

scenarios that limit the drift in both the first and upper stories to acceptable 

levels. In many cases, a building with a weak-story vulnerability can be 

retrofitted to a performance level meeting Onset of Strength Loss drift limits 

at the Maximum Considered Earthquake (MCE) for the selected drift limit 

probability of exceedance. This condition is discussed in Section 6.2.2 and 

illustrated in Figure 6-2. The strength of the upper stories is the key to 

whether this condition can be met. The equations in Chapter 6 are meant to 

estimate the strength of the first-story at which this condition might be 

expected. 

Aw=0.6

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=0.6 Aw=1.1

Aw=0.8

Aw=1.1

Aw=0.6

Aw=0.8

Aw=1.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Total Ground Floor Strength/Upper Floor Strength, V r /V U

Spectral Capacity, 

Sc

Au = 0.4

Au = 0.6

Au = 0.2

Au = 0.1

Total First-Story Retrofitted Strength/Upper-Story Strength, Vr/VU

Spectral Capacity, 

Sμ
FEMA P-807 E: Detailed Analytical Background E-33 

E.5.8 Estimating the Minimum Retrofit for Achieving Desired 

Performance 

As discussed in the previous section, a weak-story building may have upperstory strength that is sufficient for a first-story retrofit to achieve the desired 

seismic performance; i.e., one may not need to retrofit to the point that yields 

the peak spectral capacity. The minimum target strength of the retrofitted 

first-story would lead to a spectral capacity (for the specified drift criteria 

and POE) that is equal to the spectral demand, SMS. In this section, the 

evaluation equations are manipulated to derive an estimate of the minimum 

retrofitted strength of the first-story that leads to the desired spectral 

capacity. 

The evaluation equation in Chapter 5 has the general form: 

   , , 1 0.5 U

c POE U W W x T s U x S AC Q A     (E-8) 

where the coefficients U , W , and U are computed to minimize the error of 

the fit to the analytical results. Equation E-8 can be rewritten for strength 

degradation ratios, CD, of one and zero as: 

c W 11 2 S XA X   for CD = 1.0, and (E-9) 

c W 01 2 S YA Y   for CD = 0.0. (E-10) 

Figure E-31 Plot of maximum strength of total retrofitted first-story, Vr max, divided 

by upper-story strength, VU, as a function of base-normalized upperstory strength, along with a plot of a linear-fit equation. 

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Upper-Story Strength Ratio, A U

Vr max/VU

CD = 1.0 CD = 0.0 Fit

V r max /V U = 0.11A U +1.22 

Base-Normalized Upper-Story Strength, AU
E-34 E: Detailed Analytical Background FEMA P-807 

where: 

  0.48

0 ,1 1 0.5 X    POE U s AQ CT (E-11) 

1 0 X  2.24X , and 2 0 X  0.525X . (E-12) 

  0.6

0 ,0 1 0.5 Y AQ C    POE U s T (E-13) 

1 0 Y Y 1.59 , and 2 0 Y Y  0.122 (E-14) 

As discussed in previous sections, a cubic model is deemed appropriate for 

interpolating for intermediate values of CD, so the final relation for spectral 

capacity becomes: 

     3 3

1 2 12 1 S C X A X C YA Y cD W     D W (E-15) 

Substituting SMS for Sc in Equation E-15 and solving for AW leads to an 

estimate of the strength ratio, AW, that achieves the desired seismic 

performance: 

 

 

3 3

2 2

3 3

1 1

1

1

MSD D

W

D D

S XC Y C

A

XC Y C

    

 (E-16 

The strength of the retrofitted first story follows as Vr = AWVU, where VU is 

the limiting strength of the upper stories. 

In the above derivation, it is implied that AW changes independently of the 

other coefficients, particularly CT and CD; this is not true in general. In order 

to change AW, one must add strength to the first-story, and doing so will 

almost always affect the torsion coefficient, CT and will often affect the 

strength degradation ratio, CD. Thus, the value of AW recovered from 

Equation E-16 will not be the exact value that causes the spectral capacity, Sc

to equal the spectral acceleration demand, SMS. In fact, Equation E-16 will 

over-predict the amount of retrofit strength needed. It provides an estimate of 

the target retrofit strength, and the estimate converges with iteration. Thus, 

Chapter 6 refers to these retrofit strength values as estimates and calls for 

confirmation of the final retrofit design using the evaluation equations of 

Chapter 5. 

E.5.9 Wood-sheathed walls versus Moment Frame Retrofit 

Two types of load-drift curves were considered for retrofit elements: a full 

hysteretic loop that might come from a moment frame and wood-sheathed 

walls that would have behavior similar to the high-displacement capacity 

material form. The method used to model the plywood retrofit scenarios 
FEMA P-807 E: Detailed Analytical Background E-35 

mimics the modeling of the high-displacement capacity material form (see 

Section E.2.4). 

The optimal retrofit strength is determined using the moment frame 

assumption, and then the performance of the structure with plywood retrofit 

is compared to that with the moment frame retrofit. Typically, the difference 

in performance is small; Figure E-32 illustrates what might be the largest 

discrepancy. Thus, the Guidelines make no distinction between using 

plywood or moment frames as retrofitting elements. 

It is somewhat surprising that the plywood retrofit behaves better in some 

cases than the moment frame retrofit, and further study into this comparison 

is warranted. It should be noted that the plywood retrofit does not give better 

results in every case, but in those cases the performance is essentially 

equivalent. The reason may be that the moment frame is significantly softer 

than the plywood elastically, so the structure must move farther before the 

moment frame reaches its peak strength. For the low-displacement materials, 

the implication is that the existing materials would have lost strength by that 

point. 

Figure E-32 Plots comparing retrofit performance for moment frame (M.F.) verses plywood wall 

retrofit, as a function of earthquake shaking intensity, for base-normalized upper-story 

strength, AU = 0.4, and weak-story ratio, AW = 0.6. 

