Seismic Evaluation of 

Older Concrete Buildings

for Collapse Potential 

FEMA P-2018 / December 2018 
FEMA P-2018 / December 2018

Seismic Evaluation of Older Concrete 

Buildings for Collapse Potential 

Prepared by

APPLIED TECHNOLOGY COUNCIL

201 Redwood Shores Parkway, Suite 240

Redwood City, California 94065

www.ATCouncil.org

Prepared for

FEDERAL EMERGENCY MANAGEMENT AGENCY

Michael Mahoney, Project Officer

Robert D. Hanson, Technical Monitor

Washington, D.C. 

APPLIED TECHNOLOGY COUNCIL

Jon A. Heintz, Project Manager

PROJECT TECHNICAL COMMITTEE PROJECT REVIEW PANEL

William T. Holmes (Project Tech. Director) Terry Lundeen (Chair)

Abbie Liel Michael Cochran

Michael Mehrain Gregory G. Deierlein

Jack P. Moehle Ken Elwood

Peter Somers Josh Gebelein 

Laura N. Lowes 

WORKING GROUP MEMBERS Khalid Mosalam 

Saman A. Abdullah Robert Pekelnicky

Carlos Arteta Pui-Shum Shing 

Supratik Bose Bill Tremayne

Panagiotis Galanis Fred Turner

Cody Harrington John W. Wallace

Travis Marcilla

Pablo Parra

Siamak Sattar

Andreas Stavridis

Duy Vu To 

 
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 photograph – Older concrete building damaged in the 2010 Maule earthquake, located in Vina del Mar, Chile 

(photo courtesy of J. Heintz). 
FEMA P-2018 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.

One of the issues still of significant concern for the Program is the risk 

presented by older, seismically vulnerable concrete buildings, known as nonductile concrete buildings. These are concrete frame buildings constructed 

prior to the mid-1970s, including archaic designs dating back to the early 

1900s. One of the lessons to come out of the 1971 San Fernando earthquake 

was the poor performance of concrete frame buildings and how design codes 

of that era did not provide for sufficient steel reinforcing to confine the 

concrete within the building columns during earthquake shaking. The most 

famous example of this type of failure was the partial collapse of the new 

Olive View Hospital in Sylmar. By the mid-1970s, design codes had 

increased the amount and detailing of steel reinforcing to prevent this type of 

failure. However, these buildings still exist in great numbers and still pose 

significant risk.

Although retrofitting criteria for seismically deficient non-ductile concrete 

buildings has been developed, the problem remains one of efficient 

identification of the most hazardous buildings. Not all pre-1970s concrete 

buildings are equally hazardous; generally, only those with columns that 
iv Foreword FEMA P-2018

would fail in shear and/or compression. It is often difficult to visually 

determine which of these buildings are collapse hazards and which are not. 

Although some non-ductile concrete buildings may not be collapse hazards, 

this construction type includes some of most seismically dangerous buildings 

because of their potential occupancy load. 

This report, Seismic Evaluation of Older Concrete Buildings for Collapse 

Potential (FEMA P-2018), provides a simplified methodology for evaluating 

collapse resistance using simplified estimates of drift demand. The 

calculations have been intentionally simplified; however, the underlying 

criteria are based on probabilistic concepts and structural reliability theory. 

Development of the procedures included testing of the methodology by 

practicing engineers in several rounds of trial evaluations, and vetting of the 

methodology in a series of annual workshops. All of this was used to adjust 

and improve the methodology throughout the development process. 

This project also coordinated with, and included, the results of other ongoing 

research in this area. This includes the National Science Foundation’s

Network for Earthquake Engineering Simulation (NSF/NEES) Grand 

Challenge Project with the Pacific Earthquake Engineering Research Center 

(PEER). In addition, this project also worked closely with the Concrete 

Coalition, a group formed by the Earthquake Engineering Research Institute 

(EERI) to coordinate low-cost mitigation of the risks from this building type.

FEMA is indebted to the leadership of Bill Holmes, Project Technical 

Director, and to the members of the project technical team, trial evaluators, 

and workshop participants, for their efforts in the development of this 

methodology. The Project Management Committee, consisting of Abbie 

Liel, Mike Mehrain, Jack Moehle, and Peter Somers, led the technical 

development efforts, and guided the investigations of the Project Working 

Groups. 

FEMA also wishes to thank the Project Review Panel, which consisted of 

Terry Lundeen (Chair), Mike Cochran, Greg Deierlein, Ken Elwood, Josh 

Gebelein, Laura Lowes, Khalid Mosalam, Bob Pekelnicky, Benson Shing, 

Bill Tremayne, Fred Turner, and John Wallace. This group provided 

significant technical advice and consultation over the duration of the work. 

The names and affiliations of all who contributed to this report are provided 

in the list of Project Participants at the end of this report.

Without their dedication and hard work, this publication would not have been 

possible. 

Federal Emergency Management Agency
FEMA P-2018 Preface v 

Preface 

In 2009, the Applied Technology Council (ATC) was awarded the first in a 

series of contracts with the Federal Emergency Management Agency 

(FEMA) for “Identification and Mitigation of Non-Ductile Concrete 

Buildings,” identified as the ATC-78 Project Series. The overall purpose of 

this series of projects was to develop an evaluation methodology that could 

be used to identify and prioritize the most seismically hazardous non-ductile 

concrete buildings in an inventory of buildings in a way that was easier and 

less expensive to apply than evaluation and retrofit methodologies currently 

available and in use at the time.

The need to address non-ductile concrete buildings was identified as a 

national imperative in the early 2000s, and the work on this project was 

coordinated with results from related projects funded by the National 

Earthquake Hazards Reduction Program (NEHRP), the National Institute of 

Standards and Technology (NIST), and the National Science Foundation 

(NSF), as well as other FEMA-sponsored projects, published in 2010 and 

later. 

The resulting methodology is based on the evolution of procedures as 

outlined in the ATC-78 series of reports published between 2011 and 2017. 

In the methodology, collapse is defined as the global loss of vertical loadcarrying ability at a story, possibly leading to the collapse of other stories. 

Procedures for evaluating collapse resistance require simplified estimates of 

drift demand to implement. Although the calculations are intentionally 

simplified, the underlying criteria are based on probabilistic concepts and 

structural reliability theory. The methodology and calculation procedures are 

based on detailed analytical study, and have taken years to develop. A key 

aspect of the developmental process has included testing of the methodology 

by practicing engineers and researchers in several rounds of trial evaluations, 

and vetting of the methodology in annual workshops. The trial evaluations 

and workshop discussions were used to adjust and enhance the methodology 

along the way, and the results have significantly impacted the final product. 

ATC is indebted to the leadership of Bill Holmes, Project Technical Director, 

and to the members of the ATC-78 Project Team, trial evaluators, and 

workshop participants, for their efforts in the development of this 
vi Preface FEMA P-2018

methodology. The Project Management Committee, consisting of Abbie 

Liel, Mike Mehrain, Jack Moehle, and Peter Somers, led the technical 

development efforts, and guided the investigations of the Project Working 

Groups, which included Saman Abdullah, Carlos Arteta, Supratik Bose, 

Panagiotis Galanis, Cody Harrington, Travis Marcilla, Pablo Parra, Siamak 

Sattar, Andreas Stavridis, and Duy Vu To. 

The Project Review Panel, consisting of Terry Lundeen (Chair), Mike 

Cochran, Greg Deierlein, Ken Elwood, Josh Gebelein, Laura Lowes, Khalid 

Mosalam, Bob Pekelnicky, Benson Shing, Bill Tremayne, Fred Turner, and 

John Wallace provided technical advice and consultation over the duration of 

the work. The names and affiliations of all who contributed to this report are 

provided in the list of Project Participants at the end of this report.

ATC also gratefully acknowledges Michael Mahoney (FEMA Project 

Officer) and Robert Hanson (FEMA Technical Monitor) for their input and 

guidance in the conduct of this work, and Carrie Perna for ATC report 

production services. 

Jon A. Heintz

ATC Executive Director
FEMA P-2018 Table of Contents vii

Table of Contents 

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

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

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

List of Tables ........................................................................................... xxvii

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

1.1 ATC-78 Project Series .............................................................. 1-1 

1.2 Evaluation Methodology .......................................................... 1-3 

1.3 Comparison with ASCE/SEI 41 ............................................... 1-5 

1.4 Policy Implications ................................................................... 1-6 

1.5 Report Organization and Content ............................................. 1-9 

2. Evaluation Methodology .................................................................. 2-1 

2.1 Scope and Applicability ........................................................... 2-1 

2.1.1 Applicability ................................................................ 2-1 

2.1.2 Seismic Deficiencies that are not Considered in the 

Methodology ............................................................... 2-3 

2.1.3 Buildings with Concrete Components that are not 

Considered in the Methodology .................................. 2-3 

2.2 Overview of the Evaluation Methodology ............................... 2-4 

2.2.1 Overview of Key Calculation Procedures ................... 2-5 

2.2.2 Early Identification of Lower Seismic Risk 

Buildings ..................................................................... 2-7 

2.2.3 Early Identification of Exceptionally High Seismic 

Risk Buildings ............................................................. 2-7 

2.3 Use of Alternate Analysis Procedures ...................................... 2-8 

3. General Requirements ..................................................................... 3-1 

3.1 As-Built Information ................................................................ 3-1 

3.2 Site Investigation ...................................................................... 3-2 

3.3 Seismic Hazard ......................................................................... 3-2 

3.4 Material Properties ................................................................... 3-3 

3.4.1 General ........................................................................ 3-3 

3.4.2 Concrete and Reinforcing Steel ................................... 3-3 

3.4.3 Masonry Infill .............................................................. 3-3 

3.5 Condition of Structural Components ........................................ 3-5 

3.6 Structural Load Path Requirements .......................................... 3-5 

3.6.1 Diaphragm Continuity ................................................. 3-5 

3.6.2 Concrete Element Interconnectivity ............................ 3-6 

3.7 Penthouse and Other Rooftop Structures ................................. 3-7 
viii Table of Contents FEMA P

-2018

4. Component Strengths ....................................................................... 4-1 

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

4.2 Axial Loads on Columns and Walls ......................................... 4-1 

4.2.1 Expected Gravity Loads .............................................. 4-1 

4.2.2 Earthquake Axial Loads .............................................. 4-1 

4.2.3 Load Combinations ...................................................... 4-2 

4.3. Component Strength Calculations ............................................ 4-2 

4.3.1 General ......................................................................... 4-2 

4.3.2 Concrete Column Strength .......................................... 4-3 

4.3.3 Beam-Column Joint Shear Strength ............................ 4-4 

4.3.4 Slab-Column Frame Strength and Integrity 

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

4.3.5 Concrete Wall Strength................................................ 4-6 

4.3.6 Infilled Frame Strength ................................................ 4-6 

4.4 Column Shear Strength Ratio ................................................... 4-9 

4.4.1 Column Shear Capacity in a Typical Story ................. 4-9 

4.4.2 Slab-Column Frames ................................................. 4-10 

5. Structural Classification .................................................................. 5-1 

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

5.2 Classification of Concrete Components ................................... 5-2 

5.2.1 Reinforced Concrete Columns ..................................... 5-2 

5.2.2 Reinforced Concrete Structural Walls ......................... 5-2 

5.3 Classification of Building Systems ........................................... 5-3 

5.3.1 Frame Systems ............................................................. 5-3 

5.3.2 Frame-Wall Systems .................................................... 5-3 

5.3.3 Bearing Wall Systems.................................................. 5-4 

5.3.4 Infilled Frame Systems ................................................ 5-4 

5.4 Wall Index and Wall Strength Index ........................................ 5-5 

5.4.1 Wall Index ................................................................... 5-5 

5.4.2 Wall Strength Index ..................................................... 5-6 

5.4.3 Identification of Lower Seismic Risk Buildings 

using the Wall Strength Index ..................................... 5-6 

5.5 Effective Yield Strength ........................................................... 5-7 

5.5.1 Plastic Mechanism Base-Shear Strength for Frames 

and Walls ..................................................................... 5-7 

5.5.2 Plastic Mechanism Base-Shear Strength for Infilled 

Frame Systems ........................................................... 5-15 

5.5.3 Plastic Mechanism Base-Shear Strength for 

Mezzanines and Other Configurations ...................... 5-17 

5.5.4 Three-Dimensional Considerations ........................... 5-18 

5.5.5 Base Shear Ratio ........................................................ 5-19 

5.6 Effective Fundamental Period ................................................ 5-19 

5.6.1 Determination of Effective Period by Formula ......... 5-20 

5.6.2 Determination of Effective Period by Structural 

Analysis ..................................................................... 5-21 

5.7 Global Demand-to-Capacity Ratio ......................................... 5-21 

5.8 Identification of Lower Seismic Risk Buildings ..................... 5-22 

5.8.1 Essentially Elastic Buildings ..................................... 5-22 

5.9 Identification of Exceptionally High Seismic Risk 

Buildings ................................................................................. 5-22 

5.9.1 Exceptionally Weak Buildings .................................. 5-22 
FEMA P-2018 Table of Contents ix

5.9.2 Discontinuous Walls Supported on Columns, Wall 

Piers, or Girders ......................................................... 5-23 

5.10 Pounding ................................................................................. 5-25 

5.10.1 Shorter Interfering Building ...................................... 5-25 

5.10.2 Taller Interfering Building ........................................ 5-25 

6. Evaluation Procedure for Frame Systems ..................................... 6-1 

6.1 Introduction .............................................................................. 6-1 

6.2 Identify Critical Stories ............................................................ 6-1 

6.3 Identify Critical Components ................................................... 6-2 

6.3.1 Critical Columns ......................................................... 6-2 

6.3.2 Critical Slab-Column Connections .............................. 6-2 

6.3.3 Critical Beam-Column Corner Connections ............... 6-3 

6.3.4 Discontinuous Columns .............................................. 6-3 

6.4 Calculate Global Seismic Drift Demand .................................. 6-3 

6.5 Calculate Story Drift Demand .................................................. 6-4 

6.5.1 Adjustment of Story Drift Demand for P-Delta .......... 6-5 

6.6 Calculate Drift Demands on Critical Components ................... 6-6 

6.6.1 Adjusted Drift Demand on Critical Components ........ 6-6 

6.6.2 Torsional Amplification Factor ................................... 6-6 

6.6.3 Drift Factor .................................................................. 6-6 

6.7 Calculate Drift Capacity of Critical Components..................... 6-7 

6.7.1 Drift Capacity of Critical Columns ............................. 6-7 

6.7.2 Drift Capacity of Critical Slab-Column 

Connections ................................................................. 6-9 

6.7.3 Drift Capacity of Critical Beam-Column Corner 

Connections ............................................................... 6-10 

6.8 Determine Column Ratings .................................................... 6-10 

6.8.1 Discontinuous Columns ............................................ 6-12 

6.9 Determine Story Ratings ........................................................ 6-12 

7. Evaluation Procedures for Frame-Wall Systems .......................... 7-1 

7.1 Introduction .............................................................................. 7-1 

7.2 Identify Critical Stories ............................................................ 7-1 

7.3 Identify Critical Components ................................................... 7-2 

7.3.1 Critical Columns ......................................................... 7-2 

7.3.2 Critical Walls and Vertical Wall Segments ................. 7-3 

7.3.3 Critical Slab-Column Connections .............................. 7-3 

7.3.4 Critical Beam-Column Corner Connections ............... 7-4 

7.3.5 Discontinuous Columns .............................................. 7-4 

7.4 Calculate Global Seismic Drift Demand .................................. 7-4 

7.5 Calculate Story Drift Demand .................................................. 7-5 

7.6 Calculate Drift Demands on Critical Components ................... 7-6 

7.6.1 Adjusted Drift Demand on Critical Components ........ 7-6 

7.6.2 Torsional Amplification Factor ................................... 7-7 

7.6.3 Drift Factor .................................................................. 7-8 

7.7 Calculate Drift Capacity of Critical Components..................... 7-9 

7.7.1 Drift Capacity of Critical Columns ............................. 7-9 

7.7.2 Drift Capacity of Critical Slab-Column 

Connections ............................................................... 7-11 

7.7.3 Drift Capacity of Critical Beam-Column Corner 

Connections ............................................................... 7-12 
x Table of Contents FEMA P

-2018

7.7.4 Drift Capacity of Critical Walls and Vertical Wall 

Segments .................................................................... 7-12 

7.8 Determine Column and Wall Ratings ..................................... 7-15 

7.8.1 Discontinuous Columns ............................................. 7-17 

7.9 Determine Story Ratings ......................................................... 7-17 

8. Evaluation Procedures for Bearing Wall Systems ......................... 8-1 

8.1 Introduction............................................................................... 8-1 

8.2 Identify Critical Stories ............................................................. 8-1 

8.3 Identify Critical Components.................................................... 8-2 

8.3.1 Critical Walls and Vertical Wall Segments ................. 8-2 

8.3.2 Other Critical Components .......................................... 8-3 

8.4 Calculate Global Seismic Drift Demand .................................. 8-3 

8.5 Calculate Story Drift Demand .................................................. 8-4 

8.6 Calculate Drift Demands on Critical Components ................... 8-5 

8.6.1 Adjusted Drift Demand on Critical Components ........ 8-5 

8.6.2 Torsional Amplification Factor ................................... 8-5 

8.6.3 Drift Factor .................................................................. 8-5 

8.7 Calculate Drift Capacity of Critical Components ..................... 8-6 

8.7.1 Drift Capacity of Critical Walls and Vertical Wall 

Segments ...................................................................... 8-6 

8.7.2 Drift Capacity of Other Critical Components .............. 8-9 

8.8 Determine Wall and Column Ratings ....................................... 8-9 

8.8.1 Determine Wall Ratings .............................................. 8-9 

8.8.2 Determine Column Ratings ......................................... 8-9 

8.9 Determine Story Ratings ........................................................... 8-9 

9. Evaluation Procedures for Infilled Frame Systems ....................... 9-1 

9.1 Introduction............................................................................... 9-1 

9.2 Identify Critical Stories ............................................................. 9-2 

9.3 Identify Critical Components.................................................... 9-2 

9.3.1 Critical Columns in Infilled Frame Systems................ 9-2 

9.3.2 Other Critical Components .......................................... 9-2 

9.4 Calculate Global Seismic Drift Demand .................................. 9-3 

9.5 Calculate Story Drift Demand .................................................. 9-4 

9.6 Calculate Drift Demands in Critical Components .................... 9-4 

9.6.1 Adjusted Drift Demand on Critical Components ........ 9-4 

9.6.2 Torsional Amplification Factor ................................... 9-5 

9.6.3 Drift Factor .................................................................. 9-6 

9.7 Calculate Drift Capacity of Critical Components ..................... 9-7 

9.7.1 Drift Capacity of Critical Columns in Infilled Frame 

Systems ........................................................................ 9-7 

9.7.2 Drift Capacity of Other Critical Components .............. 9-9 

9.7.3 Drift Capacity of Critical Walls and Vertical Wall 

Segments ...................................................................... 9-9 

9.8 Determine Column and Wall Ratings ..................................... 9-10 

9.8.1 Determine Ratings for Columns in Infilled Frame 

Systems ...................................................................... 9-10 

9.8.2 Determine Ratings for Other Critical Components ... 9-11 

9.9 Determine Story Ratings ......................................................... 9-11 
FEMA P-2018 Table of Contents xi

10. Determination of Building Rating................................................. 10-1 

10.1 Introduction ............................................................................ 10-1 

10.2 Determine Building Rating .................................................... 10-1 

10.3 Recommended Building Risk Levels ..................................... 10-1 

10.3.1 Exceptionally High Seismic Risk Buildings ............. 10-2 

10.3.2 High Seismic Risk Buildings .................................... 10-2 

10.3.3 Lower Seismic Risk Buildings .................................. 10-2 

Appendix A: Development of Column Drift Capacities ....................... A-1 

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

A.2 Column Plastic Rotation Capacity Determination .................. A-1 

A.2.1 Plastic Rotation Capacities for Flexure-Critical 

Columns ..................................................................... A-2 

A.2.2 Plastic Rotation Capacities for Flexure-Shear and 

Shear-Critical Columns .............................................. A-2 

A.2.3 Bias in Plastic Rotation Capacity Predictions ............ A-2 

A.2.4 Comparison of Plastic Rotation Capacity Prediction 

Methods ...................................................................... A-4 

A.2.5 Uncertainty in Plastic Rotation Capacities ................. A-6 

A.2.6 Elastic Component of Column Drift Capacity ........... A-7 

A.2.7 Drift Capacity of Columns with Inadequate Lap 

Splices ........................................................................ A-7 

A.3 Slab-Column Connection Drift Capacity Determination ........ A-7 

Appendix B: Development of Method for Determining Column 

Ratings ...............................................................................................B-1 

B.1 Overview ..................................................................................B-1 

B.2 Structural Reliability Methods for Computing the Column 

Rating .......................................................................................B-1 

Appendix C: Development of Method for Determining Story 

Ratings .............................................................................................. C-1 

C.1 Overview ..................................................................................C-1 

C.2 Probability Theory for Determining Probability of Story 

Collapse ....................................................................................C-1 

C.3 Development of Story Ratings .................................................C-2 

Appendix D: Wall Strength Index (WSI) Method ................................ D-1 

D.1 Overview ................................................................................. D-1 

D.2 Numerical Simulation .............................................................. D-2 

D.2.1 Buildings Analyzed .................................................... D-2 

D.2.2 Modeling .................................................................... D-3 

D.2.3 Ground Motion Selection and Scaling ....................... D-4 

D.2.4 Collapse ...................................................................... D-4 

D.2.5 Results ........................................................................ D-5 

D.3 Analytical Investigation of WSI .............................................. D-7 

D.4 Limitations .............................................................................. D-9 

D.5 Conclusions ........................................................................... D-10 

Appendix E: Exceptionally Weak Building Criteria .............................E-1 

E.1 Overview .................................................................................. E-1 

E.2 Modeling .................................................................................. E-2 

E.3 Ground Motion Selection and Scaling ..................................... E-2 
xii Table of Contents FEMA P-2018

E.4 Collapse ................................................................................... E-2 

E.5 Development of Criteria for Exceptionally Weak Frame 

Buildings .................................................................................. E-2 

E.6 Investigation of Criteria for Exceptionally Weak FrameWall Buildings ......................................................................... E-5 

Appendix F: Beam-Column Joints ......................................................... F-1 

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

F.2 Performance of Connections with Discontinuous Beam 

Bottom Longitudinal Reinforcement ........................................ F-1 

F.3 Strength of Joints in Beam-Column Connections without 

Joint Transverse Reinforcement ............................................... F-2 

F.4 Effect of Joint Eccentricity on Joint and Column Behavior ..... F-3 

F.5 Axial Failure of Beam-Column Connections ........................... F-5 

Appendix G: Effective Fundamental Period .......................................... G-1 

G.1 Frame Buildings....................................................................... G-1 

G.2 Frames with Deep Spandrels ................................................... G-4 

G.3 Pier-Spandrel Systems ............................................................. G-4 

G.4 Wall and Frame-Wall Buildings .............................................. G-8 

Appendix H: Development of Procedures to Estimate Story Drift 

Demands ........................................................................................... H-1 

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

H.2 Studies of the SDOF Drift Demand ......................................... H-1 

H.2.1 Basic Procedure to Calculate SDOF Drift Demand .... H-1 

H.2.2 Comparison with Results of Nonlinear Response 

History Analyses ......................................................... H-2 

H.3 Studies of the Story Drift Demand .......................................... H-5 

H.3.1 Basic Procedure to Calculate Story Drift Demand ..... H-5 

H.3.2 Bare Frames ................................................................ H-5 

H.3.3 Frames and Walls ..................................................... H-14 

H.3.4 Frames with Walls Discontinuous in the First 

Story.......................................................................... H-19 

H.3.5 Frames with Walls Discontinuous in Upper 

Stories ....................................................................... H-22 

H.3.6 Buildings with Shear-Critical Walls ......................... H-27 

Appendix I: Torsion Studies ..................................................................... I-1 

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

I.2 Identify Critical Stories ..............................................................I-2 

I.3 Simulation of Collapse of Torsionally-Sensitive Buildings ......I-4 

I.3.1 Buildings Analyzed ......................................................I-4 

I.3.2 Modeling .......................................................................I-6 

I.3.3 Analysis Procedures......................................................I-7 

I.3.4 Detailed Results for Selected Buildings .......................I-8 

I.3.5 Normalization of Results for Comparison between 

Buildings .......................................................................I-9 

I.4 Extreme Torsion ......................................................................I-10 

I.5 Neglecting Torsion ..................................................................I-11 

I.6 Torsional Amplification ...........................................................I-13 

I.6.1 Torsional Amplification Overview .............................I-13 

I.6.2 Extraction of Torsional Amplification from 

Analytical Models .......................................................I-13 
FEMA P-2018 Table of Contents xiii

I.6.3 Torsional Amplification Results ................................ I-15 

I.6.4 Torsional Amplification Calculations in Each 

Column ....................................................................... I-16 

I.7 Comparison of Results to Other Torsion Studies .................... I-16 

Appendix J: Determination of Drift Factors .......................................... J-1 

J.1 Overview ................................................................................... J-1 

J.2 Drift Factor for Critical Columns .............................................. J-1 

J.2.1 Buildings Analyzed ...................................................... J-1 

J.2.2 Results .......................................................................... J-1 

J.3 Drift Factor for Critical Slab-Column Connections and 

Beam-Column Corner Connections .......................................... J-3 

J.4 Drift Factor for Critical Wall and Wall Segments ..................... J-3 

Appendix K: Archetype Building Analysis Methods ............................ K-1 

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

K.2 Nonlinear Static Analysis ........................................................ K-1 

K.3 Incremental Dynamic Analysis ............................................... K-1 

K.4 Dynamic Analyses with Hazard-Consistent Ground 

Motions .................................................................................... K-4 

K.5 Dynamic Analyses for Torsion Studies ................................... K-9 

Appendix L: Frame and Wall Modeling Procedures.............................L-1 

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

L.2 Bare Frames Models ................................................................. L-1 

L.2.1 Building with Flexure-Controlled Columns ................ L-2 

L.2.2 Building with Shear-Critical Columns ........................ L-3 

L.3 Modeling Criteria of Frame-Wall Systems .............................. L-3 

L.3.1 Frame-Wall Definition ................................................ L-4 

L.3.2 Wall Modeling Approach for Frame-Wall Systems .... L-5 

L.3.3 Frame Modeling Approach for Frame-Wall 

Systems...................................................................... L-11 

Appendix M: Column Shear Strength .................................................. M-1 

M.1 Column Shear Strength Equation ............................................ M-1 

Appendix N: Development of Wall Drift Capacities ............................. N-1 

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

N.2 Expected Wall Behavior and Failure Mode ............................ N-1 

N.3 Drift Capacity of Poorly Detailed Flexure-Controlled 

Walls ........................................................................................ N-3 

N.4 Drift Capacity of Shear-Controlled Walls/Piers ...................... N-6 

N.5 Drift Capacity of Walls with Inadequate Lap Splices ............. N-9 

N.6 Drift Capacity of Walls with L-Shaped, T-Shaped, and HalfBarbell Cross-Sections ............................................................ N-9 

N.7 Drift Capacity of Walls Spirally Reinforced Columns at the 

Boundary Regions ................................................................. N-10 

N.7.1 Flexure-Controlled Walls with Spirally Reinforced 

Columns ................................................................... N-11 

N.7.2 Shear-Controlled Walls with Spirally Reinforced 

Columns ................................................................... N-11 
xiv Table of Contents FEMA P-2018

Appendix O: Studies on Infilled Frames ................................................ O-1 

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

O.2 Simulation of Collapse of Buildings Infilled with Solid 

Infills ........................................................................................ O-2 

O.2.1 Details of the Prototype Buildings .............................. O-2 

O.2.2 Development of Numerical Models ............................ O-4 

O.2.3 Nonlinear Time-History Analyses .............................. O-6 

O.2.4 Detailed Results for Prototype Buildings ................... O-7 

O.3 Calculation of Strength of Infilled Frame Buildings ............... O-9 

O.3.1 Default Material Properties ......................................... O-9 

O.3.2 Plastic Mechanism of Infilled Frames ...................... O-10 

O.3.3 Column Effective Length ......................................... O-10 

O.3.4 Classification of Infilled Frames based on Failure 

Mechanism ................................................................ O-12 

O.3.5 Strength of Single Infilled Bay with Solid Panel ...... O-13 

O.3.6 Strength of Single Infilled Bay with Openings ......... O-15 

O.3.7 When to Ignore Infills in Strength ............................ O-19 

O.3.8 Calculation of Story-Shear Strength ......................... O-21 

O.4 Estimation of Effective Periods ............................................. O-23 

O.5 Determination of Story-Drifts ................................................ O-24 

O.6 Impact of Infill on Column Ratings ....................................... O-25 

Symbols ...................................................................................................... P-1 

References .................................................................................................. Q-1 

Project Participants ................................................................................... R-1 
FEMA P-2018 List of Figures xv

List of Figures 

Figure 4-1 Illustration of slab-column structural integrity 

requirements ...................................................................... 4-5 

Figure 4-2 Illustration of symbols defining the geometry of masonry 

infill panels ........................................................................ 4-7 

Figure 5-1 Illustration of terms in Equation 5-4 and Equation 5-5 ..... 5-8 

Figure 5-2 Mechanism 1 for calculation of plastic mechanism 

base-shear strength ............................................................. 5-9 

Figure 5-3 Mechanism 2 for calculation of plastic mechanism 

base-shear strength ........................................................... 5-10 

Figure 5-4 Mechanism 3 for calculation of plastic mechanism 

base-shear strength ........................................................... 5-12 

Figure 5-5 Mechanism 4 for calculation of plastic mechanism 

base-shear strength ........................................................... 5-14 

Figure 5-6 Possible mechanisms for calculation of plastic 

mechanism base-shear strength of frames with 

mezzanines ....................................................................... 5-17 

Figure 5-7 Kinematically compatible three-dimensional plastic 

mechanisms ...................................................................... 5-18 

Figure 5-8 Mechanisms in buildings with extreme torsion ............... 5-18 

Figure 5-9 Force-displacement curve, showing the definition of 

effective stiffness, Ke, for calculation of the effective 

fundamental period .......................................................... 5-19 

Figure 6-1 Illustration of possible critical conditions for a column 

in a slab-column frame .................................................... 6-12 

Figure 7-1 Illustration of possible critical conditions for a column 

in a slab-column frame .................................................... 7-16 

Figure A-1 Ratio of measured to predicted plastic rotation at axial 

failure for columns other than spirally-reinforced 

circular columns as a function of: (a) axial load ratio; 

(b) transverse reinforcement ratio; and (c) Vp/Vn .............. A-3 
xvi List of Figures FEMA P-2018

Figure A-2 Ratio of measured to predicted plastic rotation at axial 

failure for spirally-reinforced circular columns as a 

function of: (a) axial load ratio; (b) transverse 

reinforcement ratio; and (c) Vp/Vn ..................................... A-4 

Figure A-3 Comparison of relationship between axial load ratio 

and plastic rotation capacity using different prediction 

methods for columns other than spirally-reinforced 

circular columns with transverse reinforcement ratio 

equal to: (a) 0.002; and (b) 0.006 ...................................... A-5 

Figure A-4 Comparison of relationship between axial load ratio 

and plastic rotation capacity using different prediction 

methods for spirally-reinforced circular columns with 

transverse reinforcement ratio equal to: (a) 0.002; and 

(b) 0.006 ............................................................................ A-6 

Figure A-5 Relationship between gravity shear ratio and drift 

capacity for slab-column connections ............................... A-8 

Figure A-6 Ratio of measured versus predicted drift at punching 

shear failure for slab-column connections with different 

gravity shear ratios ............................................................ A-9 

Figure C-1 Assumed model of correlation in column/wall drift 

capacities for failure of columns i and j, as a function of 

column/wall separation distance ....................................... C-2 

Figure C-2 Relationship between adjusted average column rating, 

Ravg, and the story rating, SR, for frame structures ........... C-3 

Figure C-3 Relationship between adjusted average column and wall 

rating, CRavg, and the story rating, SR, from Monte Carlo 

simulation, and showing the simplified equation 

developed for the purpose of this methodology ................ C-3 

Figure D-1 Modeling overview for pure frame buildings ................... D-4 

Figure D-2 Modeling overview for frame-wall buildings ................... D-4 

Figure D-3 Collapse definition for 6-story, 6-bay, frame-wall 

system with a single 20 ft wall and shear critical 

columns ............................................................................. D-5 

Figure D-4 Relationship between WSI and probability of collapse 

for 32 building models ...................................................... D-6 

Figure D-5 Relationship between WSI and probability of collapse 

for wall-frame buildings with flexurally-governed 

columns ............................................................................. D-6 
FEMA P-2018 List of Figures xvii

Figure D-6 Relationship between WSI and probability of collapse 

for wall-frame buildings with shear-controlled 

columns ............................................................................. D-7 

Figure E-1 Collapse fragilities for pure frame buildings from 

Table E-1 plotted as a function of μstrength .......................... E-3 

Figure E-2 Limiting values of Vp/Vn and μstrength that identify 

exceptionally weak pure frame buildings .......................... E-4 

Figure E-3 Collapse fragilities for frame-wall buildings plotted as 

a function of: (a) spectral acceleration at each building’s 

fundamental period, shown in Table E-2; and 

(b) μstrength ........................................................................... E-5 

Figure E-4 Relationship between WI and: (a) Vy/W; (b) median 

collapse Sa(T1); and (c) the ratio of median collapse 

Sa(T1) to Vy/W ..................................................................... E-6 

Figure F-1 Shear strength of unreinforced interior joints .................... F-2 

Figure F-2 Measured and calculated strengths for exterior joints 

loaded perpendicular to the edge, including corner 

joints .................................................................................. F-3 

Figure F-3 Measured and calculated strengths for exterior joints 

loaded perpendicular to the edge, including corner 

joints .................................................................................. F-3 

Figure F-4 Force transfer at eccentric beam-column connections ...... F-4 

Figure F-5 Maximum observed drift ratios and axial load ratios of 

corner beam-column connections ...................................... F-5 

Figure G-1 Example planar frame and fishbone idealizations of a 

four-story building ............................................................ G-2 

Figure G-2 Calculated periods for all buildings studied ..................... G-3 

Figure G-3 Comparison of calculated periods .................................... G-4 

Figure G-4 Example of pier-spandrel system and model 

idealizations of a four-story building ................................ G-5 

Figure G-5 Illustration of variables and constants in the parametric 

study .................................................................................. G-6 

Figure G-6 Comparison of calculated periods .................................... G-7 

Figure H-1 Schematic elevation of the simulated 4-story frames ....... H-2 
xviii List of Figures FEMA P-2018

Figure H-2 Ratio of (maximum displacement at effective modal 

height of non-linear analysis) / (estimated displacement 

at effective modal height) for different μstrength values ...... H-4 

Figure H-3 Alpha factor story profiles for different variations of the 

4-story idealized building .................................................. H-6 

Figure H-4 Alpha factor mean value at 1st story for different 

variations of the 4-story idealized building....................... H-6 

Figure H-5 Alpha factor story profiles for different variations of 

the 8-story idealized building ............................................ H-7 

Figure H-6 Alpha factor mean value at 1st story for different 

variations of the 8-story idealized building....................... H-7 

Figure H-7 Alpha factor story profiles for different variations of 

the 6-story idealized building with a critical 4th story ....... H-9 

Figure H-8 Alpha factor mean value at 1st story for different 

variations of the 6-story idealized building with a 

critical 4th story ................................................................ H-10 

Figure H-9 Alpha factor mean value at 4th story for different 

variations of the 6-story idealized building with a 

critical 4th story ................................................................ H-10 

Figure H-10 Zero-length plastic hinge rotational behavior for 

adequate and inadequate lap splicing conditions ............ H-10 

Figure H-11 Alpha factor story profiles for different variations of 

the 8-story building with and without inadequate 

lap-splicing conditions .................................................... H-11 

Figure H-12 Alpha factor story profiles for different variations of 

the 8-story building with and without inadequate 

lap-splicing conditions .................................................... H-12 

Figure H-13 Alpha factor story profiles for different variations of 

the 8-story building with inadequate lap-splicing 

conditions at the 1st and 4th critical story......................... H-13 

Figure H-14 Schematic elevation view of the simulated 8-story 

frame plus one rectangular wall ...................................... H-14 

Figure H-15 Typical wall cross section ............................................... H-14 

Figure H-16 Collapse mechanism for a 4-story structure .................... H-16 

Figure H-17 Schematic elevation view of the simulated 4-story 

frame plus two rectangular walls .................................... H-18 
FEMA P-2018 List of Figures xix

Figure H-18 Schematic elevation view of the simulated 8-story 

frame plus two rectangular walls, one discontinuous 

in the first story ............................................................... H-20 

Figure H-19 8-story frame plus two 50 in. walls building, one 

discontinuous and supported by discontinuous 

columns ........................................................................... H-21 

Figure H-20 8-story frame plus two 50 in. walls building, one 

discontinuous and supported by ductile columns ........... H-22 

Figure H-21 Schematic elevation view of the simulated 8-story 

frame plus two rectangular walls, one discontinuous 

in upper story .................................................................. H-22 

Figure H-22 Schematic elevation view of an 8-story wall with a 

shear critical story ........................................................... H-28 

Figure H-23 (a) Two-spring in series model. (b) Response of each

individual component representing flexure and shear .... H-28 

Figure H-24 Response of the 8-story archetype frame-wall structure 

for wall length Lw = 200 in. with a shear critical section 

at the wall base. Simulation for a strong spring 

Vns/Vspr,min = 1.5 ............................................................... H-30 

Figure H-25 Response of the 8-story archetype frame-wall structure 

for wall length Lw = 200 in. with a shear critical section 

at the wall base. Simulation for Vns/Vspr,min = 1.1 ........... H-30 

Figure H-26 Response of the 8-story archetype frame-wall structure 

for wall length Lw = 200 in. with a shear critical section 

at the wall base. Simulation for a weak spring 

Vns/Vspr,min = 0.5 ............................................................... H-31 

Figure H-27 Earthquake scenarios for shear critical models 

evaluation ........................................................................ H-32 

Figure H-28 Dynamic response of the BWS model under the LH 

set .................................................................................... H-32 

Figure H-29 Dynamic response of the BAS model under the LH 

set .................................................................................... H-33 

Figure H-30 Dynamic response of the BAS model under the IH 

set .................................................................................... H-33 

Figure H-31 Dynamic response of the BAS model under the HH 

set .................................................................................... H-34 

Figure H-32 Dynamic response of the BSS model under the LH 

set .................................................................................... H-35 
xx List of Figures FEMA P-2018

Figure H-33 Dynamic response of the BSS model under the IH 

set .................................................................................... H-35 

Figure H-34 Dynamic response of the BSS model under the HH 

set .................................................................................... H-36 

Figure H-35 Dynamic response of the BWS, BAS and the BSS 

models under the LH, IH, and HH sets ........................... H-37 

Figure I-1 Illustration of the calculation of the center of strength 

for an example frame line ................................................... I-3 

Figure I-2 Illustration of the calculation of torsional capacity ............ I-4 

Figure I-3 Buildings analyzed in torsional study, showing variation 

in Torsional Ratio due the length of the walls .................... I-5 

Figure I-4 Diagram of 3D models used for torsional simulation ......... I-6 

Figure I-5 Steel material behavior used in fiber models ...................... I-7 

Figure I-6 Response of columns in a torsionally-irregular building 

model, showing how the 1% story drift collapse 

definition was determined ................................................... I-8 

Figure I-7 Pushover results for case E, deaggregated to show 

contributions from frame and wall lines ............................. I-8 

Figure I-8 Incremental dynamic analysis results for Case E, 

showing response of the building with the symmetricallyplaced wall and the asymmetrically-placed wall, and the 

lower collapse capacity of the torsionally-irregular 

building ............................................................................... I-9 

Figure I-9 Median collapse capacities of all the building cases 

analyzed in this study ........................................................ I-10 

Figure I-10 Collapse fragility for the torsionally-irregular buildings 

shown in Figure I-3, plotted in terms of μStrength ................ I-10 

Figure I-11 Buildings that are define to have “Extreme Torsion” are 

shown in the shaded area, identifying cases that may 

exceed 70% collapse probability ...................................... I-11 

Figure I-12 Buildings for which torsional effects can be neglected 

are shown in the shaded area as a function of the 

torsional ratio .................................................................... I-12 

Figure I-13 Buildings for which torsional effects can be neglected 

are shown in the shaded area as a function of the wall 

index .................................................................................. I-12 
FEMA P-2018 List of Figures xxi

Figure I-14 Buildings that are required to undergo a full torsional 

analysis are defined by the shaded area ............................ I-13 

Figure I-15 Column drift amplification due to torsion is the 

multiplier required to convert story drift to edge drift ..... I-14 

Figure I-16 3D portal frame used to examine estimates of e ............... I-14 

Figure I-17 Difference between stiffness based eccentricity and 

strength based eccentricity compared to eccentricity 

extracted from a model 3D portal frame with a wall on 

one side ............................................................................. I-15 

Figure I-18 Torsional amplification curve ........................................... I-15 

Figure I-19 Illustration of torsional amplifications computed for 

earthquake loading in the N-S direction ........................... I-16 

Figure I-20 Collapse capacities from buildings analyzed by DeBock 

(2017), compared to the results of this study.................... I-17 

Figure J-1 Portion of drift taken by the column, γ, during nonlinear 

response from incremental dynamic analysis of selected 

6-story buildings ................................................................. J-2 

Figure J-2 Portion of drift taken by the column, γ, assuming a linear 

relationship with ΣMc/ΣMb ................................................. J-2 

Figure K-1 IDA results and corresponding fragility curve 

estimation .......................................................................... K-2 

Figure K-2 Incremental Dynamic Analysis (IDA) curves for an 

8-story modern code design building model ..................... K-3 

Figure K-3 Collapse fragility functions for the “modern code 

design” building models ................................................... K-4 

Figure K-4 Scenario spectra ................................................................ K-5 

Figure K-5 Hazard curves at different periods recovered with the 

CSS set .............................................................................. K-5 

Figure K-6 Static and dynamic response of two 8-story buildings ..... K-6 

Figure K-7 Risk curves of maximum roof drift ratio for two 8-story 

buildings ........................................................................... K-7 

Figure K-8 Fragility curves construction ............................................ K-8 

Figure K-9 Dynamic alphas, 4-story building ..................................... K-8 

Figure K-10 Dynamic alphas, 8-story building ..................................... K-9 
xxii List of Figures FEMA P-2018

Figure L-1 Beam column element with concentrated flexural 

plasticity at the ends .......................................................... L-2 

Figure L-2 Backbone and cyclic response rule of the rotational 

spring representative of the flexural plastic hinge 

region ................................................................................ L-2 

Figure L-3 Limit state shear-axial-spring material introduced ........... L-3 

Figure L-4 Elevation and wall reinforcement detailing of the 

frame-wall structure used for this study ............................ L-4 

Figure L-5 Nonlinear force-based element with distributed 

plasticity formulation for the wall..................................... L-6 

Figure L-6 Wall response under triangular load pattern for GaussLobatto rule with three integration points ......................... L-8 

Figure L-7 Wall response under triangular load pattern for GaussLobatto rule with four integration points .......................... L-8 

Figure L-8 Wall response under triangular load pattern for GaussLobatto rule with five integration points .......................... L-8 

Figure L-9 Wall response under triangular load pattern for GaussRadaue rule with two integration points in the first story 

and three Gauss-Legendre integration points upstairs ...... L-9 

Figure L-10 Wall response under triangular load pattern with a 

reversed load at the roof for Gauss-Radaue rule with 

2IPs at the first story, and 3 Gauss-Legendre IPs 

upstairs .............................................................................. L-9 

Figure L-11 Normalized curvature demand at the first integration 

point (critical section at the base) for the inverted 

triangular load pattern ..................................................... L-10 

Figure M-1 Column shear strength ..................................................... M-1 

Figure N-1 Definition of flexure-controlled and shear-controlled 

walls based on results from a dataset of 990 wall tests .... N-2 

Figure N-2 Histograms of the reduced dataset of 80 flexurecontrolled walls ................................................................. N-3 

Figure N-3 Variation of drift capacity at axial failure as a function 

of λb and / P Af g c′ ............................................................. N-4 

Figure N-4 Drift capacity at axial failure for poorly detailed 

flexure-controlled walls .................................................... N-5 
FEMA P-2018 List of Figures xxiii

Figure N-5 Comparison of predicted drift capacities from 

Equation N-1 and Figure N-4 with experimentally 

obtained drift capacities .................................................... N-5 

Figure N-6 Comparison of neutral axis depth, c, computed from 

Equation N-2 with that from detailed sectional 

analysis ............................................................................. N-6 

Figure N-7 Drift capacity of shear-controlled walls/piers as a 

function of / P Af g c′ and minimum web reinforcement 

ratio ................................................................................... N-7 

Figure N-8 Drift capacity of shear-controlled walls/piers as a 

function of / P Af g c′with a natural log fit ........................ N-7 

Figure N-9 Drift capacity of shear-controlled walls/piers as a 

function of / P Af g c′with a bi-linear fit ............................ N-8 

Figure N-10 Comparison of predicted drift capacities from 

Equation N-4 with experimentally obtained drift 

capacities at axial failure .................................................. N-9 

Figure N-11 Examples of asymmetric wall cross-sections ................. N-10 

Figure N-12 Damage in walls with asymmetric wall crosssections ........................................................................... N-10 

Figure N-13 Drift capacity of flexure-controlled walls with spirally 

reinforced boundary columns ......................................... N-11 

Figure N-14 Damage of shear-controlled walls with spirally 

reinforced boundary columns at some level of lateral 

strength loss .................................................................... N-12 

Figure N-15 Drift capacity of shear-controlled walls with spirally 

reinforced boundary columns ......................................... N-13 

Figure O-1 Building details of the six-story San Diego warehouse 

with infilled RC frames .................................................... O-3 

Figure O-2 Floor plans of the prototype structures and design 

details of the columns and the beams of the first two 

stories of the 4-story prototype ......................................... O-3 

Figure O-3 Lateral force-drift ratio curves for the infilled bays and 

calibration of struts ........................................................... O-5 

Figure O-4 Three-dimensional numerical model with infill struts ..... O-6 
xxiv List of Figures FEMA P-2018

Figure O-5 Pushover analyses results of the models (M1 to M5) 

and deaggregated response of interior and exterior 

frames for models M1 and M3 .......................................... O-8 

Figure O-6 Incremental dynamic analysis results of the infilled 

frame models M1 to M6 .................................................... O-9 

Figure O-7 Displacement profiles of the buildings M1 to M6 just 

before collapse ................................................................ O-10 

Figure O-8 Damage in infill panel with opening causing shear 

failure in bounding column ............................................. O-11 

Figure O-9 Classification of infills based on relative stiffness of 

infill and bounding frame ................................................ O-12 

Figure O-10 Classification of infills based on relative strength of 

infill and bounding frame ................................................ O-12 

Figure O-11 Results of detailed FE analyses single-story single bay 

frames for the prototypes structures considered here ..... O-13 

Figure O-12 Deformed meshes at 1.0% drift of panels with 

openings for mf ′ = 0.4 ksi ................................................. O-17 

Figure O-13 Deformed meshes at 1.0% drift of panels with 

openings for mf ′ = 0.8 ksi .................................................. O-17 

Figure O-14 Deformed meshes at 1.0% drift of panels with 

openings for mf ′ = 1.4 ksi .................................................. O-18 

Figure O-15 Lateral force-vs.-drift behavior of the infilled panels 

with openings of different size and locations ................. O-18 

Figure O-16 Strength reduction of infilled frames as a function of 

opening location compared to the frame with a solid 

panel ................................................................................ O-19 

Figure O-17 Strength reduction of infilled frames as a function of 

opening area compared to the frame with a solid 

panel ................................................................................ O-19 

Figure O-18 Comparison of strength of infilled bays with openings 

obtained from Equation O-3 and detailed FE analyses 

in FEAP ........................................................................... O-19 

Figure O-19 Contribution of non-infilled columns at the peak 

strength of infilled frames ............................................... O-22 

Figure O-20 Variation of Te with increase in seismic excitation of 

the infilled frame models M1 to M6 ............................... O-24 
FEMA P-2018 List of Figures xxv

Figure O-21 Estimation of effective period of infilled frames ........... O-24 

Figure O-22 Normalized displacement profile of the infilled frame 

buildings with δeff = 1.0 ................................................... O-25 

Figure O-23 Damage to an infilled frame building, showing 

severely damaged columns, but no collapse ................... O-26 
FEMA P-2018 List of Tables xxvii

List of Tables

Table 3-1 Default Expected Properties for Masonry Infill ................. 3-4 

Table 5-1 Classification of Infill ........................................................ 5-5 

Table 5-2 Drift at which Infill is Assumed to Reach Peak Lateral 

Strength, ∆peak (in Percent Drift Ratio) ............................. 5-17 

Table 5-3 Values for Effective Mass Factor, Cm .............................. 5-21 

Table 6-1 Values of Coefficient a for Frame Systems ....................... 6-5 

Table 6-2 Drift Factor, γ, for Columns ............................................... 6-7 

Table 6-3 Plastic Rotation Capacities for Tied Columns ................... 6-8 

Table 6-4 Plastic Rotation Capacities for Spiral-Reinforced 

Columns ............................................................................. 6-9 

Table 6-5 Drift Capacity of Critical Slab-Column Connections ........ 6-9 

Table 6-6 Column Rating, CR .......................................................... 6-11 

Table 7-1 Values of Coefficient α for Frame-Wall Systems ............. 7-6

Table 7-2 Drift Factor, γ, for Columns ............................................... 7-9 

Table 7-3 Plastic Rotation Capacities for Tied Columns ................. 7-10 

Table 7-4 Plastic Rotation Capacities for Spiral-Reinforced 

Columns ........................................................................... 7-11 

Table 7-5 Drift Capacity of Critical Slab-Column Connections ...... 7-11 

Table 7-6 Drift Capacity of Flexure-Critical Walls or Vertical 

Wall Segments ................................................................. 7-13 

Table 7-7 Drift Capacity of Shear-Critical Walls or Vertical Wall 

Segments .......................................................................... 7-13 

Table 7-8 Coefficients for Calculation of Neutral Axis Depth, c ..... 7-14 

Table 7-9 Minimum Transverse Reinforcement in Integral 

Columns or Boundary Elements Required to be 

Classified as Confined ..................................................... 7-15 
xxviii List of Tables FEMA P-2018

Table 7-10 Column Rating, CR, and Wall Rating, WR ......................7-16

Table 8-1 Values of Coefficient α for Bearing Wall Systems............8-4

Table 8-2 Drift Capacity of Flexure-Critical Walls or Vertical Wall 

Segments............................................................................8-6

Table 8-3 Drift Capacity of Shear-Critical Walls or Vertical Wall 

Segments............................................................................8-7

Table 8-4 Coefficients for Calculation of Neutral Axis Depth, c.......8-7

Table 8-5 Minimum Transverse Reinforcement in Integral 

Columns or Boundary Elements Required to be 

Classified as Confined........................................................8-8

Table 8-6 Wall Rating, WR.................................................................8-9

Table 9-1 Values of Coefficient α for Infilled Frame Systems..........9-4

Table 9-2 Effective Height of Columns in Infilled Frame 

Systems ..............................................................................9-7

Table 9-3 Plastic Rotation Capacities for Tied Columns ...................9-8

Table 9-4 Plastic Rotation Capacities for Spiral-Reinforced 

Columns .............................................................................9-9

Table 9-5 Column Rating, CR..........................................................9-10

Table 9-6 Assistance to Column Ratings Based on Infill Panel 

Response ..........................................................................9-11

Table 9-7 Drift at Onset of Residual Strength, ∆res, for Infilled 

Bays..................................................................................9-11

Table A-1 Uncertainty in Predictions of Column Plastic Rotation 

Capacity, Obtained from Comparison with 

Experimental Data.............................................................A-6

Table D-1 Frame-Wall Building Properties .......................................D-2

Table D-2 WSI Required to Satisfy ASCE 41-13 Tier 1 Shear 

Stress Check......................................................................D-9

Table E-1 Properties of Pure Frame Building Set.............................. E-1

Table E-2 Properties of Frame-Wall Building Set............................. E-2

Table E-3 Table of Collapse Probabilities (from ATC-78-1) for 

Pure Frame Buildings........................................................ E-4

Table H-1 Coefficients C0, C1, and C2 of the Studied Buildings........H-3
FEMA P-2018 List of Tables xxix

Table H-2 Average Ratio of (Maximum Displacement at Effective 

Modal Height of Non-Linear Analysis) / (Estimated 

Displacement at Effective Modal Height) for Different 

Vp/Vn and Mc/Mb Ratios of the 6-Story Idealized 

Building ............................................................................ H-3

Table H-3 Mean Values for αα Factor for the 1st Story only for a 

6-story Idealized Building with Critical 1st Story ............. H-8

Table H-4 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Archetype Frame Plus One 

Continuous Wall ............................................................. H-15

Table H-5 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Modified Frame I Plus One 

Continuous Wall ............................................................. H-15

Table H-6 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Modified Frame 2 Plus One 

Continuous Wall ............................................................. H-16

Table H-7 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Frame Plus One 

Continuous Wall ............................................................. H-17

Table H-8 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Modified Frame I Plus One 

Continuous Wall ............................................................. H-17

Table H-9 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Modified Frame II Plus One 

Continuous Wall ............................................................. H-18

Table H-10 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Archetype Plus Two Continuous 

Walls............................................................................... H-19

Table H-11 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus Two 

Continuous Walls............................................................ H-19

Table H-12 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Archetype Plus One Continuous 

Wall and One Discontinuous Wall in the First Story...... H-20

Table H-13 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Discontinuous Wall in the 

First Story ....................................................................... H-20
xxx List of Tables FEMA P-2018

Table H-14 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Archetype Plus One Continuous 

Wall and One Wall That Ends in the Third Story ...........H-23

Table H-15 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Archetype Plus One Continuous 

Wall and One Wall That Ends in the Second Story ........H-23

Table H-16 Values of Coefficient α Estimated from Pushover 

Analysis for a 4-Story Archetype Plus One Continuous 

Wall and One Wall That Ends in the First Story.............H-23

Table H-17 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Wall That Ends in the 

Seventh Story ..................................................................H-24

Table H-18 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Wall That Ends in the Sixth 

Story................................................................................H-24

Table H-19 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and one Wall That Ends in the Fifth 

Story................................................................................H-25

Table H-20 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Wall That Ends in the 

Fourth Story ....................................................................H-25

Table H-21 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Wall That Ends in the Third 

Story................................................................................H-26

Table H-22 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Wall That Ends in the 

Second Story ...................................................................H-26

Table H-23 Values of Coefficient α Estimated from Pushover 

Analysis for an 8-Story Archetype Plus One 

Continuous Wall and One Wall That Ends in the First 

Story................................................................................H-27

Table N-1 Neutral Axis Depth (c) Parameters Used in 

Equation N-2 .....................................................................N-6

Table N-2 Drift Capacity for Shear-Controlled Walls/Piers at 

Axial Collapse...................................................................N-8
FEMA P-2018 List of Tables xxxi

Table O-1 Details of the Archetype Models Considered in This 

Study to Evaluate Seismic Behavior of Infilled 

Buildings........................................................................... O-2

Table O-2 Column Dimensions and Design Details of the

Prototypes......................................................................... O-4

Table O-3 Calibrated Concrete and Strut Properties of the Models’ 

Elements............................................................................ O-5

Table O-4 Collapse Potential of the Infilled Buildings and Frame 

Counterparts...................................................................... O-8

Table O-5 Collapse Potential of the Infilled Buildings and Frame 

Counterparts...................................................................... O-8

Table O-6 Effective Height of Columns in Infilled Frame .............. O-11

Table O-7 grav Pinf and max Pinf Values of the Models ............................... O-13

Table O-8 Comparison of Strength of Single Infilled Bays 

Obtained.......................................................................... O-14

Table O-9 Geometric Details of the Openings Considered in the 

Parametric Study............................................................. O-15

Table O-10 Classification of Infill in Each Infilled Bay.................... O-20

Table O-11 When Infill Panels with Openings Can Be Ignored for 

Calculation of Strength? ................................................. O-20

Table O-12 Collapse Potential of the Infilled Buildings and Frame 

Counterparts.................................................................... O-23

Table O-13 Fraction of the Drift Demand in the First Story.............. O-25
FEMA P-2018 1: Introduction 1-1

Chapter 1

Introduction

A wide variety of concrete buildings exist in regions of significant seismicity 

in the United States, and many were constructed prior to the enactment of 

modern seismic provisions in building codes. Known as non-ductile concrete 

buildings, these buildings were constructed prior to the late-1970s, and 

include archaic construction dating back to the early 1900s. Problematic 

issues include inadequate steel reinforcing details, system irregularities, and 

element discontinuities that can result in sudden failure and loss of vertical 

load-carrying ability. Large earthquakes have demonstrated the seismic 

vulnerability of these older, concrete buildings, but not all such buildings are 

at risk of global collapse.

Following the 1971 San Fernando earthquake, the 1976 Uniform Building 

Code (ICBO, 1976) introduced requirements for more robust detailing of 

reinforced concrete systems along with larger seismic design loads than in 

previous editions of the UBC. As a result, the 1976 UBC is often used as a 

benchmark, and concrete buildings that were designed and constructed in 

accordance with codes prior to the 1976 UBC are considered to be high 

seismic risk buildings that should be evaluated and potentially retrofitted.

Visual inspection alone, as is performed in FEMA P-154 Rapid Visual 

Screening of Buildings for Potential Seismic Hazards: A Handbook, Third 

Edition (FEMA, 2016) cannot reliably evaluate the significance of seismic 

deficiencies that are often present in older concrete buildings. In most cases, 

an engineer must perform a detailed analytical evaluation to differentiate the 

potential collapse vulnerability among concrete buildings subjected to strong 

ground shaking. Because current evaluation methods and retrofit techniques 

are complex and expensive to perform, a new evaluation methodology was

needed to more efficiently screen an inventory of older concrete buildings for 

potential collapse risk.

1.1 ATC-78 Project Series

The purpose of the FEMA-funded ATC-78 Project Series, “Identification and 

Mitigation of Non-Ductile Concrete Buildings,” is to develop an evaluation 

methodology that will: (1) identify the most seismically hazardous nonductile concrete buildings; and (2) be easier and less expensive to apply than 
1-2 1: Introduction FEMA P-2018

the detailed analysis procedures of ASCE/SEI 41-17, Seismic Evaluation and 

Retrofit of Existing Buildings (ASCE, 2017b).

The efforts to develop this methodology were coordinated with, and built on, 

the results of related projects funded by the National Earthquake Hazards 

Reduction Program (NEHRP), the National Institute of Standards and 

Technology (NIST), the National Science Foundation (NSF), and other 

FEMA-sponsored work, including the following:

• The NEES Grand Challenge for the Mitigation of Collapse Risk of Older 

Concrete Buildings (NEES, 2010), identified the extent of the collapse 

hazard present in existing reinforced concrete buildings, conducted 

laboratory testing of selected concrete building systems and components, 

and developed an inventory of older concrete buildings.

• The NIST GCR 10-917-7 Report, Program Plan for the Development of 

Collapse Assessment and Mitigation Strategies for Existing Reinforced 

Concrete Buildings (NIST, 2010b), defined a broad program to 

systematically investigate and mitigate the vulnerability of non-ductile 

concrete buildings. The NIST Program Plan also suggested a 

methodology for determining the relative importance of various 

conditions known to be deficient, termed collapse indicators.

• The NIST-funded project conducted by the Building Seismic Safety 

Council (BSSC) of the National Institute of Building Sciences (NIBS) 

identified subclasses of non-ductile concrete buildings with common and 

quantifiable characteristic deficiencies in the NIST GCR 10-917-6 

Report, Concrete Model Building Subtypes Recommended for Use in 

Collecting Inventory Data (NIST, 2010a).

Early phases of development investigated the collapse indicator concept 

identified in the NIST Program Plan, with the purpose of calculating a 

probability of collapse based on the severity of a collapse indicator. 

Although the collapse indicator concept proved insightful for the prediction 

of global collapse, use of collapse indicators as a predictive tool was more 

complex than originally envisioned and found to be impractical for the 

purposes of a simplified evaluation methodology for all types of concrete 

buildings (ATC, 2012; NIST, 2014).

As a result, later phases of development focused on story drifts and their 

relation to the collapse potential of concrete components such as columns

and walls, and on developing criteria for linking component collapse to 

global collapse of concrete buildings overall. Project findings and evolving
FEMA P-2018 1: Introduction 1-3

efforts defining the evaluation methodology have been documented in the 

ATC-78 series of reports:

• ATC-78, Identification and Mitigation of Seismically Hazardous Older 

Concrete Buildings: Interim Methodology Evaluation (ATC, 2011);

• ATC-78-1, Evaluation of the Methodology to Select and Prioritize 

Collapse Indicators in Older Concrete Buildings (ATC, 2012);

• ATC-78-2, Seismic Evaluation for Collapse Potential of Older Concrete 

Frame Buildings (ATC, 2013);

• ATC-78-3, Seismic Evaluation of Older Concrete Frame Buildings for 

Collapse Potential (ATC, 2015);

• ATC-78-4, Seismic Evaluation of Older Concrete Frame and Shear Wall 

Buildings for Collapse Potential (ATC, 2016); 

• ATC-78-5, Seismic Evaluation of Older Concrete Frame, Wall, and 

Frame-Wall Buildings for Collapse Potential (ATC, 2016); and

• ATC-78-6, Seismic Evaluation of Older Concrete Frame, Frame-Wall, 

and Bearing Wall Buildings for Collapse Potential (ATC, 2017).

1.2 Evaluation Methodology

This report presents an evaluation methodology intended to determine the 

relative risk of collapse of older concrete buildings in strong earthquake 

shaking. The purpose of this methodology is to enable identification of the 

subset of buildings in this class that are expected to have a high risk of 

collapse without the need for extensive testing or nonlinear analysis. 

Significant features of the evaluation methodology are:

• Definition of collapse as a global loss of gravity support at a story, 

possibly leading to the collapse of other stories.

• Singular intent of determining the relative risk of global collapse among 

an inventory of older concrete buildings. Other performance measures, 

(e.g., extent of damage, functionality, or downtime) are not considered.

• Probabilistic characterization of demand (as story drift) and the capacity 

limit (as column or wall collapse), allowing estimation of the probability 

of collapse for column or wall components in each story.

• Estimation of the probability of collapse in a given story through

consideration of global criteria based on the collapse probability of

column and wall components in that story.
1-4 1: Introduction FEMA P-2018

• Use of the probability of story collapse as a relative measure for ranking 

the seismic risk and screening an inventory of older concrete buildings to 

set priorities for further action.

For the purposes of this methodology, all concrete buildings designed to 

codes that are not equivalent to the 1976 Uniform Building Code, or not 

known to meet other locally accepted evaluation or retrofit standards, are 

considered high seismic risk buildings. This evaluation methodology is 

intended to identify the subsets of these buildings that are of lower relative 

risk of collapse, termed lower seismic risk buildings, or are considered to be

of significantly higher relative risk of collapse, termed exceptionally high 

seismic risk buildings.

The evaluation methodology addresses reinforced concrete frame, framewall, bearing wall, and infilled frame structures with rigid diaphragms and 

heights less than 160 feet. The resulting methodology is based on the 

evolution of procedures as outlined in the ATC-78 series of reports, and have 

been refined by results obtained from trial evaluations and testing of the 

methodology. Collapse is defined as the global loss of vertical load-carrying 

ability at a story, possibly leading to the collapse of other stories. Procedures 

for assessing collapse in this methodology require simplified estimates of 

drift demand to implement. Although the resulting calculations are 

intentionally simplified, the underlying criteria are based on probabilistic 

concepts and structural reliability theory.

A mechanism-based method for estimating base shear strength, which can be 

generally applied to different concrete building types and configurations, has 

been incorporated in the methodology. This has the added advantage of 

identifying potential lateral mechanisms that influence story drifts. 

Procedures to identify conditions under which concrete columns and concrete 

walls will lose vertical load-carrying capacity have been based on limited 

available test data and structural reliability concepts.

Story drift demand is calculated probabilistically and combined with a 

capacity limit, resulting in a probabilistic measure of collapse for critical

column and wall components in each story, and for the collapse of a story as 

a whole. Because extensive testing and nonlinear analysis is not required by 

the calculation procedures, the engineering time for evaluation is expected to 

be no greater than that for a Tier 2 evaluation in accordance with ASCE/SEI 

41-17, and significantly less than Tier 3 nonlinear analysis procedures.

Other estimates of drift demand that are more extensive (and presumably 

more accurate) than the procedures recommended in this report can be used 
FEMA P-2018 1: Introduction 1-5

in the methodology. Similarly, other, more detailed methods of estimating 

the effective building period can be used. It is unclear at this time if risk 

ratings obtained using input parameters from other engineering procedures

would be consistent with ratings obtained using the calculation procedures

defined herein. For decision making at the public policy level, and 

implementation in mandatory evaluation and retrofit programs, it is 

recommended that the complete methodology be used with input parameters 

from a common engineering basis to ensure consistency in the relative 

rankings across an inventory of buildings.

1.3 Comparison with ASCE/SEI 41

Until recently, ASCE/SEI 31-03, Seismic Evaluation of Existing Buildings

(ASCE, 2003), has been the standard for seismic evaluation, and ASCE/SEI 

41-06, Seismic Rehabilitation of Existing Buildings (ASCE, 2007) has been 

the standard for seismic retrofit. In the 2013 update of these standards, the 

evaluation (ASCE/SEI 31) and retrofit (ASCE/SEI 41) standards were 

combined into a single standard (ASCE/SEI 41-13), and made more 

internally consistent (ASCE, 2013). The current version of these standards is 

ASCE/SEI 41-17 (ASCE, 2017).

The protection of life safety has been used as a seismic evaluation and 

retrofit performance objective for decades. Current standards for seismic 

evaluation and retrofit were originally developed with “life safety” as a 

conceptual basis, although higher and lower performance objectives have

also been defined. Historically, the level of risk to life safety for existing 

buildings has been permitted to be somewhat higher than for new buildings 

due to the anticipated cost and disruption of retrofit. This elevated level of 

risk for existing buildings, however, has not been quantitatively defined in

life-safety terms (i.e., acceptable risk of incurring serious injuries or deaths). 

Quantification and calibration of acceptable risk among different design and 

evaluation methods may eventually be possible with the FEMA P-58 Seismic 

Performance Assessment of Buildings, Methodology and Implementation

(FEMA, 2012 and 2018).

Separate from the notion of “life safety,” the “collapse prevention” 

performance level in ASCE/SEI 41 is based on the prevention of structural 

collapse. The criteria used to define “collapse prevention” are based on the 

performance of individual building components (e.g., beams, columns, walls, 

and slabs) rather than global collapse. Often, the failure of one or more 

components relative to ASCE/SEI 41 criteria is not expected to result in 

global collapse, and some engineers experienced in evaluation and retrofit of 

older concrete buildings estimate that only a small percentage of concrete 
1-6 1: Introduction FEMA P-2018

buildings that fail the criteria in ASCE/SEI 41 will actually collapse, even in 

very rare earthquake shaking. Recent studies of building collapse 

performance, such as those embodied in the FEMA P-695 Methodology

(FEMA, 2009), consider global collapse more explicitly and describe 

collapse performance probabilistically. These studies recognize that most 

serious injuries and deaths in earthquakes are caused by global structural 

collapse.

This evaluation methodology focuses on structural failures in vertical loadcarrying elements that are expected to lead to global collapse. As a result, it 

does not directly address other seismic deficiencies that have been observed 

to cause structural damage (but not necessarily collapse) in past earthquakes. 

Evaluation using this methodology will result in an approximation of the 

probability of collapse of a building, subject to a specified ground motion. 

This result is not directly related to “collapse prevention” as defined in 

ASCE/SEI 41 because it is an approximation of global structural collapse. 

Results are considered approximate because of significant uncertainties in the 

determination of ground motion, the methods used to calculate story drifts, 

the prediction of the probability of failure of individual column and wall 

components, and the criteria used to estimate story collapse based on column 

and wall component collapse. Although approximate, the results of 

individual building evaluations within a group of buildings are expected to

provide a useful indication of the relative potential for collapse across an 

inventory of buildings.

This evaluation methodology was developed for use as a screening tool. It is 

intended as a complement to, not a replacement for, ASCE/SEI 41, and

results can be used to prioritize buildings for more detailed evaluation using 

ASCE/SEI 41. It is expected that results could eventually be used in future 

calibration of ASCE/SEI 41 evaluation and retrofit criteria for structural 

collapse, through comparisons with the probabilistic results obtained from

this methodology.

1.4 Policy Implications

Application of this evaluation methodology is expected to include use by 

political jurisdictions in setting priorities for mandatory seismic risk 

reduction within their communities, considering collapse as the overriding 

loss to be avoided. 

Concrete buildings designed and constructed to codes that are not equivalent 

to the 1976 Uniform Building Code, or not known to meet other locally 

accepted evaluation or retrofit standards, are considered to be highly 
FEMA P-2018 1: Introduction 1-7

vulnerable to earthquake shaking and are herein classified as high seismic 

risk buildings. The methodology described in this report is intended to 

enable relatively efficient identification of older concrete buildings with a 

high probability of collapse, termed exceptionally high seismic risk buildings, 

as well as those with a probability of collapse lower than most older concrete 

buildings, termed lower seismic risk buildings.

For any level of earthquake ground motion selected, this methodology can be 

used to rank buildings based on an approximate probability of collapse. The 

probability of collapse for any building is highly dependent on the severity of 

ground motion expected at the site, and the probability of occurrence for the 

selected ground motion, which can include smaller, more frequent 

earthquakes (72-year return period), or larger, less frequent earthquakes 

(500-year, 1000-year or 2500-year return periods).

The Basic Safety Earthquake, BSE-2E, from ASCE/SEI 41-17 is the seismic 

hazard level recommended herein for measuring collapse performance. In 

general, more intense (i.e., less frequent) ground motions will increase the 

collapse probability of all buildings in a region, but the relative ranking 

between buildings is expected to be the same. This general trend, however, 

may not be the case in areas with a steeply sloping hazard curve, such as the 

New Madrid seismic hazard region in and around Memphis, Tennessee. This 

region has a relatively low threat from frequent earthquakes, but the ground 

motion intensity for very rare earthquakes is very high. In areas with special 

seismic hazard concerns, selection of an earthquake hazard level that is most 

representative of the local seismic hazard setting should be considered.

A threshold for defining exceptionally high seismic risk, which presumably 

would identify the highest priority buildings for mitigation, has been 

judgmentally set in this methodology to be a building rating greater than or 

equal to 0.7, approximately corresponding to a 70% (or higher) probability of 

collapse given the selected ground motion level. Based on observed 

performance of U.S. style construction in past earthquakes, it is expected that 

a relatively low percentage of buildings will be placed in the exceptionally 

high seismic risk category, however, this percentage is not known. More 

extensive evaluation using the nonlinear analysis methods of ASCE/SEI 41 

could be used to further evaluate, and possibly reclassify, buildings that have 

been identified as exceptionally high seismic risk using this methodology.

Threshold rankings that would define “acceptable” levels of collapse risk

have not been established. Levels of collapse risk that would be deemed 

acceptable are difficult to determine, and complicated by societal needs and 

differences between the definition of collapse used in this methodology and 
1-8 1: Introduction FEMA P-2018

those used in current codes and standards for new and existing buildings. It 

is anticipated that use of this methodology on buildings with known collapse 

characteristics (i.e., from analysis, laboratory testing, or observed 

performance) will help in setting threshold values for acceptable risk in the 

future.

A reasonable approach for using this methodology in a program for reducing 

the seismic risk associated with older concrete buildings could include the 

following:

• Using sidewalk surveys, assessors’ files, or other available jurisdictional 

records, develop a preliminary inventory of older concrete buildings (i.e., 

buildings not conforming to the 1976 Uniform Building Code, or not 

meeting other locally accepted evaluation or retrofit standards).

• Within the first year of a program, require building owners in the 

preliminary inventory to submit a simple building data collection form, 

with input from an engineer or architect, to confirm the building status, 

and possibly identify additional risk factors. For example, such a form 

could be used to confirm that the building is of concrete construction, 

does not comply with acceptable building codes, and has not be 

retrofitted to acceptable standards. In addition, the form could also be 

used to identify the building height, area, and occupancy, as well as other 

risk factors, such as unstable soil conditions and structural irregularities. 

Owners of older concrete buildings that were not included in the 

preliminary inventory should also be required to submit a form, but 

identification and enforcement of such a requirement would require more 

effort, such as ongoing monitoring of building permit applications.

• Develop a refined inventory of older concrete buildings based on 

information contained in building data collection forms.

• Within approximately three years, require building owners in the refined 

building inventory to evaluate and classify their buildings using this 

methodology.

• Develop a prioritized inventory of older concrete buildings based on 

information obtained from the building evaluations.

• Within approximately five years, require mitigation of the risk associated 

with exceptionally high seismic risk buildings through more detailed 

evaluation or retrofit, if needed, using ASCE/SEI 41 or other locally 

accepted evaluation or retrofit standards.

• Over a longer period of time, require mitigation of the risk associated 

with high seismic risk buildings and lower seismic risk buildings through
FEMA P-2018 1: Introduction 1-9

more detailed evaluation or retrofit, if needed. It is expected that the 

state of knowledge in ASCE/SEI 41 will continue to evolve over time, 

and that many buildings in lower seismic risk categories could be 

deemed to be acceptably safe in the future. It is also possible that 

additional information gained from the use of this methodology over 

time will demonstrate that the criteria are sufficiently reliable for 

identifying buildings that are acceptably safe without further evaluation

(at least in the case of lower seismic risk buildings).

Because this methodology has not been calibrated to traditional life safety 

standards, it is not intended, and should not be used, to determine retrofit 

requirements.

1.5 Report Organization and Content

This report outlines a methodology to evaluate the collapse potential of older 

concrete frame, frame-wall, bearing wall, and infilled frame buildings.

Chapter 2 outlines the evaluation methodology, including applicability and 

limitations on its use.

Chapter 3 defines the general requirements for use of the methodology.

Chapter 4 defines the recommended methods for calculating component 

strengths that are part of the methodology.

Chapter 5 includes guidance for classifying building systems based on their

expected response characteristics. The primary response characteristic of 

interest is the lateral deformation pattern, which is used to estimate story 

drift. Based on the classification of a system, methods for calculating the 

structural period are provided, along with simplified methods for identifying

certain exceptionally high seismic risk buildings, or buildings judged to be of 

lower seismic risk, relative to other older concrete buildings.

Chapter 6 describes the method of evaluation for concrete frame systems.

Chapter 7 describes the method of evaluation for concrete frame-wall 

systems.

Chapter 8 describes the method of evaluation for concrete bearing wall 

systems.

Chapter 9 describes the method of evaluation for concrete systems with 

masonry infill walls.
1-10 1: Introduction FEMA P-2018

Chapter 10 describes the method of assigning building ratings based on the 

results of Chapters 5, 6, 7, 8, and 9.

The appendices to this report provide additional information on the 

background and derivation of the calculation procedures and criteria 

comprising the methodology.

A list of symbols used throughout this report, along with a list of references, 

are provided at the end of this report.
FEMA P-2018 2: Evaluation Methodology 2-1 

Chapter 2 

Evaluation Methodology

Older concrete buildings not in compliance with the strength and detailing 

requirements of the 1976 or later editions of the Uniform Building Code

(ICBO, 1976), and not otherwise determined to have acceptable seismic 

performance through evaluation or retrofit to locally accepted standards, 

could be susceptible to significant structural damage in an earthquake and 

should be considered high seismic risk buildings. 

This chapter provides an overview of an evaluation methodology that can be 

used to identify subsets of these buildings that are of lower relative risk of 

collapse, termed lower seismic risk buildings, or are considered to be of 

significantly higher relative risk of collapse, termed exceptionally high 

seismic risk buildings. It describes the intended scope, summarizes 

limitations on applicability, and identifies explicit exclusions for use of the 

evaluation methodology. 

Buildings categorized as exceptionally high seismic risk using this 

methodology should be prioritized for more detailed seismic evaluation or 

seismic retrofit.

2.1 Scope and Applicability

This evaluation methodology is intended for use in determining the relative 

risk of collapse within an inventory of buildings, prioritizing buildings for 

further evaluation, and guiding prudent risk-reduction policy decisions. It is 

not intended for use in developing or implementing seismic retrofits to 

improve the seismic performance, or reduce the risk of collapse, of an 

individual building. 

2.1.1 Applicability

This methodology is applicable to reinforced concrete buildings 160 feet or 

less in height, with concrete diaphragms, and with or without structural loadbearing walls, reinforced concrete shear walls, or masonry infill walls. 

Reinforced concrete elements that can be evaluated using this methodology 

include: 

• frame lines (or bays) that are designed to resist gravity loads, including 

beam-column systems, slab-column systems, or joist-column systems;
2-2 2: Evaluation Methodology FEMA P-2018

• frame lines (or bays) that are designed to resist gravity plus lateral loads, 

regardless of the level of ductile detailing;

• frame lines with masonry infill walls of hollow clay tile, brick masonry, 

or concrete masonry units (CMU), with or without openings (note: infill 

masonry panels that have been previously retrofitted or reinforced are 

outside the scope of application of the infill procedures in this 

methodology);

• wall lines with structural reinforced concrete walls, generally 4 inches or 

greater thickness and with a horizontal reinforcement ratio equal or 

greater than 0.0015 (see also Section 5.2.2);

• concrete elements retrofitted using materials and components that are 

compatible with concrete behavior and strength calculation procedures, 

and compatible with the mechanism analysis procedures of Section 5.5;

• post-tensioned concrete systems with reinforced concrete columns. In 

such cases, procedures for determining column capacity as a function of 

the beam or slab capacity, and any other calculation related to the 

capacity of beams and slabs, must be appropriately determined from ACI 

318-14, Building Code Requirements for Structural Concrete and 

Commentary (ACI, 2014).

Additional requirements for use of this methodology include:

• a complete load path that includes diaphragms and adequate connections 

between lateral force-resisting elements, including adequate reinforcing 

at construction joints in walls and at column and wall connections to 

foundations; and

• beam-column joints with limited eccentricity, in which the centerline of 

the beam is located within the width of the column and at least some of 

the beam longitudinal reinforcement passes within the column core (as 

defined by the boundaries of the column longitudinal reinforcement). Up 

to 10% of the beam-column joints may exceed this requirement if it is 

judged that overall building response will not be adversely affected.

The evaluation methodology is not applicable to precast frame or wall 

structures in which the capacity of a system or component is limited by its 

connection to other structural elements.

Older concrete buildings that do not qualify for evaluation using this 

methodology should be considered to be exceptionally high seismic risk 

buildings, and prioritized for detailed seismic evaluation by other means.
FEMA P-2018 2: Evaluation Methodology 2-3 

2.1.2 Seismic Deficiencies that are not Considered in the

Methodology

Because the evaluation methodology is focused on structural collapse, certain 

characteristics considered in other seismic evaluation procedures (e.g., 

ASCE/SEI 41), which identify sources of potential seismic damage, are not 

evaluated in this methodology. These include:

• Nonstructural components and systems (see section 5.2.2 for 

nonstructural walls that may affect response). 

• Prescriptive minimum reinforcing ratios and configurations (the effects 

of these characteristics on component strengths, however, are considered 

in this methodology). 

• Prescriptive minimum requirements on foundation configuration. For 

example, the effect of foundation ties on collapse probability is difficult 

to define and has not been considered.

• Precast concrete or stone cladding with brittle or drift-intolerant 

connections (note: estimated story drifts can be used to evaluate potential

damage to the panels or their connections; however, potential falling 

hazards due to cladding are not considered in the ratings of this 

methodology). 

• Geologic site hazards associated with earthquake-induced ground failure 

or tsunami effects. Such hazards require detailed analysis to determine 

the potential for collapse or other life safety risks. For the purposes of 

ranking an inventory of buildings, these buildings could initially be rated 

exceptionally high seismic risk requiring further detailed analysis.

2.1.3 Buildings with Concrete Components that are not 

Considered in the Methodology 

The evaluation methodology is intended to address specific classes of 

reinforced concrete buildings. There are other types of pre-1976 UBC 

buildings with concrete components that are not considered in this 

methodology. For the purposes of ranking an inventory, individual buildings 

of the following types could be a collapse risk, and might be considered 

exceptionally high seismic risk; however, the unique conditions associated 

with these types of buildings are not addressed by the procedures in this

methodology. 

2.1.3.1 Tilt-Up Buildings

Tilt-up buildings are one to three stories tall with walls (normally exterior 

walls, but sometimes also interior walls) precast on the ground and “tilted 
2-4 2: Evaluation Methodology FEMA P-2018

up” into place. The connections between the tilt-up walls and the 

diaphragms are often poor, and walls have often been observed to be 

collapsed or leaning outward following an earthquake. This type of failure is 

a load path issue that is not covered by this methodology. 

2.1.3.2 Residential Bearing Wall Buildings with Precast Slabs

Residential bearing wall buildings are typically motels, hotels, or apartments 

with demising walls of concrete or concrete masonry. When floors are 

constructed of precast concrete planks, with or without a concrete topping 

slab, the plank-to-wall bearing connection is often inadequate and can fail, 

leading to collapse of the floors. This type of failure is a load path issue that 

is not predictable by global building analysis, and is not covered by this 

methodology. 

2.1.3.3 Lift-Slab Buildings

Lift-slab buildings typically have a concrete core tower and are constructed 

by casting the floors stacked on the ground. Steel or concrete columns are 

erected, and the floor slabs are lifted into place, sliding up the columns. A 

gravity connection is then added at each column at each level. These gravity 

connections often have little or no drift tolerance and can fail, leading to 

collapse of the floors. Connections between the floor slabs and the concrete 

core are variable in quality. The drift tolerance of the column-to-slab gravity

connections is building-specific, and not covered by this methodology. 

2.2 Overview of the Evaluation Methodology

The evaluation methodology is intended to rate the relative probability of 

global structural collapse of older concrete buildings subjected to earthquake 

shaking at a specified seismic hazard level. Implementation of this 

methodology does not require a structural analysis model, instead relying on 

approximate period and strength calculations that are intended to require less 

effort to implement than other more detailed seismic evaluation procedures 

(e.g., ASCE/SEI 41). These features are intended to ensure, through 

prescriptive criteria, that results for one building can be easily compared to 

results for another building, enabling consistent ranking of a building 

inventory in terms of relative collapse risk. By evaluating the likelihood of 

global collapse, rather than individual component failures, this methodology 

attempts to avoid some of the conservatisms inherent in other seismic 

evaluation procedures, such as ASCE/SEI 41. 

The evaluation methodology uses a mechanism-based procedure to estimate 

strength and period, along with a prescribed approximation of story drifts as 

a function of global roof drifts derived from spectral displacements. Torsion, 
FEMA P-2018 2: Evaluation Methodology 2-5 

along with other considerations, are used to estimate inelastic rotation 

demands on individual columns and drift demands on walls, including 

consideration of uncertainty. Drift capacities and uncertainties for each 

column and wall have been based on experimental data (where available)

quantifying the failure of different types of reinforced concrete components 

with varying levels of axial load and ductile detailing, including 

consideration of lap splice deficiencies. 

Drift demands and drift capacities are used to compute column and wall 

ratings, which are then used to determine story ratings, and finally, an overall 

building rating. These ratings represent the likelihood of collapse, and vary 

between 0.1 and 0.9, with 0.1 representing a low likelihood of collapse and 

0.9 representing a high likelihood of collapse. Numerical building ratings 

can then be used to rank a group of buildings, or to separate the inventory 

into classes (i.e., groups) of lower seismic risk buildings, high seismic risk

buildings, and exceptionally high seismic risk buildings, for the purposes of

setting risk mitigation priorities. 

Certain buildings can be quickly classified as lower seismic risk (relative to 

all older concrete buildings), and others as exceptionally high seismic risk, 

using global considerations, including strength and configuration. Other 

buildings may undergo a more complete, but still abbreviated, evaluation 

procedure. The following sections highlight key calculation procedures for 

full application of the evaluation methodology, and summarize criteria used 

for early identification and classification of buildings. 