A U = 0.4, A W = 0.6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Spectral Acceleration Response

Cumulative Probability

Existing buildings with highdisplacement capacity

Plywood Retrofit

M.F. Retrofit

Existing buildings with

low-displacement 

capacity
E-36 E: Detailed Analytical Background FEMA P-807 

E.5.10 First-Story Height 

The seismic performance of a weak-story building will depend on the height 

of the first story. Given two buildings that are identical with the exception of 

different first-story heights, the building with the shorter first story will have 

worse seismic performance. A small analytical study was done to verify and 

explore this effect. For this study, a simple building model was selected (AU

= 0.4, AW = 0.6) for each material form, with and without optimal retrofit: 

four models, total. The first-story height was varied from 15 inches (1’-3”) to 

200 inches (16’-8”). The backbone curves were kept constant relative to 

interstory drift. 

Figure E-33 shows the median spectral acceleration capacity plotted against 

first-story height for each model. Clearly, the median spectral acceleration 

capacity increases for increasing first-story height. In Figure E-34, the 

median spectral acceleration capacity is normalized by dividing the median 

spectral acceleration capacity for a building of given first-story height by that 

of the building with 100-inch first-story height. This implies that a linear fit 

might adequately represent the trend irrespective of retrofit and strength 

degradation ratio, CD. Figure E-35 shows the normalized median spectral 

acceleration capacities with a linear fit based on a first-story height of 100 

inches. Chapters 3 and 4 use a similar equation, adjusted slightly to be based 

on a first-story height of 8 ft. 

Figure E-33 Plots of median spectral acceleration capacity (spectral capacity) 

versus first-story height for four building models considered. 

CD = strength degradation ratio. 

Cd=0, original

Cd=0, retrofitted

Cd=1, original

Cd=1, retrofitted

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250

Height of First Story, in.

Median Spectral Capacity
FEMA P-807 E: Detailed Analytical Background E-37 

Figure E-34 Plots of normalized median spectral acceleration capacity 

(spectral capacity) versus first-story height for four buildings 

considered. Spectral capacity is normalized by dividing spectral 

capacity at a given height by the spectral capacity of the 

building with a 100-inch height. C

D = strength degradation 

ratio. 

Figure E-35 Plots of normalized median spectral acceleration capacity 

(spectral capacity) versus first-story height for four buildings 

considered with linear fit. Spectral capacity is normalized by 

dividing spectral capacity at a given height by the spectral 

capacity of the building with a 100-inch height. C

D = strength 

degradation ratio. 

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

0 50 100 150 200 250

Height of First Story, in.

Normalized Median Spectral Capacity

Linear fit for Story-Height Adjustment Factor, Qs:

Q

s = 0.55 + 0.0045 

H

where 

H is the median first-story height in inches.

Cd=0, original

Cd=0, retrofitted

Cd=1, original

Cd=1, retrofitted

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

0 50 100 150 200 250

Height of First Story, in.

Normalized Median Spectral Capacity

Spectral capacities normalized by the spectral capacity of the 

corresponding building with a bottom story height of 100 in.
E-38 E: Detailed Analytical Background FEMA P-807 

E.6 Torsional Analyses 

E.6.1 Discussion on Torsional Behavior 

Torsional behavior is distinctly more complicated than translational behavior 

because the two directions of motion are coupled. Thus, even if the center of 

strength aligns with the center of mass (the center of the seismic inertial 

loading), in one direction, the spectral acceleration capacity in that direction 

will be affected by eccentricity in the other direction. Torsional behavior is 

also coupled with translational force input. Earthquakes do not deliver 

torsional moment to the base of the building (assuming the buildings are 

small), but it is the eccentricity that exists between the centers of strength and 

mass that causes twisting to occur. Because of these complexities, a 

comprehensive treatment of torsional behavior would probably require more 

study. Because a limited treatment of torsion is presented and incorporated 

into the Guidelines, an engineer designing a retrofit should strive to remove 

torsion in the first story to the extent practical. 

E.6.2 Torsion Coefficient, CT

Torsional vulnerability is treated as another phenomenon that can be 

parameterized by a coefficient like the other coefficients used in the 

Guidelines. This approach allows simple recommendations, based on the 

lateral load-drift characteristics of the existing and retrofitted first story. 

The center of strength is, by definition, the point at which the application of 

lateral force causes no rotation. A simplified understanding of the torsional 

response would be that there is a translational force imparted from the firststory to the upper stories through the center of strength of the first story. As 

the force is applied, the upper stories apply an inertial reaction through their 

center of strength, which is often uniform among the upper stories and 

coincides near the center of mass. This causes a torsional couple. Assuming 

the upper stories rotate about the first-story center of strength, the torsional 

resistance stabilizing the upper stories is characterized by the torsional 

strength of the first story, T1, computed in Chapter 4. 

The lateral strength of the first story has two orthogonal components; a force 

vector that will potentially occur during any response-history as the structure 

reaches its peak strength and yields in the two directions simultaneously. In 

general, the relationship between the centers of strength at the first story and 

the upper stories can be characterized as a position vector with two 

orthogonal components. Torsional moment is defined to be the cross-product 

of the eccentricity vector and the force vector. Thus, the definition of the 

Torsional Demand, , emerges in Chapter 4. 
FEMA P-807 E: Detailed Analytical Background E-39 

The natural next step is to divide the torsional demand by the capacity to 

arrive at the unitless torsion coefficient, CT. 

E.6.3 Modeling 

Building models were devised that vary CT while holding other parameters 

constant. Values of CT considered range from 0.0 (no torsion) to 1.0 

(unretrofitted) and 1.58 (retrofitted). The following list summarizes the range 

of other parameters considered: 

 Base-normalized upper-story strength, AU: 0.4; 

 Weak-story ratio, AW: 0.6, 0.8; and 

 Both low-displacement capacity (Ld) and high-displacement (Hd) 

capacity material forms. 