2.2.1 Overview of Key Calculation Procedures 

Full application of the evaluation methodology consists of the following 

steps:

• Complete the general requirements including a site visit.

• Classify the structural system among pure frame, frame-wall, bearing 

wall, and infilled frame systems.

• Identify lower seismic risk buildings and exceptionally high seismic risk 

buildings using approximate global characteristics. 

• Determine global lateral mechanisms and the governing base shear 

strength. 

• Estimate the effective period of vibration. 

• Estimate global drift demands based on the spectral demands at the site.

• Estimate story drift demands as a function of global drift demands.
2-6 2: Evaluation Methodology FEMA P-2018

• Evaluate column and wall components for collapse based on drift 

demand to drift capacity ratios, and assign column and wall component 

ratings.

• Establish the story rating as a measure of story collapse probability based 

on the ratings of all gravity load-carrying components.

• Determine building rating and risk classification based on the largest 

story rating in either direction.

The methodology also includes special procedures for evaluating pounding 

between buildings, slab-column frames, corner-column conditions, 

discontinuous columns, and mezzanines. Key calculation procedures are 

provided in the following chapters and sections:

• Chapters 2 through 4 provide scope, applicability, general requirements, 

and general strength calculations for basic application of the 

methodology.

• Chapter 5 covers procedures for classifying building type, configuration, 

and behavior, which are critical and necessary for application of the 

methodology. It includes a mechanism procedure for estimating the 

effective base shear strength (Section 5.5), which is used to estimate the 

effective fundamental period (Section 5.6). It also includes estimation of 

a global demand-to-capacity ratio (Section 5.7), which is used as a key 

indicator of behavior, and is also used in early identification and 

classification of buildings (Sections 5.8 and 5.9).

• Chapters 6, 7, 8, and 9 provide system-specific evaluation procedures for 

frame, frame-wall, bearing wall, and infilled frame systems, respectively,

based on the classification of buildings in Chapter 5. Each of these 

chapters is parallel in content and organization, and information is 

repeated so that each chapter is largely self-contained and essentially 

complete for evaluation of the system of interest. System-specific 

evaluation procedures include: identification of critical components 

(Section *.3), estimation of global drift demand (Section *.4), calculation 

of story and component drift demands (Sections *.5 and *.6), calculation 

of drift capacities (Section *.7), and determination of component and 

story ratings (Sections *.8 and *.9).

• Chapter 10 describes the determination of the overall building rating, and 

classification of buildings based on building rating.
FEMA P-2018 2: Evaluation Methodology 2-7 

2.2.2 Early Identification of Lower Seismic Risk Buildings 

Buildings can be identified as lower seismic risk buildings with limited 

effort, and without the need for further evaluation, based on criteria in the 

following sections: 

• Section 5.4.3 – identifies frame-wall or wall systems with regular 

configurations that can be classified as lower seismic risk buildings if a 

parameter called the wall strength index (WSI) meets certain 

requirements.

• Section 5.8.1 – identifies strength requirements for buildings to be 

classified as exceptionally strong (i.e., essentially elastic), and, therefore, 

lower seismic risk buildings. 

2.2.3 Early Identification of Exceptionally High Seismic Risk 

Buildings 

Buildings can be identified as exceptionally high seismic risk buildings with 

limited effort, and without the need for further evaluation, based on criteria 

in the following sections: 

• Section 3.1 – specifies that concrete buildings for which detailed 

structural drawings are not available should be considered exceptionally 

high seismic risk buildings by default, unless structural details can be 

confirmed by other means. 

• Section 3.6 – identifies structural load path requirements along with 

conditions that, if present, result in the designation of an exceptionally 

high seismic risk building. 

• Section 5.9.1 – identifies strength requirements for buildings to be 

classified as exceptionally weak, and, therefore, exceptionally high 

seismic risk buildings. 

• Section 5.9.2 – identifies conditions for discontinuous walls supported on 

columns, wall piers, or girders that, if present, can result in the 

designation of an exceptionally high seismic risk building; also provides 

criteria for further evaluation of elements supporting discontinuous 

walls. 

• Section 7.6.2.3 and Section 9.6.2.3 – identifies criteria for extreme 

torsion resulting in the designation of an exceptionally high seismic risk 

building. 
2-8 2: Evaluation Methodology FEMA P-2018

2.3 Use of Alternate Analysis Procedures

The evaluation methodology includes simplified calculation procedures for 

estimation of important structural properties and response characteristics,

such as building strength, period of vibration, and drift demands. Although it 

is intended to be easier and less expensive to implement than other 

evaluation and retrofit methods, it does not preclude the use of alternate

analysis procedures for determining structural parameters used in the 

evaluation methodology.

The use of alternate procedures is permitted, as long as the resulting 

structural parameters are compatible and consistent with the basis of this 

methodology, as follows:

• Effective Fundamental Period. Use of an accepted analysis procedure, 

such as the Nonlinear Static Procedure in ASCE/SEI 41-17 Section 7.4.3,

is permitted for computing the effective fundamental period of the 

structure. The elastic period is not an acceptable substitute for the 

effective period.

• Effective Yield Strength. Use of an accepted analysis procedure, such 

as the Nonlinear Static Procedure in ASCE/SEI 41-17 Section 7.4.3, is 

permitted for computing the effective yield strength of the structure.

• Story Drift Demand. Use of an accepted analysis procedure, such as 

the Nonlinear Static Procedure in ASCE/SEI 41-17 Section 7.4.3, or the 

Nonlinear Dynamic Procedure in ASCE/SEI 41-17 Section 7.4.4, is 

permitted for determining the story drift demand including torsional 

effects, where required, in lieu of the approximate procedure in this 

methodology. Column drift demands may be determined directly from 

the analysis or from the procedures in this methodology.

It is unclear at this time if risk ratings obtained using input parameters from 

other engineering procedures would be consistent with ratings obtained using 

the calculation procedures defined herein. For decision making at the public 

policy level, and implementation in mandatory evaluation and retrofit 

programs, it is recommended that the complete methodology be used with 

input parameters from a common engineering basis to ensure consistency in 

the relative rankings across an inventory of buildings.
FEMA P-2018 3: General Requirements 3-1 

Chapter 3 

General Requirements

The evaluation methodology requires specific knowledge of the as-built 

configuration and condition of in-place materials and components. This 

chapter describes the general requirements for use of the methodology, 

including the presence of a complete load path.

3.1 As-Built Information

Documentation of the as-built configuration of a building is necessary for 

implementation of the evaluation methodology. Required as-built 

information includes: (a) building size and configuration; (b) structural 

component size, reinforcement, and detailing; material properties; and (c) site 

and foundation information. This information is best obtained from complete 

structural design drawings or as-built drawings. Other potential sources of 

information include construction specifications, geotechnical reports, 

structural calculations, and shop drawings.

In the case of older concrete buildings, sources of as-built information are 

often not available. Because it is potentially misleading to make assumptions 

regarding reinforcement details and member proportioning, it is 

recommended that any concrete building for which detailed structural 

drawings are not available should be considered an exceptionally high 

seismic risk building by default, unless structural details can be confirmed by 

other means (e.g., destructive and non-destructive site investigations).

An exception to the need for complete data as described above is contained 

in Section 5.4.3, where certain buildings could be classified as lower seismic 

risk based on the ratio of cross sectional area of structural walls and total 

building area. 

Where concrete buildings contain masonry infill, the configuration of the 

masonry (e.g., thickness and dimensions of openings) is often shown only in

architectural drawings, specifications, or shop drawings, which may not be 

available with the structural drawings. In addition, masonry material 

properties are seldom identified in any construction documents. In the 

absence of available construction documents or material tests, estimates for 

default masonry material properties are provided, but should be considered as 

highly uncertain. 
3-2 3: General Requirements FEMA P-2018

3.2 Site Investigation

A site investigation consists of visual observation of the condition of the 

building to verify that as-built information is representative of the existing 

conditions. The following should be confirmed as part of a site investigation: 

(a) building configuration, including the presence (or not) of structural 

additions, alterations, or modifications; (b) layout, proportioning, and 

condition of structural components; (c) site characteristics; (d) foundation 

conditions; and (e) where present, infill characteristics (e.g., infill panel 

locations, materials, thickness/number of wythes, and size of openings). 

It is intended that site investigations be performed using non-destructive 

means. Concealed conditions should be exposed where feasible and practical 

(e.g., above suspended ceilings). In general, destructive removal of finishes 

and in-situ testing of materials are not required as part of the methodology, 

although information from destructive investigations could be used to 

enhance available as-built information. The condition of masonry infill can 

have a significant influence on the response of buildings with infill walls. 

Site investigation of masonry infill materials, including characterization of 

the mortar with a scratch test, is necessary for determining infill material 

properties. 

3.3 Seismic Hazard

Seismic hazard due to ground shaking is defined as an acceleration response 

spectrum based on either a probabilistic or deterministic assessment of 

hazard presented in United States Geological Survey (USGS) seismic maps.

The recommended seismic hazard level for evaluation is the ASCE/SEI

41-17 Basic Safety Earthquake BSE-2E, which corresponds to a 5% 

probability of exceedance in a 50-year period. The USGS National Seismic 

Hazard Mapping Project provides spectral response acceleration parameters 

(SS, S1) adjusted for site class at the latitude and longitude of the building. 

Site class (A through F) should be determined in accordance with ASCE/SEI 

7-16, Minimum Design Loads and Associated Criteria for Buildings and 

Other Structures, Provisions (ASCE, 2017a). Site class as documented in a 

geotechnical report is acceptable for use. If insufficient information is 

available to classify the site, default Site Class D shall be used.

For the purposes of this methodology the BSE-2E parameters (SXS, SX1) need 

not be greater than those for the risk-targeted maximum considered 

earthquake (MCER) ground motion (also modified for site class) determined 

in accordance with ASCE/SEI 7-16. 
FEMA P-2018 3: General Requirements 3-3 

Evaluation using this methodology at other levels of seismic hazard is 

permitted. 

3.4 Material Properties

3.4.1 General

Properties of cast-in-place concrete, reinforcing steel, and masonry infill 

materials shall be taken from design drawings or other as-built information. 

Physical testing of in-situ materials is not required as part of the 

methodology. 

Although not required, testing can result in higher material strengths than 

minimum values specified on the drawings or default values provided in 

ASCE/SEI 41-17 or as part of this methodology. As a result, physical testing 

could be used to improve material strength values, and could be considered 

as part of an enhanced investigation of as-built information. Regardless of 

the source of material property information and level of testing and 

investigation performed, the methodology does not incorporate the use of a 

knowledge factor as prescribed in ASCE/SEI 41-17. 

3.4.2 Concrete and Reinforcing Steel

If material properties are not identified in the design drawings or documented 

in other as-built information, default material properties may be used in 

accordance with ASCE/SEI 41-17 Section 10.2.2.5.

Concrete and reinforcing steel properties used in component strength 

calculations shall be expected material properties, determined as follows:

• expected compressive strength of concrete, ce f ′ , taken as the specified or 

nominal compressive strength, cf ′ , multiplied by 1.5; and 

• expected yield strength of reinforcement, fye, taken as the specified or 

nominal yield strength, fy, multiplied by 1.25. 

3.4.3 Masonry Infill

Properties of infill masonry panels shall be taken from design drawings, 

other as-built information, or site investigation. At a minimum, information 

on infill panel locations, masonry unit material (clay or concrete) and type 

(brick, hollow clay tile, concrete masonry unit), thickness and number of 

wythes, confinement, and mortar condition are necessary.

Masonry infill properties used in component strength calculations shall be 

expected material properties, determined as follows:
3-4 3: General Requirements FEMA P-2018

• Expected cohesion of the masonry-mortar interface, C, defined in 

ASCE/SEI 41-17 Section 11.4.2.3. If no information is available, 

expected values can be taken from Table 3-1. 

• Expected initial friction coefficient of masonry mortar joints, μ, defined 

in ASCE/SEI 41-17 Section 11.4.2.3. If no information is available, 

expected values can be taken from Table 3-1. 

• Expected compressive strength of the masonry assembly, f ′m. If the 

mortar and masonry units are in good condition, and information about 

the type of mortar and the strength of the masonry units are available, f ′m

is taken as the specified or nominal compressive strength, or from the 

unit strength method in Section 1.4 of TMS 602-13/ACI 530.1-13/ASCE 

6-13 Specification for Masonry Structures (MSJC, 2013). If no other 

information is available, expected values can be taken from Table 3-1. 

Table 3-1 Default Expected Properties for Masonry Infill

Mortar Description

C

(psi) μ

f′m

Solid Fired 

Clay Brick

Concrete 

Masonry 

Unit (CMU)

Hollow 

Clay Tile (1)

Raked out by finger pressure 

(i.e., very soft/ lime mortar) 15 0.3 400 n/a 200

Scratches easily with finger 

nails (i.e., soft) 45 0.3 850 n/a 500

Scratches with finger nails 

(i.e., medium) 70 0.6 1000 1600 500

Scratches using aluminum 

pick or does not scratch with 

tools (i.e., hard/very hard)

100 0.8 1200 2000 600

(1) Hollow clay tile refers to clay tile in architectural or nonstructural applications. Structural clay tile 

should use the values under solid fired clay brick.

Default properties in Table 3-1 were developed as described in Appendix O. 

Significant uncertainties are present in masonry infill properties, which are

not captured in the values provided in Table 3-1. Although physical testing 

is not explicitly required as part of this methodology, other information (if 

available), or results from physical tests (even if limited), should be used in 

lieu of the values in Table 3-1. Evaluation of infilled frame systems using 

default properties should consider the potential impact of variation in 

masonry infill parameters. Users are cautioned that it is not always 

conservative to assume the weakest (worst) condition for masonry infill. 
FEMA P-2018 3: General Requirements 3-5 

3.5 Condition of Structural Components

The methodology assumes that the building and structure are in generally 

good condition. Although site investigations do not require destructive 

investigation or detailed condition assessment, visual observations should 

include assessment of the general condition of significant structural 

component in accessible areas. If the overall building or significant 

structural components are judged to be in poor condition, then the evaluation 

results should be adjusted to characterize the potentially weakened state of 

the building. 

Concrete buildings constructed in the 1940s and earlier are particularly likely 

to have experienced inadequate quality control on concrete mixing and 

placement procedures during construction. As a result, the as-built condition 

of such buildings, and the condition of the concrete columns in particular, 

should be investigated in greater detail. Guidance on more detailed condition 

assessment is available in ASCE/SEI 41-17 Section 10.2.3, FEMA 306, 

Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings

(FEMA, 1998), or ACI 201.2R, Guide to Durable Concrete (ACI, 2008). 

3.6 Structural Load Path Requirements

The evaluation methodology assumes the existence of a complete load path. 

Prior to implementing the methodology, it is important to understand the load 

path for lateral and vertical forces. Significant gaps in the load path can lead 

to catastrophic failure even if most structural components would remain 

undamaged. Assessment of the load path is primarily qualitative in nature, 

based on identification of gaps in the seismic-force resisting system rather 

than quantitative analysis of structural elements. This is consistent with the 

philosophy of the Tier 1 Screening assessment in ASCE/SEI 41-17 

Chapter 4. 

Load path deficiencies that would cause an older concrete building to be 

considered an exceptionally high seismic risk building are identified in the 

following sections. Other load path considerations, such as discontinuous 

wall or frame elements, or excessive weakness in wall or frame elements, are 

explicitly addressed in the evaluation methodology.

3.6.1 Diaphragm Continuity

Except for buildings classified as frame structures, buildings should be 

evaluated for adequate connection between the diaphragms and shear walls. 

In general, it is assumed that frame structures have distributed lateral systems 

and that there is sufficient interconnection between the frames and floor slabs 
3-6 3: General Requirements FEMA P-2018

to provide at least a nominal load path for transferring diaphragm forces to 

the frame elements.

If any of the following conditions are present, the building should be 

considered an exceptionally high seismic risk building: 

• Any individual shear wall or combined shear core that is located at the 

exterior of the building with less than 50 percent of the total wall length 

engaging the diaphragm at any level in either primary direction, unless 

collector reinforcing is present with minimum tensile capacity of 0.10SXS

times the weight of the floor tributary to the wall. SXS is the spectral 

response acceleration parameter at 0.2 second period using the seismic 

hazard determined in Section 3.3. 

• Diaphragm openings immediately adjacent to interior shear walls 

exceeding 75 percent of the shear wall length on both sides of the wall, 

unless collector reinforcing is present with minimum tensile capacity of 

0.10SXS times the weight of the floor tributary to the wall.

• Diaphragms lacking a positive connection to shear walls by means of 

reinforcing steel dowels between the wall and slab. 

• Diaphragms in ramped parking structures, or buildings with ramped 

parking levels above grade, that consist of split-level floors in which the 

sections of the diaphragm are not engaged by seismic force-resisting 

elements on at least three sides of each section. 

If individual walls with inadequate engagement to diaphragms exist in a 

building, the exceptionally high seismic risk designation can be set aside and 

the full methodology can be used to evaluate the building if the walls are not 

considered in the analysis and it can be shown that the presence of the walls 

does not result in any negative impacts on building response, such as a soft or 

weak story or significant torsion.

3.6.2 Concrete Element Interconnectivity

Basic interconnection of concrete frame and wall elements is necessary for a 

complete load path. If present in a building, the following conditions are 

indications of poor interconnectivity, but are not necessarily an indication of 

exceptionally high seismic risk buildings. The evaluating engineer should 

determine the effects of such conditions on the expected seismic performance 

of the building under consideration.

• Concrete columns are not doweled into foundations with a minimum of 

four dowels. 
FEMA P-2018 3: General Requirements 3-7 

• Concrete walls are not doweled into foundations with vertical dowels

equal to the size and spacing of vertical wall reinforcement immediately 

above the foundation.

3.7 Penthouse and Other Rooftop Structures

Penthouses and other rooftop structures need not be explicitly evaluated in 

this methodology if the weight is no more than 25 percent of the effective 

seismic weight of the main roof level, and the area of the footprint is no more 

than 30 percent of the total area of the main roof level. Where these 

conditions are not met, a penthouse or rooftop structure shall be considered a 

story and evaluated as such using this methodology. 
FEMA P-2018 4: Component Strengths 4-1 

Chapter 4 

Component Strengths

This chapter specifies methods for determining the strengths of individual 

concrete components. 

4.1 Introduction

For most concrete components, strengths are determined in accordance with

ASCE/SEI 41-17 and ACI 318-14, Building Code Requirements for 

Structural Concrete and Commentary (ACI, 2014). Because of differences 

in proportioning and detailing between older concrete structures and current 

construction practices, clarifications and alternate provisions for some types 

of concrete components are provided. Because the strength of some concrete 

components depends on axial load, procedures for determining axial load are 

also provided. 

4.2 Axial Loads on Columns and Walls

4.2.1 Expected Gravity Loads

For the purposes of this methodology, the determination of expected gravity 

loads on concrete columns, concrete walls, concrete slab-column 

connections, and masonry infill panels shall be determined in accordance 

with this section. Dead loads include the structure self-weight and 

appropriate superimposed dead loads. Live loads shall be taken as 25% of 

the unreduced design live loads listed in ASCE/SEI 7-10 Table 4-1. Vertical 

loads due to expected gravity load effects, Pg, are calculated as: 

Pg = PD + 0.25PL (4-1) 

where PD is the axial load due to tributary dead loads, and PL is the axial load 

due to unreduced tributary live loads.

4.2.2 Earthquake Axial Loads

Consideration of column and wall component axial loads due to earthquake, 

Peq, is required only where explicitly specified. Column axial load due to 

earthquake overturning effects, Peq, at each story x is calculated as:

( ) y eff x

eq

Vh h

P

L

− = (4-2) 
4-2 4: Component Strengths FEMA P-2018

where:

Vy = base shear strength of a structure 

heff = effective height of the building, defined as the height from the 

base to the centroid of lateral forces (same as the effective 

height of an equivalent single-degree-of-freedom system, which 

may be taken as 0.7hn in multistory buildings having uniform 

distribution of effective weight over the building height, and hn

in single-story buildings) 

hn = height from the base of the building to the highest level of the 

seismic force-resisting system (i.e., level n) 

hx = height from the base of the building to level x (i.e., the bottom 

of story x) 

L = plan dimension between the outermost frame columns in the 

direction of interest at story x

Axial load, Peq, is taken as positive in compression, and can be distributed in 

proportion to contribution of each frame line to total building Vy. Tension 

loads due to earthquake overturning are not critical and need not be 

considered. For columns located in a story above the effective height of the

equivalent single-degree-of-freedom system, or for interior columns in a 

frame line (i.e., not the outermost columns in the frame line), Peq may be 

taken as zero. If heff falls within a story, Peq should be computed for the 

columns within that story.

Where explicitly required in the methodology, axial loads due to earthquake 

overturning effects on walls and vertical wall segments shall be estimated by 

accepted principles of mechanics.

4.2.3 Load Combinations

Where gravity loads are combined with earthquake forces, all load 

combinations shall be unfactored, with gravity loads determined in 

accordance with Equation 4-1. Evaluation of components for gravity loads 

in the absence of earthquake forces is beyond the scope of this methodology. 

4.3 Component Strength Calculations

4.3.1 General

Component strengths used in this evaluation methodology shall be taken as 

expected strengths. Expected strengths shall be calculated using expected 

material properties, determined in accordance with Section 3.4. 
FEMA P-2018 4: Component Strengths 4-3 

Concrete column, beam, slab, joint, and wall component strengths shall be 

determined using expected material properties and accepted principles of 

mechanics. Unless specifically indicated otherwise in the sections that 

follow, the procedures of ACI 318-14 may be used to calculate the strength 

of concrete components, except that the strength reduction factor, φ, should 

be taken as unity (i.e., φ = 1.0). For components constructed using 

lightweight concrete, strength calculations should be modified in accordance 

with ACI 318-14 procedures for lightweight concrete. 

Expected strength of masonry infill panels shall be determined in accordance 

with Section 4.3.6. 

4.3.2 Concrete Column Strength

4.3.2.1 Column Shear Strength

Column shear strength, Vn, is calculated based on ASCE/SEI 41-17, as 

follows: 

6

1 0.8

/ 6

v ye ce g

n g

inf ce g

Af d f P

V k A

s ld f A

λ

    ′ =+ +     ′    

 (4-3) 

where:

k = factor related to displacement ductility demand; can be taken as 

1.0 for the purpose of calculating column shear strength in this 

methodology 

s = spacing of transverse reinforcement

Av = area of transverse reinforcement within spacing s

d = effective depth of the column section

fye = expected yield strength of reinforcement 

λ = 0.75 for lightweight concrete, and 1.0 for normal weight 

concrete

ce f ′ = expected compressive strength of concrete

linf = clear height of an equivalent cantilever column from the face of 

a joint to the point of inflection (or zero moment); in a typical 

story, linf may be taken as half of the column clear height, lu

Pg = column axial load (in compression) due to expected gravity load 

effects (equal to zero if in tension) 

Ag = gross area of concrete column section

It is permitted to assume d = 0.8hc, where hc is the overall dimension of the 

column in the direction of shear. The ratio linf /d should not be taken greater 
4-4 4: Component Strengths FEMA P-2018

than 4, nor less than 2. For columns satisfying the detailing and 

proportioning requirements of ACI 318-14 Chapter 18, the shear strength 

equations of ACI 318-14 Chapter 22 are permitted.

Where the longitudinal spacing of transverse reinforcement is less than the 

component effective depth measured in the direction of shear, transverse 

reinforcement is assumed to be fully effective in resisting shear, and the 

limitations in ASCE/SEI 41-17 Section 10.3.4 related to spacing of 

transverse reinforcement need not apply. 

4.3.2.2 Column Flexural Strength

The expected flexural strength of a column section, Mn, is calculated in 

accordance with ACI 318-14 Chapter 22 using expected material properties 

and φ = 1.0. The axial load for determining flexural strength shall be the 

expected gravity loads on the column determined in accordance with 

Section 4.2.1. 

4.3.2.3 Effects of Column Lap Splices on Flexural Strength

For the purpose of determining the effective base shear strength and 

controlling building mechanism in accordance with Section 5.5, if the lap 

splices in the vertical reinforcement of the columns do not meet the 

minimum length requirements in ASCE/SEI 41-17 Section 10.3.5, the 

expected flexural strength shall be modified to account for a reduction in the 

strength of vertical reinforcement in accordance with ASCE/SEI 41-17 

Section 10.5.3. 

4.3.3 Beam-Column Joint Shear Strength

Beam-column joints satisfying the following conditions may be assumed to 

have sufficient strength to develop the flexural strength of the beams and 

columns framing into the joint: 

• interior beam-column joints where beams frame into all four faces of the 

joint; and

• any joint with hoop reinforcement within the joint at a spacing not 

exceeding the lesser of: h/3, where h is the overall dimension of the 

column in the direction of shear, or 8 inches.

For other joints, shear strength should be calculated in accordance with 

ASCE/SEI 41-17 Section 10.4.2.2, except that the joint shear strength, Vnj, 

need not be taken less than: 

10 c

nj ce j

b

h V fA h = λ ′ (4-4) 
FEMA P-2018 4: Component Strengths 4-5 

where:

hc = overall dimension of the column in the direction of shear

hb = overall depth of the beam

Aj = effective cross-sectional area of the beam-column joint 

The ratio hc/hb shall be taken less than or equal to 1.0. The effective area of 

the joint, Aj, can be taken as hc (bc + wb′ )/2, where bc is overall width of the 

column in the direction perpendicular to joint shear; and wb′ is the web width 

of the beam, excluding portions of the web that extend beyond the width of 

the column. Joint shear strength calculated in accordance with ASCE/SEI 

41-17 is typically less than the value in the exception noted above. Thus, Vnj

calculated using Equation 4-4 is generally expected to control. 

4.3.4 Slab-Column Frame Strength and Integrity Requirements

The flexural strength of a slab, and the shear and moment transfer strength of 

slab-column connections, shall be calculated in accordance with ASCE/SEI 

41-17 Section 10.4.4.3. The flexural strength of the slab, and the flexural 

strength of a joist system, is based on the strength of the column strip, as 

defined in ASCE/SEI 41-17. The shear and moment transfer strength of 

slab-column connections must consider the combined action of flexure, 

shear, and torsion in accordance with ASCE/SEI 41-17. 

Where required in this methodology, slab-column joints are considered to 

satisfy minimum structural integrity requirements if the total area of main 

slab bottom bars passing through, or anchored within, the column cage, Asb, 

is more than 2Vg/fye, where Vg is the shear demand based on gravity loads 

computed in accordance with Equation 4-1, and fye is the expected strength of 

the slab bottom bars (Section 3.4). This is illustrated in Figure 4-1 where Ab

is the area if an individual bottom bar and Asb represents the total area of 

main slab bottom bars. 

(a) Interior connection (b) Exterior connections

Figure 4-1 Illustration of slab-column structural integrity requirements: (a) interior connection; 

and (b) exterior connections. 
4-6 4: Component Strengths FEMA P-2018

4.3.5 Concrete Wall Strength

In calculating expected shear and flexural strengths of concrete walls, 

expected material properties shall be used and the strength reduction factors,

φ, should be taken as unity (i.e., φ = 1.0). 

4.3.5.1 Wall Shear Strength

The shear strength of a wall section shall be calculated as the expected shear 

strength using the procedures of ACI 318-14 Section 18.10, except that the 

restriction on spacing, reinforcement ratio, and number of curtains of 

reinforcement need not apply. If the transverse reinforcement ratio, ρn, is 

less than 0.0015, the contribution of wall reinforcement to the shear strength 

of the wall may be computed using ρn = 0.0015. 

The shear strength of a wall shall be limited by the sliding strength at 

horizontal construction joints. Sliding strength shall be taken as twice the 

value determined in accordance with the shear friction provisions in ACI 

318-14 using expected material properties, and taking the friction coefficient 

and strength reduction factor as unity (i.e., μ = φ = 1.0). Shear friction 

capacity shall be modified to account for the effects of non-conforming lap 

splice lengths as described below.

4.3.5.2 Wall Flexural Strength

The expected flexural strength of a wall section, Mn, is calculated in 

accordance with ACI 318-14 Chapter 22. The axial load for determining 

flexural strength shall be the expected gravity loads on the wall determined 

in accordance with Section 4.2.1. 

For the purpose of determining the effective base shear strength and 

controlling building mechanism in accordance with Section 5.5, if the lap 

splices in the vertical reinforcement of a wall do not meet the minimum 

length requirements in ASCE/SEI 41-17 Section 10.3.5, the expected flexural 

strength shall be modified to account for a reduction in the strength of 

vertical reinforcement in accordance with ASCE/SEI 41-17 Section 10.3.5. 

4.3.6 Infilled Frame Strength

4.3.6.1 Masonry Infill Panel Strength

Where masonry infill is present, the shear strength of a masonry infill panel, 

Vm, is calculated as:

Vm = grav P AC inf μ + w,inf (4-5) 
FEMA P-2018 4: Component Strengths 4-7 

but not taken greater than: 

6

inf

m inf s

h

ft n ′ (4-6) 

where:

grav Pinf = gravity load carried by the infill 

μ = initial friction coefficient

Aw,inf = horizontal cross-sectional area of an infill panel

C = cohesion, as defined in Section 3.4.3

f ′m = expected compressive strength of the masonry assembly

tinf = net thickness of the masonry panel

hinf = height of the masonry panel

ns = number of struts expected to develop in the masonry panel, 

taken as 1 for solid panels with Linf/hinf < 1.0, and 2 otherwise

and infill panel dimensions are as defined in Figure 4-2. The horizontal 

cross-sectional area of an infill panel, Aw,inf, is taken as the product (tinf × Linf) 

of the thickness of the infill, tinf, and the length of the infill, Linf. The vertical 

load carried by the infill, grav Pinf , is calculated from the total expected gravity 

load, PT, based on the tributary areas above the panel and story of interest, 

which can be estimated based on the relative stiffness of columns and infill in 

accordance with ASCE/SEI 41-17. In cases with wall lengths, Linf, between 

15 feet and 25 feet, and story heights, hsx, between 10 feet and 14 feet, the 

vertical load carried by the infill can be estimated as grav Pinf = 0.5PT.

Figure 4-2 Illustration of symbols defining the geometry of masonry 

infill panels. 

As shown in Figure 4-2, Linf is the length of the infill wall, hinf is the height 

of the infill panel, and tinf is the net thickness of the panel. Wythes 
4-8 4: Component Strengths FEMA P-2018

protruding beyond the column face are not well-confined and are ignored in 

the calculation of shear strength. 

4.3.6.2 Infilled Bay Strength

Where masonry infill is classified as “strong” or “weak” in accordance with 

Section 5.3.4, the shear strength of a single, solid infilled bay, Vinf,solid, is 

taken as the maximum of the shear strength of the masonry infill panel in 

accordance with Section 4.3.6.1, and a combination of frictional resistance in 

the masonry plus a governing, lower value of shear strength in a column: 

Vinf,solid = ( , ) max max V P V m inf lc μ + (4-7) 

where:

Vm = shear strength of the masonry panel (Section 4.3.6.1)

max Pinf = expected gravity load supported by the infill when the 

maximum lateral strength is reached

μ = initial friction coefficient

Vlc = lower governing shear strength of the weaker of the two 

columns bounding the infill panel of interest, taken as the lesser 

of Vn (Section 4.3.2.1) and Vp (Section 4.4.1) considering the 

role of the infill in reducing the effective height of the column 

In Equation 4-7, max Pinf is the expected gravity load supported by the infill when 

the maximum lateral strength is reached. Studies indicate that this value is 

higher than the vertical load carried by the infill, grav Pinf , calculated in Section 

4.3.6.1, and can be calculated in accordance with ASCE/SEI 41-17 Table 

11-9. In cases with wall lengths, Linf, between 15 feet and 25 feet, and story 

heights, hsx, between 10 feet and 14 feet, the expected gravity load at 

maximum lateral strength can be taken as max Pinf = 0.7PT. 

In the case of an infill panel with openings, the strength of a single, solid

infilled bay shall be reduced to Vinf,open, calculated as:

Vinf,open = 1 op

inf,solid

inf

A

V

A

    −

 

 (4-8) 

where:

Vinf,solid = shear strength of a single, solid infilled bay (Equation 4-7)

Aop = area of openings in an infill panel, in elevation, ft2

Ainf = area of an infill panel, in elevation, ft2

In cases where Aop/Ainf > 0.6, Vinf,open shall be taken as 0. 
FEMA P-2018 4: Component Strengths 4-9 

4.4 Column Shear Strength Ratio

To determine the column shear strength ratio, Vp/Vn, column shear strength, 

Vn, is determined in accordance with Section 4.3.2.1, and the column plastic 

shear capacity controlled by flexure, Vp, is calculated based on the expected 

flexural strengths of the members framing into the joints at the top and 

bottom of each story. 

To provide an upper bound assessment of column flexural strength in

determining the column shear strength ratio, the strength of vertical 

reinforcement in the column shall not be reduced to account for inadequate 

lap splice length (Section 4.3.2.3). 

4.4.1 Column Shear Capacity in a Typical Story

For columns in a typical story, the column capacity-limited (plastic) shear 

strength, Vp, is:

cT cB

p

u

M M V

l

+ = (4-9) 

where: 

McT = flexural strength at the top of the column

McB = flexural strength at the bottom of the column 

lu = clear height of the column

McT and McB are taken as the lesser of the expected flexural strength of the 

column section, Mn, calculated in accordance with Section 4.3.3 and the 

flexural strength controlled by the beams or slabs at the top or bottom of the 

column, respectively. The column clear height, lu, shall account for 

translational or rotational restraint provided by concrete spandrel beams, 

partial height concrete walls, and masonry infill panels. Where the moment 

is controlled by the beams or slabs, lu shall be replaced by the story height.

Alternatively, if the beams are shear-controlled, the expected flexural 

strength of the beam can be limited by the shear strength of the beam. 

Additionally, the flexural strength at the top or bottom of the column need

not be taken greater than the capacity associated with the joint shear strength, 

taken as Vnjhb/2, where Vnj is the expected shear strength of the joint

determined in accordance with Equation 4-4, and hb is the overall depth of 

the beam.

In T-beam construction, where slab reinforcement is in tension due to 

moments at the face of the joint, reinforcement located within an effective 
4-10 4: Component Strengths FEMA P-2018

flange width determined in accordance with ACI 318-14 Section 9.2.4 should 

be assumed to contribute to the flexural strength of the beam.

4.4.2 Slab-Column Frames

In slab-column frames, the flexural strength at the top and bottom of the

column will be limited by the expected flexural strength of the slab or the 

shear and moment transfer strength of slab-column connection as determined 

in Section 4.3.4.
FEMA P-2018 5: Structural Classification 5-1

Chapter 5

Structural Classification

This chapter provides rules for classifying buildings into systems of similar 

seismic response characteristics to enable the use of more efficient evaluation 

methods. This chapter also provides criteria for identifying the lowest and 

the highest risk buildings that are at the extreme ends of the strength and 

configuration ranges of these systems.

5.1 Introduction

Older concrete buildings come in many sizes, heights, and structural system

types. Gravity frame systems include floors of flat slabs, shallow joists, and 

beams and girders supported on columns that can be round, rectangular,

square, or other shape, with varying levels of confinement provided by 

spirals or hoops with crossties. Some gravity frame systems are explicitly

designed to resist seismic forces, but all gravity framing must safely 

accommodate expected seismic drift demands. Concrete walls, which can 

resist seismic forces, are present in many older concrete buildings. A 

specific type of building, usually used in residential occupancies, has very 

few, if any, columns, with the majority of gravity loads supported by 

structural concrete walls.

The seismic risk presented by different types of buildings varies widely. 

Many buildings have limited ductility under lateral loading, particularly 

those governed by members failing in shear. Lateral strength also varies, and 

buildings with structural walls are generally stronger than buildings with 

frames. However, some frame systems designed for high gravity loads, such 

as those used in warehouse occupancies, also have relatively high strength, 

and frames with round columns and spiral transverse reinforcing can be quite 

ductile in response to earthquake shaking.

Regardless of the type of structural system, the performance of many 

buildings is largely influenced by the building configuration. Tall first 

stories, used to create lobbies or first-floor commercial spaces, are often also 

soft and/or weak stories that concentrate lateral displacement at that level. 

Other vertical irregularities, such as discontinuous walls supported on 

columns or girders, or columns supported on transfer girders, can be a local 

collapse risk that could lead to global collapse. Plan irregularities, especially 
5-2 5: Structural Classification FEMA P-2018

in buildings with walls, induce torsional response that can amplify lateral 

displacement demands on frame and wall lines. 

5.2 Classification of Concrete Components

5.2.1 Reinforced Concrete Columns

For the purposes of this methodology, a reinforced concrete column is a 

vertically oriented concrete component with an elevation aspect ratio of:

lu/hmax ≥ 2.0 

where:

lu = clear height of the column

hmax = largest cross-sectional dimension

and the section is tied with hoops, crossties, or spirals in accordance with 

minimum requirements for non-seismic columns.

Test data for collapse of columns used as a basis for this methodology were

generally limited to cross section aspect ratios of hmax/hmin ≤ 2.5, where hmax

and hmin are the maximum and minimum cross-sectional dimensions of the 

component, respectively. Extrapolation of this methodology to column 

components with larger aspect ratios should be carefully considered for 

applicability by the evaluating engineer.

5.2.2 Reinforced Concrete Structural Walls

For the purposes of this methodology, vertically oriented reinforced concrete 

components that are not otherwise classified as columns, and that possess the 

following characteristics, shall be considered as structural concrete walls:

1. Thickness of at least 4 inches, or thickness at least 1/25 of the distance 

between supporting or enclosing members. 

2. Ratios of distributed longitudinal and transverse reinforcement to gross 

concrete area perpendicular to that reinforcement of at least 0.0015. 

3. Sufficient anchorage to the floor diaphragms such that they can be 

considered as altering the lateral behavior of the structural system.

4. Sufficient strength to significantly impact other structural members (e.g., 

a spandrel that reduces the clear height of a column).

Concrete walls not meeting the requirements of this section need not be 

considered. Concrete walls not meeting requirements 1 and 2, above, may be 

considered at the option of the evaluating engineer if the effects of

requirements 3 and 4 are judged to be significant. 
FEMA P-2018 5: Structural Classification 5-3 

Wall piers are vertical wall segments, typically not exceeding 8 feet in 

length, used as piers in pier-spandrel systems, as shorter vertical wall 

segments within longer walls, or located at the ends of longer walls in framewall or bearing wall systems.

5.3 Classification of Building Systems

Classification of buildings into structural systems of similar seismic response

is necessary for implementation of the evaluation methodology. Each 

principal horizontal direction in a building can have a different structural 

system classification. Categories include frame systems (Section 5.3.1), 

frame-wall systems (Section 5.3.2), bearing wall systems (Section 5.3.3), and 

infilled frame systems (Section 5.3.4). 

5.3.1 Frame Systems

Frame systems are systems composed of frames without structural walls or 

effective infill walls. Frame lines composing frame systems may include the 

following: 

• Frame lines (or bays) that are designed to resist gravity loads, including 

beam-column systems, slab-column systems, or joist-column systems. 

• Frame lines (or bays) that are designed to resist gravity plus lateral loads, 

regardless of the level of ductile detailing. 

• Frame lines with partial-height concrete or masonry infill walls that can 

potentially create short column effects. 

The evaluation procedure for frame systems includes Sections 5.5 to 5.9 and 

Chapter 6. 

5.3.2 Frame-Wall Systems

Frame-wall systems are systems with both frame lines, as identified in

Section 5.3.1, and structural walls, as defined in Section 5.2.2. 

Pier-spandrel systems are a subset of frame-wall systems in which structural 

walls, usually extending around the entire building perimeter, have a regular 

or nearly regular set of openings that subdivide the surface of the walls into a 

series of vertical piers and horizontal spandrels. A pier-spandrel system, as 

defined in this methodology, shall have piers with typical horizontal length 

not less than one-third of the bay width and spandrels with typical vertical 

depth not less than one-third of the story height. Minor or occasional 

deviations from these span-to-depth ratios are permitted in pier-spandrel 

systems, subject to the judgment of the evaluating engineer. 
5-4 5: Structural Classification FEMA P-2018

Walls with openings are sometimes referred to as punched shear walls or 

punched wall systems. Typically, such systems feature concrete walls

around the perimeter of the building with a regular pattern of window 

openings. Punched wall openings are usually smaller, and the walls thinner

than elements in a pier-spandrel system, and punched walls would be 

expected to behave more like a solid wall rather than a frame. In general, it 

is recommended that punched walls be treated as solid walls in this 

methodology. If the dimensions of openings in a punched wall system 

approach the dimensions of a pier-spandrel system, the building should also 

be evaluated assuming pier-spandrel behavior, and the controlling case

determined.

The evaluation procedure for frame-wall systems includes Sections 5.4 to 5.9 

and Chapter 7.

5.3.3 Bearing Wall Systems

Bearing wall systems are systems configured such that the majority of gravity 

loads are supported on structural concrete bearing walls. Isolated columns 

supporting up to 25% of the gravity load in the building can be present in a 

bearing wall system. If columns are used to support more than 25% of the 

gravity load, the structure shall be classified as a frame-wall system.

The evaluation procedure for bearing wall systems includes Sections 5.4 to 

5.9 and Chapter 8.

5.3.4 Infilled Frame Systems

Infilled frame systems are systems that satisfy the requirements for frames in

Section 5.3.1, or frame-walls in Section 5.3.2, and also include one or more 

masonry infill panels confined within the beam and column framing. 

Classification of infill in accordance with Table 5-1 affects the strength of 

the infilled bay, how the infill is presumed to interact with the columns, and 

how the infill is considered in the evaluation methodology.

In Table 5-1, Vm is the shear strength of the masonry infill panel, as 

calculated in Section 4.3.6.1, Aop is the area of openings in an infill panel (in 

elevation), Ainf is the area of an infill panel (in elevation), and Vlc is the lower 

governing shear strength of the weaker of the two columns bounding the 

infill panel of interest, as calculated in Section 4.3.6.2.

To be considered in this methodology, infill panels must be tightly confined 

within columns on both sides, but a small gap (< 0.25 inches) between the 

panels and the beam above is permitted. Infill panels classified as ineffective

in Table 5-1 are not considered structural infill and may be ignored.
FEMA P-2018 5: Structural Classification 5-5 

Table 5-1 Classification of Infill 

Ratio of Masonry Infill Strength 

to Column Strength Infill classification Consideration

  −     ≥

op

m inf

lc

A V A

V

1

3 Strong Infill requires full 

consideration

.

  −     > ≥

op

m inf

lc

A V A

V

1

3 1 4 Weak Infill requires full 

consideration

.

  −     <

op

m inf

lc

A V A

V

1

1 4

Very weak due to 

openings(1)

Infill not considered in 

strength calculations, but 

considered in Chapter 9 

evaluation procedures

Vm/Vlc < 1.4 Ineffective

Infill not considered in 

strength calculations, nor for 

short column effects

(1) Also applies when Aop/Ainf > 0.6, or when Aop/Ainf > 0.2 and openings are within 2 feet 

of a column.

Buildings with infill panels that are not classified as ineffective in Table 5-1, 

and are not tightly confined, can be evaluated both with and without 

considering the effects of infill, and the building rating determined by the 

governing case. Infill panels that have been previously retrofitted or 

reinforced are outside the scope of application of the methodology for 

evaluation of infilled frame systems. The evaluation procedure for infilled 

frame systems includes Sections 5.4 to 5.9 and Chapter 9. 

5.4 Wall Index and Wall Strength Index 

The wall index and wall strength index are used as criteria for identifying 

lower seismic risk buildings that have many walls (Section 5.4.3), or 

identifying cases where torsion need not be considered (Section 7.6.2.1). 

5.4.1 Wall Index

The effect of structural walls including wall piers on the response of the 

structure can be measured by the wall index, WI: 

w

f

A

WI

A = ∑

∑ (5-1) 

where:

∑Aw = the sum of the cross-sectional area of structural walls including 

wall piers in the story of interest oriented in the direction under 

consideration 

∑Af = the total area of floors above the story under consideration 
5-6 5: Structural Classification FEMA P-2018

The ∑Aw shall include the webs and associated boundary elements of all 

vertically-oriented reinforced concrete components that are classified as 

structural walls in accordance with Section 5.2.2. Flanges of T-, L-, and 

other similarly shaped walls are not counted in the direction under 

consideration, but are counted when considering the wall index in the 

perpendicular horizontal direction. Where the axis of an individual wall is 

not aligned with the direction under consideration, it is acceptable to use the 

component in the direction under consideration.

Values of the wall index must be calculated in each of two principal 

horizontal directions in stories identified as follows: (a) the first story of a

building; (b) other stories where walls are discontinued or reduced in size 

going up the building; and (c) stories immediately below floors having 

increased floor area as compared to lower floor levels. The lowest value of 

the wall index calculated in any story of the building, and in either of the two 

principal horizontal directions, is taken as the governing value of the wall 

index, WI, for the building.

5.4.2 Wall Strength Index

The wall strength index (WSI) is defined as:

( ) e a T

WI WSI

S = (5-2)

where:

WI = the governing value of WI from Section 5.4.1

Sa = the horizontal spectral acceleration at the site (in g), taken at the 

approximate effective structural period, Te, determined for the 

direction corresponding to the governing wall index WI

For the purposes of calculating the wall strength index, the effective 

fundamental period of the building (in seconds) may be approximated using 

the following equation:

Te = 0.015hn

0.75 (5-3)

where hn is the total height of the building in feet. Alternatively, the effective 

fundamental period may be determined using Equation 5-19, but shall not be

taken less than the value given by Equation 5-3.

5.4.3 Identification of Lower Seismic Risk Buildings using the 

Wall Strength Index

Some frame-wall or wall systems with regular configurations can be 

classified as lower seismic risk buildings without further evaluation using the 
FEMA P-2018 5: Structural Classification 5-7 

wall strength index (WSI). The WSI can be used to determine the level of 

seismic risk in buildings satisfying the following conditions: (a) there is no 

extreme torsional irregularity (as defined in this methodology); (b) there are

no significant vertical irregularities (identified by extreme soft-story or weakstory irregularity as defined in ASCE/SEI 7-10 Chapter 12); and (c) there are

no discontinuous walls supported on columns or beams (see Section 5.9.2). 

If the above conditions are met, a frame-wall or wall structure may be 

classified as a lower seismic risk building without further evaluation if the 

WSI meets one of the following criteria: 

• WSI ≥ 0.002; or 

• WSI ≥ 0.0015 and Vp/Vn < 0.8 for columns comprising 50% or more of 

the gravity load support in the story and in the direction of the governing 

wall index, WI, 

where the column shear strength ratio, Vp/Vn, is calculated in accordance with 

Section 4.4. 

5.5 Effective Yield Strength

The effective yield strength of a structure, Vy, is defined as the base-shear 

strength under static lateral loading, considering expected member strengths 

in accordance with Chapter 4, calculated along each principal direction of the 

building. It is permitted to calculate the effective yield strength, Vy, using 

established principles of mechanics. 

The nonlinear static procedure of ASCE/SEI 41-17, with a lateral force

distribution in accordance with Equation 5-4, is an acceptable procedure for 

calculating the effective yield strength. Alternatively, it is permitted to 

estimate the effective yield strength based on the plastic mechanism baseshear strength, Vp1, using the steps outlined in Sections 5.5.1 to 5.5.5. For 

frame and wall systems, the mechanism procedures of Section 5.5.1 apply. 

For infilled frame systems, the mechanism procedures of Section 5.5.2 apply, 

but it is also necessary to evaluate the bare frame using Section 5.5.1. 

Special conditions are considered in Section 5.5.3 and 5.5.4.

5.5.1 Plastic Mechanism Base-Shear Strength for Frames and 

Walls

Step 1. Define the building geometry and the distribution of lateral forces as 

shown in Figure 5-1. 

The plastic mechanism base-shear strength, Vp1, is calculated under static 

lateral loading, not including P-delta effects. The plastic mechanism base- 
5-8 5: Structural Classification FEMA P-2018

(a) Lateral forces (b) Building elevation (c) Story shears

Figure 5-1 Illustration of terms in Equation 5-4 and Equation 5-5.

shear strength, Vp1, is the sum of lateral forces Fx that are concentrated at 

each floor level x. Values at each floor level are defined by:

Fx = CvxVp1 (5-4) 

where Vp1 is a plastic mechanism base-shear strength (yet to be determined) 

and Cvx is the vertical distribution factor for story forces determined as:

1

x x

vx n

i i

i

w h C

w h

=

=

∑

(5-5) 

where:

x = level under consideration, with level 1 designating the first 

level above the base 

wi and wx = the portion of the total effective seismic weight of the 

structure (W) located or assigned to Level i or x

hi and hx = the height (ft or m) from the base to Level i or x

n = designation for the uppermost level in the main portion of 

the building 

For the lateral loading defined by Equation 5-4, the story shear in story x

(i.e., the story below level x) is related to the story shear in the first story 

through the following expression: 

1

n

px vi p

i x

V CV =

  =     ∑ (5-6) 

Step 2. Calculate the plastic mechanism base-shear strength, Vp1, for 

Mechanism 1 shown in Figure 5-2. 

Mechanism 1 assumes that the building strength is controlled by the strength 

of structural elements in the first story. It requires calculation of the 

strengths of the columns and walls in the first story. The lateral strength of 

an individual column in the first story is the smaller of the column 
FEMA P-2018 5: Structural Classification 5-9 

(a) bare frame (b) frame-wall

Figure 5-2 Mechanism 1 for calculation of plastic mechanism base-shear 

strength. 

shear strength and the shear associated with development of the column 

flexural strength, that is: 

Vnc1 = min [Vnc, ∑Mnc/lu] (5-7) 

where: 

Vnc1 = lateral strength of a column in story 1 

Vnc = shear strength of a column in story 1, calculated in accordance 

with Equation 4-3 

Mnc = flexural strength of a column, where the summation applies to 

the flexural strengths at the top and bottom of a column, 

considering the strength of the connection with the foundation 

where that condition applies 

lu = clear height of column in first story

The shear strength of the walls in the first story, is Vnw1, where:

Vnw1 = shear strength of walls in the first story calculated in accordance 

with Section 4.3.5, but not exceeding the shear corresponding to 

development of flexural strengths at the top and bottom of the 

wall

The plastic mechanism base-shear strength in story 1, Vp1, corresponding to 

Mechanism 1 is:

Vp1 = ∑Vnc1 + ∑Vnw1 (5-8) 

where the summation applies to all the columns and walls in the first story. 

Step 3. Calculate the plastic mechanism base-shear strength for Mechanism 2 

shown in Figure 5-3. 

Mechanism 2 assumes that the vertical elements have sufficient strength to 

force yielding throughout the building height. This mechanism (or 

mechanisms approaching this mechanism) may occur in frames with walls or 

in frames having columns much stronger than the beams. Mechanism 2

should be checked in frames with walls (Figure 5-3a) and in pure frames 
5-10 5: Structural Classification FEMA P-2018

having ∑Mnc/∑Mnb ≥ 1.5 in typical stories within the lower half of the 

building height (Figure 5-3b). 

(a) frame-wall building (b) frame building

Figure 5-3 Mechanism 2 for calculation of plastic mechanism base-shear 

strength. 

To determine the base-shear strength according to this mechanism, it is 

necessary to calculate the framing strengths resolved at column-footing 

connections, beam-column (and slab-column) connections, and beam-wall 

(slab-wall) connections, plus moment strengths of the walls in the first story, 

as follows:

Mnc1 = flexural strength at the bottom of a column, considering the 

strength of the connection with the foundation where that 

condition applies, but not exceeding the moment corresponding 

to column shear failure 

Mnjx = flexural strength of beam-column, slab-column, beam-wall, and 

slab-wall connections (joints) at level x

Mnw1 = flexural strength at the bottom of a wall, considering the 

strength of the connection with the foundation where that 

condition applies 

At a beam-column connection, Mnjx is the smallest moment that can be 

developed at the joint at level x, as limited by the column flexural strength 

and the beam flexural strength, that is:

Mnjx = min [∑Mnc, ∑Mnb] (5-9) 

where:

Mnc = flexural strength of columns, summed above and below the 

beam-column joints at level x, but not exceeding the moments 

corresponding to column shear failure

Mnb = flexural strength of beams, summed on both sides of the beamcolumn joint in the direction of framing at level x; it is 

acceptable, but not required, to limit the beam moments to 

values corresponding to beam shear failure 
FEMA P-2018 5: Structural Classification 5-11

In a frame building, Mechanism 2 will determine building strength only if the 

columns generally have strengths that exceed the strengths of the beams by a 

considerable margin. Therefore, it is acceptable to take Mnjx = ΣMnb in 

Equation 5-9.

It is possible that the maximum moment that can be developed at a beamcolumn connection will be limited by the strength of the beam-column joint 

itself. Therefore, it is acceptable, but not required, to limit the value of Mnjx

to the value given by Equation 5-9, or to the moment corresponding to 

development of beam-column joint shear strength, whichever is less.

At a slab-column connection, Mnjx is the smallest moment that can be 

developed at the joint, as limited by the column flexural strength and the 

slab-column connection strength, that is:

Mnjx = min [∑Mnc, ∑Mns] (5-10)

where: 

Mnc = flexural strength of columns, summed above and below the 

beam-column joints at level x, but not exceeding column 

moments corresponding to column shear failure

Mns = moment transfer strength of the slab-column connection at 

level x

At a beam-wall (or slab-wall) connection, Mnjx is the moment that can be 

transferred from the beam (or slab) to the wall. It is acceptable, but not 

required, to limit the moment that can be generated by a beam to the moment 

corresponding to development of beam shear strength.

Beam and column flexural strengths are calculated at faces of joints, walls, or 

footings. For beams and columns framing into joints or walls, it is 

acceptable to project the moments to the centerline of the joint or wall. This 

can be accomplished with reasonable accuracy by assuming that the beam (or 

column) moment is the negative value on one end of the beam (or column) 

and the positive value on the other end of the beam (or column), and then 

using a straight-line through these two points to extrapolate values at the 

centerlines of the joint or wall. 

Extrapolation of moments to the centerline of members is important where 

vertical or horizontal members have relatively large dimensions. Because of 

the significant impact that large members have on pier-spandrel system

response, it is required to extend pier and spandrel strengths to the joint 

centerlines in pier-spandrel systems, as described above.
5-12 5: Structural Classification FEMA P-2018

In buildings with combinations of beam-column, slab-column, and beamwall framing, values of Mnjx are determined at each beam-column, slabcolumn, and beam-wall joint, and the results are then summed.

The plastic mechanism base-shear strength corresponding to Mechanism 2 is:

1 1

1

nc njx nw

p

eff

MMM

V

h

∑ +∑ +∑ = (5-11) 

where:

Mnc1 = flexural strength at the bottom of a column, considering the 

strength of the connection with the foundation where that 

condition applies, but not exceeding the moment corresponding 

to column shear failure 

Mnjx = values of Mnjx from Equation 5-9 and 5-10, or from connections 

between beams and walls

Mnw1 = flexural strength at the bottom of a wall, considering the 

strength of the connection with the foundation where that 

condition applies, calculated in accordance with Section 4.3.5 

heff = effective height of the building, defined as the height from the 

base to the centroid of lateral forces (same as the effective 

height of an equivalent single-degree-of-freedom system, which 

may be taken as 0.7hn in multistory buildings having uniform 

distribution of effective weight over the building height, and hn

in single-story buildings) 

Step 4. Calculate the plastic mechanism base-shear strength for Mechanism 3 

shown in Figure 5-4. 

(a) vertically irregular structure (b) Mechanism 3

Figure 5-4 Mechanism 3 for calculation of plastic mechanism base-shear 

strength. 

Mechanism 3 applies only to buildings with an obvious strength irregularity 

in which one story or multiple stories have story shear strengths that are

significantly reduced relative to adjacent stories. This may occur due to 

reduction in strength of columns, walls, or both. Mechanism 3 need only be 

considered where the rate of reduction in story shear strength exceeds the 
FEMA P-2018 5: Structural Classification 5-13

rate of reduction in the story shear demand (Figure 5-1) by more than 20%. 

Note that Mechanism 3 is similar to Mechanism 1, except the weak story is 

in the upper stories of a building. Therefore, the steps to determine baseshear strength for Mechanism 1 and Mechanism 3 are similar.

To determine the plastic mechanism base-shear strength corresponding to 

Mechanism 3, it is necessary to first identify the weak story, and then 

calculate the strengths of the columns and walls in the weak story. The 

lateral strength of an individual column in the weak story is the smaller of the 

column shear strength and the shear associated with development of the 

column moment strength, that is: 

Vncx = min [Vnc, ∑Mnc/lu] (5-12) 

where:

Vncx = lateral strength of a column in weak story x

Vnc = shear strength of a column in weak story x calculated in 

accordance with Equation 4-3 

Mnc = flexural strength of a column, where the summation applies to 

the flexural strengths at the top and bottom of the weak story x

lu = clear height of the columns in weak story x

The shear strength of the walls in story x, is Vnwx, where:

Vnwx = shear strength of wall in weak story x calculated in accordance 

with Section 4.3.5, but not exceeding the shear corresponding to 

development of wall flexural strengths 

The plastic mechanism shear strength at story x corresponding to Mechanism 3 

is:

Vpx = ∑Vncx + ∑Vnwx (5-13) 

where the summation applies to all the columns and walls in the weak story 

x. Given the shear Vpx at story x, the corresponding plastic mechanism baseshear strength, Vp1, is:

1

x

px

n

i

p

v

i

V

V

C

=

=

∑

(5-14) 

where:

Vp1 = plastic mechanism base shear strength at story 1

Vpx = plastic mechanism shear strength at story x according to 

Equation 5-13 
5-14 5: Structural Classification FEMA P-2018

Step 5. Calculate the plastic mechanism base-shear strength for Mechanism 4 

shown in Figure 5-5. 

Similar to Mechanism 3, Mechanism 4 applies only to buildings with an 

obvious strength irregularity. In this case, the strength irregularity is 

associated with a significant reduction in the moment strength of columns, 

walls, or both. Note that Mechanism 4 is similar to Mechanism 2, except that 

the sidesway mechanism occurs in the upper stories of the building. 

Therefore, the steps to determine base-shear strength for Mechanism 2 and 

Mechanism 4 are similar.

(a) vertically irregular structure (b) Mechanism 4

Figure 5-5 Mechanism 4 for calculation of plastic mechanism base-shear 

strength. 

To determine the plastic mechanism base-shear strength corresponding to 

Mechanism 4, it is necessary to calculate the framing strengths of columns 

and walls at the level of the strength irregularity, as well as framing strengths 

resolved at beam-column (and slab-column), and beam-wall (slab-wall) 

connections. The procedures are analogous to those for Mechanism 2 and 

are not repeated here.

The plastic mechanism shear strength at story x corresponding to Mechanism 4 

is:

*

ncx 1 nj nwx 1

px

eff

M MM

V

h

∑ +∑ +∑ − − = (5-15) 

where:

Mncx-1 = flexural strength of a column at level x – 1, that is, bottom of 

story x, but not exceeding the moment corresponding to column 

shear failure

Mnj = values of moment that can be resisted at each joint, based on the 

limiting strength of beams, columns, and joints, similar to 

Mechanism 2

Mnwx-1= flexural strength of wall at level x – 1, that is, bottom of story x, 

calculated in accordance with Section 4.3.5 
FEMA P-2018 5: Structural Classification 5-15

* heff = height of centroid of lateral forces acting above level x – 1, 

which is the same as the centroid of the vertical distribution 

factors Cvx from level x to roof n

Given the shear Vpx at story x, the corresponding plastic mechanism baseshear strength, Vp1, is:

1

px

p n

vi

i x

V

V

C

=

=

∑

(5-16) 

where:

Vp1 = plastic mechanism base shear strength at story 1

Vpx = plastic mechanism shear strength at story x according to 

Equation 5-15 

Step 6. Calculate the plastic mechanism base-shear strength for the building 

as the minimum value of Vp1 for all applicable mechanisms, as given by 

Equations 5-8, 5-11, 5-14, and 5-16, and use this value as the effective yield 

strength, Vy. 

Variations in lateral force distributions during dynamic loading can result in 

actual yielding mechanisms that shift from one mechanism to another, so the 

yielding mechanisms calculated above are uncertain and not absolutely 

defined. In cases where Mechanism 2 controls for determination of effective 

yield strength, if the calculated plastic mechanism base-shear strength for 

Mechanism 2 is equal to or greater than three-quarters (3/4) of the calculated 

plastic mechanism base-shear strength for Mechanism 1, Mechanism 1 

should be taken as the controlling mechanism for the purposes of identifying 

critical stories and calculating drift demands in Chapters 6 and 7. 

5.5.2 Plastic Mechanism Base-Shear Strength for Infilled Frame 

Systems

The strength of an infilled frame system is a function of the strength of the 

infilled bays and the strength of other (reinforced concrete) components in

the critical story. 

Step 1. Define the building geometry and the distribution of lateral forces as 

shown in Figure 5-1. 

Step 2. Identify the controlling mechanism by inspection. Infilled frame 

systems can be presumed to be controlled by Mechanism 1, unless a 

significant discontinuity in infill strength or configuration along the height of 

the building warrants consideration of Mechanism 3. 
5-16 5: Structural Classification FEMA P-2018

Step 3. Classify each infill bay in the building into one of four groups using 

Table 5-1. 

Step 4. Calculate strength of all infilled bays with and without openings, in 

accordance with Section 4.3.6.2. 

Step 5. Calculate the plastic mechanism base shear strength of the building. 

The effective yield strength of an infilled frame building in each direction of 

loading can be taken as the sum of contributions from the infilled bays, and 

all reinforced concrete columns and walls in the balance of the building that 

are not part of infilled bays:

Vpx = ,

1 11

inf c wall n n n

inf ncx nw i

i ii

V VV β = = =

∑ ∑∑ + + (5-17) 

where:

ninfx ,ninfy = number of infilled bays at the critical story in each 

orthogonal direction 

Vinf = shear strength of the infilled bay, with or without openings

β = factor representing the contribution of frame elements to the 

total strength of an infilled frame system

nc = number of columns in the critical story that are not adjacent 

to infill panels in the direction of loading, or are adjacent to 

infill panels classified as ineffective for calculation of 

strength in Table 5-1 

Vnc = shear strength of a column, taken as the smaller of the 

column shear strength and the shear associated with 

development of the column flexural strength, as limited by 

the strength of the beams or slab-column connections 

nw = number of structural walls in the critical story in the 

direction of loading

Vnw = shear strength of a wall, taken as the smaller of the shear 

strength and the shear associated with development of the 

wall flexural strength

Calculations are carried out at the first story, which is assumed to be critical

unless Mechanism 3 must be evaluated due to a strength or configuration 

discontinuity in an upper story. If Mechanism 3 controls at an upper story x, 

the corresponding plastic mechanism base-shear strength, Vp1, at the base 

must be calculated using Equation 5-14. 
FEMA P-2018 5: Structural Classification 5-17

To determine the factor, β, drift ratios (in percent) at which the peak strength 

of the infilled bays are reached, ∆peak, are estimated from Table 5-2. The 

factor, β, varies linearly from 0.4 to 0.9 for ∆peak from 0.15% to 0.4%, and is

equal to 0.9 for ∆peak > 0.4%. In this determination, ∆peak is the minimum of 

the values computed for all infilled bays at the critical story along each 

direction (i.e., the drift is determined by the strongest panel). 

Table 5-2 Drift at which Infill is Assumed to Reach Peak Lateral Strength, ∆peak (in Percent 

Drift Ratio)

Vp/Vn of the 

Weakest Column in 

the Infilled Bay

∆peak, 

Weak Infill

∆peak, 

Strong Infill

Vp/Vn < 1 

0.6 – 0.23(Linf/hinf), for (Linf/hinf) < 1.3

0.30, otherwise 0.82 – (1/3)(Linf/hinf), for (Linf/hinf) < 2

0.15, otherwise

Vp/Vn > 1 0.35

Step 6. Calculate the plastic mechanism base-shear strength for the building 

as the minimum value of Vp1 for all applicable mechanisms, and use this 

value as the effective yield strength, Vy, for the infilled frame system.

Note that for the purposes of determining the effective fundamental period of 

the infilled frame system in Section 5.6.1, the plastic mechanism base-shear 

strength for the bare-frame system must also be determined in accordance 

with Section 5.5.1, ignoring the presence of the infill. 

5.5.3 Plastic Mechanism Base-Shear Strength for Mezzanines 

and Other Configurations

Mezzanines and other framing configurations may require modifications of 

the basic procedures outlined in Section 5.5.1. Figure 5-6 illustrates 

application of Mechanisms 1 and 2 for a frame with a mezzanine.

(a) Mechanism 1a (b) Mechanism 1b (c) Mechanism 2

Figure 5-6 Possible mechanisms for calculation of plastic mechanism base-shear 

strength of frames with mezzanines.

As discussed in Section 5.5.1, mechanisms can be controlled by flexural or 

shear failures in members. Not all possible mechanisms are shown.
5-18 5: Structural Classification FEMA P-2018

5.5.4 Three-Dimensional Considerations

In general, cast-in-place concrete diaphragms will impose deflection 

compatibility for all frames aligned in a given direction. Common threedimensional behaviors are illustrated in Figures 5-7 and 5-8. 

Figure 5-7 Kinematically compatible three-dimensional 

plastic mechanisms.

Figure 5-8 Mechanisms in buildings with extreme torsion.

In the absence of torsion, the assumed mechanism (Mechanism 1, 2, 3, or 4) 

should be imposed on all frame lines simultaneously. Figure 5-7 illustrates 

Mechanism 1 applied to three frame lines. This is repeated for each assumed 

mechanism, and the controlling mechanism is the one with the smallest

plastic mechanism base-shear strength.
FEMA P-2018 5: Structural Classification 5-19

In cases with significant torsion, building response can result in different 

displacements and different mechanisms in different frames. Figure 5-8 

illustrates the common case of a wall along one side of a building that is very 

strong and stiff, leading to a torsional mechanism in which other frame lines 

develop mechanisms per their individual strength distributions. 

Although base-shear strength of such a building is difficult to define uniquely 

using the simplified techniques described herein, the methodology enables 

identification of the critical story mechanisms for individual frames. 

5.5.5 Base Shear Ratio

The base shear ratio shall be taken as Vy/W, where Vy is the effective yield 

strength, and W is the total effective seismic weight of a structure. Values of 

Vy are calculated in each of two principal horizontal directions of the 

building. 

5.6 Effective Fundamental Period

The effective fundamental periods in each of two principal horizontal 

directions is used to estimate the pseudo-acceleration spectral demands and 

spectral displacements in a building. Figure 5-9 illustrates the effective 

stiffness, Ke, intended for determination of fundamental period in this 

methodology. 

Figure 5-9 Force-displacement curve, showing the definition of 

effective stiffness, Ke, for calculation of the effective 

fundamental period (adapted from ASCE/SEI 41-17).

The effective fundamental period in this methodology is conceptually similar 

to the effective fundamental period defined in the Nonlinear Static Procedure 

of ASCE/SEI 41-17, which corresponds to an effective initial stiffness that 

accounts for concrete cracking and failure of more brittle elements prior to 

overall effective yielding of the structural system.
5-20 5: Structural Classification FEMA P-2018

5.6.1 Determination of Effective Period by Formula

Frame Systems. For frame systems, the effective fundamental period, Te, 

may be taken as:

( )

0.5

0.5 0.07 y

e n

V

T h

W

−

  =    

(5-18) 

For frame systems with deep spandrel beams, the period obtained by 

Equation 5-18 may be adjusted by the ratio (lu/l), where l is the typical floorto-floor column height and lu is the typical clear height of the column. 

Frame-Wall Systems. For frame-wall systems other than pier-spandrel 

systems, and for bearing wall systems, Te may be taken as:

0.0026 n

e

w

h T

C = ≤ Te from Equation 5-18 (5-19) 

where: 

2

1

100

1 0.83

j

wi

w

base i wi

wi

A C

A h

l

=

=

 

+    

∑ (5-20) 

hn = height from the base of the building to the highest level of the 

seismic force-resisting system, ft

Abase = area of the base of a structure, ft2

Awi = area of the web of wall i, ft2

hwi = height of wall i, ft

lwi = length of wall i, ft

j = number of walls in the building effective in resisting lateral 

forces in the direction under consideration 

Pier-Spandrel Systems. For pier-spandrel systems, Te may be taken as:

1.5 0.5

0.5 0.001 opening base

e n i

we wp

A A T hl

A A

    =          

≤ Te from Equation 5-18 (5-21) 

where: 0.15 0.5 opening

we

A

A

≤ ≤ 

and: 

li = typical or average bay width measured center-to-center of wall 

piers, ft

Aopening = total area of openings in all pier-spandrel walls in direction 

under consideration, ft2
FEMA P-2018 5: Structural Classification 5-21

Awe = total area of pier-spandrel wall, measured in elevation, 

including openings, in direction under consideration, ft2

Awp = total area of pier-spandrel wall, measured in plan, including 

openings, in direction under consideration, ft2

Infilled Frame Systems. For infilled frame systems, the effective 

fundamental period, Te may be taken as:

Te = 1

,

1,

1.6 0.6 p

e bare

p bare

V

T

V

    −

 

(5-22) 

where Vp1 and Vp1,bare are the base shear strengths of the building calculated 

with infill (Section 5.5.2) and without infill (Section 5.5.1), respectively, and 

Te,bare is the effective fundamental period of the building without infill based 

on Equation 5-18 and Vp1,bare. In Equation 5-22, the ratio Vp1/Vp1,bare shall not 

be taken greater than 2.0.

The effective fundamental period for frame-wall or bearing wall systems

(Equation 5-19), pier-spandrel systems (Equation 5-21), or infilled frame 

systems (Equation 5-22) shall not be taken longer than the effective 

fundamental period for frame systems (Equation 5-20).

5.6.2 Determination of Effective Period by Structural Analysis

The effective fundamental period may also be determined in accordance with 

the Nonlinear Static Procedure in ASCE/SEI 41-17. 

5.7 Global Demand-to-Capacity Ratio

The global demand-to-capacity ratio, μstrength, for a given direction of 

earthquake loading, is calculated as:

/

a

strength m

y

S C

V W μ = (5-23) 

where Sa is the spectral acceleration at the effective fundamental period, Te, 

Vy is the effective yield strength, and Cm is the effective mass factor 

determined in accordance with ASCE/SEI 41-17, as provided in Table 5-1. 

Table 5-3 Values for Effective Mass Factor, Cm

No. 

of stories

Frame 

System

Wall or FrameWall System

PierSpandrel 

System

Infill Wall 

System

1-2 1.0 1.0 1.0 1.0

≥ 3 0.9 0.8 0.8 1.0

Note: Cm shall be taken as 1.0 if the fundamental period, Te, in the direction under 

consideration is greater than 1.0 sec.
5-22 5: Structural Classification FEMA P-2018

5.8 Identification of Lower Seismic Risk Buildings 

Some buildings can be classified as lower seismic risk buildings without 

further evaluation based on the global demand-to-capacity ratio, μstrength. 

5.8.1 Essentially Elastic Buildings

Buildings that are exceptionally strong (essentially elastic) can be classified 

as lower seismic risk buildings without further evaluation. A building is 

considered to be essentially elastic if the global demand-to-capacity ratio, 

μstrength, meets one of the following criteria in each of the two principal 

horizontal directions: 

• μstrength ≤ 0.75 in the case of frame systems with average column shear 

strength ratio in the critical story of Vp/Vn > 0.6; or

• μstrength ≤ 1.5 in all other cases.

5.9 Identification of Exceptionally High Seismic Risk 

Buildings

Some buildings can be classified as exceptionally high seismic risk buildings

without further evaluation based on the presence of certain seismic 

deficiencies. Correction of individual seismic deficiencies, however, should 

not be used as a strategy for changing the level of seismic risk determined 

using this methodology. 

5.9.1 Exceptionally Weak Buildings

Buildings that are exceptionally weak shall be classified as exceptionally 

high seismic risk buildings. A building is considered to be exceptionally 

weak if the global demand-to-capacity ratio, μstrength, meets one of the 

following criteria in either of the two principal horizontal directions: 

• Frame systems with μstrength > 2.0, and average column shear strength 

ratio in the critical story of Vp/Vn > 1.5; or 

• Frame systems with μstrength > 5.5, and average column shear strength 

ratio in the critical story of Vp/Vn < 0.6. 

Columns in the stories participating in the mechanism analysis are to be 

considered in computing the average shear strength ratio. In frame buildings 

with a combination of shear-controlled and flexure-controlled columns in the 

critical story, the threshold value of μstrength for exceptionally weak buildings 

can be linearly interpolated between the values of 2.0 and 5.5, based on the 

average value of shear strength ratio, Vp/Vn, in the critical story, ranging from

1.5 to 0.6. 
FEMA P-2018 5: Structural Classification 5-23

5.9.2 Discontinuous Walls Supported on Columns, Wall Piers, or 

Girders

Buildings with discontinuous walls supported on columns, wall piers, or 

girders can be further evaluated using this methodology, or classified as 

exceptionally high seismic risk buildings without further evaluation, based on 

the criteria in this section.

Conservatism is necessary when using simplified procedures to analyze 

buildings with discontinuous walls supported on columns, wall piers, or 

girders. Such conditions can be especially susceptible to effects of vertical 

acceleration and, in the case of columns, P-M interaction that reduces the 

axial capacity to well below the pure axial compressive strength, which can 

lead to brittle failures and loss of gravity-load-carrying ability (i.e., local 

collapse). 

Although consideration of discontinuous walls is required in the case of 

concrete walls, one or more panels of discontinuous masonry infill supported 

on bare-frame columns may also be a concern. For masonry infill classified 

as strong in Table 5-1, the overturning moment generated by the 

discontinuous infill configuration must be estimated, and the adequacy of the 

supporting columns checked in accordance with Section 5.9.2.1. 

5.9.2.1 Vertical Capacity Check on Columns and Wall Piers

Calculate the nominal axial force in columns and wall piers supporting 

discontinuous walls. In buildings not braced with shear walls in the first 

story in the direction under consideration, but with discontinuous walls 

extending above the first story, calculate the plastic base-shear strength for 

the frame in question for Mechanism 1. Calculate the axial force on columns 

and wall piers supporting discontinuous walls assuming those columns and 

wall piers resist the entire overturning moment for Mechanism 1, except that 

the moment demand need not exceed the expected flexural strength of the 

wall, or the moment corresponding to development of the wall shear strength, 

whichever is less. 

In buildings braced with shear walls in the first story in the direction under 

consideration, calculate the axial force on columns and wall piers based on 

the expected flexural strength of the supported wall, or the moment 

corresponding to development of the wall shear strength, whichever is less. 

Alternatively, it is acceptable to calculate building base-shear strength in 

accordance with Section 5.5, and then calculate the axial force on columns 

and wall piers supporting discontinuous walls assuming that those columns 

and wall piers resist the overturning moment for the controlling mechanism 
5-24 5: Structural Classification FEMA P-2018

in proportion to the relative resistance of the various walls in the structural

system. One of the following conditions shall apply:

• Where the calculated axial force is less than the balanced axial force

(which may be approximated as 0.3Agfce′), the columns and wall piers can 

be assumed capable of supporting the axial force, and can be further 

evaluated in accordance with procedures of Chapter 7. This condition 

applies regardless of column or wall pier confinement detailing.

• Where a column or wall pier is confined in accordance with ACI 318-14 

(or equivalent) requirements for special moment frame columns, the 

column or wall pier can be assumed capable of supporting axial force up 

to the nominal axial strength, and the building can be further evaluated in 

accordance with the procedures of Chapter 7.

• Columns and wall piers not confined in accordance with ACI 318-14 

requirements for special moment frame columns, with calculated axial 

force equal to or exceeding the balanced axial force (which may be 

approximated as 0.3Agfce′), columns shall be assumed to lose gravityload-carrying capacity. Where the gravity loads cannot be redistributed 

to adjacent vertical elements, the building shall be classified as an 

exceptionally high seismic risk building. Where the gravity loads can be 

redistributed to adjacent vertical elements, the building rating shall be 

determined in accordance with this methodology, excluding 

consideration of the supporting columns or wall piers.

In cases were columns or wall piers are determined to be inadequate, it is 

recommended that the full evaluation methodology be completed to more 

completely identify the extent of deficiencies in the building that contribute 

to a high or exceptionally high seismic risk rating. Non-conforming columns 

or wall piers can be efficiently retrofitted (e.g., jacketed to achieve 

confinement equivalent of ACI 318-14 requirements) if these are the only 

deficiencies causing a high or exceptionally high seismic risk rating. 

5.9.2.2 Girder Vertical Capacity Check

Calculate the moment and shear forces in girders supporting discontinuous 

walls based on the expected flexural strength of the wall, or the moment 

corresponding to development of wall shear strength, whichever is less. 

Where the girder strength exceeds the forces corresponding to the strength of 

the wall, the girder can be assumed capable of supporting the discontinuous 

wall. Where the girder strength is less than the forces corresponding to the 

strength of the wall, the girder shall be assumed to lose gravity-load-carrying 

ability. Where the gravity loads cannot be redistributed to adjacent vertical 

elements, the building shall be classified as an exceptionally high seismic risk 
FEMA P-2018 5: Structural Classification 5-25

building. Where the gravity loads can be redistributed to adjacent vertical 

elements, the building rating shall be determined in accordance with this 

methodology, excluding consideration of the girder. 

5.10 Pounding

Consideration of pounding applies to frame, frame-wall, and infilled frame 

systems. Pounding between buildings requires the potential consideration of 

additional controlling mechanisms and critical stories, which are in addition 

to results from the mechanism analyses of Section 5.5. If adjacent buildings 

are separated by at least 1.5% of the height of the shorter building, further 

consideration of pounding is not required as part of this methodology. 

If an adjacent building is separated from the building under consideration by 

less than 1.5% of the height of the shorter building, the adjacent building 

shall be considered an interfering building and considered in accordance with 

the requirements of this section. 

5.10.1 Shorter Interfering Building

5.10.1.1 Floors Align

If the floors of the shorter interfering building align within the depth of the 

floor framing of the building under consideration, the story immediately 

above the roof of the shorter interfering building shall be designated a critical 

story per Mechanism 3 and evaluated in accordance with the procedures of 

Chapters 6, 7, and 9. 

5.10.1.2 Floors Not Aligned

If the floors of the shorter interfering building do not align in accordance 

with Section 5.10.1.1, the story at the level of the roof of the shorter 

interfering building shall be designated a critical story, the exterior columns 

along the line of potential impact shall be given a rating of CR = 0.7, and the 

building shall be further evaluated in accordance with procedures of Chapters 

6, 7, and 9. 

5.10.2 Taller Interfering Building

5.10.2.1 Floors Aligned

If the floors of the taller interfering building align within the depth of the 

floor framing of the building under consideration, further consideration of 

pounding is not required as part of this methodology. 
5-26 5: Structural Classification FEMA P-2018

5.10.2.2 Floors Not Aligned

If the floors of the taller interfering building do not align in accordance with 

Section 5.10.2.1, the top story of the building under consideration shall be 

designated a critical story, the exterior columns along the line of potential 

impact shall be given a rating of CR = 0.7, and the building shall be further 

evaluated in accordance with procedures of Chapters 6, 7, and 9. 
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-1 

Chapter 6

 Evaluation Procedure for 

Frame Systems 

The chapter covers the evaluation of buildings classified as frame systems, as 

defined in Section 5.3.1. 

6.1 Introduction

Evaluation of frame systems is focused on comparing drift demands with 

drift capacities of columns and slab-column connections, and using 

component demand-to-capacity ratios to define column ratings. Column 

ratings determine story ratings, which are used in Chapter 10 to determine 

the building rating.

Section 6.2 defines critical stories along each of two horizontal earthquake 

loading directions based on the results of the mechanism analyses in Section 

5.5. Section 6.3 defines critical components, which include columns located 

in critical stories, as well as slab-column connections, corner beam-column 

connections, and discontinuous columns satisfying certain criteria. Sections 

6.4 through 6.6 define the drift demands that are considered for each critical 

frame component. Section 6.7 defines drift capacities, and a comparison of 

drift demands to drift capacities in Section 6.8 establishes individual column 

ratings for critical components. 

6.2 Identify Critical Stories

Using the controlling plastic mechanism calculated in Section 5.5 in each of 

the two principal framing directions, critical stories are defined in 

accordance with the following: 

• Where Mechanism 1 or 2 controls the strength along a principal framing 

direction, the critical story in that direction is the first story above the 

base. Where Mechanism 2 is calculated to be the controlling 

mechanism, but the plastic mechanism base-shear strength for 

Mechanism 2 is three-quarters (3/4) or more of the plastic mechanism 

base-shear strength for Mechanism 1, Mechanism 1 should be taken as 

controlling for calculation of story drift demands (because variations in 

lateral force distributions during dynamic loading have a high probability 

of producing Mechanism 1 failures in such cases). 
6-2 6: Evaluation Procedure for Frame Systems FEMA P-2018

• Where Mechanism 3 controls the strength along a principal framing 

direction, the critical story in that direction is the story in which

Mechanism 3 forms. 

• Where Mechanism 4 controls the strength along a principal framing 

direction, the critical story in that direction is the lowest story in which

yielding occurs in Mechanism 4.

It is possible for different plastic mechanisms to control along each of the 

two principal framing directions. In such cases, the critical story in one 

principal direction may differ from the critical story in the other principal 

direction. 

Critical stories are also defined where adjacent buildings require pounding 

considerations in accordance with Section 5.10. 

6.3 Identify Critical Components

Critical components are those components deemed to be most vulnerable to 

damage and loss of vertical load-carrying ability. Critical components are 

evaluated in accordance with the procedures in Sections 6.6 through 6.8.

6.3.1 Critical Columns

Columns in critical stories (defined in Section 6.2) are designated as critical 

components. Columns in other stories are not designated as critical, except 

where changes in column geometry or detailing create an increased 

vulnerability for column failure. In such cases, columns at other levels 

should also be designated as critical. 

6.3.2 Critical Slab-Column Connections

In two-way slabs without beams, slab-column connections at the top of 

columns in critical stories are designated as critical components where the 

following condition applies: 

• The slab moment transfer strength is less than the sum of column flexural

strengths immediately above and below the slab. The slab moment 

transfer strength is the smaller of strengths calculated considering slab 

flexural strength and slab shear strength. Column flexural strength need 

not be taken greater than the moment corresponding to column shear 

failure.

Additionally, slab-column connections satisfying this condition should be 

designated as critical components at other levels where unusual conditions 

create an increased vulnerability for punching shear failure of the connection. 
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-3 

Such conditions typically include levels where there is a decrease in slab 

thickness, increase in floor loading, or significant change in slab-column 

connection geometry or detailing.

6.3.3 Critical Beam-Column Corner Connections

In beam-column frames, beam-column corner connections at the top of 

columns in critical stories are designated as critical components where both 

conditions (a) and (b) apply:

(a) The beam-column joint lacks transverse reinforcement.

(b) The joint shear strength calculated in accordance with Section 4.3.3 is 

less than the joint shear generated by the controlling mechanism.

Additionally, beam-column connections satisfying both (a) and (b) should be 

designated as critical components at other levels where unusual conditions 

create an increased vulnerability for joint shear failure. Such conditions 

typically include levels where there is a sudden change in the column 

dimensions or joint detailing. 

6.3.4 Discontinuous Columns

A column is considered discontinuous at a level where there is no supporting 

column in the story below. A discontinuous column is designated as a 

critical component where both conditions (a) and (b) apply: 

(a) The discontinuous columns supports loads from two or more levels. 

(b) The plastic capacity of the column, Vp, calculated in accordance with 

Section 4.4.1, is controlled by the shear strength of the supporting beam 

or slab. 