Each building model was also re-analyzed with the optimal retrofit strength 

placed at the original center of strength. This causes the increase in CT from 

1.5 (unretrofitted) to 1.58 (retrofitted) noted above. 

The building models for torsion were analyzed with two translational and one 

rotational degree of freedom on each level. They comprise four lateral 

bracing systems similar to what was described in detail in Section E.3.2 

representing four wall lines. The weight of the entire building was 1 kip, 

distributed evenly to each of the four levels (0.25 kips per level). The nodes 

at each level were constrained by a rigid diaphragm assumption. 

In general, the value of CT depends on many factors including the locations 

of the walls, the relationship of the lateral strength of walls in one direction 

versus the other, and the distribution of the wall strengths. Also, the torsional 

moment of inertia depends upon the geometry of the floors. For these 

analyses, for a given building model, the strength and weak-story ratio in 

each horizontal direction was equal. In order to increase CT, the wall line 

elements in the longitudinal direction on the front façade on the first story 

was moved toward the back in four increments, and the transverse walls lines 

were moved in toward the center. Figure E-36 and Figure E-37 illustrate each 

building model form for the four increments of CT considered. 

E.6.4 Response-History Input 

The response-history input for the torsional analyses differs from that of the 

translational analyses. It was deemed appropriate to simultaneously run the 

ground-motion records considering both components of motion. However, 

since the orientation of the records should be random, the building models 
E-40 E: Detailed Analytical Background FEMA P-807 

Figure E-36 Schematic illustration of floor plans and values of weak-story ratio, AW, used in Perform 3D 

models of unretrofitted buildings for various torsion coefficients, CT. 

Figure E-37 Schematic illustration of floor plans and values of weak-story ratio, , AW, used in Perform 3D 

models of retrofitted buildings for various torsion coefficients, CT. 

Ground Floor Plans Upper Floor Plans eq. eq.

L

0.2L L

0.0

Lateral strength proportional

to building length in each

direction

Edge of floor above

0.00

0.00

AW

0.60

0.80

C

0.33

0.33

0.60

0.80

0.67

0.67

0.60

0.80

1.00

1.00

0.60

0.80

T

Ground Floor Plans Upper Floor Plans

0.00

0.00

eq. eq.

L

0.2L L

0.0

Lateral strength proportional

to building length in each

direction

Edge of floor above

AW

0.60

0.80

CT

0.41

0.38

0.60

0.80

0.90

0.79

0.60

0.80

1.58

1.31

0.60

0.80

Optimal retrofit

element
FEMA P-807 E: Detailed Analytical Background E-41 

were analyzed once with an orientation angle of zero degrees and re-analyzed 

with an orientation angle of 90 degrees. Thus, the total number of records 

considered in the incremental dynamic analysis (IDA) remained at 44. 

E.6.5 Assessing the Effect of Torsion 

Analyzing the results of the IDA on the building models for torsion, a 

correlation was found between increasing CT and reduction in spectral 

acceleration capacity for the Onset of Strength Loss set of drift criteria, 

considering the longitudinal direction of the building models, i.e., the 

direction perpendicular to the movement of the front façade wall line. The 

correlation is characterized fairly well with a simple linear approximation as 

illustrated in Figure E-38. 

The results, considering drift in the transverse direction, also showed a 

correlation between increasing CT and reduction in spectral capacity. A 

somewhat different trend is illustrated in Figure E-39. The reduction starts 

more steeply and appears to level off at CT near 1.0. 

The load-drift behavior in each direction is exactly the same if torsion is 

ignored. Because the time-histories are run in two orthogonal orientations as 

separate analyses, the translational demand on the building is the same in 

Figure E-38 Plots of spectral acceleration capacity reduction versus torsion 

coefficient, CT, for the Onset of Strength Loss set of drift criteria, 

considering the longitudinal direction for various values of weak-story 

ratio, AW. “AB” indicates unretrofitted model; “R” indicates model 

with optimal retrofit. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Torsion Coefficient, C T

Spectral Acceleration Capacity Reduction

Ductile, Aw = 0.60AB

Ductile, Aw = 0.60R

Ductile, Aw = 0.80AB

Ductile, Aw = 0.80R

Brittle, Aw = 0.60AB

Brittle, Aw = 0.60R

Brittle, Aw = 0.80AB

Brittle, Aw = 0.80R

Direction of drift assessment
E-42 E: Detailed Analytical Background FEMA P-807 

Figure E-39 Plots of spectral acceleration capacity reduction versus CT, for the Onset 

of Strength Loss set of drift criteria, considering the transverse direction 

for various values of weak-story ratio, AW. “AB” indicates expected 

model; “R” indicates model with optimal retrofit. 

each direction. Thus, there appears to be an interesting effect wherein the 

transverse walls are taxed more heavily than the longitudinal walls due to the 

torsional demand caused by the forces acting longitudinally. This is because 

the greatest resistance to rotation comes from the walls the greatest distance 

from the center of rotation. Thus, for the building plan shown, the transverse 

walls will carry more of the torsional forces. 

E.6.6 Simplified Torsion Coefficient, CTs

The simplified torsion coefficient, CTs is derived from the torsion coefficient, 

CT by making certain assumptions that are considered appropriate in the 

context of the simplified evaluation in Chapter 3 of the Guidelines. The 

torsional coefficient, CT is the ratio of torsional pseudo-demand,  to 

torsional strength of first-story, T1, as defined in Chapter 4: 

CT T

  ; need not be greater than 1.4 (E-17) 

As described in Section 4.6.8, the torsional demand,  is calculated by 

multiplying the translational strength of the ground story by the eccentricity 

(as illustrated in Figure 4-14). It is given by:

x 1, 1, y yx   eV eV  (E-18) 

0.0

0.2

0.4

0.6

1.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Torsion Coefficient, CT

Spectral Acceleration Capacity Reduction

Ductile, Aw = 0.60AB

Ductile, Aw = 0.60R

Ductile, Aw = 0.80AB

Ductile, Aw = 0.80R

Brittle, Aw = 0.60AB

Brittle, Aw = 0.60R

Brittle, Aw = 0.80AB

Brittle, Aw = 0.80R

Direction of drift

assessment
FEMA P-807 E: Detailed Analytical Background E-43 

Figure E-40 Illustration of the simplified torsional strength, Ts. 

Computing the torsional strength of the first story, T1, in accordance with 

Chapter 4 is not trivial. Therefore, a simplifying assumption is made to 

estimate the torsional strength, as illustrated in Figure E-40. The torsional 

strength is computed by applying a twist about the center of strength, and 

computing the corresponding torque. In this simplified approach, the first 

story is twisted about the geometrical centroid of the floors above, assuming 

that the resultant of one-half the wall shear in each direction will act through 

a point located one-quarter of the building dimension away from the center. 

With this assumption, the torsional strength becomes: 

4 4

x y

sy x

L L

TV V             

 (E-19) 

A further assumption is made, that Vx  Vy; Equation E-18 and Equation E-19 

become: 

   Ve e  x y  (E-20) 

  4 s x y

V T LL   (E-21) 

Thus, the simplified torsion coefficient, CTs, as used in Chapter 3, becomes: 

4 x y

Ts

x y

e e

C

L L

     

  

 (E-22) 

FEMA P-807 F: Validation of Analysis Methods F-1 

Appendix F 

Validation of Analysis Methods 

F.1 Purpose 

Early on in the Guidelines developmental effort, members of the project team 

performed preliminary analytical work to verify the concept of the “Relative 

Strength Method.” The results of that effort are documented in an internal 

ATC report, “Task 2: Detailed Analytical Verification.” This analysis is 

referred to herein as the Task 2 Analysis. The conclusions of that work 

support the validity of the concept. The analytical framework described in 

Appendix E of the Guidelines broadened the scope of results by considering 

a large number of simple idealized buildings. The analysis work described in 

Appendix E is referred to herein as the Broad-Scope Analysis. 

The purpose of this appendix is to compare and contrast the results of these 

two sets of analysis to validate the analysis methods used in Appendix E of 

the Guidelines. The details of each body of work are sufficiently described 

elsewhere; this appendix supplements those details from the perspective of 

comparison. 

F.2 The Building Under Consideration 

The Task 2 Analysis focused on a rectangular, wood-framed, three-story 

apartment building that had been studied previously as part of the CUREECaltech Wood-Frame Project (Reitherman et al., 2003), which was carried 

out by California Universities for Research in Earthquake Engineering (now 

the Consortium of Universities for Research in Earthquake Engineering) and 

the California Institute of Technology, with funding from FEMA. This 

building is referred to herein as the CUREE Apartment Building. The 

building (Figure F-1) is assumed to have been constructed prior to 1970 in 

Northern or Southern California, designed according to the 1964 edition of 

the Uniform Building Code (ICBO, 1964) and ‘engineered’ to a minimal 

extent. The floor-to-floor height of the apartment building is about 9’-0”. 

The total dead load, W, is about 348.5 kips. 

The Task 2 Analysis focused mainly on response in the long (east-west) 

direction, which has a greater weak-story character than in the north-south 

direction. Torsion was eliminated from the analysis because the pushover 

curves for the east-west direction were not significantly affected by 
F-2 F: Validation of Analysis Methods FEMA P-807 

torsion. Following is a list of the building’s characteristics in the east-west 

direction in terms of the Guidelines coefficients: 

1. First-story strength, V1 = 0.452W

2. Second-story strength, V2 = 0.6W

3. Base-normalized upper-story strength, AU = 0.6 

4. Weak-story ratio, AW = 0.75 

5. Strength degradation ratio, CD = 0.66 

F.3 Differences in Scope of Analysis 

Whereas the Task 2 Analysis focused in detail on one particular building, the 

Guidelines cover a broad scope of structures. It was deemed appropriate that 

the Broad-Scope Analysis sufficiently cover the whole range of buildings that 

could potentially be covered by the requirements of the Guidelines. In the 

following subsections, various characteristics of the buildings under 

consideration are described, with discussion about how the Broad-Scope and 

Task 2 Analyses differ. 

Figure F-1 CUREE Apartment Building used in ATC-71-1 Task 2 Analysis (from Christovasilis et al., 2009).
FEMA P-807 F: Validation of Analysis Methods F-3 

F.3.1 Number of Stories 

Whereas the CUREE Apartment Building is three stories tall, many buildings 

covered by the Guidelines have four stories. For the Broad-Scope Analysis, it 

was assumed that the four-story structure should be modeled and that the 

results should be applicable to the three-story structure, if the results were 

normalized by the total building mass. 

F.3.2 Sheathing Assemblies 

The sheathing materials in the CUREE Apartment Building include both 

structural wood sheathing and finish materials. This leads to load-deflection 

curves that are a composite of high- and low-deformation capacity materials. 

In the parlance of the Guidelines, the strength degradation ratio, CD, is 

between 0.0 and 1.0. For the Broad-Scope Analysis, the permutations of 

building models considered the two extreme possible strength degradation 

ratios (0.0 and 1.0), but nothing in between. This was done for the practical 

purpose of limiting the analysis work to what was possible to achieve within 

the budgetary and time limitations of the project. It is assumed that having 

the results for the extreme strength degradation ratios, one can adequately 

estimate for intermediate ratios using linear interpolation. 

F.4 Differences in Analytical Methods 

The two analysis efforts were done by different teams with distinct 

perspectives and approaches related to the work involved. The following 

subsections describe some of the differences related to the analytical 

methods. 