6.4 Calculate Global Seismic Drift Demand 

Calculate the global seismic drift (displacement) demand for an equivalent 

single-degree-of-freedom (SDOF) system, δeff, as:

2

2 4

e

eff 1 2 a

T δ CCS g

π = (6-1) 

where:

C1 = modification factor to relate expected maximum inelastic 

displacement to displacement calculated for linear elastic 

response

C2 = modification factor to represent the effect of pinched hysteresis 

shape, cyclic stiffness degradation, and strength deterioration on 

maximum displacement response
6-4 6: Evaluation Procedure for Frame Systems FEMA P-2018

Te = effective fundamental period determined in Section 5.6

Sa = spectral acceleration at period, Te

g = acceleration of gravity

Calculate coefficient C1 in accordance with ASCE/SEI 41-17 as:

C1 = 2

1

1 strength

e aT

μ − + (6-2) 

where a is a site class factor equal to: 130 for Site Class A or B; 90 for Site 

Class C; 60 for Site Class D, E, or F; and all other terms are as previously 

defined. For Te < 0.2 seconds, C1 need not be taken greater than the value at 

Te = 0.2 seconds. For Te ≥ 1 second, C1 = 1.0.

Calculate coefficient C2 in accordance with ASCE/SEI 41-17 as:

C2 =

2

1 1

1

800

strength

Te

  μ − +    

(6-3) 

where all terms are as previously defined. For Te > 0.7 seconds, C2 = 1.0.

Global seismic drift demands are calculated in each direction of earthquake 

loading.

6.5 Calculate Story Drift Demand

Calculate story drift demand, δx, of story x as:

eff

x x sx eff

eff

h

h

δ

δα δ

  =   ≤    

(6-4) 

where:

αx = coefficient to modify story drifts at story x for building 

configuration and strength characteristics

hsx = height of story x

δeff = global drift demand of the equivalent SDOF system

(Equation 6-1)

heff = effective height of the building, defined as the height from the 

base to the centroid of lateral forces (same as the effective 

height of an equivalent single-degree-of-freedom system, which 

may be taken as 0.7hn in multistory buildings having uniform 

distribution of effective weight over the building height, and hn

in single-story buildings)

hn = height from the base of the building to the highest level of the 

seismic force-resisting system
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-5 

Story drift demands are calculated in each direction of earthquake loading. 

Coefficient α modifies story drifts considering number of stories in a 

building, the yield mechanism, and whether the story is a critical story. 

Values of coefficient α for frame systems are provided in Table 6-1. 

Table 6-1 Values of Coefficient α for Frame Systems

No. of 

Stories in the 

Building 

Yield 

Mechanism(2)

Values of α (1)

Critical Stories Other Stories(3)

1 (any) 1.0 (n/a)

2 

1, 3 2.0 0.5

2, 4 1.5 1.0

3-6 

1, 3 2.0 . − − −

x

n

2 1 05

2

2, 4 1.5 1.0

7-8 

1, 3 Linearly interpolate between the values

for 6 and 9 stories

2, 4 1.5 1.0

≥ 9

1, 3 2.5 1.5

2, 4 1.5 1.0

(1) x is the story under consideration; n is the total number of stories.

(2) Where Mechanism 2 is calculated to be the controlling mechanism, but the calculated 

plastic mechanism base-shear strength for Mechanism 2 is three-quarters (3/4) or more 

of the calculated plastic mechanism base-shear strength for Mechanism 1, Mechanism 1 

should be taken as the controlling mechanism for selection of α values. 

(3) Values of α for “Other Stories” are generally not used, except where components in 

other stories are designated as critical because of increased local vulnerability, as 

required in Section 6.3.

6.5.1 Adjustment of Story Drift Demand for P-Delta

For frame systems, to account for the P-delta effect of gravity loads acting 

through lateral displacements, story drift demand, δx, calculated using 

Equation 6-4 shall be increased in accordance with Equation 6-5: 

1

1 x1 x x x

px x

W

V h

δ δ δ

 

  =   −    

(6-5)

where:

δx1 = story drift demand of story x amplified for P-delta effects

δx = story drift demand (Equation 6-4)
6-6 6: Evaluation Procedure for Frame Systems FEMA P-2018

Wx = gravity load, approximated as the seismic weight of the stories 

above level x 

Vpx = plastic mechanism shear strength at story x 

hx = height from the base of a building to level x 

6.6 Calculate Drift Demands on Critical Components

6.6.1 Adjusted Drift Demand on Critical Components

For each critical component defined in Section 6.3, calculate the adjusted drift 

demand, ∆D, as: 

ΔD = ATγδx1 (6-6) 

where:

ΑT = torsional amplification factor (Section 6.6.2)

γ = drift factor representing fraction of story drift affecting the 

critical component (Section 6.6.3) 

δx1 = story drift demand amplified for P-delta effects (Section 6.5.1) 

6.6.2 Torsional Amplification Factor

Because frame systems generally include evenly distributed and proportioned 

frame elements and foundation conditions, inherent torsion is expected to be 

low. Therefore, torsion need not be considered in buildings classified as 

frame systems, and the torsional amplification factor, AT, is taken as 1.0, 

except as noted below. 

If the building under consideration possesses an unusual structural 

configuration that results in a torsional irregularity due to plan configuration, 

changes in foundation fixity, or other condition, column drifts should be 

amplified for torsion using the torsional amplification factor, AT, in 

accordance with Section 7.6.2.

6.6.3 Drift Factor

The drift factor, γ, defines the fraction of story drift demand, δx1, affecting 

critical components. Values of drift factor, γ, for critical components are 

defined in the sections that follow. 

6.6.3.1 Drift Factor for Columns

The column drift factor, γ, defines the portion of the story drift demand, δx, 

attributable to column deformations. Drift factors for columns are provided 

in Table 6-2. Values are required in critical stories for each column in each 

direction of earthquake loading. 
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-7 

In Table 6-2, the drift factor for columns depends on the ratio of the strengths 

of columns to the strengths of horizontal members framing into the column. 

This ratio is calculated for the beam-column or slab-column connection at the 

top of the critical story. For beam-column framing, this is represented by 

∑Mc/∑Mb, where ∑Mc is the sum of column strengths above and below the 

beam-column joint, and ∑Mb is the sum of the strengths of beams framing 

into the joint in the direction under consideration. For slab-column framing, 

the slab-column connection strength is substituted for the sum of the 

strengths of beams. 

Table 6-2 Drift Factor, γ, for Columns(1)

Ratio of Column Strengths to Beam Strengths(2)

∑Mc/∑Mb

Column Drift Factor

γ

≤ 0.6 0.85 

1 0.70 

≥ 2.4 0.30 

(1) For intermediate values of ∑Mc/∑Mb, the drift factor, γ, may be calculated by linear 

interpolation or the larger value used directly. 

(2) For columns below slab-column connections, substitute slab-column connection 

strength for the sum of the strengths of beams. 

6.6.3.2 Drift Factor for Slab-Column Connections and BeamColumn Corner Connections

For slab-column connections and beam-column corner connections, the drift 

factor, γ, is taken as 1.0. This applies to slab-column connections of slabcolumn frames and to beam-column corner connections when the 

connections are being evaluated as critical components. It does not apply to 

columns of slab-column or beam-column frames. For columns, the drift 

factor, γ, is defined in Section 6.6.3.1.

6.7 Calculate Drift Capacity of Critical Components

6.7.1 Drift Capacity of Critical Columns

Calculate the drift capacity of critical columns as:

Δc = lu(θc + 0.01) (6-7) 

where:

lu = clear height of the column

θc = column plastic rotation capacity

Calculate column plastic rotation capacity, θc, in accordance with Table 6-3 

for tied columns and Table 6-4 for spirally reinforced columns. Column 

plastic rotation capacity, θc, is based on the column shear strength ratio, 
6-8 6: Evaluation Procedure for Frame Systems FEMA P-2018

Vp/Vn, axial load ratio, P/Ag ce f ′ , and shear reinforcement ratio, ρt. Except for 

corner columns, the axial load ratio is based on the gravity load, Pg, 

determined in accordance with Section 4.2. For corner columns, the axial 

load ratio is based on the total column axial load, P = Pg + Peq, where P is 

positive in compression, and Pg and Peq are determined in accordance with 

Section 4.2.

Tables 6-3 and 6-4 are divided between flexure-critical columns and other 

columns (flexure-shear or shear-critical columns). Flexure-critical columns 

are columns with Vp/Vn ≤ 0.6, ρt > 0.002 and s/d < 0.5. Flexure-shear or 

shear-critical columns are defined as columns not classified as flexurecritical.

Table 6-3 Plastic Rotation Capacities for Tied Columns (1), (2), (3), (4)

Flexure-Critical Columns (Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5)

For .     ≥     ′ g ce

P

A f

0 1 θ ρ ( ρ )  

= +− + ≥       ′ c t t

g ce

P

A f

11.4 0.034 14 0.036 0.0

For .     <     ′ g ce

P

A f

0 1 θ ρ = +≥ . . c t 10 0 03 0 0

Flexure-Shear and Shear-Critical Columns (i.e., Columns not classified as Flexure-Critical Columns) 

For .     ≤     ′ g ce

P

A f

0 5

,min

. .

.

θ θ

ρ

′

′

= − ≥

+

c c

ce

g ce t ye

P f

A f f

0 5 0 01 1 5

0 8

P/Ag f′ce should not be taken smaller than 0.1

θc should be reduced linearly for .     >     ′ g ce

P

A f

0 5 from its value at .     =     ′ g ce

P

A f

0 5 to zero at .     =     ′ g ce

P

A f

0 7

,min θ ρ .. . . .    

=− + − ≥           ′

p

c t

g ce n

P V

A f V

0 042 0 023 0 63 0 023 0 0

P/Ag f′ce should not be taken smaller than 0.1

(1) ρt should not be taken greater than 0.0175 in any case, nor greater than 0.0075 when ties are not adequately 

anchored in the core.

(2) Vp/Vn should not be taken less than 0.2.

(3) θc for flexure-shear and shear-critical columns shall not exceed θc for a flexure-critical column with the same 

condition. 

(4) P = Pg, except for corner columns where P = Pg + Peq. 
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-9 

Table 6-4 Plastic Rotation Capacities for Spiral-Reinforced Columns (1), (2), (3), (4)

Flexure-Critical Columns (Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5)

For .     ≥     ′ g ce

P

A f

0 1 θρ ρ .. . ( . . )

    =  + −   +  ≥         ′ c t t

g ce

P

A f

1 15 11 4 0 034 14 0 036 0 0

For .     <     ′ g ce

P

A f

0 1 θ ρ c t = +≥ 1 15 10 0 03 0 0 . .. [ ]

Flexure-Shear and Shear-Critical Columns (i.e., Columns not classified as Flexure-Critical Columns)

For .     ≤     ′ g ce

P

A f

0 5

,min

. .

.

θ θ

ρ

= − ≥ ′ + ′

c c

ce

g ce t ye

P f

Af f

0 65 0 01 1 5

0 8

P/Ag f′ce should not be taken smaller than 0.1

θc should be reduced linearly for .     >     ′ g ce

P

A f

0 5 from its value at .     =     ′ g ce

P

A f

0 5 to zero at .     =     ′ g ce

P

A f

0 7

θ ρ .. . . .     =− + − ≥           ′

p

c,min t

g ce n

P V

A f V

0 06 0 06 1 3 0 037 0 0

P/Ag f′ce should not be taken smaller than 0.1

(1) ρt should not be taken greater than 0.0175 in any case, nor greater than 0.0075 when ties are not adequately 

anchored in the core.

(2) Vp/Vn should not be taken less than 0.2.

(3) θc for flexure-shear and shear-critical columns shall not exceed θc for a flexure-critical column with the same 

condition. 

(4) P = Pg, except for corner columns where P = Pg + Peq. 

6.7.2 Drift Capacity of Critical Slab-Column Connections

Calculate the drift capacity, ∆c, of critical slab-column connections based on 

structural integrity requirements. If the reinforcement at slab-column connections 

satisfies the structural integrity requirements of ACI 318-14 or Section 4.3.4, the 

drift capacity is taken as 0.12hsx. If the structural integrity requirements are not 

met, the drift capacity is calculated in accordance with Table 6-5. 

Table 6-5 Drift Capacity of Critical Slab-Column Connections(1)

Gravity Shear Ratio (2)

Vg/Vc Drift Capacity, ∆c

≤ 0.1 0.045hsx

≥ 0.6 0.01hsx

(1) For intermediate values of gravity load, the drift capacity may be calculated using linear 

interpolation.

(2) The gravity shear ratio is the unfactored gravity shear, Vg, divided by the theoretical 

punching shear strength, without moment transfer, Vc, determined in accordance with 

ACI 318-14 Section 22.6.5.2. 
6-10 6: Evaluation Procedure for Frame Systems FEMA P-2018

The drift capacity in Table 6-5 is calculated for the slab at level x, that is, the 

level at the top of story x (see Figure 5-1 for definitions of story x and level x). 

6.7.3 Drift Capacity of Critical Beam-Column Corner 

Connections

Calculate the drift capacity, ∆c, of critical beam-column corner connections 

as:

0.1 0.33 c sx

g ce

P h

A f

∆

 

= −   ′  

(6-8) 

where all terms are as previously defined. Story drift capacity, ∆c, need not 

be taken less than 0.025hsx. Note that story drift capacity refers to story x

while the drift capacity ratio is calculated for the beam-column connection at 

level x, that is, the level at the top of story x. See Figure 5-1 for definitions 

of story x and level x. 

Column axial load, P, is calculated considering combined gravity and 

earthquake loading in both orthogonal directions (X and Y) as:

P = Pg + Peq,X + Peq,Y (6-9) 

where:

Pg = axial load due to gravity, determined in accordance with 

Equation 4-1 

Peq = axial load due to earthquake overturning effects, determined in 

accordance with Section 4.2.2

6.8 Determine Column Ratings 

Determine column ratings, CR, for critical columns, slab-column connections 

and corner beam-column connections, as the ratio of drift demand to drift 

capacity, ∆D/∆C, in accordance with Table 6-6, for earthquake loading in each 

direction. 

The column rating, CR, represents the relative likelihood that an individual 

column, or the slab that it supports, will lose its ability to support vertical 

loads under the assumed earthquake loading. Column ratings near 0.0 

indicate a low likelihood of failure, while column ratings near 1.0 indicate a 

high likelihood of failure. 
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-11 

Table 6-6 Column Rating, CR

Drift Demand to Drift Capacity Ratio

∆D/∆C

Column Rating

CR

∆D/∆C ≤ 0.25 0.0

0.4 ≥ ∆D/∆C > 0.25 0.1

0.5 ≥ ∆D/∆C > 0.4 0.2

0.7 ≥ ∆D/∆C > 0.5 0.3

0.9 ≥ ∆D/∆C > 0.7 0.4

1.1 ≥ ∆D/∆C > 0.9 0.5

1.4 ≥ ∆D/∆C > 1.1 0.6

1.8 ≥ ∆D/∆C > 1.4 0.7

2.5 ≥ ∆D/∆C > 1.8 0.8

3.0 ≥ ∆D/∆C > 2.5 0.9

∆D/∆C > 3.0 0.93

In beam-column frames, the column rating is determined for both: 

(a) columns designated as critical components in critical stories; and 

(b) columns located in the story immediately below beam-column corner 

connections designated as critical components.

In slab-column frames, the column rating is determined for both: 

(a) columns designated as critical components in critical stories; and

(a) columns located in the story immediately below slab-column connections 

designated as critical components.

Figure 6-1 illustrates possible critical conditions for slab-column frames. It 

is possible for a column to be critical in both horizontal directions. It is also 

possible for the column to be critical, and for the supported beam-column 

corner connection or the slab-column connection to also be critical. In such 

cases, determine the column rating individually for all applicable conditions

in either horizontal direction, and then determine the final column rating as 

the maximum of the individual ratings.
6-12 6: Evaluation Procedure for Frame Systems FEMA P-2018

(a) Critical column (b) Critical slab-column connection (c) critical column and critical 

slab-column at same column

Figure 6-1 Illustration of possible critical conditions for a column in a slab-column frame. In (a), 

the column rating is equal to the rating of the critical column. In (b), the column rating 

is equal to the rating of the slab-column connection supported by the column. In (c) 

the column rating is equal to the maximum value of the ratings for the column and for 

the slab-column connection. A similar situation applies to beam-column corner 

connections.

Critical column 

in critical story

Beam or noncritical slab Critical

slab

Column in 

non-critical 

story

Critical

slab

Critical column 

in critical story

6.8.1 Discontinuous Columns

For discontinuous columns, column ratings, CR, are determined as follows:

• For critical discontinuous columns supported by a beam or slab that is 

not a cantilever, CR = 0.8. 

• For critical discontinuous columns supported by a cantilever beam or 

slab, if the demand-to-capacity ratio of the cantilever element for Vp in 

combination with expected vertical loads is greater than 0.7, the 

discontinuous column shall be assigned a column rating of 0.8, otherwise 

column ratings shall be determined in accordance with Section 6.8. 

Expected vertical loads shall be as defined in Section 4.2, considering 

axial loads due to overturning in addition to gravity loads.

6.9 Determine Story Ratings 

The story rating is a number representing the relative likelihood that an 

individual story will lose its ability to support vertical loads under the 

assumed earthquake loading. Determine the story rating, SR, as:

SR = 1.5Radj – 0.1 (6-10)

where:

Radj = the adjusted average of column ratings in the story, defined by 

Equation (6-11) 

 
FEMA P-2018 6: Evaluation Procedure for Frame Systems 6-13 

The story rating, SR, shall not be taken less than 0.1 nor greater than 0.9. 

Low values of story rating, SR, indicate a low likelihood of failure, while 

high values indicate a high likelihood of failure. 

The adjusted average column in the story, Radj, is defined as:

Radj = Ravg + 0.625Ravg(COV – 0.4) (6-11)

where:

Ravg = ,

1

col n

col i i

i

f CR =

∑ (6-12)

and:

Ravg = the weighted average column rating for all columns in the story, 

in which the values are weighted by the gravity load taken by 

each column

fcol,i = fraction of gravity loads supported by column i in a story (note: 

the sum of the fraction of gravity loads supported by all 

columns must equal 1.0 in each story) 

ncol = number of columns in a story

COV = the standard deviation of all the column ratings at a story 

divided by the weighted average column rating, Ravg, at that 

story

In Equations 6-11 and 6-12, Radj shall not be taken less than Ravg, nor greater 

than 1.25Ravg. 

In calculating Ravg, every column location in a story is assigned a column 

rating, CRi, determined by the highest rating for any critical column at that 

location, or for any supported critical beam-column corner connection or 

critical slab-column connection at that location, in either horizontal direction. 

The fraction of the gravity load taken by the column at each location, fcol,i, is 

used to weight the calculation of the average, regardless of whether column, 

slab-column connection, or beam-column connection is critical. 
FEMA P-2018 7: Evaluation Procedures for 7-1 

Frame-Wall Systems

Chapter 7

Evaluation Procedures for

Frame-Wall Systems 

This chapter covers the evaluation of buildings classified as frame-wall 

systems, as defined in Section 5.3.2. 

7.1 Introduction

The procedures for frame-wall systems parallel the procedures for bare frame 

systems in Chapter 6. Evaluation of frame-wall systems is focused on 

comparing drift demands with drift capacities of columns, slab-column 

connections, walls, and vertical wall segments (or wall piers). Component 

demand-to-capacity ratios are used to define column, wall, and wall segment

ratings. Column and wall ratings are combined to determine story ratings, 

which are used in Chapter 10 to determine the building rating.

Section 7.2 defines critical stories along each of two horizontal earthquake 

loading directions based on the results of the mechanism analyses of Section 

5.5. Section 7.3 defines critical components, which include columns located 

in critical stories, slab-column connections, corner beam-column 

connections, discontinuous columns satisfying certain criteria, and vertical 

wall segments. Sections 7.4 through 7.6 define the drift demands that are 

considered for each critical component. Section 7.7 defines drift capacities, 

and a comparison of drift demands to drift capacities in Section 7.8 

establishes individual column and wall ratings for critical components. 

7.2 Identify Critical Stories

Using the controlling plastic mechanism calculated in Section 5.5 in each of 

the two principal framing directions, critical stories are defined in 

accordance with the following:

• Where Mechanism 1 or 2 controls the strength along a principal framing 

direction, the critical story in that direction is the first story above the 

base. Where Mechanism 2 is calculated to be the controlling 

mechanism, but the plastic mechanism base-shear strength for 

Mechanism 2 is three-quarters (3/4) or more of the plastic mechanism 

base-shear strength for Mechanism 1, Mechanism 1 should be taken as 

controlling for calculation of story drift demands (because variations in 
7-2 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

lateral force distributions during dynamic loading have a high probability 

of producing Mechanism 1 failures in such cases). 

• Where Mechanism 3 controls the strength along a principal framing 

direction, the critical story in that direction is the story in which 

Mechanism 3 forms.

• Where Mechanism 4 controls the strength along a principal framing 

direction, the critical story in that direction is the lowest story in which 

yielding occurs in Mechanism 4.

It is possible for different plastic mechanisms to control along each of the 

two principal framing directions. In such cases, the critical story in one 

principal direction may differ from the critical story in the other principal 

direction. 

Critical stories are also defined where adjacent buildings require pounding 

considerations in accordance with Section 5.10. 

7.3 Identify Critical Components

Critical components are those components deemed to be most vulnerable to 

damage and loss of vertical load-carrying ability. Critical components are 

evaluated in accordance with the procedures in Sections 7.6 through 7.8.

7.3.1 Critical Columns

Columns in critical stories (defined in Section 7.2) and columns below 

discontinuous walls are designated as critical components. Columns in other 

stories are not designated as critical, except where changes in column 

geometry or detailing create an increased vulnerability for column failure. In 

such cases, columns at other levels should also be designated as critical. 

7.3.1.1 Critical Columns Integral with Walls

Treatment of columns that are integral with walls depends on the direction of 

loading, and the dimension of the column relative to the wall thickness. 

Columns integral with walls that have an out-of-plane dimension (parallel to 

the thickness of the wall web) equal to or greater than 1.5 times the thickness 

of the wall are designated as critical columns in the out-of-plane direction of 

the wall. In the in-plane direction, the columns are considered part of the 

wall. 

Columns integral with walls that have an out-of-plane dimension less than 

1.5 times the thickness of the wall are considered part of the wall in both the 

in-plane and out-of-plane directions of the wall. 
FEMA P-2018 7: Evaluation Procedures for 7-3 

Frame-Wall Systems

7.3.2 Critical Walls and Vertical Wall Segments

For the purpose of evaluation, critical walls must be separated, where 

appropriate, into identifiable vertical wall segments. Vertical wall segments 

can be differentiated when there is a substantial opening (e.g., a door) 

separating one portion of a wall from another in a given story. Vertical wall 

segments in critical stories (defined in Section 7.2) are designated as critical 

components. Vertical wall segments in stories other than critical stories, as 

well as horizontal wall segments, are not designated as critical.

Critical wall segments are evaluated based on drift demands and axial 

demands. Seismic overturning forces shall be estimated and added to gravity 

loads to determine P/Ag cf ′ on vertical wall segments with hw/lw ≥ 2 and lw/bw

≤ 6 occurring at the ends of critical walls, where hw is the clear height, lw is 

the horizontal length, and bw is the thickness of the wall segment. In other 

cases, tributary gravity loads can be used without seismic overturning forces. 

7.3.2.1 Critical Walls with Integral Columns

Critical walls can have integral columns located at one or both ends, or 

within the length of the wall. Walls with integral columns are evaluated in 

accordance with Section 7.7.4.1.

Axial demands, P/Ag ce f ′ , on critical walls with integral columns shall be 

calculated including the loads supported by the columns.

7.3.3 Critical Slab-Column Connections

In two-way slabs without beams, slab-column connections at the top of 

columns in critical stories are designated as critical components where the 

following condition applies:

• The slab moment transfer strength is less than the sum of column flexural 

strengths immediately above and below the slab. The slab moment 

transfer strength is the smaller of strengths calculated considering slab 

flexural strength and slab shear strength. Column flexural strength need 

not be taken greater than the moment corresponding to column shear 

failure.

Additionally, slab-column connections satisfying this condition should be 

designated as critical components at other levels where unusual conditions 

create an increased vulnerability for punching shear failure of the connection. 

Such conditions typically include levels where there is a decrease in slab 

thickness, increase in floor loading, or significant change in slab-column 

connection geometry or detailing.
7-4 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

7.3.4 Critical Beam-Column Corner Connections

In beam-column frames, beam-column corner connections at the top of 

columns in critical stories are designated as critical components where both 

conditions (a) and (b) apply:

(a) The beam-column joint lacks transverse reinforcement.

(b) The joint shear strength calculated in accordance with Section 4.3.3 is 

less than the joint shear generated by the controlling mechanism.

Additionally, beam-column connections satisfying both (a) and (b) should be 

designated as critical components at other levels where unusual conditions 

create an increased vulnerability for joint shear failure. Such conditions 

typically include levels where there is a sudden change in the column 

dimensions or joint detailing.

7.3.5 Discontinuous Columns

A column is considered discontinuous at a level where there is no supporting 

column in the story below. A discontinuous column is designated as a 

critical component where both conditions (a) and (b) apply:

(a) The discontinuous column supports loads from two or more levels. 

(b) The plastic capacity of the column, Vp, calculated in accordance with 

Section 4.4.1, is controlled by the shear strength of the supporting beam 

or slab.

7.4 Calculate Global Seismic Drift Demand 

Calculate the global seismic drift (displacement) demand for an equivalent 

single-degree-of-freedom (SDOF) system, δeff, as:

2

2 4

e

eff 1 2 a

T δ CCS g

π = (7-1)

where:

C1 = modification factor to relate expected maximum inelastic 

displacement to displacement calculated for linear elastic 

response

C2 = modification factor to represent the effect of pinched hysteresis 

shape, cyclic stiffness degradation, and strength deterioration on 

maximum displacement response

Te = effective fundamental period determined in Section 5.6

Sa = spectral acceleration at period, Te

g = acceleration of gravity
FEMA P-2018 7: Evaluation Procedures for 7-5 

Frame-Wall Systems

Calculate coefficient C1 in accordance with ASCE/SEI 41-17 as:

C1 = 2

1

1 strength

e aT

μ − + (7-2)

where a is a site class factor equal to: 130 for Site Class A or B; 90 for Site 

Class C; 60 for Site Class D, E, or F; and all other terms are as previously 

defined. For Te < 0.2 seconds, C1 need not be taken greater than the value at 

Te = 0.2 seconds. For Te ≥ 1 second, C1 = 1.0.

Calculate coefficient C2 in accordance with ASCE/SEI 41-17 as:

C2 =

2

1 1

1

800

strength

Te

  μ − +    

(7-3)

where all terms are as previously defined. For Te > 0.7 seconds, C2 = 1.0.

Global seismic drift demands are calculated in each direction of earthquake 

loading.

7.5 Calculate Story Drift Demand

Calculate story drift demand, δx, of story x as:

eff

x x sx eff

eff

h

h

δ

δα δ

  =   ≤    

(7-4)

where:

αx = coefficient to modify story drifts at story x for building 

configuration and strength characteristics

hsx = height of story x

δeff = global displacement demand of the equivalent SDOF system

(Equation 7-1)

heff = effective height of the building, defined as the height from the 

base to the centroid of lateral forces (same as the effective 

height of an equivalent single-degree-of-freedom system, which 

may be taken as 0.7hn in multistory buildings having uniform 

distribution of effective weight over the building height, and hn

in single-story buildings)

hn = height from the base of the building to the highest level of the

seismic force-resisting system

Story drift demands are calculated in each direction of earthquake loading.
7-6 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

Coefficient α modifies story drifts considering number of stories in a 

building, the yield mechanism, and whether the story is a critical story. 

Values of coefficient α for frame-wall systems are provided in Table 7-1.

Table 7-1 Values of Coefficient α for Frame-Wall Systems

No. of 

Stories in the 

Building 

Yield 

Mechanism(1)

Values of α

Critical Stories Other Stories(2)

1 (any) 1.0 (n/a)

2 

1 1.4 0.5

2 1.2 1.0

3, 4 1.5 1.0

≥3 

1 0.8heff/hsx 0.5

2 1.2 1.0

3 0.8heff/hsx 0.5

4 1.5

Stories below

critical story 0.5

Stories above 

critical story 1.0

 (1) Where Mechanism 2 is calculated to be the controlling mechanism, but the calculated plastic mechanism 

base-shear strength for Mechanism 2 is three-quarters (3/4) or more of the calculated plastic mechanism 

base-shear strength for Mechanism 1, Mechanism 1 should be taken as the controlling mechanism for 

selection of α values. 

(2) Values of α for “Other Stories” are generally not used, except where components in other stories are 

designated as critical because of increased local vulnerability, as required in Section 7.3. 

7.6 Calculate Drift Demands on Critical Components

7.6.1 Adjusted Drift Demand on Critical Components

For each critical component defined in Section 7.3, calculate the adjusted 

drift demand, ∆D, as follows: 

ΔD = ATγδx (7-5) 

where:

ΑT = torsional amplification factor (Section 7.6.2)

γ = drift factor representing the fraction of story drift affecting the 

critical component (Section 7.6.3)

δx = the story drift demand (Section 7.5) 
FEMA P-2018 7: Evaluation Procedures for 7-7 

Frame-Wall Systems

7.6.2 Torsional Amplification Factor

Determine the torsional amplification, ΑT, at the location of each critical 

component. The torsional amplification, ΑT, varies linearly in plan between 

a value of 1.0 at the center of strength and a value of AT,max at the edge of the 

building furthest from the center of strength (i.e., the weak or flexible side of 

the building). For all components located on the strong or stiff side of the 

building (between the center of strength and the edge of the building closest 

to the center of strength), ΑΤ = 1.0. 

7.6.2.1 Calculation of the Maximum Torsional Amplification 

Factor 

The maximum torsional amplification factor, AT,max, is calculated in 

accordance with Equation 7-6, but should not be taken less than 1.0. 

AT,max = 2.75(TR) + 0.5 (7-6)

where TR is the torsional ratio. The maximum torsional amplification factor, 

AT,max, may be taken as 1.0 if the wall index, WI < 0.0004, or if the torsional 

ratio, TR < 0.25. 

7.6.2.2 Calculation of Torsional Ratio

In Equation 7-6, TR shall be taken as the value of torsional ratio, TRx, at the 

critical story, unless there is a significant torsional irregularity in another 

story. TRx is the torsional ratio for story x, calculated as: 

Dx

x

Cx

T TR

T = (7-7)

where TDx is the torsion demand on story x, and TCx is the torsion capacity 

(strength) of story x. Torsion demand, TDx, is directional, and must be 

calculated for each direction of earthquake loading:

TDx = Vpxe (7-8)

where:

Vpx = plastic shear capacity of the critical story, as calculated in 

Chapter 5

e = eccentricity between the center of mass and the center of 

strength in the direction perpendicular to the direction of 

earthquake loading; e may not be taken as less than 5% of L

(i.e., 0.05L), where L is the overall plan dimension 

perpendicular to the direction of earthquake loading

The coordinates of the center of strength, ( ) x y, , are calculated from: 
7-8 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

1

1

f

f

n

i pfi

i

n

pfi

i

xV

x

V

=

=

=

∑

∑

, 1

1

f

f

n

i pfi

i

n

pfi

i

y V

y

V

=

=

=

∑

∑

(7-9)

where:

x, y = are the orthogonal distances from between the column or wall 

line of interest and an established reference point

Vpfi = is the plastic capacity of frame or wall line i

nf = is the number of frame or wall lines in story x, considering all 

frame or wall lines that resist torsion

Torsion capacity, TC, is calculated considering the capacity of all frame or 

wall lines in all orientations, and is the same regardless of the direction of 

loading considered:

1

f n

Cx fi pfi

i

T RV == ∑ (7-10)

where Rf is the orthogonal distance between frame or wall line i and the 

center of strength, and all other terms are as previously defined.

7.6.2.3 Identification of Exceptionally High Seismic Risk 

Buildings based on the Torsional Ratio 

Frame-wall systems with extreme torsion shall be classified as exceptionally 

high seismic risk buildings without further evaluation. A building is 

considered to have extreme torsion if the torsional ratio, TR > 1.5. 

7.6.3 Drift Factor

The drift factor, γ, defines the fraction of story drift demand, δx, affecting 

critical components. Values of drift factor, γ, for critical components are 

defined in the sections that follow. 

7.6.3.1 Drift Factor for Columns

The column drift factor, γ, defines the portion of the story drift demand, δx, 

attributable to deformations in critical columns. Drift factors for columns are 

provided in Table 7-2. Values are required in critical stories for each column 

in each direction of earthquake loading. 

In Table 7-2, the drift factor for columns depends on the ratio of the strengths 

of columns to the strengths of horizontal members framing into the column. 

This ratio is calculated for each column at the beam-column or slab-column 

connection at the top of the critical story. For beam-column framing, this is 
FEMA P-2018 7: Evaluation Procedures for 7-9 

Frame-Wall Systems

represented by ∑Mc/∑Mb, where ∑Mc is the sum of column strengths above 

and below the beam-column joint and ∑Mb is the sum of the strengths of 

beams framing into the joint in the direction under consideration. For slabcolumn framing, the slab-column connection strength is substituted for the 

sum of the strengths of beams.

Table 7-2 Drift Factor, γ, for Columns(1)

Ratio of Column Strengths to Beam Strengths(2)

∑Mc/∑Mb

Column Drift Factor

γ

≤ 0.6 0.85

1 0.70

≥ 2.4 0.30 

(1) For intermediate values of ∑Mc/∑Mb, the drift factor, γ, may be calculated by linear 

interpolation or the larger value used directly.

(2) For columns below slab-column connections, substitute slab-column connection 

strength for the sum of the strengths of beams.

7.6.3.2 Drift Factor for Slab-Column Connections and BeamColumn Corner Connections

For slab-column connections and beam-column corner connections, the drift 

factor, γ, is taken as 1.0. This applies to slab-column connections of slabcolumn frames and to beam-column corner connections when the 

connections are being evaluated as critical components. It does not apply to 

columns of slab-column or beam-column frames. For columns, the drift 

factor, γ, is defined in Section 7.6.3.1.

7.6.3.3 Drift Factor for Vertical Wall Segments

For critical vertical wall segments, the drift factor, γ, is taken as 1.0. 

7.7 Calculate Drift Capacity of Critical Components

Calculate drift capacities of critical columns, slab-column connections, and 

corner beam-column connections in accordance with this section.

7.7.1 Drift Capacity of Critical Columns

Calculate the drift capacity of critical columns as: 

Δc = lu(θc + 0.01) (7-11) 

where:

lu = clear height of the column 

θc = column plastic rotation capacity
7-10 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

Calculate column plastic rotation capacity θc in accordance with Table 7-3 

for tied columns and Table 7-4 for spiral-reinforced columns. Column 

plastic rotation capacity, θc, is based on the column shear strength ratio, 

Vp/Vn, axial load ratio, P/Ag ce f ′ , and shear reinforcement ratio, ρt. Except for 

corner columns, the axial load ratio is based on the gravity load, Pg, 

determined in accordance with Section 4.2. For corner columns, the axial 

load ratio is based on the total column axial load, P = Pg + Peq, where P is 

positive in compression, and Pg and Peq are determined in accordance with 

Section 4.2.

Table 7-3 Plastic Rotation Capacities for Tied Columns(1), (2), (3), (4)

Flexure-Critical Columns (Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5)

For .     ≥     ′ g ce

P

A f

0 1 θ ρ ( ρ )  

= +− + ≥       ′ c t t

g ce

P

A f

11.4 0.034 14 0.036 0.0

For .     <     ′ g ce

P

A f

0 1 θ ρ = +≥ . . c t 10 0 03 0 0

Flexure-Shear and Shear-Critical Columns (i.e., Columns not classified as Flexure-Critical Columns)

For .     ≤     ′ g ce

P

A f

0 5

,min

. .

.

θ θ

ρ

′

′

= − ≥

+

c c

ce

g ce t ye

P f

A f f

0 5 0 01 1 5

0 8

/ ′ g ce P Af should not be taken smaller than 0.1

θc should be reduced linearly for .     >     ′ g ce

P

A f

0 5 from its value at .     =     ′ g ce

P

A f

0 5 to zero at .     =     ′ g ce

P

A f

0 7

,min θ ρ .. . . .    

=− + − ≥           ′

p

c t

g ce n

P V

A f V

0 042 0 023 0 63 0 023 0 0

/ ′ g ce P Af should not be taken smaller than 0.1

(1) ρt should not be taken greater than 0.0175 in any case, nor greater than 0.0075 when ties are not adequately 

anchored in the core.

(2) Vp/Vn should not be taken less than 0.2.

(3) θc for flexure-shear and shear-critical columns shall not exceed θc for a flexure-critical column with the same 

condition. 

(4) P = Pg, except for corner columns where P = Pg + Peq. 

Tables 7-3 and 7-4 are divided between flexure-critical columns and other 

columns (flexure-shear or shear-critical columns). Flexure-critical columns 

are columns with Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5. Flexure-shear or 

shear-critical columns are defined as columns not classified as flexurecritical.
FEMA P-2018 7: Evaluation Procedures for 7-11 

Frame-Wall Systems

Table 7-4 Plastic Rotation Capacities for Spiral-Reinforced Columns(1), (2), (3), (4)

Flexure-Critical Columns (Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5)

For .     ≥     ′ g ce

P

A f

0 1 θρ ρ .. . ( . . )

    =  + −   +  ≥         ′ c t t

g ce

P

A f

1 15 11 4 0 034 14 0 036 0 0

For .     <     ′ g ce

P

A f

0 1 θ ρ c t = +≥ 1 15 10 0 03 0 0 . .. [ ]

Flexure-Shear and Shear-Critical Columns (i.e., Columns not classified as Flexure-Critical Columns)

For .     ≤     ′ g ce

P

A f

0 5

,min

. .

.

θ θ

ρ

= − ≥ ′ + ′

c c

ce

g ce t ye

P f

Af f

0 65 0 01 1 5

0 8

/ ′ g ce P Af should not be taken smaller than 0.1

θc should be reduced linearly for .     >     ′ g ce

P

A f

0 5 from its value at .     =     ′ g ce

P

A f

0 5 to zero at .     =     ′ g ce

P

A f

0 7

θ ρ .. . . .     =− + − ≥           ′

p

c,min t

g ce n

P V

A f V

0 06 0 06 1 3 0 037 0 0

/ ′ g ce P Af should not be taken smaller than 0.1

(1) ρt should not be taken greater than 0.0175 in any case, nor greater than 0.0075 when ties are not adequately 

anchored in the core.

(2) Vp/Vn should not be taken less than 0.2.

(3) θc for flexure-shear and shear-critical columns shall not exceed θc for a flexure-critical column with the same 

condition. 

(4) P = Pg, except for corner columns where P = Pg + Peq. 

7.7.2 Drift Capacity of Critical Slab-Column Connections

Calculate the drift capacity, ∆c, of critical slab-column connections based on 

structural integrity requirements. If the reinforcement at slab-column connections 

satisfies the structural integrity requirements of ACI 318-14 or Section 4.3.4, the 

drift capacity is taken as 0.12hsx. If the structural integrity requirements are not 

met, the drift capacity is calculated in accordance with Table 7-5. 

Table 7-5 Drift Capacity of Critical Slab-Column Connections(1)

Gravity Shear Ratio (2)

Vg/Vc

Drift Capacity

∆c

≤ 0.1 0.045hsx

≥ 0.6 0.01hsx

(1) For intermediate values of gravity load, the drift capacity may be calculated using linear 

interpolation.

(2) The gravity shear ratio is the unfactored gravity shear, Vg, divided by the theoretical 

punching shear strength, without moment transfer, Vc, determined in accordance with 

ACI 318-14 Section 22.6.5.2.
7-12 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

The drift capacity in Table 7-5 is calculated for the slab at level x, that is, the 

level at the top of story x (see Figure 5-1 for definitions of story x and level x). 

7.7.3 Drift Capacity of Critical Beam-Column Corner 

Connections

Calculate the drift capacity ∆c of critical beam-column corner connections as: 

0.1 0.33 c sx

g ce

P h

A f

∆

 

= −   ′  

(7-12) 

where all terms are as previously defined. Story drift capacity, ∆c, need not 

be taken less than 0.025hsx. Note that story drift capacity refers to story x

while the drift capacity ratio is calculated for the beam-column connection at 

level x, that is, the level at the top of story x. See Figure 5-1 for definitions 

of story x and level x. 

Column axial load, P, is calculated considering combined gravity and 

earthquake loading in both orthogonal directions (X and Y) as:

P = Pg + Peq, X + Peq, Y (7-13) 

where:

Pg = axial load due to gravity, determined in accordance with 

Equation 4-1 

Peq = axial load due to earthquake overturning effects, determined in 

accordance with Section 4.2.2

7.7.4 Drift Capacity of Critical Walls and Vertical Wall Segments

Calculate drift capacity, ∆c, of critical walls and vertical wall segments in 

accordance with Table 7-6, for flexure-critical walls, and Table 7-7, for 

shear-critical walls. If Mechanism 2 or 4 controls, walls and vertical wall 

segments can be assumed to be flexure-critical. If Mechanism 1 or 3 

controls, walls and vertical wall segments are generally shear-critical, except 

when the calculation of wall shear strength, Vnwx, in Chapter 5 is controlled 

by the shear corresponding to the development of the wall flexural strength. 

In Table 7-6, lw is the horizontal length, bw is the thickness, and c is the 

neutral axis depth of the vertical wall segment. The neutral axis depth, c, can 

be computed from moment curvature analysis or approximated by:

100 w g ce

ca P b

l Af

= + ′ (7-14)
FEMA P-2018 7: Evaluation Procedures for 7-13 

Frame-Wall Systems

where a and b are coefficients provided in Table 7-8. If the thickness of the 

wall varies over the compression zone, a weighted average value of bw shall 

be used for wall thickness. 

Table 7-6 Drift Capacity of Flexure-Critical Walls or Vertical Wall Segments (%)(1)

lw/bw

(2)

c/lw(2)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

≤6 3.50 3.50 3.50 3.50 3.25 3.00 2.67 2.62 1.85 1.80 1.76 1.71

9 3.50 3.50 3.42 3.28 3.00 2.50 2.20 2.00 1.34 1.24 1.14 1.04

12 3.50 3.35 3.09 2.84 2.59 2.00 1.54 1.32 1.00 0.75 0.75 0.75

15 3.46 3.06 2.67 2.28 1.88 1.75 1.50 1.25 1.00 0.75 0.75 0.75

18 3.28 2.72 2.15 1.75 1.75 1.50 1.25 1.00 0.75 0.75 0.75 0.75

21 3.08 2.31 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

24 2.84 1.83 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

27 2.57 1.75 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

30 2.28 1.75 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

>35 1.75 1.75 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

(1) For walls with confined boundaries, drift capacity may be increased by 25%.

(2) For intermediate values, drift capacity may be calculated using linear interpolation.

Table 7-7 Drift Capacity of Shear-Critical Walls or Vertical Wall

Segments(1)

P/Agf’c

 (2) Drift Capacity (%)

0.0 4.00

0.005 3.50

0.01 3.00

0.03 2.30

0.05 2.00

0.10 1.50

0.15 1.25

0.20 1.00

0.30 0.75

0.40 0.60

0.50 0.45

(1) For walls with confined boundaries, drift capacity may be increased by 50%.

(2) For intermediate values, drift capacity may be calculated using linear interpolation.

Except for vertical wall segments occurring at the ends of critical walls, as 

identified in Section 7.3.2, the axial load is based on the gravity load, Pg, 

determined in accordance with Section 4.2. For vertical wall segments at the 
7-14 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

ends of critical walls, the axial load is based on the total axial load, P = Pg + 

Peq, where P is positive in compression, and Pg and Peq are determined in 

accordance with Section 4.2.

Table 7-8 Coefficients for Calculation of Neutral Axis Depth, c

Cross-Section a b 

Rectangular 10 1.2

I-shaped and Barbell 3 1.4

T-shaped, L-shaped and Half-Barbell 

(web in compression) 30 0.7

T-shaped, L-shaped and Half-Barbell 

(web in tension) 20 2.0

For walls with asymmetric cross-sections (e.g., T-shaped, L-shaped, and 

half-barbell configurations), the drift capacity should be evaluated in both 

directions of loading (i.e., flange in compression and flange in tension), and 

the larger value used to determine the drift capacity of the wall.

Alternatively, drift capacity (in percent) may be determined by calculation, 

using Equation 7-15 for flexure-critical walls and Equation 7-16 for shearcritical walls: 

( ) 2 3.85 3.5 0.75

30 c %

c

w

w g e

l c P

b A f

∆ ′ = − − ≥ (7-15)

where lwc/bw

2 should not be taken greater than 60, and

(%) 2.50 10 for 0.1

(%) 1.75 2.6 for 0.1

c

g ce g ce

c

g ce g ce

P P

Af Af

P P

Af Af

∆

∆

= − ≤ ′ ′

= − > ′ ′

 (7-16)

7.7.4.1 Walls with Integral Columns or Boundary Elements

Where the ends of walls and vertical wall segments are confined by spirally 

reinforced columns or confined boundaries as defined in Table 7-9, the drift 

capacity may be increased by 25% for flexure-critical walls and by 50% for 

shear-critical walls.

Where integral concrete columns are located within the length of a wall or 

vertical wall segment, the drift capacity shall be determined as follows:

• For walls that are not more than 15 feet in length, with an axial load ratio 

of 0.30 or less, with an integral concrete column conforming to the 

confinement requirements in Table 7-9, located within the middle third 

of the wall length, the drift capacity may be taken as 4%.
FEMA P-2018 7: Evaluation Procedures for 7-15

Frame-Wall Systems

• For other cases of walls with integral concrete columns, the drift capacity 

may be taken as the larger of:

o the drift capacity determined for the wall or vertical wall segment, 

excluding consideration of the integral concrete column; or

o the drift capacity determined for a segment of wall on either side of 

the column, treated as a half-barbell section, with the column 

assumed to be located at the compression end of the segment.

Table 7-9 Minimum Transverse Reinforcement in Integral Columns or 

Boundary Elements Required to be Classified as Confined

Transverse 

Reinforcement

Applicable 

Expression

sh

c

A

sb

for rectilinear hoops(1) Greater of: .   ′   −

 

g c

ch yt

A f

A f

02 1 and . ′

c

yt

f

f

0 06

ρs for spiral or circular hoops Greater of: .   ′   −

 

g c

ch yt

A f

A f

03 1 and . ′

c

yt

f

f

0 08

(1) To be considered for purposes of confinement, transverse reinforcement must have 135 

degree hooks and spacing of no more than 8 inches.

7.8 Determine Column and Wall Ratings

Determine column ratings, CR, for critical columns, slab-column connections 

and corner beam-column connections, and determine wall ratings, WR, for 

critical walls and vertical wall segments, as the ratio of drift demand to drift 

capacity, ∆D/∆C, in accordance with Table 7-10, for earthquake loading in 

each direction.

Column and wall ratings represents the relative likelihood that an individual 

column, supported slab, or wall will lose its ability to support vertical loads 

under the assumed earthquake loading. Ratings near 0.0 indicate a low 

likelihood of failure, while ratings near 1.0 indicate a high likelihood of 

failure.

In beam-column frames, the column rating is determined for both:

(a) columns designated as critical components in critical stories; and

(b) columns located in the story immediately below beam-column corner 

connections designated as critical components.

In slab-column frames, the column rating is determined for both:

(a) columns designated as critical components in critical stories; and
7-16 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

(b) columns located in the story immediately below slab-column connections 

designated as critical components.

Table 7-10 Column Rating, CR, and Wall Rating, WR

Drift Demand to Drift Capacity Ratio

∆D/∆C

Column Rating, CR

Wall Rating, WR

∆D/∆C ≤ 0.25 0.0

0.4 ≥ ∆D/∆C > 0.25 0.1

0.5 ≥ ∆D/∆C > 0.4 0.2

0.7 ≥ ∆D/∆C > 0.5 0.3

0.9 ≥ ∆D/∆C > 0.7 0.4

1.1 ≥ ∆D/∆C > 0.9 0.5

1.4 ≥ ∆D/∆C > 1.1 0.6

1.8 ≥ ∆D/∆C > 1.4 0.7

2.5 ≥ ∆D/∆C > 1.8 0.8

3.0 ≥ ∆D/∆C > 2.5 0.9

∆D/∆C > 3.0 0.93

Figure 7-1 illustrates possible critical conditions for slab-column frames. It 

is possible for a column to be critical in both horizontal directions. It is also 

possible for the column to be critical, and for the supported beam-column 

corner connection or the slab-column connection to also be critical. 

(a) Critical column (b) Critical slab-column connection (c) Critical column and critical 

slab-column at same column

Figure 7-1 Illustration of possible critical conditions for a column in a slab-column frame. In (a), 

the column rating is equal to the rating of the critical column. In (b), the column rating 

is equal to the rating of the slab-column connection supported by the column. In (c) 

the column rating is equal to the maximum value of the ratings for the column and for 

the slab-column connection. A similar situation applies to beam-column corner 

connections. 

Critical column 

in critical story

Beam or noncritical slab Critical

slab

Column in 

non-critical 

story

Critical

slab

Critical column 

in critical story

 
FEMA P-2018 7: Evaluation Procedures for 7-17 

Frame-Wall Systems

In such cases, determine the column rating individually for all applicable 

conditions in either horizontal direction, and then determine the final column 

rating as the maximum of the individual ratings.

7.8.1 Discontinuous Columns

For discontinuous columns, column ratings, CR, are determined as follows:

• For critical discontinuous columns supported by a beam or slab that is 

not a cantilever, CR = 0.8. 

• For critical discontinuous columns supported by a cantilever beam or 

slab, if the demand-to-capacity ratio of the cantilever element for Vp in 

combination with expected vertical loads is greater than 0.7, the 

discontinuous column shall be assigned a column rating of 0.8, otherwise 

column ratings shall be determined in accordance with Section 7.8. 

Expected vertical loads shall be as defined in Section 4.2, considering 

axial loads due to overturning in addition to gravity loads.

7.9 Determine Story Ratings 

The story rating is a number representing the relative likelihood that an 

individual story will lose its ability to support vertical loads under the 

assumed earthquake loading. Determine the story rating, SR, as:

SR = 1.5Radj – 0.1 (7-17)

where:

Radj = the adjusted average of column and wall ratings in the story, 

defined by Equation (7-18) 

The story rating, SR, shall not be taken less than 0.1 nor greater than 0.9. 

Low values of story rating, SR, indicate a low likelihood of failure, while 

high values indicate a high likelihood of failure.

The adjusted average of column and wall ratings in the story, Radj, is defined 

as:

Radj = Ravg + 0.625Ravg(COV – 0.4) (7-18)

where:

Ravg = , ,

1 1

col wall n n

col i i wall j j

i j

f CR f WR = =

∑ ∑+ (7-19)

and:

Ravg = the weighted average rating for all columns, walls, and vertical 

wall segments in the story, in which the values are weighted by 

the gravity load taken by each column, wall, or wall segment

fcol,j = fraction of gravity loads supported by column i
7-18 7: Evaluation Procedures for FEMA P-2018

Frame-Wall Systems

fwall,j = fraction of gravity loads in a story supported by wall j (note: 

the sum of the fraction of gravity loads supported by all 

columns and walls must equal 1.0 in each story)

ncol = number of columns in a story

nwall = number of walls in a story

COV = the standard deviation of all the column and wall ratings at a 

story divided by the weighted average rating, Ravg, at that story

In Equations 7-18 and 7-19, Radj shall not be taken less than Ravg, nor greater 

than 1.25Ravg. 

In calculating Ravg, every column location in a story is assigned a column 

rating, CRi, and each wall and vertical wall segment in a story is assigned a 

wall rating, WRj, determined by the highest rating for any critical column or 

wall element at that location, or for any supported critical beam-column 

corner connection or critical slab-column connection at that location, in 

either horizontal direction. The fraction of the gravity load taken by the 

column, fcol,i, or wall, fwall,j, at each location is used to weight the calculation 

of the average. 
FEMA P-2018 8: Evaluation Procedures for Bearing Wall Systems 8-1 

Chapter 8

Evaluation Procedures for 

Bearing Wall Systems

This chapter covers the evaluation of buildings classified as bearing wall 

systems, as defined in Section 5.3.3. 

8.1 Introduction

The procedures for bearing wall systems parallel the procedures for framewall systems in Chapter 7. Evaluation of bearing wall systems is focused on 

comparing drift demands with drift capacities of walls and vertical wall 

segments (or wall piers). Wall drift capacities are a function of the wall 

geometry, axial load ratio, and whether the wall is estimated to be flexurecritical or shear-critical. The evaluation also considers drift demands and 

capacities for isolated columns and slab-column connections present in 

bearing wall buildings. Although columns are considered in the evaluation, 

column performance is not expected to control global collapse, and columns 

that, together, support less than 10% of the gravity load in a story need not be 

explicitly considered in the evaluation. Wall ratings are combined with 

column ratings (if applicable) to determine story ratings, which are used in 

Chapter 10 to determine the building rating. 

Section 8.2 defines critical stories along each of two horizontal earthquake 

loading directions based on the results of the mechanism analyses of Section 

5.5. Section 8.3 defines critical components, which are vertical wall 

segments and columns supporting significant gravity loads. Sections 8.4 

through 8.6 define the drift demands that are considered for each wall. 

Section 8.7 defines drift capacities, and a comparison of wall drift demands 

to drift capacities in Section 8.8 establishes individual wall ratings. 

8.2 Identify Critical Stories

Using the controlling plastic mechanism along each of the two principal 

framing directions determined in Section 5.5, critical stories are defined in 

accordance with the following:

• Where Mechanism 1 or 2 controls strength along a principal framing 

direction, the critical story in that direction is the first story above the 

base. Where Mechanism 2 is calculated to be the controlling 
8-2 8: Evaluation Procedures for Bearing Wall Systems FEMA P-2018

mechanism, but the plastic mechanism base-shear strength for 

Mechanism 2 is three-quarters (3/4) or more of the plastic mechanism 

base-shear strength for Mechanism 1, Mechanism 1 should be taken as 

controlling for calculation of story drift demands (because variations in 

lateral force distributions during dynamic loading have a high probability 

of producing Mechanism 1 failures in such cases). 

• Where Mechanism 3 controls strength along a principal framing 

direction, the critical story in that direction is the story where Mechanism 

3 forms. 

• Where Mechanism 4 controls strength along a principal framing 

direction, the critical story in that direction is the lowest story where 

yielding occurs in Mechanism 4.

It is possible for different controlling plastic mechanisms to occur along each 

of the two principal framing directions. In such cases, the critical story for 

loading in one principal direction may differ from the critical story for 

loading in the other principal direction. 

8.3 Identify Critical Components

Critical components are those components deemed to be most vulnerable to 

damage and loss of vertical load-carrying ability, eventually contributing to 

collapse. Critical components are evaluated in accordance with procedures 

in Section 8.7.

8.3.1 Critical Walls and Vertical Wall Segments

For the purposes of evaluation, critical walls must be separated, where 

appropriate, into identifiable vertical wall segments. Vertical wall segments 

can be differentiated when there is a substantial opening (e.g., a door) 

separating one portion of a wall from another in a given story. Vertical wall 

segments in critical stories of bearing wall buildings (defined in Section 8.2) 

are designated as critical components. Vertical wall segments in stories other 

than critical stories, as well as horizontal wall segments, are not designated 

as critical.

Critical wall segments are evaluated based on drift demands and axial 

demands. Seismic overturning forces shall be estimated and added to gravity 

loads to determine P/Ag cf ′ on vertical wall segments with hw/lw ≥ 2 and lw/bw

≤ 6 occurring at the ends of critical walls, where hw is the clear height, lw is 

the horizontal length, and bw is the thickness of the wall segment. In other 

cases, tributary gravity loads can be used. 
FEMA P-2018 8: Evaluation Procedures for Bearing Wall Systems 8-3 

8.3.2 Other Critical Components

Columns in critical stories (defined in Section 8.2) and columns below 

discontinuous walls are designated as critical components. Where they 

occur, columns in other stories, columns integral with walls, slab-column 

connections, beam-column corner connections, and discontinuous columns 

and walls are identified as critical in accordance with Section 7.3.

8.4 Calculate Global Seismic Drift Demand

Calculate the global seismic drift (displacement) demand for an equivalent 

single-degree-of-freedom (SDOF) system, δeff, as:

2

2 4

e

eff 1 2 a

T δ CCS g

π = (8-1) 

where:

C1 = modification factor to relate expected maximum inelastic 

displacement to displacement calculated for linear elastic 

response

C2 = modification factor to represent the effect of pinched hysteresis 

shape, cyclic stiffness degradation, and strength deterioration on 

maximum displacement response 

Te = effective fundamental period determined in Section 5.6

Sa = spectral acceleration at period, Te

g = acceleration of gravity

Calculate coefficient C1 in accordance with ASCE/SEI 41-17 as:

C1 = 2

1

1 strength

e aT

μ − + (8-2) 

where a is a site class factor equal to: 130 for Site Class A or B; 90 for Site 

Class C; 60 for Site Class D, E, or F; and all other terms are as previously 

defined. For Te < 0.2 seconds, C1 need not be taken greater than the value at 

Te = 0.2 seconds. For Te ≥ 1 second, C1 = 1.0. 

Calculate coefficient C2 in accordance with ASCE/SEI 41-17 as:

C2 =

2

1 1

1

800

strength

Te

  μ − +    

(8-3) 

where all terms are as previously defined. For Te > 0.7 seconds, C2 = 1.0. 

Global seismic drift demands are calculated in each direction of earthquake 

loading.
8-4 8: Evaluation Procedures for Bearing Wall Systems FEMA P-2018

8.5 Calculate Story Drift Demand

Calculate story drift demand, δx, of story x as:

eff

x x sx eff

eff

h

h

δ

δα δ

  =   ≤    

(8-4) 

where:

αx = coefficient to modify story drifts at story x for building 

configuration and strength characteristics (Table 8-1) 

hsx = height of story x

δeff = global displacement demand of the equivalent SDOF system 

(Equation 8-1)

heff = effective height of the building, defined as the height from the 

base to the centroid of lateral forces (may be taken as 0.7hn in 

multistory buildings having uniform distribution of effective 

weight over the building height and hn in single-story buildings) 

hn = height from the base of the building to the highest level of the 

seismic force-resisting system

Table 8-1 Values of Coefficient α for Bearing Wall Systems 

No. of 

Stories in the 

Building

Yield 

Mechanism(1)

Values of α

Critical Stories Other Stories(2)

1 (any) 1.0 (n/a)

2 

1 1.4 0.5

2 1.2 1.0

3, 4 1.5 1.0

≥3 

1 0.8heff/hsx 0.5

2 1.2 1.0

3 0.8heff/hsx 0.5

4 1.5

Stories below 

critical story 0.5

Stories above 

critical story 1.0

 (1)Where Mechanism 2 is calculated to be the controlling mechanism, but the calculated plastic mechanism 

base-shear strength for Mechanism 2 is three-quarters (3/4) or more of the calculated plastic mechanism 

base-shear strength for Mechanism 1, Mechanism 1 should be taken as the controlling mechanism for 

selection of α values. 

(2) Values of α for “Other Stories” are generally not used, except where components in other stories are 

designated as critical because of increased local vulnerability, as required in Section 8.3.
FEMA P-2018 8: Evaluation Procedures for Bearing Wall Systems 8-5 

Coefficient α modifies story drifts considering number of stories in a 

building, the yield mechanism, and whether the story is a critical story. 

Table 8-1 provides values of coefficient α for bearing wall systems.

Story drift demands are calculated in each direction of earthquake loading.

8.6 Calculate Drift Demands on Critical Components

8.6.1 Adjusted Drift Demand on Critical Components

For each critical component defined in Section 8.3, calculate the adjusted 

drift demand, ∆D, as:

ΔD = ATγδx (8-5) 

where:

ΑT = torsional amplification factor 

γ = drift factor representing fraction of story drift affecting the 

critical component 

δx = the story drift demand (Section 8.5) 

8.6.2 Torsional Amplification Factor

Inherent torsion is expected to be low in bearing wall systems because such 

systems generally include well-distributed wall elements and relatively 

uniform foundation conditions. Therefore, torsion need not be considered in 

buildings classified as bearing wall systems, and the torsional amplification 

factor, AT, is taken as 1.0, except as noted below. 

If the building under consideration possesses an unusual structural 

configuration that results in a torsional irregularity due to plan configuration, 

changes in foundation fixity, or other condition, column drifts should be 

amplified for torsion using the torsional amplification factor, AT, in 

accordance with Section 7.6.2. 

8.6.3 Drift Factor

The drift factor, γ, defines the fraction of story drift demand, δx, affecting 

critical components. The drift factor, γ, for critical walls and vertical wall

segments is taken as 1.0.

If columns and other related components (e.g., slab-column connections, 

beam-column connections, and discontinuous columns) are designated as 

critical, drift factors shall be determined in accordance with Section 7.6.3. 
8-6 8: Evaluation Procedures for Bearing Wall Systems FEMA P-2018

8.7 Calculate Drift Capacity of Critical Components

8.7.1 Drift Capacity of Critical Walls and Vertical Wall Segments

Calculate drift capacity, ∆c, of critical walls and vertical wall segments in 

accordance with Table 8-2, for flexure-critical walls, and Table 8-3, for 

shear-critical walls. If Mechanism 2 or 4 controls, walls and vertical wall 

segments can be assumed to be flexure-critical. If Mechanism 1 or 3 

controls, walls and vertical wall segments are generally shear-critical, except 

when the calculation of wall shear strength, Vnwx, in Chapter 5 is controlled 

by the shear corresponding to the development of the wall flexural strength. 

Table 8-2 Drift Capacity of Flexure-Critical Walls or Vertical Wall Segments (%)(1)

lw/bw

(2)

c/lw(2)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

≤6 3.50 3.50 3.50 3.50 3.25 3.00 2.67 2.62 1.85 1.80 1.76 1.71

9 3.50 3.50 3.42 3.28 3.00 2.50 2.20 2.00 1.34 1.24 1.14 1.04

12 3.50 3.35 3.09 2.84 2.59 2.00 1.54 1.32 1.00 0.75 0.75 0.75

15 3.46 3.06 2.67 2.28 1.88 1.75 1.50 1.25 1.00 0.75 0.75 0.75

18 3.28 2.72 2.15 1.75 1.75 1.50 1.25 1.00 0.75 0.75 0.75 0.75

21 3.08 2.31 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

24 2.84 1.83 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

27 2.57 1.75 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

30 2.28 1.75 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

>35 1.75 1.75 1.75 1.75 1.50 1.25 1.25 1.00 0.75 0.75 0.75 0.75

(1) For walls with confined boundaries, drift capacity may be increased by 25%.

(2) For intermediate values, drift capacity may be calculated using linear interpolation.

In Table 8-2, lw is the horizontal length, bw is the thickness, and c is the 

neutral axis depth of the vertical wall segment. The neutral axis depth, c, can 

be computed from moment curvature analysis or approximated by: 

100 w g ce

ca P b

l Af

= + ′ (8-6) 

where a and b are coefficients provided in Table 8-4. If the thickness of the 

wall varies over the compression zone an average value of bw shall be used.

Except for vertical wall segments occurring at the ends of critical walls, as 

identified in Section 8.3.2, the axial load is based on the gravity load, Pg, 

determined in accordance with Section 4.2. For vertical wall segments at the 

ends of critical walls, the axial load is based on the total axial load, P = Pg + 
FEMA P-2018 8: Evaluation Procedures for Bearing Wall Systems 8-7 

Peq, where P is positive in compression, and Pg and Peq are determined in 

accordance with Section 4.2.

Table 8-3 Drift Capacity of Shear-Critical Walls or Vertical Wall 

Segments(1)

P/Agf’c

 (2) Drift Capacity (%)

0.0 4.00

0.005 3.50

0.01 3.00

0.03 2.30

0.05 2.00

0.10 1.50

0.15 1.25

0.20 1.00

0.30 0.75

0.40 0.60

0.50 0.45

(1) For walls with confined boundaries, drift capacity may be increased by 50%.

(2) For intermediate values, drift capacity may be calculated using linear interpolation.

Table 8-4 Coefficients for Calculation of Neutral Axis Depth, c

Cross-Section a b 

Rectangular 10 1.2

I-shaped and Barbell 3 1.4

T-shaped, L-shaped and Half-Barbell 

(web in compression) 30 0.7

T-shaped, L-shaped and Half-Barbell 

(web in tension) 20 2.0

For walls with asymmetric cross-sections (e.g., T-shaped, L-shaped, and 

half-barbell configurations), the drift capacity should be evaluated in both 

directions of loading (i.e., flange in compression and flange in tension), and 

the larger value used to determine the drift capacity of the wall.

Alternatively, drift capacity (in percent) may be determined by calculation, 

using Equation 8-7 for flexure-critical walls and Equation 8-8 for shearcritical walls:

( ) 2 3.85 3.5 0.75

30 c %

c

w

w g

l c P

b A f

∆ ′ = − − ≥ (8-7) 

where lwc/bw

2

 should not be taken greater than 60, and: 
8-8 8: Evaluation Procedures for Bearing Wall Systems FEMA P-2018

(%) 2.50 10 for 0.1

(%) 1.75 2.6 for 0.1

c

g c g c

c

g c g c

P P

Af Af

P P

Af Af

∆

∆

= − ≤ ′ ′

= − > ′ ′

(8-8) 

8.7.1.1 Walls with Integral Columns or Boundary Elements

Where the ends of walls and vertical wall segments are confined by spirally 

reinforced columns or confined boundaries as defined in Table 8-5, the drift 

capacity may be increased by 25% for flexure-critical walls and by 50% for 

shear-critical walls.

Where integral concrete columns are located within the length of a wall or 

vertical wall segment, the drift capacity shall be determined as follows:

• For walls that are not more than 15 feet in length, with an axial load ratio 

of 0.30 or less, with an integral concrete column conforming to the 

confinement requirements in Table 8-5, located within the middle third 

of the wall length, the drift capacity may be taken as 4%.

• For other cases of walls with integral concrete columns, the drift capacity 

may be taken as the larger of:

o the drift capacity determined for the wall or vertical wall segment, 

excluding consideration of the integral concrete column; or 

o the drift capacity determined for a segment of wall on either side of 

the column, treated as a half-barbell section, with the column 

assumed to be located at the compression end of the segment.

Table 8-5 Minimum Transverse Reinforcement in Integral Columns or 

Boundary Elements Required to be Classified as Confined

Transverse 

Reinforcement

Applicable 

Expression

sh

c

A

sb

 for rectilinear hoops(1) Greater of: .   ′   −

 

g c

ch yt

A f

A f

02 1 and . ′

c

yt

f

f

0 06

ρs for spiral or circular hoops Greater of: .   ′   −

 

g c

ch yt

A f

A f

03 1 and . ′

c

yt

f

f

0 08

(1) To be considered for purposes of confinement, transverse reinforcement must have 135 

degree hooks and spacing of no more than 8 inches.
FEMA P-2018 8: Evaluation Procedures for Bearing Wall Systems 8-9 

8.7.2 Drift Capacity of Other Critical Components

If columns and other related components (e.g., slab-column connections, 

beam-column corner connections, and discontinuous columns) are designated 

as critical, drift capacities shall be determined in accordance with Section 7.7.

8.8 Determine Wall and Column Ratings

8.8.1 Determine Wall Ratings 

Determine wall ratings, WR, for critical walls and vertical wall segments, as 

the ratio of drift demand to drift capacity, ∆D/∆C, in accordance with Table 

8-6, for earthquake loading in each direction. 

Table 8-6 Wall Rating, WR

Drift Demand to Drift Capacity Ratio

∆D/∆C Wall Rating, WR

∆D/∆C ≤ 0.25 0.0

0.4 ≥ ∆D/∆C > 0.25 0.1

0.5 ≥ ∆D/∆C > 0.4 0.2

0.7 ≥ ∆D/∆C > 0.5 0.3

0.9 ≥ ∆D/∆C > 0.7 0.4

1.1 ≥ ∆D/∆C > 0.9 0.5

1.4 ≥ ∆D/∆C > 1.1 0.6

1.8 ≥ ∆D/∆C > 1.4 0.7

2.5 ≥ ∆D/∆C > 1.8 0.8

3.0 ≥ ∆D/∆C > 2.5 0.9

∆D/∆C > 3.0 0.93

8.8.2 Determine Column Ratings

If columns and other related components (e.g., slab-column connections, 

beam-column connections, and discontinuous columns) are designated as 

critical, column ratings, CR, shall be determined in accordance with Section 

7.8. 

For the purpose of calculating the story rating, SR, in Equation 8-9, unrated 

columns should be assigned a CR of 0. 

8.9 Determine Story Ratings

The story rating is a number representing the relative likelihood that an 

individual story will lose its ability to support vertical loads under the 

assumed earthquake loading. Determine the story rating, SR, as:
8-10 8: Evaluation Procedures for Bearing Wall Systems FEMA P-2018

SR = 1.5Radj – 0.1 (8-9) 

where:

Radj = the adjusted average of column and wall ratings in the story, 

defined by Equation 8-10 

The story rating, SR, shall not be taken less than 0.1 nor greater than 0.9. 

Low values of story rating, SR, indicate a low likelihood of failure, while 

high values indicate a high likelihood of failure. 

The adjusted average of column and wall ratings in the story, Radj, is defined:

Radj = Ravg + 0.625Ravg(COV – 0.4) (8-10) 

where:

Ravg = , ,

1 1

col wall n n

col i i wall j j

i j

f CR f WR = =

∑ ∑+ (8-11) 

and: 

Ravg = the weighted average rating for all columns and walls in the 

story, in which the values are weighted by the gravity load 

taken by each column or wall at the critical story

fcol,i = fraction of gravity loads in the critical story supported by 

column i

fwall,j = fraction of gravity loads in the story supported by wall j (note: 

the sum of the fraction of gravity loads supported by all 

columns and walls must equal 1.0 in each story) 

ncol = number of columns in a story 

nwall = number of walls in a story 

COV = the standard deviation of all the column and wall ratings at the 

critical story, divided by the weighted average rating, Ravg, at 

that story 

In Equations 8-10 and 8-11, Radj shall not be taken less than Ravg, nor greater 

than 1.25Ravg. 

In calculating Ravg, every column location in a story is assigned a column 

rating, CRi, and each wall location in a story is assigned a wall rating, WRj, 

determined by the highest rating for any critical column or wall element at 

that location, or for any supported critical beam-column corner connection or 

critical slab-column connection at that location, in either horizontal direction. 

The fraction of the gravity load taken by the column, fcol,i, or wall, fwall,j, at 

each location is used to weight the calculations of the average. 
FEMA P-2018 9: Evaluation Procedures for 9-1 

Infilled Frame Systems

Chapter 9 

Evaluation Procedures for 

Infilled Frame Systems

This chapter covers the evaluation of buildings classified as infilled frame 

systems, as defined in Section 5.3.4. 

9.1 Introduction

The procedures for infilled frame systems parallel the procedures for frame 

systems in Chapter 6 and frame-wall systems in Chapter 7. Infilled frame 

systems include masonry infill walls, referred to as panels, and could include 

reinforced concrete structural walls, referred to as walls. Infilled frame 

systems also include infilled-frame columns, with infill panels abutting the 

column on one or both sides in the direction of loading, and bare-frame 

columns, without abutting infill panels. Classification of infill in accordance 

with Section 5.3.4 affects the strength of the infilled bay, how the infill is 

presumed to interact with the columns, and how the infill is considered in the 

evaluation methodology. 

Evaluation of infilled frame systems is focused on comparing drift demands 

with drift capacities of infilled-frame columns and bare-frame columns, as 

well as slab-column connections, walls, and vertical wall segments (or wall 

piers) where they exist in the building. Component demand-to-capacity 

ratios are used to define column, wall, and wall segment ratings. Column 

ratings for infilled-frame columns include consideration of the presence of 

infill panels assisting in the gravity load-carrying capacity of the columns. 

Column and wall ratings are combined to determine story ratings, which are 

used in Chapter 10 to determine the building rating. 

Section 9.2 defines critical stories along each of two horizontal earthquake 

loading directions based on the results of the mechanism analyses of Section 

5.5. Section 9.3 defines critical components, which include infilled-frame 

columns and bare-frame columns located in critical stories. Other critical 

components could include slab-column connections, corner beam-column 

connections, discontinuous columns satisfying certain criteria, walls, and 

vertical wall segments. Sections 9.4 through 9.6 define the drift demands 

that are considered for each critical component. Section 9.7 defines drift 
9-2 9: Evaluation Procedures for FEMA P-2018

Infilled Frame Systems

capacities, and a comparison of drift demands to drift capacities in Section 

9.8 establishes individual column and wall ratings for critical components. 

9.2 Identify Critical Stories

Using the controlling plastic mechanism along each of the two principal 

framing directions determined in Section 5.5, critical stories are defined in

infilled frame systems in accordance with the following: 

• Where Mechanism 1 controls the strength along a principal framing 

direction, the critical story in that direction is the first story above the 

base. 

• Where Mechanism 3 controls the strength along a principal framing 

direction, the critical story in that direction is the story in which 

Mechanism 3 forms.

Infilled frame systems can be presumed to be controlled by Mechanism 1, 

unless a significant discontinuity in infill strength or configuration along the 

height, or potential out-of-plane failure, warrants consideration of 

Mechanism 3. It is possible for different plastic mechanisms to control along 

each of the two principal framing directions. In such cases, the critical story 

in one principal direction may differ from the critical story in the other 

principal direction. 

Critical stories are also defined where adjacent buildings require pounding 

considerations in accordance with Section 5.10. 

9.3 Identify Critical Components

Critical components are those components deemed to be most vulnerable to 

damage and loss of vertical load-carrying ability. Critical components are 

evaluated in accordance with the procedures in Sections 9.6 through 9.8. 

9.3.1 Critical Columns in Infilled Frame Systems

Columns in critical stories of infilled frame systems (defined in Section 9.2) 

are designated as critical components. Critical columns in infilled frame

systems include columns with infill walls abutting the column on one or both 

sides in the direction of loading and bare-frame columns. Infill wall panels 

are not considered critical components and are not rated. The effects of infill 

panels are considered in the rating of critical columns in Section 9.8.1. 

9.3.2 Other Critical Components

Bare-frame columns below one or more panels of discontinuous masonry 

infill can be critical. Columns below discontinuous masonry infill classified 
FEMA P-2018 9: Evaluation Procedures for 9-3 

Infilled Frame Systems

as strong in Section 5.4.3, should be evaluated in accordance with Section 

5.9.2. Where they occur, other bare-frame columns, walls and vertical wall 

segments, columns integral with walls, slab-column connections, beamcolumn corner connections, and discontinuous columns and walls are 

identified as critical in accordance with Section 7.3. 

9.4 Calculate Global Seismic Drift Demand

Calculate the global seismic drift (displacement) demand for an equivalent 

single-degree-of-freedom (SDOF) system, δeff, as:

2

2 4

e

eff 1 2 a

T δ CCS g

π = (9-1) 

where:

C1 = modification factor to relate expected maximum inelastic 

displacement to displacement calculated for linear elastic 

response

C2 = modification factor to represent the effect of pinched hysteresis 

shape, cyclic stiffness degradation, and strength deterioration on 

maximum displacement response 

Te = effective fundamental period determined in Section 5.6

Sa = spectral acceleration at period, Te

g = acceleration of gravity

Calculate coefficient C1 in accordance with ASCE/SEI 41-17 as:

C1 = 2

1

1 strength

e aT

μ − + (9-2) 

where a is a site class factor equal to: 130 for Site Class A or B; 90 for Site 

Class C; 60 for Site Class D, E, or F; and all other terms are as previously 

defined. For Te < 0.2 seconds, C1 need not be taken greater than the value at 

Te = 0.2 seconds. For Te ≥ 1 second, C1 = 1.0. 

Calculate coefficient C2 in accordance with ASCE/SEI 41-17 as:

C2 =

2

1 1

1

800

strength

Te

  μ − +    

(9-3) 

where all terms are as previously defined. For Te > 0.7 seconds, C2 = 1.0. 

Global seismic drift demands are calculated in each direction of earthquake 

loading.
9-4 9: Evaluation Procedures for FEMA P-2018

Infilled Frame Systems

9.5 Calculate Story Drift Demand

Calculate story drift demand, δx, of story x as:

eff

x x sx eff

eff

h

h

δ

δα δ

  =   ≤    

(9-4) 

where:

αx = coefficient to modify story drifts at story x for building 

configuration and strength characteristics

hsx = height of story x

δeff = global displacement demand of the equivalent SDOF system

(Equation 9-1)

heff = effective height of the building, defined as the height from the 

base to the centroid of lateral forces (may be taken as 0.7hn in 

multistory buildings having uniform distribution of effective 

weight over the building height and hn in single-story buildings) 

hn = height from the base of the building to the highest level of the 

seismic force-resisting system

Story drift demands are calculated in each direction of earthquake loading.

Coefficient α modifies story drifts considering number of stories in a 

building, the yield mechanism, and whether the story is a critical story. 

Values of coefficient α for infilled frame systems are provided in Table 9-1. 

Table 9-1 Values of Coefficient α for Infilled Frame Systems

(1) Values of α for “Other Stories” are generally not used, except where components in 

other stories are designated as critical because of increased local vulnerability, as 

required in Section 9.3. 

9.6 Calculate Drift Demands in Critical Components

9.6.1 Adjusted Drift Demand on Critical Components

For each critical component (see Section 9.3), calculate the adjusted drift 

demand, ∆D, as follows:

ΔD = ATγ δx (9-5) 

No. of 

Stories in the 

Building

Yield 

Mechanism

Values of α

Critical Stories Other Stories(1)

1 (any) 1.0 (n/a)

≥2 1, 3 0.8heff/hsx 0.5
FEMA P-2018 9: Evaluation Procedures for 9-5 

Infilled Frame Systems

where: 

ΑT = torsional amplification factor (Section 9.6.2) 

γ = fraction of story drift affecting the critical component 

(Section 9.6.3)

δx = story drift demand (Section 9.5) 

9.6.2 Torsional Amplification Factor

Determine the torsional amplification, ΑT, at the location of each critical 

component. The torsional amplification, ΑT, varies linearly in plan between 

a value of 1.0 at the center of strength and a value of AT,max at the edge of the 

building furthest from the center of strength (i.e., the weak or flexible side of 

the building). For all components located on the strong or stiff side of the 

building (between the center of strength and the edge of the building closest 

to the center of strength), ΑΤ = 1.0. 

9.6.2.1 Calculation of Maximum Torsional Amplification 

Factor 

The maximum torsional amplification factor, AT,max, is calculated in 

accordance with Equation 7-6, but should not be taken less than 1. 

AT,max = 2.75(TR) + 0.5 (9-6) 

where TR is the torsional ratio. The maximum torsional amplification factor, 

AT,max, may be taken as 1.0 if the wall index, WI < 0.0004, or if the torsional 

ratio, TR < 0.25. 

9.6.2.2 Calculation of Torsional Ratio

In Equation 9-6, TR shall be taken as the value of torsional ratio, TRx, at the 

critical story, unless there is a significant torsional irregularity in another 

story. TRx is the torsional ratio for story x, calculated as:

Dx

x

Cx

T TR

T = (9-7) 

where TDx is the torsion demand on story x, and TCx is the torsion capacity 

(strength) of story x. Torsion demand, TDx, is directional, and must be 

calculated for each direction of earthquake loading:

TDx = Vpxe (9-8) 

where:

Vpx = plastic shear capacity of the critical story, as calculated in 

Chapter 5 
9-6 9: Evaluation Procedures for FEMA P-2018

Infilled Frame Systems

e = eccentricity between the center of mass and the center of 

strength in the direction perpendicular to the direction of 

earthquake loading; e may not be taken as less than 5% of L

(i.e., 0.05L), where L is the overall plan dimension 

perpendicular to the direction of earthquake loading 

The coordinates of the center of strength, ( ) x y, , are calculated from:

1

1

f

f

n

i pfi

i

n

pfi

i

xV

x

V

=

=

=

∑

∑

, 1

1

f

f

n

i pfi

i

n

pfi

i

y V

y

V

=

=

=

∑

∑

(9-9) 

where:

x, y = are the orthogonal distance between the frame, infilled frame, or 

wall line of interest and an established reference point 

Vpfi = is the plastic capacity of frame, infilled frame, or wall line i

nf = is the number of frame or wall lines in story x, considering all 

frame, infilled frame, or wall lines that resist torsion. 

Torsion capacity, TC, is calculated considering the capacity of all frame, 

infilled frame or wall line in all orientations, and is the same regardless of the 

direction of loading considered: 

1

f n

Cx fi pfi

i

T RV =

= ∑ (9-10) 

where Rf is the orthogonal distance between frame, infilled frame, or wall 

line line i and the center of strength, and all other terms are as previously 

defined. 

9.6.2.3 Identification of Exceptionally High Seismic Risk 

Buildings based on the Torsional Ratio

Infilled frame systems with extreme torsion shall be classified as 

exceptionally high seismic risk buildings without further evaluation. A 

building is considered to have extreme torsion if the torsional ratio, TR > 1.5. 

9.6.3 Drift Factor

The drift factor, γ, defines the fraction of story drift demand, δx, affecting 

critical components. Values of drift factor, γ, for critical components are 

defined in the sections that follow. 
FEMA P-2018 9: Evaluation Procedures for 9-7 

Infilled Frame Systems

9.6.3.1 Drift Factor for Infilled-Frame Columns

For columns with infill panels abutting the column on one or both sides in 

the direction of loading, γ = 1.0. 

9.6.3.2 Drift Factor for Other Components

If other bare-frame columns, walls and vertical wall segments, columns 

integral with walls, slab-column connections, beam-column corner 

connections, and discontinuous columns and walls are identified as critical, 

drift factors shall be determined in accordance with Section 7.6.3. 

The drift factor for other columns, in general, depends on the ratio of the 

strength of columns to the strengths of horizontal members framing into the 

column. For bare-frame columns in infilled frame systems, if the movement 

of beams framing into the column in the direction of loading is restrained by 

infill walls, γ = 1.0. 

9.7 Calculate Drift Capacity of Critical Components

Calculate drift capacities of critical components in accordance with this 

section.

9.7.1 Drift Capacity of Critical Columns in Infilled Frame

Systems 

Calculate the drift capacity of critical columns in infilled frame systems as:

Δc = lu,inf(θc + 0.01) (9-11) 

where:

lu,inf = effective height of column in infilled frame (Table 9-2) 

θc = column plastic rotation capacity 

Table 9-2 Effective Height of Columns in Infilled Frame Systems

Effective Height of Column lu,inf

Bare-frame column lu

Columns with abutting infill on one 

or both sides in the direction of 

loading 

lu/2

Partial height infills Clear height of the column that does not have 

abutting infill

Columns with abutting infill with 

openings on one or both sides in the 

direction of loading

Where an opening exists within a 

distance of dop < hinf/2 of the column, the 

effective height of the column is taken as 

the height of the opening, hop. 

Otherwise, use lu/2.
9-8 9: Evaluation Procedures for FEMA P-2018

Infilled Frame Systems

In Table 9-2, lu is the clear height of the column, and infill panel dimensions, 

dop, hinf, and hop are as defined in Section 4.3.6. 

Calculate column plastic rotation capacity θc in accordance with Table 9-3 

for tied columns and Table 9-4 for spiral-reinforced columns. Column 

plastic rotation capacity, θc, is based on the column shear strength ratio, 

Vp/Vn, axial load ratio, P/Ag ce f ′ , and shear reinforcement ratio, ρt. Except for 

corner columns, the axial load ratio is based on the gravity load, Pg, 

determined in accordance with Section 4.2. For corner columns, the axial 

load ratio is based on the total column axial load, P = Pg + Peq, where P is 

positive in compression, and Pg and Peq are determined in accordance with 

Section 4.2. For the purpose of calculating the plastic rotation capacity of 

infilled-frame columns, the infill panel is assumed to support no gravity load. 

Table 9-3 Plastic Rotation Capacities for Tied Columns(1), (2), (3), (4)

Flexure-Critical Columns (Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5)

For .     ≥     ′ g ce

P

A f

0 1 θ ρ ( ρ )  

= +− + ≥       ′ c t t

g ce

P

A f

11.4 0.034 14 0.036 0.0

For .     <     ′ g ce

P

A f

0 1 θ ρ = +≥ . . c t 10 0 03 0 0

Flexure-Shear and Shear-Critical Columns (i.e., Columns not classified as Flexure-Critical Columns)

For .     ≤     ′ g ce

P

A f

0 5

,min

. .

.