F.4.1 Software 

The Task 2 Analysis team used SAWS (Seismic Analysis of Wood-frame 

Structures) computer software (Folz and Filiatrault, 2004a,b) to perform the 

analyses. SAWS features sophisticated hysteretic behavior tailored for 

modeling wood-framed structures. One key aspect of this behavior is to 

dissipate energy at low displacements as opposed to having a range of elastic 

strength (see Figure F-2). SAWS can also model hysteretic behavior 

characteristic of ductile moment frames with full hysteretic loops. The 

backbone for these elements is bilinear with an elastic range and post-yield 

range with strain hardening (see Figure F-3). 

The Broad-Scope Analysis was done using CSI (2006) Perform-3D software, 

a general purpose nonlinear structural analysis application. Because 

Perform-3D does not have a built-in wood-frame wall element, as SAWS 
F-4 F: Validation of Analysis Methods FEMA P-807 

O

A

B

D

E

F

G

H

I

1 C

1

1

(u,Fu)

r2K0

K0

r4K0

r3K0

FI 1

Kp

1

F0

120

Force

Displacement

Nonlinear

Backbone Curve

Capping Strength

Pinching and 

Re-Loading Stiffness

In-Cycle

Degrading Strength

r2k0 Degrading

Capping Strength

Failure

Displacement

f

-400

-300

-200

-100

0

100

200

300

400

-5 -4 -3 -2 -1 0 1 2 3 4 5

Deflection, in.

Force, kips

does, non-linear “concrete” material (a zero-tension material with tri-linear 

and strength-loss 

 

Figure F-2 Hysteretic behavior of wood-framed elements in SAWS (after Folz and 

Filiatrault (2004a,b). Parameters shown are defined in Folz and Filiatrault 

(2004a,b). 

Figure F-3 Hysteretic behavior of moment frame elements in SAWS. 
FEMA P-807 F: Validation of Analysis Methods F-5 

backbone options) was modeled as cross-struts calibrated to emulate the 

expected hysteretic behavior of wood. Each floor level had four 

compression-only cross-struts, with staggered yield points (see Figure F-4 

and Figure F-5). The ductile moment frames were modeled using inelastic 

diagonal bar elements with a trilinear backbone curve (see Figure F-6). 

Figure F-4 Hysteretic behavior of elements emulating wood-frame walls in Perform3D, where the strength degradation ratio, CD = 0.0. 

Figure F-5 Hysteretic behavior of elements emulating wood-frame walls in Perform3D, where the strength degradation ratio, CD = 1.0. 

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Force

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift Ratio, %

Force
F-6 F: Validation of Analysis Methods FEMA P-807 

F.4.2 Viscous Damping 

The Task 2 Analysis included Rayleigh (also known as alpha-M, beta-K) 

viscous damping. This models damping as a constant velocity damping 

matrix composed of adding particular fractions of the mass and elastic 

stiffness matrices. The user inputs a damping ratio for the first two modes of 

vibration, and the software determines the corresponding coefficients for 

each matrix. In the Task 2 Analysis, 1% damping was chosen for the first two 

modes; damping for the third mode was computed to be 1.28% for the 

existing structure and 1.24% for the retrofitted. 

In the Broad-Scope Analysis, viscous damping was modeled using modal 

damping. In this approach the damping matrix was computed by combining 

the mass matrix in a special way. One can specify the damping ratio to be 

constant for all modes, as opposed to Rayleigh damping, where only the 

damping is constant for two modes but varies for all others. In the BroadScope Analysis, 2% modal damping was used for all modes. 

It was decided to not re-run the analysis with a damping model to match the 

Task 2 Analysis. As is shown in later sections of this appendix, the results 

appear unaffected by the choice between these two damping models when 

other aspects of the models are constructed to match. 

Figure F-6 Hysteretic behavior elements emulating ductile moment 

frames in Perform-3D. 

-400

-300

-200

-100

0

100

200

300

400

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

Deflection, in.

Force, kips
FEMA P-807 F: Validation of Analysis Methods F-7 

F.4.3 Backbone of Increasing Retrofit 

In the Task 2 Analysis, the elastic and strain hardening stiffnesses were held 

constant irrespective of retrofit strength. The elastic stiffness corresponded to 

four W14×90 cantilevered columns, and the post yield stiffness was set at 

0.02 times the elastic stiffness. The base yield strength, Vy, was set at 322 

kips (0.92W or 1.6V2). There was no plateau modeled. The range of yield 

strengths modeled varied between 0.2Vy (0.12W) and 1.2Vy (0.7W), as shown 

in Figure F-7. 

In the Broad-Scope Analysis, the drift ratio at yield and ultimate plateau were 

held constant at 1% and 5%, respectively. The ratio of yield to ultimate 

strength was held constant at 0.75, and the elastic and hardening stiffnesses 

vary. In the Task 2 Analysis, retrofit strength was keyed at the yield strength 

of the retrofit, but in the Broad-Scope Analysis, the retrofit strength was 

keyed off of the ultimate strength, Vu. Figure F-8 shows the range of retrofit 

strengths in the Task 2 Analysis. 

Figure F-9 compares backbone curves for three selected retrofit strengths for 

each analysis. It is clear that there is a significant distinction between the two 

analysis approaches, both in terms of what is a reasonable model of the 

retrofit (constant stiffness versus constant yield drift and ratio Vu/Vy) and how 

it is described (based on Vy versus Vu). One must be careful when comparing 

the results that the terms are defined on the same basis. 

Figure F-7 Backbone curves for varying retrofits modeled in the Task 2 

Analysis. 

1.14 Vy

1.0 Vy

0.35 Vy

0.2 Vy

0.55 Vy

0.4 Vy

0.74 Vy

0.6 Vy

0.94 Vy

0.8 Vy

1.2 Vy

1.33 Vy

0

0.2

0.4

0.6

0.8

1

1.2

1.4

012345

Interstory Drift Ratio, %

Force in Terms of Building Weight, 

W
F-8 F: Validation of Analysis Methods FEMA P-807 

0

0.2

0.4

0.6

0.8

1

1.2

0123456

Interstory Drift Ratio, %

Force in Terms of Building Weight, 

W

Task 2 Analysis Broad-Scope Analysis

0.75 Vu

1.0 Vu

0.15 Vu

0.2 Vu

0.30 Vu

0.45 Vu 0.4 Vu

0.6 Vu

0.60 Vu

0.8 Vu

1.2 Vu

0.90 Vu

0

0.2

0.4

0.6

0.8

1

1.2

0123456

Interstory Drift Ratio, %

Force in Terms of Building Weight, 

W

Figure F-8 Backbone curves for varying retrofits modeled in the BroadScope Analysis.

F.5 Comparison of Results

As noted above there were many differences between the two analysis 

approaches that may lead to different results. It was decided to build a model 

in Perform-3D that matches the properties of the building as documented in 

the Task 2 report but using the modeling methods of the Broad-Scope 

Analysis. Thus, cross-strut and retrofit elements were calibrated to match the 

Figure F-9 Comparison of selected backbone curves for varying retrofits 

modeled.
FEMA P-807 F: Validation of Analysis Methods F-9 

backbone curves shown in the Task 2 Report. The number of stories was set 

at three. The damping model was left unchanged. The Incremental Dynamic 

Analysis (IDA) was re-run using the suite of 44 acceleration records, and the 

median earthquake intensities were recovered and compared with the results 

documented in the Task 2 Report at three drift ratios: 1%, 2% and 3%. This 

was done for increasing levels of retrofit strength. The same analyses were 

then re-run for the four-story case, and then both the 3- and 4-story cases 

were re-run with the retrofit backbones used in the Broad-Scope Analysis. 

Following is a discussion of differences in the results and the perceived causes. 

F.5.1 Existing Building 

Given the differences between the Task 2 and Broad-Scope Analyses in 

viscous damping and hysteretic behavior, one might expect some difference 

in the results for models of the existing (unretrofitted) building. Figure F-10 

shows plots of the results for the three sets of analyses. The variation among 

the median spectral accelerations is small at 1% or 2% drift ratios and is 

negligible at 3% drift. Interestingly, there is no discernable difference 

between the results for the 3- and 4-story buildings. 

Figure F-10 Comparison of analysis results for the existing building. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1.0 1.5 2.0 2.5 3.0

Drift Ratio, %

Median Spectral Acceleratio

n

Task 2

Broad-Scope, 3 Stories

Broad-Scope, 4 Stories

Data Table

Drift Task 2 3 Stories 4 Stories

1% 0.95 0.85 0.85

2% 1.21 1.10 1.10

3% 1.31 1.29 1.29

Broad Scope
F-10 F: Validation of Analysis Methods FEMA P-807 

F.5.2 Retrofitted Building 

As discussed above, there are several significant differences in the backbone 

curves for the retrofitted building between the Task 2 and Broad-Scope 

Analyses. The first difference is how the retrofit strength is defined. One 

would expect a difference in results if the definition of strength in one case is 

based on yield strength and, in the other case, is based on ultimate strength. 

Consider the lowest retrofit strength in Figure F-9. The yield strength in the 

Task 2 backbone and the ultimate strength in the Broad-Scope Analysis are 

both equal to 0.18W. The Task 2 backbone yields at a larger force and 

smaller deflection than the corresponding Broad-Scope backbone, and 

though the backbones approach each other post-yield, they remain separated 

significantly. 

Figure F-11 illustrates the difference in performance that arises from the two 

different retrofit modeling approaches and it verifies that, given equivalent 

assumptions, the Task 2 and Broad-Scope Analyses lead to the same 

conclusions. The four curves plotted each represent results from the lowest 

level of retrofit shown in Figure F-9. The grey, upper-most curve illustrates 

the results from the Task 2 Report. The purple graph labeled Task 2 

Emulation is the analysis done the same as in the Broad-Scope Analyses with 

Figure F-11 Comparison of analysis results for the building with retrofit 

strength of Vy/V2 of 0.2 for Task 2 and emulation of Task 2 and 

Vu/V2 of 0.2 for the Broad-Scope Analysis. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1.0 1.5 2.0 2.5 3.0

Drift Ratio, %

Median Spectral Acceleratio

n

Task 2

Task 2 Emulation

Broad-Scope, 3 Stories

Broad-Scope, 4 Stories

Data Table

Broad Scope

Drift U.B. Emulation 4 Stories

1% 1.29 1.22 0.94

2% 1.62 1.60 1.22

3% 1.81 1.85 1.46

Task 2
FEMA P-807 F: Validation of Analysis Methods F-11 

three stories instead of four and with the retrofit backbone matching the Task 

2 Analysis. The dashed, bottom-most purple graph illustrates the results using 

the retrofit as modeled in the Broad-Scope Analyses. The fact that the Task 2 

and Task 2 Emulation graphs are so close shows that the two analysis 

methods yield very similar results if the retrofit backbone curves are 

identical. The difference illustrated by the Broad-Scope Analysis model must 

then arise from the difference in retrofit backbone. Note again the 

imperceptible difference arising from modeling three versus four stories. 

A comparison of the Task 2 backbone curve for the retrofitted building, with 

Vy/V2 equal to 0.2, and the Broad-Scope Analysis backbone curve for the 

retrofitted building, with Vu/V2 equal to 0.4, is provided in Figure F-12. The 

performance results are illustrated in Figure F-13. Again, the only difference 

between the models represented by the dashed and solid lines is the 

difference in retrofit backbone curves illustrated in Figure F-12. The 

performance results show better but still not very close agreement, differing 

by 20% at 1% drift and 10% at 3% drift. 

Figure F-12 Comparison of backbone curves for Task 2 retrofit set with ratio 

Vy/V2 = 0.2, and Broad-Scope Analysis retrofit set at Vu/V2 = 0.4. 