θ θ

ρ

′

′

= − ≥

+

c c

ce

g ce t ye

P f

A f f

0 5 0 01 1 5

0 8

P/Ag f′ce should not be taken smaller than 0.1

θc should be reduced linearly for .     >     ′ g ce

P

A f

0 5 from its value at .     =     ′ g ce

P

A f

0 5 to zero at .     =     ′ g ce

P

A f

0 7

,min θ ρ .. . . .    

=− + − ≥           ′

p

c t

g ce n

P V

A f V

0 042 0 023 0 63 0 023 0 0

P/Ag f′ce should not be taken smaller than 0.1

(1) ρt should not be taken greater than 0.0175 in any case, nor greater than 0.0075 when ties are not adequately 

anchored in the core.

(2) Vp/Vn should not be taken less than 0.2.

(3) θc for flexure-shear and shear-critical columns shall not exceed θc for a flexure-critical column with the same 

condition. 

(4) P = Pg, except for corner columns where P = Pg + Peq. 

Tables 9-3 and 9-4 are divided between flexure-critical columns and other 

columns (flexure-shear or shear-critical columns). Flexure-critical columns 

are columns with Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5. Flexure-shear or 

shear-critical columns are defined as columns not classified as flexure-
FEMA P-2018 9: Evaluation Procedures for 9-9 

Infilled Frame Systems

critical. The calculation of Vp/Vn should consider the impact of the infill in 

reducing the effective height of the column. The effective height of columns 

in infilled frame systems is provided in Table 9-2. Effective heights should 

be used when the infill panel is classified as “strong,” “weak,” or “very weak 

with openings” in Section 5.3.4, even if the infill panel strength is ignored in 

strength calculations. 

Table 9-4 Plastic Rotation Capacities for Spiral-Reinforced Columns(1), (2), (3), (4)

Flexure-Critical Columns (Vp/Vn ≤ 0.6, ρt > 0.002, and s/d < 0.5)

For .     ≥     ′ g ce

P

A f

0 1 θρ ρ .. . ( . . )

    =  + −   +  ≥         ′ c t t

g ce

P

A f

1 15 11 4 0 034 14 0 036 0 0

For .     <     ′ g ce

P

A f

0 1 θ ρ c t = +≥ 1 15 10 0 03 0 0 . .. [ ]

Flexure-Shear and Shear-Critical Columns (i.e., Columns not classified as Flexure-Critical Columns)

For .     ≤     ′ g ce

P

A f

0 5

,min

. .

.

θ θ

ρ

= − ≥ ′ + ′

c c

ce

g ce t ye

P f

Af f

0 65 0 01 1 5

0 8

P/Ag f′ce should not be taken smaller than 0.1

θc should be reduced linearly for .     >     ′ g ce

P

A f

0 5 from its value at .     =     ′ g ce

P

A f

0 5 to zero at .     =     ′ g ce

P

A f

0 7

θ ρ .. . . .     =− + − ≥           ′

p

c,min t

g ce n

P V

A f V

0 06 0 06 1 3 0 037 0 0

P/Ag f′ce should not be taken smaller than 0.1

(1) ρt should not be taken greater than 0.0175 in any case, nor greater than 0.0075 when ties are not adequately 

anchored in the core.

(2) Vp/Vn should not be taken less than 0.2.

(3) θc for flexure-shear and shear-critical columns shall not exceed θc for a flexure-critical column with the same 

condition. 

(4) P = Pg, except for corner columns where P = Pg + Peq. 

9.7.2 Drift Capacity of Other Critical Components

If other columns and related components (e.g., slab-column connections, 

beam-column corner connections, and discontinuous columns) are designated 

as critical, drift capacities shall be determined in accordance with Section 7.7.

9.7.3 Drift Capacity of Critical Walls and Vertical Wall Segments

If walls and wall segments are identified as critical, drift capacities shall be 

determined in accordance with Section 7.7.4. 
9-10 9: Evaluation Procedures for FEMA P-2018

Infilled Frame Systems

9.8 Determine Column and Wall Ratings

Column and wall ratings represents the relative likelihood that an individual 

column, supported slab, or wall will lose its ability to support vertical loads 

under the assumed earthquake loading. Ratings near 0.0 indicate a low 

likelihood of failure, while ratings near 1.0 indicate a high likelihood of 

failure.

9.8.1 Determine Ratings for Columns in Infilled Frame Systems

Determine column ratings, CR, for critical columns in infilled frame systems, 

as the ratio of drift demand to drift capacity, ∆D/∆C, in accordance with Table 

9-5, for earthquake loading in each direction. 

Table 9-5 Column Rating, CR

Drift Demand to Drift Capacity Ratio

∆D/∆C Column Rating, CR

∆D/∆C ≤ 0.25 0.0

0.4 ≥ ∆D/∆C > 0.25 0.1

0.5 ≥ ∆D/∆C > 0.4 0.2

0.7 ≥ ∆D/∆C > 0.5 0.3

0.9 ≥ ∆D/∆C > 0.7 0.4

1.1 ≥ ∆D/∆C > 0.9 0.5

1.4 ≥ ∆D/∆C > 1.1 0.6

1.8 ≥ ∆D/∆C > 1.4 0.7

2.5 ≥ ∆D/∆C > 1.8 0.8

3.0 ≥ ∆D/∆C > 2.5 0.9

∆D/∆C > 3.0 0.93

If a column has infill panels that remain intact on both sides in the direction 

of loading, and there is no gap between the infill panel and the beam, the 

infill panels can be assumed to provide assistance in supporting gravity 

loads. Table 9-6 provides criteria for measuring the integrity of the infill 

panels based on in-plane and out-of-plane response, based on the drift at 

onset of residual strength, provided in Table 9-7. 

Values in Table 9-6 are added to values provided in Table 9-5 to obtain a 

total rating for infilled-frame columns. In no case shall the total column 

rating, CR, including assistance provided by the infill panels, be taken less 

than zero. 
FEMA P-2018 9: Evaluation Procedures for 9-11

Infilled Frame Systems

Table 9-6 Assistance to Column Ratings Based on Infill Panel Response(1) (2)

Measure of out-of-plane 

response

Measure of In-Plane Response 

δ < Δres δ ≥ 2Δres (3)

hinf/tinf < 25 -0.3 0 

hinf/tinf ≥ 35 0 0 

(1) Assistance is taken as 0 if there are openings within a distance of 2 feet on either side of 

the column in the direction of loading.

(2) For intermediate values, assistance can be calculated by linear interpolation.

(3) ∆res is the drift at the onset of residual strength, provided in Table 9-7.

Table 9-7 Drift at Onset of Residual Strength, ∆res, for Infilled Bays

Aspect 

Ratio Weak Infill Strong Infill(1) 

hinf/Linf <1 

for column Vp/Vn < 1, Δres = 0.01hsx

for column Vp/Vn ≥ 1, Δres = 0.0055hsx

1.6Δpeakhsx

hinf/Linf ≥ 1 Δres = 0.01hsx

(1) Δpeak is the drift at which the infill reaches peak strength, provided in Table 5-2.

9.8.2 Determine Ratings for Other Critical Components

If other columns, walls, and other related components (e.g., slab-column 

connections, beam-column connections, and discontinuous columns) are 

designated as critical, column ratings, CR, and wall ratings, WR, shall be 

determined in accordance with Section 7.8.

9.9 Determine Story Ratings

The story rating is a number representing the relative likelihood that an 

individual story will lose its ability to support vertical loads under the 

assumed earthquake loading. Determine the story rating, SR, as:

SR = 1.5Radj – 0.1 (9-12) 

where:

Radj = the adjusted average of column and wall ratings in the story, 

defined by Equation (9-13) 

The story rating, SR, shall not be taken less than 0.1 nor greater than 0.9. 

Low values of story rating, SR, indicate a low likelihood of failure, while 

high values indicate a high likelihood of failure. 

The adjusted average of column and wall ratings in the story, Radj, is defined 

as:

Radj = Ravg + 0.625Ravg(COV – 0.4) (9-13) 
9-12 9: Evaluation Procedures for FEMA P-2018

Infilled Frame Systems

where:

Ravg = , ,

1 1

col wall n n

col i i wall j j

i j

f CR f WR = =

∑ ∑+ (9-14) 

and: 

Ravg = the weighted average rating for all columns and walls in the 

story, in which the values are weighted by the gravity load 

taken by each column or wall 

fcol,i = fraction of gravity loads supported by column i. For the 

purpose of weighting column ratings, infill panels are not 

assumed to carry gravity load, and the columns are assumed to 

carry all tributary gravity load

fwall,j = fraction of gravity loads in a story supported by wall j (note: the 

sum of the fraction of gravity loads supported by all columns 

and walls must equal 1.0 in each story) 

ncol = number of columns in a story 

nwall = number of walls in a story 

COV = the standard deviation of all the column and wall ratings at a 

story divided by the weighted average rating, Ravg, at that story

In Equations 9-13 and 9-14, Radj shall not be taken less than Ravg, nor greater 

than 1.25Ravg. 

In calculating Ravg, every column location in a story is assigned a column 

rating, CRi, and each wall location in a story is assigned a wall rating, WRj, 

determined by the highest rating for any critical infilled frame column, bareframe column, or wall element at that location, or for any supported critical 

beam-column corner connection or critical slab-column connection at that 

location, in either horizontal direction. The fraction of the gravity load taken 

by the column, fcol,i, or wall, fwall,j, at each location is used to weight the 

calculation of the average. 
FEMA P-2018 10: Determination of Building Rating 10-1 

Chapter 10

Determination of

Building Rating

This chapter describes the determination of building ratings based on story 

ratings for frame, frame-wall, bearing wall, and infilled frame systems

calculated in the preceding chapters. It also describes the recommended use 

of building ratings in ranking buildings within an inventory, and prioritizing 

buildings for future work. 

10.1 Introduction

The building rating, BR, is a number between 0.1 and 0.9, inclusive, 

representing the relative likelihood that the building will lose its ability to 

support vertical loads under the assumed earthquake loading. Building 

ratings can be used to rank the relative risk of partial or complete collapse 

among buildings in an inventory of buildings. Use of building ratings in a 

program to reduce the seismic risk associated with older concrete buildings is 

described in Section 1.4. 

10.2 Determine Building Rating

The building rating, BR, is taken as the maximum story rating, SR, 

determined in either direction, for critical stories over the height of a 

building. Story ratings between 0.1 and 0.9 for frame, frame-wall, bearing 

wall, and infill frame systems calculated in Chapters 6 through 9 are used to 

determine the building rating, BR. 

10.3 Recommended Building Risk Levels

In some cases, classification of buildings in Chapter 5 results in the early 

identification of buildings as either lower seismic risk buildings or 

exceptionally high seismic risk buildings based on certain features or 

characteristics.

In other cases, the building rating, BR, is used to rank the relative risk of 

buildings in an inventory of buildings, and to assign buildings within three 

relative risk levels: exceptionally high seismic risk buildings, high seismic 

risk buildings, and lower seismic risk buildings. 
10-2 10: Determination of Building Rating FEMA P-2018

10.3.1 Exceptionally High Seismic Risk Buildings

Buildings identified as exceptionally high seismic risk buildings in Chapter 5, 

or assigned a building rating, BR, greater than or equal to 0.7 shall be 

considered as a class, exceptionally high seismic risk buildings. 

Exceptionally high seismic risk buildings are considered the highest level of 

relative risk and should be given the highest priority for further evaluation 

(or mitigation) among older concrete buildings in an inventory.

10.3.2 High Seismic Risk Buildings

Buildings assigned a building rating, BR, greater than 0.3 but less than 0.7 

shall be considered as a class, high seismic risk buildings. 

High seismic risk buildings should be given an intermediate priority for 

further evaluation (or mitigation) among older concrete buildings in an 

inventory. 

10.3.3 Lower Seismic Risk Buildings

Buildings identified as lower seismic risk buildings in Chapter 5, or assigned 

a building rating, BR, less than or equal to 0.3 shall be considered as a class, 

lower seismic risk buildings. 

Lower seismic risk buildings are considered the lowest level of relative risk 

and could include buildings of very low risk meeting conventional life safety 

standards. Lower seismic risk buildings should be given the lowest priority 

for further evaluation (or mitigation) among older concrete buildings in an 

inventory. 
FEMA P-2018 A: Development of Column Drift Capacities A-1 

Appendix A 

Development of Column Drift 

Capacities

A.1 Introduction

Column ratings are a critical input to the determination of story ratings and 

building ratings in this methodology. Column drift capacities are used in the 

calculation of column ratings. This appendix describes how column drift 

capacities, which are a combination of plastic rotation capacity and the 

elastic drift capacity, were determined, and how uncertainty was included in 

the determination of column ratings. 

A.2 Column Plastic Rotation Capacity Determination

Column plastic rotation capacities, θc, are intended to represent the 

deformation at which the column is expected to lose its gravity-load bearing 

capacity. In all cases, drift capacities are based on experimental test data of 

reinforced concrete components, and intended to represent median capacities 

(i.e., there is a 50% chance that the true capacity is higher - or lower - than 

the value reported). As a result, the drift capacities may differ from those 

published elsewhere in cases where other publications intended to produce 

lower bound or conservative estimates of drift capacity.

The derivation of column plastic rotation capacities, θc, in this methodology 

differs depending on the expected failure mode of the column. For columns 

expected to fail in flexure, θc was obtained by adapting the tables provided in 

ASCE/SEI 41-13, Seismic Evaluation and Retrofit of Existing Buildings

(ASCE, 2013). For flexure-shear and shear critical columns, mechanicsbased equations are used, as proposed by the ACI 369 committee

(Ghannoum, 2017). For both sets of equations, predictions of θc are intended 

to produce a consistent 50% probability that the observed value will exceed 

the predicted value, such that all values are medians. These predictions were 

investigated to ensure that there was no bias with respect to axial load ratio, 

transverse reinforcement ratio, and other column design parameters. As a 

result, the equations are intended to provide median values, regardless of the 

properties of a column.
A-2 A: Development of Column Drift Capacities FEMA P-2018

A.2.1 Plastic Rotation Capacities for Flexure-Critical Columns 

Flexure-critical columns are those with Vp/Vn ≤ 0.6, ρt > 0.002 and s/d < 0.5. 

Equations defining column plastic rotation capacities for flexure-critical 

columns in this methodology were obtained by adapting the tables provided 

in ASCE/SEI 41-13. Values of θc were based on b (rather than a) values, as 

defined in ASCE/SEI 41-13, because this methodology is aimed at

quantifying column failure, and the axial limit state is judged to occur at, or 

near, the time of failure. Values of θc in this methodology are based on the 

same experimental tests of rectangular columns used to develop b values in

ASCE/SEI 41-13, but reported values differ in two ways: (1) they represent 

median values; and (2) they are equation-based rather than tabular. An 

adjustment for circular columns based on additional data is also proposed. 

A.2.2 Plastic Rotation Capacities for Flexure-Shear and ShearCritical Columns 

Flexure-shear or shear-critical columns are defined as those columns not 

classified as flexure-critical. Plastic rotation capacity equations for 

rectangular and circular columns are based on a mechanics-based equation

developed by Elwood and Moehle (2005). A mechanics-based equation was

better suited for this purpose than a statistics-based equation because of the 

limited amount of experimental shear-critical column tests carried out to 

axial failure. The model is further simplified based upon recommendations 

in Ghannoum and Matamoros (2014) by assuming a critical shear crack angle 

of 65 degrees from horizontal. The provided equations are taken from 

Ghannoum and Matamoros (2014) and also printed in Ghannoum (2017). 

These equations are not used for flexure-critical columns because of the 

mechanics-based approach used to develop the equations, which presumes a 

shear or flexure-shear failure.

A.2.3 Bias in Plastic Rotation Capacity Predictions

The prediction equations for θc are evaluated through comparison with a 

database of experimental column tests. The database of column tests that 

was assembled for use in development of deformation capacity predictions in

ASCE/SEI 41-13 was leveraged here (Ghannoum, 2017; Ghannoum and 

Sivaramakrishnan, 2012a and 2012b). All tests were conducted quasistatically on columns that did not contain splice or anchorage deficiencies. 

In the test data, the point of axial failure was identified as either the 

deformation at which axial collapse was observed during the experiment, or 

the deformation at which the lateral strength degrades to 25% of its peak 

strength. A more detailed description of the experimental database is 

provided in Ghannoum (2017). 
FEMA P-2018 A: Development of Column Drift Capacities A-3 

The relationship between the predicted values for θc and those observed 

during experimental testing (quantified as the ratio of the measured to 

predicted θc) is presented for columns other than spirally-reinforced circular 

columns in Figure A-1, and for spirally-reinforced circular columns in Figure 

A-2. Figure A-1 shows that prediction equations for columns other than 

spirally-reinforced circular columns are not biased with respect to axial load 

ratio (Figure A-1a), transverse reinforcement ratio (Figure A-1b), and 

column Vp/Vn (Figure A-1c). Figure A-2 indicates that prediction equations 

for spirally-reinforced circular columns are also not biased with respect to 

axial load ratio (Figure A-2a), transverse reinforcement ratio (Figure A-2b), 

and Vp/Vn (Figure A-2c).

(a) (b)

(c)

Figure A-1 Ratio of measured to predicted plastic rotation at axial failure for columns 

other than spirally-reinforced circular columns as a function of: (a) axial load 

ratio; (b) transverse reinforcement ratio; and (c) Vp/Vn. 
A-4 A: Development of Column Drift Capacities FEMA P-2018

(a) (b)

(c)

Figure A-2 Ratio of measured to predicted plastic rotation at axial failure for spirallyreinforced circular columns as a function of: (a) axial load ratio; (b) transverse 

reinforcement ratio; and (c) Vp/Vn. 

A.2.4 Comparison of Plastic Rotation Capacity Prediction

Methods

The characteristics of the final deformation capacity prediction equations

used in this methodology were compared against alternative methods in

Figure A-3 and Figure A-4. Figure A-3 compares predicted values of plastic 

rotation capacity for for columns other than spirally-reinforced circular 

columns, and Figure A-4 compares plastic rotation capacities for spirallyreinforced circular columns.

Three different methods for prediction of plastic rotation capacity are 

compared in Figure A-3 and Figure A-4: (1) the plastic rotation capacity as 

predicted in ATC-78-3, Seismic Evaluation of Older Concrete Frame 

Buildings for Collapse Potential (ATC, 2015); (2) equations in Ghannoum 

(2017); and (3) the final deformation capacity prediction equations developed 

in ATC-78-5, Seismic Evaluation of Older Concrete Frame, Wall, and 

Frame-Wall Buildings for Collapse Potential (ATC, 2016) and used herein, 
FEMA P-2018 A: Development of Column Drift Capacities A-5 

labeled ATC-78-5. Tables in ATC-78-3 are based on the data used in 

ASCE/SEI 41-13 for both flexural and shear-critical columns, but are in 

tabular form rather than equation form. Prediction equations from 

Ghannoum (2017) have been used by ACI Committee 369 and implemented 

in ASCE/SEI 41-17 (which supersedes the 2013 edition of ASCE/SEI 41). 

(a)

(b)

Figure A-3 Comparison of relationship between axial load ratio and plastic 

rotation capacity using different prediction methods for columns 

other than spirally-reinforced circular columns with transverse 

reinforcement ratio equal to: (a) 0.002; and (b) 0.006. 

The form of the ATC-78-3 and Ghannoum (2017) prediction methods are 

quite different with respect to axial load ratio, and the form of the ATC-78-5 

prediction equations is a modified combination of the two. The following

observations highlight the differences between the three prediction methods:

• The ATC-78-5 prediction for θc follows the form of the ATC-78-3 

prediction for flexure controlled columns (i.e., Vp/Vn = 0.6 in Figure A-3 

and Figure A-4). However, the ATC-78-5 prediction decreases to zero 

for column axial load ratios greater than or equal to 0.7. Furthermore, 

the ATC-78-5 prediction is 15% larger than the ATC-78-3 prediction for 

flexurally controlled, spirally-reinforced, circular columns. This 

adjustment was made based upon new experimental test results used in 

the development of the ATC-78-5 method. 

• For flexure-shear and shear critical columns (i.e., Vp/Vn = 0.8 and Vp/Vn = 

1.2 in Figure A-3 and Figure A-4), the ATC-78-5 prediction follows the 

form of the Ghannoum (2017) equations. However, for columns with 
A-6 A: Development of Column Drift Capacities FEMA P-2018

low axial load ratios (< 0.1) and low transverse reinforcement ratios 

(0.002), the value of θc is limited to the value of θc computed for flexural 

controlled columns.

(a)

(b)

Figure A-4 Comparison of relationship between axial load ratio and plastic 

rotation capacity using different prediction methods for spirallyreinforced circular columns with transverse reinforcement ratio 

equal to: (a) 0.002; and (b) 0.006. 

A.2.5 Uncertainty in Plastic Rotation Capacities

Experimental data were used to estimate uncertainty in plastic rotation 

capacities. Values shown in Table A-1 quantify uncertainty in the ratio of 

measured to predicted capacities. Values in the table range from 0.62 to 

0.63. 

Table A-1 Uncertainty in Predictions of Column Plastic Rotation Capacity,

Obtained from Comparison with Experimental Data

Condition σln,Δc

θc for flexure-critical columns 0.63

θc for flexure-shear and shear-critical columns 0.62

Uncertainty in the plastic rotation capacity for flexure-critical columns was 

computed from the database of column tests used to develop the tables 

provided in ASCE/SEI 41-13. Uncertainty in the drift capacity prediction for 

flexure-shear and shear-critical columns was taken as the value reported in 
FEMA P-2018 A: Development of Column Drift Capacities A-7

Ghannoum and Matamoros (2014). On the basis of this data, the lognormal 

standard deviation, σln,∆c, was taken to be 0.60. This value includes 

uncertainty in test data and in the empirical model (equation) predicting the 

test result, and has been incorporated in the computation of column ratings.

A.2.6 Elastic Component of Column Drift Capacity

In Section 6.7, the drift capacity of a column is computed from the plastic 

rotation capacity, added to an estimate of the elastic drift capacity. Equation 

6-7 assumes the elastic drift capacity is 1% drift, which is a reasonable value 

from test data. The precise elastic capacity depends on whether or not a 

column fails in shear or flexure, the column stiffness, and other 

characteristics. For the purposes of this methodology, the 1% value was

considered an adequate approximation.

A.2.7 Drift Capacity of Columns with Inadequate Lap Splices

ASCE/SEI 41-13 provides conservative estimates of the deformation 

capacity of columns with inadequate lap splices in longitudinal 

reinforcement. Columns with inadequate lap splices are classified as as 

flexure-critical, or flexure-shear and shear-critical based on the ratio of 

column shear capacity controlled by flexure to column shear capacity 

controlled by shear, Vp/Vn. For this purpose, the potential for lap-splices to 

reduce flexural strength is not considered.

Limited available test data on columns with inadequate lap splices suggest 

that the bond failure of a lap splice may actually increase flexibility and 

deformation capacity in some cases. Due to the limited and scattered nature 

of available data, these columns are treated the same as columns without lap 

splices, and the presence of lap splices is essentially ignored in determining 

the column drift capacity.

A.3 Slab-Column Connection Drift Capacity 

Determination

Drift capacities for slab-column connections were based on 85 slab-column 

tests conducted by various researchers and compiled by Gogus and Wallace 

(2015) and Aslani (2005). Thirty of these tests lacked bottom reinforcement 

through the column, and 55 had bottom reinforcement through the column. 

In these tests, punching failure of the slab-column connection was assumed 

to occur at the drift at which the connection lost 20% of its lateral load 

capacity (i.e., the drift corresponding to 80% of peak lateral load). It should 

be noted that this definition of drift capacity differs somewhat from the 

citeria used to define column drift capacity, which is based on vertical (axial) 
A-8 A: Development of Column Drift Capacities FEMA P-2018

failure. A punching shear definition for slab-column connection collapse 

was used for the following reasons:

• Very few experimental slab-column tests were conducted to vertical 

failure.

• This methodology is only concerned with slab-column connections that 

do not satisfy minimum requirements for continuous bottom 

reinforcement, and vertical failure is anticipated to occur soon after 

punching failure.

The form of the relationship for predicting drift capacity of slab-column 

connections is similar to ACI 318-11, such that the drift is defined as a 

function of the gravity shear ratio, which represents the unfactored vertical 

gravity shear, Vg, divided by the theoretical punching shear strength without 

moment transfer, Vo. However, drift capacities are representative of median 

values and are, therefore, different from the values provided by ACI 318-11. 

Figure A-5 compares the proposed regression to the test data, and the curve 

provided in ACI 318-11. The regression used in this methodology has a 49% 

probability of exceedance (i.e., it represents the median of test results) with a 

lognormal standard deviation of 0.4. The ACI 318-11 regression is more 

conservative, with an 89% probability of exceedance (i.e., test results are 

more likely to be higher than the value predicted in the regression). Figure 

A-6 shows that the prediction is not biased with respect to the gravity shear 

ratio. 

Figure A-5 Relationship between gravity shear ratio and drift 

capacity for slab-column connections. 
FEMA P-2018 A: Development of Column Drift Capacities A-9 

Figure A-6 Ratio of measured versus predicted drift at punching shear 

failure for slab-column connections with different gravity 

shear ratios.

This methodology assumes that punching shear failure will only occur if 

there is insufficient continuity (bottom) reinforcement through the 

connection. Where there is sufficient bottom reinforcement, a slab-column 

connection may punch, but it is assumed that structural integrity 

requirements will prevent the slab from collapsing. As a result, large drift 

capacities are provided for slab-column connections with sufficient bottom 

reinforcement. 
FEMA P-2018 B: Development of Method for B-1

Determining Column Ratings

Appendix B

Development of Method for 

Determining Column Ratings

B.1 Overview

A column rating represents the probability that the drift demand on a column, 

ΔD, exceeds the drift capacity of the column, ΔC. Thus, a column rating 

reflects the probability of column failure (under the ground motion intensity 

that produces that drift demand). Higher column ratings indicate that the 

expected performance of columns will be worse.

Drift demands and drift capacities are both assumed to be lognormally 

distributed. A lognormal distribution is commonly used in earthquake 

engineering applications. The probability that column drift demand exceeds 

capacity depends on the mean and standard deviations of the probability 

distributions for drift demand and capacity. In this methodology, uncertainty 

in drift demand includes record-to-record variability in drift response, as well 

as uncertainty in the prediction of roof and critical story drifts. Uncertainty 

in the drift capacity includes variability in material properties, and the 

predictive model for drift capacity.

A column rating should be viewed as a representation of the probability of 

column failure for the given level of excitation, not as the true probability of 

failure. As a representation of the probability of failure, column ratings are 

comparable between different columns in a building and between different 

buildings. However, due to the simplified nature of this methodology, these 

values should not be applied in other probabilistic analyses outside of this 

methodology.

B.2 Structural Reliability Methods for Computing the 

Column Rating

A column rating is calculated using structural reliability methods to 

determine the probability that a column drift demand exceeds the column 

drift capacity (Melchers, 1999). In the formulation that follows, it is 

assumed that the random variables representing drift demand and drift 

capacity are lognormally distributed and statistically independent (Mori and 
B-2 B: Development of Method for FEMA P-2018

Determining Column Ratings

Ellingwood, 1993). In structural reliability terms, the limit state function for 

this problem can be written as:

(B-1)

where:

= drift capacity for the column of interest; and

= drift demand for the column of interest.

“Failure” occurs when G ≤ 0. Both and are random variables.

It can be shown that the reliability index, β, for this situation can be obtained 

from the following equation:

(B-2)

where: 

= drift capacity for the column of interest

= drift demand for the column of interest

ln,∆C σ = uncertainty in the column drift capacity, taken as 0.60

ln,∆D σ = uncertainty in the column drift demand, taken as 0.60

The probability of failure, pf, for each column can be computed from the 

reliability index as follows:

pf = − Φ β ( ) (B-3)

where the operator Φ indicates the cumulative standard normal probability 

distribution. As a result, the column rating, CR, is given as:

(B-4)

which is the relationship that was used to develop the values shown in 

Table 6-4 and Table 7-4.
FEMA P-2018 C: Development of Method for C-1

Determining Story Ratings

Appendix C

Development of Method for 

Determining Story Ratings

C.1 Overview

Like the column rating, the story rating represents the probability of collapse 

of a story, given the level ground shaking being considered. Higher story 

ratings indicate higher probabilities of collapse. As a representation of the 

probability of collapse, story ratings are comparable among stories and 

between buildings. However, due to the simplified nature of this 

methodology, these values should not be applied in other probabilistic 

analyses.

C.2 Probability Theory for Determining Probability of 

Story Collapse

Several different methods were explored to relate column failure ratings to 

story collapse ratings. The method used in this evaluation methodology uses

probability theory to relate the probability of failure of each column at story x

to the probability of collapse in that story. This method is employed to make 

up for the absence of a structural analysis model in the methodology.

The following assumptions are made in computing the probability of a story 

collapse:

• Story collapse is assumed to occur if at least 25% of gravity load bearing 

capacity in a story fails. In a frame building, for example, this 

corresponds to failure of columns carrying 25% of the gravity loads.

• Drift demands on all columns/walls in a story are assumed to be perfectly 

correlated, due to a rigid diaphragm assumption. Hence, if one column 

drift demand is higher than average, the other columns/walls are also 

expected to experience higher drift demands.

• Column/wall drift (deformation) capacities are correlated assuming the 

failure model shown in Figure C-1. This model captures adjacent 

column relationships, such that the failures of columns that are closer 

together are assumed to be more highly correlated (or consequential) 

than columns that are farther apart. The minimum level of correlation 

applied to the most widely-spaced columns corresponds to a correlation 
C-2 C: Development of Method for FEMA P-2018

Determining Story Ratings

coefficient of 0.20. This assumption attempts to account for progressive 

collapse and load redistribution probabilistically.

These correlations are used to in Monte Carlo simulations to develop story 

ratings based on realizations of drift demands and capacity on gravity load 

bearing elements that are consistent with these correlation models through 

multivariate random number generation. This process is described in more 

detail below.

Figure C-1 Assumed model of correlation in 

column/wall drift capacities for failure 

of columns i and j, as a function of 

column/wall separation distance.

C.3 Development of Story Ratings

These assumptions are used to generate the story rating curve shown in 

Figure C-2. This curve was obtained using 10,000 Monte Carlo simulations 

in which random realizations of the drift demand and drift capacity of each 

load bearing element (column or wall) in the story were generated. These 

realizations were generated using a multivariate random number generator 

such that the assumed correlations in both demand and capacity described in 

Section C.2 are accounted for. An individual column or wall was identified 

as failed in the Monte Carlo realization if its demand exceeded its capacity. 

Story collapse was identified in a simulation if at least 25% of the gravity 

load bearing capacity in the story was identified as having failed in the 

simulation. The curve shown was developed for a set of buildings with 

different column/wall ratings, aspect ratios, and numbers of columns/walls, 

but there was not significant variation from building to building. 

In the interest of simply representing the results shown in Figure C-3 for use 

in this methodology, these curves are presented as equations for linear trend 

lines applicable for story ratings greater than 0.1 and less than 0.9. These 

equations are a function of the average column/wall rating, Ravg, wherein the 
FEMA P-2018 C: Development of Method for C-3

Determining Story Ratings

average is weighted by the fraction of gravity loads taken by each load 

bearing element. The fitted equations are overlaid on the curves from Figure 

C-2 in Figure C-3. This is the basis for Equations 6-9 and 7-14. 

Figure C-2 Relationship between adjusted average column 

rating, Ravg, and the story rating, SR, for frame 

structures. The curve is the same for frame-wall and 

wall structures, except that the average incorporates 

the rating of walls through Equation 7-16.

Figure C-3 Relationship between adjusted average column and 

wall rating, CRavg, and the story rating, SR, from 

Monte Carlo simulation, and showing the simplified 

equation developed for the purpose of this 

methodology. 
FEMA P-2018 D: Wall Strength Index (WSI) Method D-1

Appendix D

Wall Strength Index (WSI) 

Method

D.1 Overview

A significant fraction of older buildings contain walls. The seismic 

performance of buildings containing a large number of walls is expected to 

be better than the performance of pure frame buildings because of their 

greater overstrength. Moreover, the added stiffness provided by walls may 

reduce drift demands on poorly detailed columns. The following sections 

develop the method for quickly evaluating frame-wall and wall buildings, 

such that wall-dominated buildings with large number of walls are excused 

from having to conduct a full ATC-78 evaluation based on the so-called 

“Wall Strength Index”. Two approaches are employed to support the 

development of this method based on: (1) numerical simulation; and (2) an 

analytical solution.

Sozen proposed the concept of a wall index (WI) as an indicator for building 

damage and collapse (Sozen, 2014). Sozen’s original formulation of the WI

is a ratio of wall to tributary floor area, and is computed at the base of the 

structure, not on a story-by-story basis. Additionally, Sozen proposed a 

column index (CI) which relates the cross-sectional area of all columns to the 

tributary floor area, arguing that it is the combination of the WI and CI that 

predicts a building’s seismic resistance. Sozen supported these concepts 

using post-earthquake damage observations from five events to develop 

relationships between WI, CI, and damage. Contained in this dataset were 

buildings with WI that ranged from 0 to 0.0055, showing generally lower 

damage with higher WI. However, none of the five events occurred in the 

U.S. or in areas with construction practices similar to the U.S. In this study, 

Sozen’s WI is adapted to account for the hazard level and site effects by 

including Sa(Te). The resulting metric, WSI, is used to identify frame-wall or 

wall buildings of lower seismic risk.

The Wall Strength Index (WSI) is defined as:

( ) ef a T

WI WSI

S = (D-1)
D-2 D: Wall Strength Index (WSI) Method FEMA P-2018

where: 

WI = the governing value of WI from Section 5.4.1

Sa = the horizontal spectral acceleration at the site, taken at the 

approximate structural period, Tef. determined for the direction 

corresponding to the governing wall index WI

D.2 Numerical Simulation

D.2.1 Buildings Analyzed

A set of nonlinear models of frame-wall systems is created and analyzed to 

establish a relationship between WSI and the collapse probability. As 

summarized in Table D-1, the buildings analyzed range from 2 to 6 stories in 

height; include frames with flexure, flexure-shear, and shear controlled 

columns (Vp/Vn from 0.6 to 1.2); consist of single and multiple wall systems;

and have walls with varying strengths. Typical bay widths and story heights 

are shown in Figure D-1. Wall designs are unconfined with #4 bars at 12 

inches on center, as is expected to be typical of older building; the wall 

lengths (lw) and thickness (tw) are defined in Table D-1. In total, 32 framewall models are analyzed, with 9 of them containing frames with flexurecontrolled columns and 23 having frames with shear-critical columns. 

Additionally, the analyzed building set contains WI ranging from 0.0002 to 

0.0040 as shown in Table D-1. 

Table D-1 Frame-Wall Building Properties

Num. 

Stories Vp/Vn

(2)

Num. 

Walls 

lw 

(ft) 

tw 

(in) WI

Te 

(sec)(1)

2 1.2 1 10 10 0.0007 0.43

2 1.2 1 20 10 0.0013 0.24

2 1.2 1 30 10 0.0020 0.16

2 1.2 1 40 10 0.0027 0.12

3 1.2 1 7 10 0.0003 0.60

3 1.2 1 11 10 0.0005 0.53

3 1.2 1 20 10 0.0009 0.42

3 1.2 1 30 10 0.0013 0.27

3 1.2 1 45 10 0.0020 0.17

6 0.6 1 10 10 0.0002 1.13

6 0.6 1 20 10 0.0004 0.95

6 0.6 1 30 10 0.0007 0.89

6 0.6 1 50 10 0.0011 0.49
FEMA P-2018 D: Wall Strength Index (WSI) Method D-3

Table D-1 Frame-Wall Building Properties (continued)

Num. 

Stories Vp/Vn

(2)

Num. 

Walls

lw

(ft)

tw

(in) WI

Te

(sec)(1)

6 0.6 1 60 10 0.0013 0.39

6 0.6 1 20 10 0.0004 1.20

6 0.6 1 30 10 0.0007 1.12

6 1.2 1 30 10 0.0007 0.89

6 1.2 1 40 10 0.0009 0.65

6 1.2 1 50 10 0.0011 0.50

6 1.2 1 60 10 0.0013 0.39

6 1.2 1 80 10 0.0018 0.28

6 1.2 2 30 10 0.0013 0.79

6 0.6 3 20 10 0.0013 0.65

6 0.6 5 20 10 0.0022 0.62

6 0.6 6 20 10 0.0027 0.62

2 1.2 2 20 10 0.0027 0.20

2 1.2 3 20 10 0.0040 0.19

2 1.2 3 20 10 0.0040 0.29

3 1.2 2 7 10 0.0006 0.60

3 1.2 2 11 10 0.0010 0.39

3 1.2 3 20 10 0.0027 0.36

3 1.2 4 20 10 0.0035 0.35

(1) Te is the effective period as per Eq. 7-27 of ASCE 41-13, calculated from pushover.

(2) Ratio of column flexural to shear strength, indicating degree of shear criticality.

D.2.2 Modeling

The dynamic response of each pure frame building is modeled using 

distributed plasticity elements for beams and columns and elastic springs 

representing beam-column joints, as illustrated in Figure D-1. If the 

governing failure mode of a column is shear, zero length shear and axial 

springs are included in series with the distributed plasticity element. The 

response of the shear and axial springs are governed by limit state materials, 

with relationships defined by Elwood (2004). If walls are present, they are 

modeled using a distributed plasticity element and connected to the frame 

with a rigid link as shown in Figure D-2.

In distributed plasticity elements, the constitutive relationship of concrete 

fibers is described by the modified Kent and Park model (Kent and Park,

1971); steel fibers are modeled using the relation proposed by GiuffreMenegotto-Pinto and the onset of buckling and post-bucking behavior is 
D-4 D: Wall Strength Index (WSI) Method FEMA P-2018

determined using the model proposed by Dhakal and Maekawa (2002). 

When the governing failure mode is flexure, a single force-based fiber 

element is used per flexural element and the regularized integration scheme 

presented by Scott and Hamutcuoglu (2008) is employed with five 

integration points.

Figure D-1 Modeling overview for pure frame buildings. 

Figure D-2 Modeling overview for frame-wall buildings. 

D.2.3 Ground Motion Selection and Scaling

The collapse capacity of each building, measured in terms of spectral 

acceleration, is evaluated through Incremental Dynamic Analysis or IDA 

(Vamvatsikos and Cornell, 2002). The FEMA P-695 far field ground motion 

set is used to represent the expected hazard (FEMA, 2009). 

D.2.4 Collapse

Global collapse of the system is defined as occurring when the lateral 

resistance of any story degrades to 50% of its peak capacity. To determine 

this point, first, the interstory drift ratio at which any story degrades to 50% 

of its peak capacity is identified from pushover analysis (see Figure D-3a). 

This interstory drift ratio is then used to identify the collapse point during 

subsequent dynamic analysis. Figure D-3b plots the incipient collapse points 

(i.e., one step prior to collapse) for an example building during dynamic 
FEMA P-2018 D: Wall Strength Index (WSI) Method D-5 

analysis. Collapse points from individual records are then used to develop 

the building’s collapse fragility in Figure D-3c. 

(a) (b) (c)

Figure D-3 Collapse definition for 6-story, 6-bay, frame-wall system with a single 20 ft wall and shear 

critical columns: showing (a) the point of global collapse identified during pushover 

analysis of the critical story; (b) the identification of global collapse from IDA curves; and 

(c) the building’s collapse fragility curve.

D.2.5 Results

Buildings with many walls are expected to have low collapse probabilities. 

The collapse simulation results obtained for the buildings listed above were 

used to identify a cutoff WSI is selected that corresponds with an acceptably 

low collapse probability, on average, consistent with Lower Seismic Risk 

Buildings. Here, an acceptably low collapse probability is defined as 20%. 

Figure D-4 presents collapse probabilities resulting from the dynamic 

analysis of these buildings as a function of WSI. The WSI is defined based 

on the ground motion intensities and seismic hazard at the location of Davis 

Hall on the UC Berkeley campus. A normally distributed survival function

(Kleinbaum and Klein, 2005) is used to define the form of an upper bound 

fit, i.e., upper bound probability of collapse for a given WSI. Based upon the 

upper bound fit, a WSI of greater than 0.002 is found to have a collapse 

probability of less than 20%, as shown by the star in Figure D-4. The 

buildings that govern the upper bound fit are typically frame-wall buildings 

that contain shear critical columns, and multiple walls with lengths of 20 feet 

or less. This implies that the 0.002 cutoff is conservative for buildings with 

fewer strong walls and flexure critical columns. 

Figure D-4 presents an upper bound fit for all considered buildings. 

However, frame-wall buildings that contain flexural-governed columns 

typically have lower collapse probabilities than buildings with shear-critical 

columns for a given WSI. Based upon this observation, an upper bound fit, 

specific to frame-wall buildings with only flexural-critical columns is created 

in Figure D-5. Here, a WSI of 0.0015 corresponds to a collapse probability 

of 20%. This result signifies that wall-frame systems that contain flexurallygoverned columns need fewer walls than systems with shear critical columns 
D-6 D: Wall Strength Index (WSI) Method FEMA P-2018

to produce equivalent collapse probabilities. In systems with shear critical 

columns, more walls are needed to reduce drift demands on poorly-detailed 

columns.

Figure D-4 Relationship between WSI and probability of collapse 

for 32 building models. All buildings are assumed to be 

located at the site of Davis Hall in UC Berkeley, CA 

(SD1 = 1.028g, SDS = 1.65g) and evaluated at the design 

spectrum level.

Figure D-5 Relationship between WSI and probability of collapse for 

wall-frame buildings with flexurally-governed columns. 

All buildings are assumed to be located at Davis Hall in 

UC Berkeley, CA (SD1 = 1.028g, SDS = 1.65g). 

Thus far, results have been presented for a single site (Davis Hall on the UC 

Berkeley campus). Accordingly, Figure D-6 varies the site hazard to 

investigate the effect of site location on the selected cutoff WSI. Figure D-6a

presents collapse probabilities as a function of WSI for frame-wall buildings 

with shear-critical columns located at Davis Hall on the UC Berkeley campus

(same site and subset of buildings from Figure D-4). Figure D-6b presents 

collapse probabilities for the same building set when the site hazard is taken 
FEMA P-2018 D: Wall Strength Index (WSI) Method D-7 

as half the design hazard at Davis Hall. In both cases, an upper bound fit is 

plotted on the data. While the upper bound fit in both plots is slightly 

different, the WSI that corresponds to a collapse probability of 20% is about 

0.002 in both cases. This signifies the cutoff WSI is relatively insensitive to 

the site hazard. This insensitivity is attributed to the fact that site hazard 

quantified in terms of Sa(T1) affects both the WSI and the collapse probability 

(the x- and y-axis in Figure D-6). Changing the site hazard in Figure D-6 

alters the location of the individual data points, but the upper bound fit and 

cutoff WSI stay relatively constant.