F.6 The Optimal Retrofit for Relative Strength 

The Task 2 Report concludes that the optimal retrofit strength ratio Vy/V2 is 

somewhere between 0.4 and 0.6. Beyond that strength, the drift in the upper 

stories controls the overall performance. To compare with the Broad-Scope 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0123456

Interstory Drift Ratio, %

Force in Terms of Building Weight, 

W

Task 2 Emulation, Vy/V2=0.2

Broad-Scope Analysis, Vu/V2=0.4
F-12 F: Validation of Analysis Methods FEMA P-807 

Figure F-13 Comparison of results for Task 2 retrofit set with ratio Vy/V2 = 

0.2, and Broad-Scope retrofit set at Vu/V2 = 0.4. 

Analyses, consider that Vu  1.2Vy. so the range of optimal retrofit strength 

ratios, Vu/V2, becomes 0.48 and 0.72. Because the ratio of the first and 

second story strength, V1/V2, is equal to 0.75, this leads to a total retrofitted 

first-story strength, on the basis of Vu, between 1.23V2 and 1.47V2. Based on 

the information provided in Appendix E, the total retrofitted ground story 

strength (new plus existing) for optimal performance is about 1.3V2. Thus, 

the optimal retrofit strength ratio Vu/V2 should be 0.55. This is within the 

range predicted by the Task 2 Report. 

F.7 Conclusions 

Though the analysis methods and assumptions used in the Task 2 Analysis 

differ in some significant ways from the Broad-Scope Analysis, the two 

approaches give results in very close agreement when the input parameters 

are the same. Thus, there is little difference in the results arising from 

differing software platforms, viscous damping and number of stories. There 

is also good agreement in regard to the strength of retrofit that optimizes 

seismic performance in the method of Relative Strength. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1.0 1.5 2.0 2.5 3.0

Drift Ratio, %

Median Spectral Acceleratio

n

Task 2

Task 2 Emulation

Broad-Scope, 3 Stories, Vu/V2=0.4

Broad-Scope, 4 Stories, Vu/V2=0.4

Data Table

Broad Scope

Drift U.B. Emulation 4 Stories

1% 1.29 1.22 1.07

2% 1.62 1.60 1.42

3% 1.81 1.85 1.66

Task 2
FEMA P-807 F: Validation of Analysis Methods F-13 

However, the predicted performance differs significantly depending on how 

the strength of the retrofit is defined and the character of the backbone curve. 

It was not in the scope of the Task 2 Analysis to study the effect of initial 

stiffness of the retrofit, and thus the initial stiffness was held constant for 

each analysis. It is noted in the Task 2 Report that the strength of the 

W14×90 frame columns can be tuned with little effect on stiffness. While 

this may be true, it is not likely that an owner will choose to use a large 

section, and cope the flanges, rather than choosing a lighter section to begin 

with. In that case, it is probably better to assume that the yield and ultimate 

drifts and the ratio of ultimate-to-yield strength are invariant for purposes of 

predicting performance. This is the approach used in the Broad-Scope 

Analysis that forms the basis for the recommendations in the Guidelines. 

FEMA P-807 References G-1 

References 

AF&PA, 2008, Special Design Provisions for Wind and Seismic, 

ANSI/AF&PA SDPW S-2008, American Forest and Paper 

Association, American Wood Council, Washington, D.C. 

AISC, 2005, Seismic Provisions for Structural Steel Buildings, Including 

Supplement No. 1, ANSI/AISC 341-05, ANSI/AISC 341s1-05, 

American Institute of Steel Construction, Chicago. 

AISC, 2011, Seismic Provisions for Structural Steel Buildings, ANSI/AISC 

341-10, American Institute of Steel Construction, Chicago, Illinois. 

APA, 1993, Wood Structural Panel Shear Walls, APA Report 154, APA – 

The Engineered Wood Association, Tacoma, Washington. 

APA, 2005, Preliminary Perforated Shear Wall Testing, APA Report T2005-

83, APA – The Engineered Wood Association, Tacoma, 

Washington. 

Arnold, A.E., Uang, C.-M., and Filiatrault, Andre, 2003, Cyclic Behavior and 

Repair of Stucco and Gypsum Woodframe Walls: Phase I, CUREE 

Publication No. EDA-03, Consortium of Universities for Research in 

Earthquake Engineering, Richmond, California. 

ASCE, 2003, Seismic Evaluation of Existing Buildings, ASCE/SEI 31-03, 

American Society of Civil Engineers, Reston, Virginia. 

ASCE, 2006a, Minimum Design Loads for Buildings and Other Structures,

ASCE/SEI 7-05, including Supplement No. 1, American Society of 

Civil Engineers, Reston, Virginia. 

ASCE, 2006b, Seismic Rehabilitation of Existing Buildings, ASCE/SEI 41-

06, American Society of Civil Engineers, Reston, Virginia. 

ASCE, in preparation, Seismic Rehabilitation of Existing Buildings, 

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ATC, 1984, Tentative Provisions for the Development of Seismic Regulations 

for Buildings, ATC-3-06 Amended, Second Printing; originally 

published in 1978, by the Applied Technology Council, Redwood 

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G-2 References FEMA P-807 

ATC, 2009a, Here Today – Here Tomorrow: The Road to Earthquake 

Resilience in San Francisco, Earthquake Safety for Soft-Story 

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Department of Building Inspection by the Applied Technology 

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ATC, 2009b, Here Today – Here Tomorrow: The Road to Earthquake 

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Bonowitz, D., and Rabinovici, S., 2011, Soft Story Risk Reduction: Best 

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under a Special Projects and Initiatives grant by the Earthquake 

Engineering Research Institute, Oakland, California. 

Chai, R., Hutchinson, T., and Vukavich, S., 2002, Seismic Behavior of Level 

and Stepped Cripple Walls, CUREE W-17 Report, Consortium of 

Universities for Research in Earthquake Engineering, Richmond, 

California. 

Christovasilis, I., Filiatrault, A., Constantinou, M., and Wanitkorkul, A., 

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Earthquake Engineering & Structural Dynamics, Vol. 38, No. 4, pp. 

477-496. 

CSI, 2006, Perform-3D, Nonlinear Analysis and Performance Assessment for 

3D Structures, Version 4, Computers and Structures, Inc., Berkeley, 

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Dolan, J. D., and Johnson, A. C., 1997a, Monotonic Tests of Long Shear 

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Dolan, J. D., and Johnson, A. C., 1997b, Cyclic Tests of Long Shear Walls 

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EERI, 1995, Northridge Earthquake of January 17, 1994 Reconnaissance 

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FEMA P-807 References G-3 

EERI, 1996, Northridge Earthquake of January 17, 1994 Reconnaissance 

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Gatto, K., and Uang, C.-M., 2002, Cyclic Response of Woodframe 

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Harris, S. K., and Egan, J. A., 1992, “Effects of Ground Conditions on the 

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ICBO, 1964, Uniform Building Code, 1964 Edition, International Conference 

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ICC, 2009a, International Building Code, International Code Council, 

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ICC, 2009b, International Existing Building Code, International Code 

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G-4 References FEMA P-807 

Johnson, A. C., 1997, Monotonic and Cyclic Performance of Long Shear 

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Karacabeyli, E., 1997, “Lateral Resistance of Nailed Shear Walls Subjected 

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Mahaney, J., and Kehoe, B., 2002, Anchorage of Woodframe Buildings: 

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Maison, B., Bonowitz, D., Kornfield, L., and McCormick, D., 2011. 

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Testing and Analysis of One-Story and Two-Story Shear Walls Under 

Cyclic Loading, CUREE W-25 Report, Consortium of Universities 

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FEMA P-807 References G-5 

Rabinovici, S. J. M., 2010, “Engineering Report Law Motivated 1 in 5 SoftStory Apartment Owners to Retrofit: Findings from an Evaluation of 

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Rabinovici, S. J. M., 2012 (forthcoming). Motivating Private Behaviors with 

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Woodframe Project Index Buildings, Report No.W-29, Consortium of 

Universities for Research in Earthquake Engineering, Richmond, 

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Washington. 

Toothman, A.J., 2003, Monotonic and Cyclic Performance of Light-Frame 

Shear Walls with Various Sheathing Materials, Virginia Polytechnic 

Institute and State University, Blacksburg, Virginia. 
G-6 References FEMA P-807 

Trayer, G.W., 1956, The Rigidity and Strength of Frame Walls, Information 

Reviewed and Reaffirmed Report, No. 896, U.S. Department of 

Agriculture, Forest Products Laboratory. 

Vamvatsikos, D., and Cornell, A. C., 2002, “The Incremental Dynamic 

Analysis and Its Application to Performance-Based Earthquake 

Engineering,” Proceedings, 12th European Conference on 

Earthquake Engineering, London, England, Paper No. 479 
FEMA P-807 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 

Thomas R. McLane (Project Manager) 

Applied Technology Council 

2111 Wilson Blvd., Suite 700 

Arlington, Virginia 22201 

William T. Holmes (Project Technical Monitor) 

Rutherford & Chekene 

55 Second Street, Suite 600 

San Francisco, California 94105 

Federal Emergency Management Agency 

Michael Mahoney (FEMA Project Officer) 

Federal Emergency Management Agency 

500 C Street, SW, Room 416 

Washington, DC 20472 

Cathleen Carlisle (FEMA Project Monitor) 

Federal Emergency Management Agency 

500 C Street SW 

Washington, DC 20024 

Daniel Shapiro (FEMA Technical Monitor) 

SOHA Engineers 

48 Colin P. Kelly Jr. Street 

San Francisco, California 94107 

Project Management Committee 

David Mar (Project Technical Director) 

Tipping Mar 

1906 Shattuck Ave 

Berkeley, California 94704 

David Bonowitz 

Consulting Structural Engineer 

605A Baker Street 

San Francisco, California 94117 

Kelly Cobeen 

Wiss, Janney, Elstner Associates 

2200 Powell Street, Suite 925 

Emeryville, California 94608 

J. Dan Dolan 

Washington State University 

Dept. of Civil and Environmental Engineering 

405 Spokane Street, Sloan 101 

Pullman, Washington 99164-2910 

Andre Filiatrault 

State University of New York 

Dept. of Civil, Structural & Environ. Engineering 

134 Ketter Hall 

Buffalo, New York 14260-4300 

H. John Price 

Curry Price Court 

444 Camino Del Rio South, #201 

San Diego, California 92108 
H-2 Project Participants FEMA P-807

Project Review Panel 

Chris D. Poland (Chair) 

Degenkolb Engineers 

235 Montgomery Street, Suite 500 

San Francisco, California 94104-2908 

Tony DeMascole 

Consulting Structural Engineer 

3420 Market St., #6 

San Francisco, California 94114 

Laurence Kornfield 

Manager, Earthquake Safety Implementation 

Program 

City and County of San Francisco 

1660 Mission Street 

San Francisco, California 94103-2414 

Bret Lizundia 

Rutherford & Chekene 

55 Second Street, Suite 600 

San Francisco, California 94105 

Joan MacQuarrie 

Chief Building Official (Retired) 

City of Berkeley 

2120 Milvia Street 

Berkeley, California 94704 

Andrew T. Merovich 

A. T. Merovich & Associates, Inc. 

1950 Addison Street, Suite 205 

Berkeley, California 94704 

Thomas Tobin 

Tobin & Associates 

444 Miller Avenue 

Mill Valley, California 94941 

Consultants 

Maikol Del Carpio (Analysis Consultant) 

State University of New York 

Dept. of Civil, Structural & Environ. Engineering 

Buffalo, New York 14260-4300 

Mike Korolyk (Analysis Consultant) 

Tipping Mar 

1906 Shattuck Ave 

Berkeley, California 94704