(a) (b)

Figure D-6 Relationship between WSI and probability of collapse for wall-frame buildings with 

shear-controlled columns. Site hazard is taken at (a) Davis Hall in UC Berkeley, CA 

(SD1 = 1.028g, SDS = 1.65g); and (b) half the hazard at Davis Hall (SD1 = 0.514g, 

SDS = 0.825g).

D.3 Analytical Investigation of WSI

An alternate approach used to support the WSI criteria is investigated by

relating the definition of the WSI to the shear stress check for shear walls 

performed during an ASCE 41-13 Tier 1 evaluation (ASCE 2013). ASCE 

41-13 Tier 1 evaluations categorize buildings by their type, then evaluates 

significant lateral load resistance characteristics through a series of checklist 

items. Checklist items are intended to be conservative measures of seismic 

risk such that buildings that pass a Tier 1 evaluation are very likely to 

perform adequately during a design level event. 

During a Tier 1 evaluation, the approximate shear stress in the shear walls is 

checked for concrete shear wall buildings. The average shear stress in a 

shear wall is defined in ASCE 41-13 Section 4.5.3.3 and is presented in 

Equation D-1: 

avg 1 j

j

s w

V

v

M A

  =    

(D-1) 
D-8 D: Wall Strength Index (WSI) Method FEMA P-2018

where, vj

avg is the average shear stress in shear walls in level j, Ms is a system 

modification factor, Vj is the story shear at level j, and Aw is the summation of 

the horizontal cross-sectional area of all shear walls in the loading direction.

To satisfy life safety criteria in the Tier 1 checklist, the average shear stress 

in each wall must be less than the maximum of 100 psi or 2 cf ′ as per 

ASCE 41-13 Section 16.10LS.

max 100 psi, 2 ( ) avg

j c v f ≤ ′ (D-2)

Substituting Equation D-2 into Equation D-1 produces Equation D-3:

( ) 1 max 100 psi, 2 j

c

s w

V

f M A

  ≤ ′    

(D-3)

The shear force demand can be estimated from ASCE 41-13 Section 4.5.2.1 

and is shown in Equation D-4:

V = CSaW (D-4)

Here, V is the seismic base shear force, C is a coefficient to relate 

displacements determined from elastic analysis to expected inelastic 

displacements, Sa is the spectral acceleration computed at the building’s 

fundamental period, and W is the building’s effective seismic weight. If we 

assume each story has the same weight, the maximum shear force will occur 

at the first story. Substituting Equation D-4 in for Vj in Equation D-3 results 

in Equation D-5:

( ) 1 max 100 psi, 2 a

c

s w

CS W f M A

  ≤ ′    

(D-5)

If we assume 200 lb/ft2 (or 1.39 psi) for the dead load plus effective live load, 

W = 1.39AT. AT is the total of the floor areas above ground, counting all of 

the stories. Substituting in for W gives Equation D-6:

( ) 1 1 39 max 100 psi, 2 a T

c

s w

. CS A f M A

  ≤ ′    

(D-6)

The definition of WSI, revised to use the terminology employed in this 

section, is presented in Equation D-7:

a T 1

w

S A

A WSI = (D-7)

Equation D-8 is obtained by substituting Equation D-7 into Equation D-6:

( ) 1 39 max 100 psi, 2 c

s

. C f M WSI

  ≤ ′     (D-8)
FEMA P-2018 D: Wall Strength Index (WSI) Method D-9

If we then assume a concrete compressive strength of 4,000 psi:

1 39 126 psi

s

. C

M WSI

    ≤   (D-9)

And rearrange Equation D-9 in terms of WSI gives Equation D-10:

WSI ≥ 1 39

126 s

. C

M (D-10)

From ASCE 41-13 Table 4-9, MS is equal to 4 for life safety. If we assume 

collapse prevention is 75% of life safety, MS is equal to 5.33, which is more 

in line with the goals of ATC 78.

Table D-2 WSI Required to Satisfy ASCE 41-13 Tier 1 Shear Stress Check

Num. Stories C (ASCE 41-13 Table 4.8) WSI Required

1 1.4 0.0029

2 1.2 0.0025

3 1.1 0.0023

4+ 1.0 0.0021

Based upon Table D-2, the WSI required to satisfy the ASCE 41-13 Tier 1 

shear stress check ranges from 0.0021 to 0.0029 depending on the number of 

stories. These results are obtained by assuming:

• equal weight per story

• seismic weight equals 200 lb/ft2

• concrete compressive strength, cf ′ = 4000 psi

• performance measure is collapse prevention (taken as 75% of life safety)

When compared with the required WSI obtained from numerical simulation 

(0.002), the required WSI in Table D-2 are slightly larger. This difference is 

attributed to the fact that the numerical simulations consider the effect of 

wall-frame interaction and the cutoff WSI corresponds with a collapse 

probability of 20%. Despite the slight differences in resulting WSI, the 

analytical solution serves to support the results obtained from numerical 

simulation.

D.4 Limitations

Building models used in the development of a cutoff WSI are regular in plan 

and contained walls that are continuous thorough the full building height. 

Therefore, additional criteria for use of the WSI within ATC-78 are enforced 
D-10 D: Wall Strength Index (WSI) Method FEMA P-2018

to ensure that building characteristics that may worsen seismic performance 

must undergo further evaluation. Additional criteria include:

• no discontinuous walls (going downward)

• no severe torsion

• no short columns

D.5 Conclusions

The collapse capacities of 32 wall-frame building models were computed 

through IDA. Based upon the results of this building set, a cutoff WSI was 

selected that corresponds with a collapse probability of less than 20%. For 

wall-frame buildings containing shear critical columns the cutoff WSI is 

0.002 and for buildings containing flexurally-governed columns the cutoff 

WSI is 0.0015. These results are shown to be relatively independent of the 

site hazard and are further supported by an analytical solution that relates the 

cutoff WSI to the shear stress check for shear walls performed during an 

ASCE 41-13 Tier 1 evaluation.
FEMA P-2018 E: Exceptionally Weak Building Criteria E-1

Appendix E

Exceptionally Weak Building 

Criteria

E.1 Overview

Buildings that are exceptionally weak are expected to earn a high building 

rating, which is indicative of a relatively high probability of collapse. Here, 

a set of criteria is created for frame, frame-wall and wall buildings that 

identify exceptionally weak buildings during an early screening process. 

Buildings that are identified as exceptionally weak are then classified as 

Exceptionally High Risk (Building Rating > 0.7).

To develop the criteria for these buildings, first, a set of pure frame buildings 

of varying strengths was designed to the 1967 UBC. This building set has

columns ranging from flexure-critical to shear-critical as shown in Table E-1. 

Next, flexure-critical walls with varying lengths and detailing (i.e.,

deformation capacities and moments of inertia) were added to the pure frame 

models. Properties of frame-wall buildings are presented in Table E-2. The 

collapse capacity of each building is then estimated through IDA and limits 

for exceptionally high risk weak buildings are proposed based on Vp/Vn.

Table E-1 Properties of Pure Frame Building Set

Num. 

Stories

Num. 

Bays

Median 

Vp/Vn

Median 

Mc/Mb Vy/W

Te

 (sec)(1)

Median Sa(T1) 

Collapse (g)

2 3 0.35 0.43 0.23 0.80 1.07

5 3 0.73 1.27 0.16 0.92 0.67

3 5 0.88 1.11 0.28 0.83 1.17

3 3 0.98 1.56 0.38 0.81 1.11

3 3 1.17 1.72 0.40 0.75 1.11

3 3 1.48 0.99 0.47 0.72 1.17

6 5 1.48 1.00 0.43 0.97 0.74

(1) Te is the effective period as per Eq. 7-27 of ASCE 41, calculated from pushover.
E-2 E: Exceptionally Weak Building Criteria FEMA P-2018

Table E-2 Properties of Frame-Wall Building Set

Num. 

Stories

Num. 

Bays

Median 

Vp/Vn WI Vy/W

Te

(sec) (1)

Median Sa(T1) 

Collapse (g)

2 3 0.24 0.0036 0.72 0.36 1.89

3 5 0.88 0.0013 0.35 0.69 1.29

3 3 1.47 0.0024 0.55 0.58 1.67

3 3 1.28 0.0024 0.53 0.59 1.74

3 3 0.50 0.0024 0.44 0.62 1.61

3 3 0.56 0.0012 0.28 0.89 1.17

3 3 0.56 0.0024 0.42 0.61 1.47

3 3 0.97 0.0024 0.52 0.60 2.06

3 3 0.97 0.0024 0.48 0.60 1.82

5 3 0.73 0.0014 0.25 1.06 0.88

6 5 0.75 0.0006 0.17 1.28 0.88

8 3 1.28 0.0009 0.13 1.58 0.61

(1) Te is the effective period as per Eq. 7-27 of ASCE 41, calculated from pushover.

E.2 Modeling

For an overview of the modeling techniques used evaluate each building’s 

dynamic response, refer to Appendix D.

E.3 Ground Motion Selection and Scaling

Refer to Appendix D.

E.4 Collapse

Different collapse criteria are used depending on whether the building’s 

columns are flexure or shear critical. For frame-wall or frame systems with 

shear-critical columns, collapse is taken as occurring in these analyses when 

25% of columns in the story fail in shear. This collapse criterion was chosen 

to be consistent with earlier analyses conducted for this project, and is a 

proxy for loss of 25% of the gravity load bearing capacity. For frame and 

frame-wall buildings with flexure-critical columns, collapse is taken as the 

point at which the IDA curve flattens to 20% of its initial slope, i.e., 

sidesway (Vamvatsikos and Cornell, 2002).

E.5 Development of Criteria for Exceptionally Weak 

Frame Buildings

Two sources are drawn upon to develop the criteria that identifies 

exceptionally weak pure frame buildings: (1) nonlinear dynamic analysis 
FEMA P-2018 E: Exceptionally Weak Building Criteria E-3 

results of pure frame models described above in Table E-1; and (2) Table 

C-10f from ATC-78-1 (ATC, 2012) which is reproduced in Table E-3, 

below. Table C-10f from ATC-78-1 is also based upon nonlinear dynamic 

analyses of RC frame buildings, however, the ATC-78-1 models used 

lumped plasticity elements to capture post-elastic behavior as opposed to the 

distributed plasticity models developed in this phase of the project and

presented in Table E-1. 

The collapse capacity of each pure frame building from Table E-1 is 

estimated through IDA. As shown in Figure E-1, there are trends in collapse 

capacity associated with the governing failure mode of the columns in the 

critical story, Vp/Vn. μstrength values corresponding to a collapse probability of 

0.7 are then extracted for each building. The 0.7 value is employed because 

it aligns conceptually with the definition of the Building Rating for 

Exceptionally High Risk buildings. These μstrength values are then used in the 

development of the criteria to identify exceptionally weak pure frame 

buildings, as discussed below.

Figure E-1 Collapse fragilities for pure frame 

buildings from Table E-1 plotted as 

a function of μstrength. 

Table C-10f from ATC-78-1 is reproduced below in Table E-3. Collapse 

probabilities for pure frame buildings are presented as a function of Vp/Vn and 

m, where m = μstrength/Cm. (Here, Cm is an effective mass factor dependent 

upon the number of stories and type of lateral load resisting system.) 

Combinations of Vp/Vn and m (which is converted to μstrength) are extracted 

from Table E-3 to quantify μstrength associated with collapse probabilities of 

0.7.
E-4 E: Exceptionally Weak Building Criteria FEMA P-2018

Table E-3 Table of Collapse Probabilities (from ATC-78-1) for Pure Frame 

Buildings

m 3 4 5 6 7 10

Vp/Vn

0.7 0.14 0.38 0.62 0.79 0.89 0.98

0.8 0.15 0.42 0.67 0.83 0.92 0.99

0.9 0.22 0.50 0.73 0.87 0.94 0.99

1.0 0.30 0.60 0.80 0.91 0.96 1.00

1.1 0.47 0.76 0.90 0.96 0.99 1.00

1.2 0.67 0.88 0.96 0.98 0.99 1.00

1.3 0.85 0.97 0.99 1.00 1.00 1.00

Combinations of Vp/Vn and μstrength that produce collapse probabilities of 0.7 

are combined from IDA analysis of the buildings in Table E-1 and Table E-3, 

and plotted in Figure E-2. Limiting values of μstrength are defined based upon 

Vp/Vn such that buildings with μstrength values greater than the limiting values 

are expected to have collapse probabilities greater than 0.7 and are classified 

as exceptionally weak. For pure frames with Vp/Vn < 0.6 in the critical story, 

μstrength must be greater than 5.5 to be considered exceptionally weak. Pure 

frames with Vp/Vn > 1.5 must have μstrength > 2. Note that these criteria imply

that buildings with shear-critical columns that are weak may be identified as 

exceptionally weak even though a frame of similar strength with flexurecritical columns is not. Linear interpolation is permitted for frames with 0.6 

≤ Vp/Vn ≤ 1.5. Limiting values of Vp/Vn and μstrength are shown by the solid 

line in Figure 2. 

Figure E-2 Limiting values of Vp/Vn and μstrength that identify exceptionally 

weak pure frame buildings.
FEMA P-2018 E: Exceptionally Weak Building Criteria E-5 

E.6 Investigation of Criteria for Exceptionally Weak 

Frame-Wall Buildings 

Collapse fragilities for the studied frame-wall buildings are plotted in Figure 

E-3 as a function of Sa(T1) and as a function of μstrength. Recall that μstrength is 

defined as [Sa(T1)/(Vy/W)]Cm. Plotting the frame-wall collapse fragilities in 

terms of μstrength (Figure E-3b) has less scatter between buildings than 

collapse fragilities plotted in terms of Sa(T1) (Figure 3a), and is therefore a 

better predictor of collapse. Based upon this observation, μstrength is chosen as 

the indicator used to identify exceptionally weak frame-wall buildings. As 

described in Section E.5, this measure is consistent with criteria used to 

identify exceptionally weak frame buildings. 

The amount of wall present in a building relative to the total floor area, 

measured by the WI, is depicted by the color in Figure E-3. When collapse 

fragilities are plotted against Sa(T1) (Figure E-3a), the results show an 

increasing probability of collapse with decreasing WI (i.e., decreasing 

contribution of walls to the structural response). Interestingly, when plotted 

as a function of μstrength (Figure E-3b), buildings with large WI have larger 

collapse probabilities for a given μstrength value than buildings with small WI. 

(a) (b)

Figure E-3 Collapse fragilities for frame-wall buildings plotted as a function of: (a) spectral acceleration 

at each building’s fundamental period, shown in Table E-2; and (b) μstrength. 

Figure E-4 explores the reason collapse fragilities for buildings with large WI

values appear more vulnerable than buildings with small WI values when 

plotted against μstrength. As expected, the addition of structural walls to a 

building with a fixed floor plan increases the building strength, or Vy/W, 

(Figure E-4a), and increases the collapse resistance of the building (Figure 

E-4b) due to the additional strength provided by the walls. However, the 

addition of structural walls to a system increases Vy/W more rapidly than the 
E-6 E: Exceptionally Weak Building Criteria FEMA P-2018

collapse resistance of the building is increased, as shown in Figure E-4c. As 

a result, in Figure E-3b, the collapse fragilities of buildings with large WI 

values to plot on the left of buildings with small WI values. Therefore, the 

WI trends are counteracted by the use of the imperfect demand-to-capacity 

ratio of μstrength. 

(a) (b) (c)

Figure E-4 Relationship between WI and: (a) Vy/W; (b) median collapse Sa(T1); and (c) the ratio of median 

collapse Sa(T1) to Vy/W. 

As a result of the trends observed in Figure E-3b and the desire to use μstrength

as an indicator for exceptionally weak buildings, the limiting value 

identifying exceptionally weak buildings was selected based upon frame-wall 

models with small WI values. This simplification was deemed appropriate

because buildings with many walls (high WI) will perform better than 

buildings with fewer walls (Figure E-3a) and are unlikely to be exceptionally 

weak. μstrength of 5.5 corresponds with a collapse probability of 0.7 for 

buildings with WSI from 0.0003 to 0.0006. Therefore, μstrength of 5.5 was

used as a criterion for identifying exceptionally weak frame-wall buildings, 

as shown in Figure E-3b. 

Unfortunately, trial evaluations on real, or realistic, test-case frame-wall 

buildings with varying amounts of concrete walls present in the buildings, 

did not show a good correlation between WI values and the building ratings 

resulting from a full application of the methodology. As a result, the wall 

index, WI, did not prove to be a reliable indicator of performance, and use of 

WI values to identify exceptionally high seismic risk buildings was 

abandoned.
FEMA P-2018 F: Beam-Column Joints F-1

Appendix F

Beam-Column Joints

F.1 Introduction

The behavior of beam-column connections in older-type construction has 

been widely studied (Moehle, 2014). Of particular interest are:

• Performance of connections with discontinuous beam bottom 

longitudinal reinforcement

• Strength of joints in beam-column connections without joint transverse 

reinforcement

• Effect of joint eccentricity on joint and column behavior

• Axial failure of beam-column connections

Each of these topics is reviewed in the following text.

F.2 Performance of Connections with Discontinuous 

Beam Bottom Longitudinal Reinforcement

Many older buildings have discontinuous beam bottom reinforcement that 

extends a short distance into the beam-column joint. A typical extension was 

6 inches (the minimum permitted by the then-current ACI building codes). 

Short embedments of this type are insufficient to develop full strength of the 

embedded bars. However, the embedded bars are well confined by the 

surrounding concrete, so they are unlikely to cause a brittle splitting failure. 

For this reason, it is reasonable to calculate the bar stress capacity of the 

embedded bar in accordance with the provisions of ASCE 41-13, to apply 

this stress to calculate the moment strength of the beam for loading that puts 

the embedded bars in tension. This reduced moment strength usually can be 

sustained through relatively large rotations.

Figure F-1 plots measured strengths for interior beam-column joints without 

transverse reinforcement, both with and without continuous beam bottom 

longitudinal reinforcement. Cracking strength is notably affected by axial 

load, whereas ultimate strength is less affected by axial load. Reduced 

strength associated with discontinuous beam bottom longitudinal 

reinforcement is apparent.
F-2 F: Beam-Column Joints FEMA P-2018

Figure F-1 Shear strength of unreinforced interior joints. Test 

specimens with continuous beam bottom bars are noted. All 

other test specimens have discontinuous bottom bars 

embedded in the joint. (Data from Pessiki et al., 1990, and 

Beres et al., 1992, after Moehle, 2014.)

F.3 Strength of Joints in Beam-Column Connections 

without Joint Transverse Reinforcement

Figure F-1 presents data for edge connections load parallel to the edge. 

Measured joint shear strength is at least 10 c j f A′ (psi), with higher strengths 

noted for connections with continuous longitudinal reinforcement. These 

joints had aspect ratio hb/hc ~ 1. 

Figure F-2 compares measured and calculated strengths for exterior 

connections with columns continuous through the joint, loaded perpendicular 

to the edge, including corner connections. Calculated strength is based on 

the ASCE 41 expression, that is, Vn = 6 c j λ f A′ . In the tests, the joints failed 

without significant inelastic flexural response in the beams or columns. The 

comparison suggests (a) ASCE 41 calculated strengths are conservative; and 

(b) joint strength is a function of joint aspect ratio hb/hc. 

The data from Figures F-1 and F-2 suggest an alternative form of joint shear 

strength could provide improved correlation between measured and 

calculated strengths. One suggested shear strength expression is: 

Vn =10 c

c

b

h f h

λ ′ (psi)

where: 

hc/hb ≤ 1.0
FEMA P-2018 F: Beam-Column Joints F-3 

Figure F-2 Measured and calculated strengths for exterior joints 

loaded perpendicular to the edge, including corner joints. 

Data are for joints failing in shear without significant 

inelastic flexural deformation in adjacent beams or 

columns (data after Hassan, 2011).

Figure F-3 compares measured and calculated results, using the same test 

data shown in Figure F-2, and using the revised expression to calculate shear 

strength. Overall correlation is improved considerably. 

Figure F-3 Measured and calculated strengths for exterior joints 

loaded perpendicular to the edge, including corner 

joints. Data are for joints failing in shear without 

significant inelastic flexural deformation in adjacent 

beams or columns (data after Hassan, 2011). 

F.4 Effect of Joint Eccentricity on Joint and Column 

Behavior

Several researchers have studied behavior of eccentric beam-column joints, 

that is, joints for which centerlines of beams and columns framing into the 
F-4 F: Beam-Column Joints FEMA P-2018

joint are eccentric. LaFave et al. (2005) provide a summary of the principal 

findings. 

Force transfer at an eccentric beam-column joint is complicated by the 

misalignment of the framing members. Figure F-4(a) depicts the local force 

transfer mechanism. The diagonal struts forming within the joint depth are 

oriented in opposite directions on opposite sides of the joint, suggesting the 

occurrence of joint torsion, which could reduce joint strength. The 

localization of force transfer at the intersection between the beam and 

column results in localization of joint damage [Figure F-4(b)], which also 

could justify reduced joint strength for eccentric connections. Some writers 

have also identified the possibility of column torsion, and have suggested 

that this column torsion could reduce column shear strength due to the 

superposition of shear stresses from shear and torsion. This effect appears to 

be ameliorated by the presence of a floor slab, which can resist any torsional 

moments through in-plane bending of the diaphragm (Figure F-4(c)). 

Physical evidence of column damage due to induced torsion is limited, and 

does not appear to justify consideration in a rapid evaluation method, if at all. 

LaFave et al. (2005) recommend including the effect of joint eccentricity by 

defining the joint area Aj = hc(bc + bw)/2. None of the joints reviewed by 

LaFave et al. had beams extending outside the plan of the column. 

Therefore, it is recommended that bw not exceed the width of the beam web 

that is contained within the outline of the column dimensions. 

Available test data do not show significant reduction in deformation capacity 

of eccentric beam-column joints compared with otherwise equivalent 

concentric joints. 

(a) Force transfer (b) Localized damage (c) Slab reduces the effect

Figure F-4 Force transfer at eccentric beam-column connections.
FEMA P-2018 F: Beam-Column Joints F-5 

F.5 Axial Failure of Beam-Column Connections

Several buildings that collapsed in past earthquakes have shown evidence of 

severe joint damage. On the other hand, physical evidence of building 

collapses having been triggered by joint failures is less clear. Laboratory 

studies also have not provided convincing proof that building collapse can be 

triggered by joint failure. One of the reasons for absence of evidence may be 

that laboratory tests may not be subjecting beam-column connections to 

sufficiently severe loadings because of limitations in testing equipment 

capabilities. 

In one study, Hassan (2011) subjected a series of corner beam-column joints 

to severe lateral and axial loading histories. The joints eventually showed 

signs of axial shortening through the joint at late stages of testing, although 

sudden axial failure was never obtained. Hassan also collected laboratory 

test data from tests conducted by other researchers, delineating, for final 

loading stages, those tests that showed signs of axial shortening within the 

joint and those that did not. Figure F-5 plots the results. The bilinear 

relation divides those connections showing axial shortening from those not 

showing axial shortening. According to Hassan, connections falling below 

the bilinear relation can be considered safe from axial collapse, while those 

falling above the relation might be suspected of triggering axial collapse. 

At the time of this writing, the writers are not aware of any test data 

providing physical evidence that axial failure can be triggered by failure of 

edge or interior connections. 

Figure F-5 Maximum observed drift ratios and axial load ratios of corner 

beam-column connections (after Hassan, 2011). 
FEMA P-2018 G: Effective Fundamental Period G-1

Appendix G

Effective Fundamental Period

ASCE/SEI 7 and ASCE/SEI 41 present equations for fundamental period of 

frame buildings as a function of either height or number of stories. These 

equations are useful for identifying a conservative set of lateral forces for 

strength design, as emphasized in ASCE/SEI 7 and the linear methods of 

ASCE/SEI 41. The methodology presented in this report places more 

emphasis on estimation of lateral drifts rather than forces. Furthermore, it is 

intended to be applied to individual buildings whose strength may vary 

widely from the minimum base-shear strength required by ASCE/SEI 7. 

Given these different objectives, it was desirable to develop alternative 

period equations.

G.1 Frame Buildings

As a starting point, an analytical study was undertaken to identify the effect 

of building strength and height on building period (Renouard, 2014). A 

series of four-, eight-, and 12-story tall frame buildings with uniform 

rectangular plans were designed for gravity loads plus a set of lateral loads 

having an inverted triangular pattern. Building heights were 46 feet, 90 feet, 

and 134 feet respectively. Target building base-shear strengths were 0.05W, 

0.10W, 0.15W, and 0.25W, where W corresponds to the building weight.

Each building was assumed to have two perimeter moment-resisting frames 

in each direction designed to resist all the earthquake forces. This 

assumption allowed for simplified analysis models in which the buildings 

were modeled as two-dimensional frames, with each perimeter frame 

providing half the required lateral resistance. Each frame included six bays. 

Furthermore, the buildings were assumed to have symmetric plans so that the 

building response to lateral forces included minimal plan torsion.

Each building was designed using an algorithm that sized the columns for 

target longitudinal reinforcement ratios of 0.01, 0.015, 0.018, 0.02, 0.025, or

0.03. Beam sizes were varied to obtain typical reinforcement ratios. The 

following parameters were used to better emulate actual construction and 

ease member size selection:

• Column and beam sizes were changed every two stories.

• Column size was limited to no smaller than 12′′ × 12′′.
G-2 G: Effective Fundamental Period FEMA P-2018

• Beam depth-to-width ratio was limited to no greater than 1.4.

All building models were analyzed using the following nominal material 

properties:

• Reinforced Concrete Strength, cf ′ = 3000 psi

• Steel Reinforcement Grade 60, fy = 60 ksi

• Reinforced Concrete modulus of elasticity, Ec = 3122 ksi 

• Steel Reinforcement modulus of elasticity, Es = 29000 ksi

The building models were further idealized as two-dimensional fishbone 

models (Luco et al., 2003). This simplified model lumps column and beam 

stiffnesses by condensing all the columns of a story into one column and all 

the beams into one rotational beam spring. This method allows for a 

simplified building model with a greatly reduced number of degrees of 

freedom. Figure G-1 depicts the planar frame and fishbone idealizations for 

a four-story building. 

Figure G-1 Example planar frame and fishbone idealizations of a 

four-story building.

The analytical models consist of line elements representing the flexibilities of 

beams and columns rigidly connected to zero-length joints. Flexibilities 

considered flexural, shear, and axial forces. Each element has flexural 

stiffness properties calculated from the member cross section, using the 

effective moment of inertia as proposed by Elwood and Eberhard (2009), 

which considered the effect of reinforcement slip from beam-column joints. 

It was assumed the beams were cast monolithic with the slabs. Therefore, 

the moment of inertia of the beams with slabs was assumed to be equal to 

twice the moment of inertia of the beams if there was no slab. The structures 

were assumed to have fixed base foundations. 

Figure G-2 depicts the calculated results for all buildings studied. Values of 

percent strength refer to the Vbase/W ratios of the buildings considered. As 

expected, period increases with increasing height and decreases with 
FEMA P-2018 G: Effective Fundamental Period G-3 

increasing strength. The target column longitudinal reinforcement ratio has 

some effect on period, but the effect is less important than other variables. 

Figure G-2 Calculated periods for all buildings studied. 

ASCE/SEI 41 uses the following expression to approximate the fundamental 

period of a concrete frame:

0.9 T h = 0.018 n (G-1)

where hn = height to the roof level n in feet. This expression is plotted in 

Figure G-2. It provides nearly a lower bound to the calculated data, as might 

be expected for an equation intended to produce a conservative (high) set of 

lateral forces. 

An approximation to the calculated results is given by: 

( )

1 0.07 n

y

T h

V W = (G-2)

where Vy = base-shear strength. Figure G-3 plots results of Equation G-2. 

Figure G-3 also plots data reported by Goel and Chopra (1997). Note that 

the data of Goel and Chopra are for responses to moderate ground motions 

and likely do not include data for response into the inelastic range. 
G-4 G: Effective Fundamental Period FEMA P-2018

Figure G-3 Comparison of calculated periods.

G.2 Frames with Deep Spandrels

Frames with deep spandrel beams will have reduced fundamental periods 

relative to typical frames because deep spandrels are stiffer than typical 

beams and deep spandrels reduce the effective length of the columns. The 

effect on overall building period will depend on the fraction of frames in the 

building that have deep spandrel beams. 

To estimate the effect of deep spandrel beams on building period, it was first 

assumed that the stiffness of a frame is inversely proportional to the cube of 

the column height. Consequently, the stiffness of a frame with deep spandrel 

beams would be approximately (l / lu)

3

 times that of a bare frame, where l is 

the floor-to-floor column height and lu is the clear height of the column. A 

small parameter study was carried out in which the fraction of spandrel 

frames was varied from one-half to one-third of the total number of frames. 

Relative stiffnesses of the combined frame and deep spandrel systems were 

calculated, and period was assumed to vary inversely with the square root of 

the system stiffness. From this study, it was observed that the period of the 

building with deep spandrels was approximately (lu / l) times the period of 

the same building without deep spandrels.

G.3 Pier-Spandrel Systems

An analytical study was undertaken to investigate the effect of geometry of a 

building with pier-spandrel system on its vibration period. Important 

geometry parameters include the building height, dimensions of deep 

spandrels and piers, and the ratio of wall thickness to the floor dimension 

transverse to direction of vibration. It was assumed that minimum 
FEMA P-2018 G: Effective Fundamental Period G-5 

reinforcement was present, so this was not considered a major variable. A 

series of four-, eight-, and twelve-story tall archetype pier-spandrel wall 

buildings with uniform rectangular plans was developed based on actual 

buildings with large openings in shear walls. The typical story height was 12 

feet, resulting in building height, hn, of 48 feet, 96 feet, and 144 feet, 

respectively. The seismic mass of the building was determined from the 

combination of (DL + 0.25LL), where DL was taken as 200 psf and LL was 

40 psf for typical office use. 

This type of building typically has perimeter walls extending full length of 

the building on all building sides. Therefore, two-dimensional simplified 

analytical models of pier-spandrel systems were developed in the computer 

software ETABS (Computers and Structures, Inc.) with the assumption that 

each perimeter system provides half the required lateral resistance with no 

resistance provided by interior framing. Additionally, the building plans 

were assumed to be symmetric such that the effects of torsion on the building 

response were negligible. Results of a two-dimensional model were 

compared with results from a full three-dimensional archetype including 

interior frames to demonstrate that the two-dimensional idealization 

produced calculated period within a few percent of the calculated period for 

the complete three-dimensional building. 

The building models were further idealized as single-bay models (Luco et al., 

2003). Figure G-4 displays the planar pier-spandrel wall system and the 

model idealization for a four-story building. Figure G-5 illustrates the 

definition of the main variables considered in the parametric study.

Figure G-4 Example of pier-spandrel system and model idealizations of a 

four-story building.
G-6 G: Effective Fundamental Period FEMA P-2018

 (a) (b)

Figure G-5 Illustration of variables and constants in the parametric 

study: (a) Elevation view; (b) Typical floor plan view.

For each single-bay model representing an archetype building with certain 

height, av and ah were varied between 0.4 to 0.8 while the bay width, li, was 

varied from 18 feet to 30 feet. The seismic mass imposed on each level of 

the simplified model was calculated as the load combination (DL + 0.25LL) 

multiplied by the bay width in the direction of vibration and half the building 

dimension in the transverse direction, W. Story height h = 12 feet, floor plan 

dimension W = 120 feet, wall thickness t = 12 inches, concrete compressive 

strength cf ′ = 5,000 psi, elastic modulus of concrete Ec = 4,030 ksi, and DL = 

200 psf and LL = 40 psf were kept constant for all single-bay models.

Piers, spandrels, and joint panels are modeled by thin-shell element with 

flexural and shear stiffnesses of 0.5EcIg and 0.3EcAg, respectively. The 

flexural stiffness is in accordance with ASCE 41 and reflects a reduction in 

stiffness associated with cracking. The shear stiffness is reduced to threequarters of the shear stiffness in ASCE 41 to reflect the effect of modest 

shear cracking on effective period—the reduction factor was established after 

discussion with a sample of practicing engineers who have analyzed these 

buildings by ASCE 41, review of test data, and judgment of the authors. The 

structures were assumed to be fixed to the base foundations.

Figure G-6 presents the calculated periods for all building models studied on 

the y-axis. Key variables were identified and organized in an algebraic form 

that would facilitate implementation in the present methodology, and a 

nonlinear regression analysis was carried out to minimize the sum of squared 

error to determine the final form of an equation that best fit the calculated 

periods. The results given by the resulting equation are shown on the x-axis. 

The coefficient of determination (R-squared) was 0.9332.
FEMA P-2018 G: Effective Fundamental Period G-7 

Figure G-6 Comparison of calculated periods.

As the gross moment of inertia Ig = td 3/12 and gross area Ag = td of the cross 

section are linear functions of the wall thickness, t, the global stiffness of the 

analytical models is known to be linearly proportional to the wall thickness. 

The seismic mass of the building can be assumed to be approximately 

linearly proportional to the floor plan dimension, W, such that the seismic 

mass of a typical floor can be expressed by (DL + 0.25LL)WL. Given that 

vibration period generally has the form Te = M K/ , it is evident that the 

period is proportional to W t / . With W and t normalized by 120 feet and 1 

foot, respectively, and L already incorporated in analytical models by the bay 

width, li, the period equation derived from nonlinear regression analysis 

shown in Figure G-6 can be extended to apply to other buildings of different 

floor dimensions and wall thickness:

Te = 1.5 0.5 /120 0.008 ( ) /1 n vh i

W h aa l

t

(G-3)

Resulting in the final form of the period equation:

Te = 

1.5 0.5

0.001 opening base

n i

we wp

A A h l

A A

   

         

(G-4)

for 0.15 ≤ opening

we

A

A

     

≤ 0.5

where: 

hn = height of building (ft)

Aopening = total area of openings in all pier-spandrel walls in direction of 

vibration (ft2

) 

Awe = total area of all pier-spandrel walls, measured in elevation, 

including openings, in direction under consideration (ft2

) 
G-8 G: Effective Fundamental Period FEMA P-2018

li = typical or average bay width measured center-to-center of wall 

piers, (ft)

Abase = WL = typical floor plan area (ft2

) 

Awp = total area of pier-spandrel wall, measured in plan, including 

openings, in direction under consideration, = 2tL assuming two 

walls of thickness t and length L in each direction, (ft2

) 

αvαh = Abase/Awp can be shown on average from elevation view of 

walls

The limits on (Aopening/Awe) are based in part on the limits of the variables 

considered in this study and in part to prevent use of the equation for 

buildings whose large openings result in the building being more like a frame 

system than a pier-spandrel system. 

G.4 Wall and Frame-Wall Buildings

Vibration periods of wall buildings are affected by building height, baseshear strength, and wall aspect ratio. Goel and Chopra (1998) present data 

and an analytical study of vibration periods of wall buildings that provides 

the starting point for developing a period equation suitable for use in this 

methodology. 

The Goel and Chopra (1998) approach incorporates the assumptions of fullheight, fixed-based walls with rectangular cross sections and with flexibility 

contributions from shear and flexure, resulting in a theoretical expression for 

vibration period. The expression was adjusted to better match measured 

periods from wall buildings shaken by earthquakes, leading to the following 

equations as a lower-bound estimate of period:

1 0.0019 n

w

T h

C = (G-5a)

2

2 1

100

1 0.83

x n i

w

B i i i

wi

h A C

A h h

l

=

  =           +        

∑ (G-5b)

where:

AB = area of base of structure, ft2

Ai = web area of shear wall i in ft2

lwi = length of shear wall i in ft

hi = height of shear wall i in ft

x = number of shear walls in the building effective in resisting 

lateral forces in the direction under consideration
FEMA P-2018 G: Effective Fundamental Period G-9

The form of Equation G-5 is based on Goel and Chopra (1998), but is taken 

from ASCE/SEI 7, which adopted the formula as one method for estimating 

vibration period of a wall building.

In this methodology, Equation G-5 is further modified by increasing the 

coefficient from 0.019 to 0.026 to obtain a period more representative of a 

heavily cracked wall. Note that Goel and Chopra (1998) identified the 

coefficient 0.026 as an upper bound to the measured wall periods from their 

database. Additionally, it is assumed that ratio hn/hi = 1.

Results of Equations G-2 and G-5 were compared for a small sample of 

typical building geometries to verify that, for a given height and base-shear 

strength, the calculated period of wall buildings is less than the calculated 

strength of frame buildings.

For the purposes of determining the wall strength index in Chapter 5, a

simpler alternative equation for buildings with walls is provided.

Te = 0.015hn

0.75 (G-6)

Equation G-6 is only to be used for determination of the wall strength index. 

It is similar in form to that provided in ASCE/SEI 41, and was found to result 

in an approximate period that was close to effective periods estimate from 

pushover analyses for a set of frame-wall building models used in other 

studies (e.g., wall strength index studies presented in Appendix D).
FEMA P-2018 H: Development of Procedures to H-1

Estimate Story Drift Demands

Appendix H

Development of Procedures to 

Estimate Story Drift Demands

H.1 Introduction

In this methodology, the collapse potential of an existing reinforced concrete 

building is estimated by comparison of the story drift demands and story drift 

capacities of critical structural components. The procedure to estimate story 

drift demands in each principal framing direction is summarized as follows:

• Estimate the effective fundamental vibration period of the building, Te, 

along a principal framing direction.

• Determine the equivalent single-degree-of-freedom (SDOF) drift demand 

δeff at an elevation heff that corresponds to the effective modal height of 

the fundamental vibration mode of the building, using a response 

spectrum representing the seismic hazard.

• Given the drift demand at the effective height and the building 

configuration, estimate the distribution of story drift demands, δi, over 

the building height based on the building configuration and strength 

distribution.

Appendix G describes the development of equations to estimate the effective 

fundamental period, Te. Section H.2 describes studies to evaluate the method 

used to calculate the SDOF drift demand δeff. The balance of this appendix 

describes studies to explore methods to estimate story drift demands.

H.2 Studies of the SDOF Drift Demand

H.2.1 Basic Procedure to Calculate SDOF Drift Demand

The equivalent SDOF displacement at the effective modal height is 

determined using a procedure mirroring the target displacement approach of 

ASCE 41. Specifically, the displacement, δeff, is calculated as follows:

δ

π =

2

2 4

e

eff 0 1 2 a

T CCCS g (H-1)

where, C0, C1, and C2 are coefficients from ASCE 41, Sa is the response 

spectrum pseudo acceleration at period Te, and g is the acceleration of 
H-2 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

gravity. In Equation H-1, the quantity Sa(Te

2

/4π2)g is the spectral 

displacement, Sd, at period Te. Coefficients C0, C1, and C2 modify the 

spectral displacement to estimate the roof displacement considering the 

effects of several modeling and nonlinear behavioral factors. 

Coefficient C0 is a modification factor to relate spectral displacement of an 

equivalent single-degree-of-freedom (SDOF) system to the displacement at 

the effective height of the building multi-degree-of-freedom (MDOF) 

system. Values of C0 were found to range from 0.9 to 1.1 for typical 

buildings. Given the small variability of C0, this term was set equal to 1.0 

and dropped from the equation in the methodology. 

Values of heff were calculated for typical multi-story frame or frame-wall 

buildings. It was found that a value of 0.7hn is a close approximation of the 

actual value of heff, except heff = 1 for one-story buildings.

Coefficient C1 and C2 are adopted directly from ASCE 41. 

H.2.2 Comparison with Results of Nonlinear Response History 

Analyses

To check the accuracy of Equation H-1, incremental dynamic analyses were 

carried out on a series of 4, 6, 8, and 12-story frames designed to be 

representative of older concrete buildings. Figure H-1 illustrates the 

configuration of an exterior frame. Interior frames were designed as gravityonly frames. The frames included columns whose failure mode was 

controlled by either inelastic flexure or by shear and axial failure. The 

frames were proportioned to have resistance in proportion with demands 

from an inverted triangular lateral loading, except weak stories were 

introduced into some of the frames for the purposes of this study. See 

Galanis and Moehle (2015) for additional details.

Figure H-1 Schematic elevation of the simulated 4-story 

frames. 

The study confirmed that cyclic degradation does not appreciably affect the 

predictive accuracy of Equation H-1 for buildings having vibration periods 
FEMA P-2018 H: Development of Procedures to H-3

Estimate Story Drift Demands

exceeding 1.0 second. Furthermore, the study showed that Equation H-1 is 

more accurate for buildings with damage distributed over height of the 

building and less accurate for buildings with a weak story leading to 

concentrated damage. Some results of the study are summarized in the 

following paragraphs.

Table H-1 presents the coefficients C0, C1, and C2 employed in Equation H-1

for the studied frame buildings.

Table H-1 Coefficients C0, C1, and C2 of the Studied Buildings

Parameter 4-Story 6-Story 8-Story 12-Story

Period Te (sec) 1.14 1.38 1.62 1.95

C0 1.09 1.05 1.11 0.94

C1 1.00 1.00 1.00 1.00

C2 1.00 1.00 1.00 1.00

Table H-2 presents the mean ratios of displacements of the 6-story idealized 

building from the inelastic dynamic analyses and those obtained from 

Equation H-1, all reported at the effective modal height, heff. In Table H-2, 

∑Mc/∑Mb refers to the ratio of the sum of column nominal moment strengths 

to the sum of beam nominal moment strengths at each beam-column joint, 

and Vp/Vn refers to the ratio of column plastic shear demand (determined as 

twice the nominal moment strength Mn divided by the column clear height lu) 

divided by the column nominal shear strength calculated in accordance with 

ASCE 41 with cyclic strength degradation factor k = 1. Similar results were 

found for the 4, 8, and 12-story frames.

Table H-2 Average Ratio of (Maximum Displacement at Effective Modal 

Height of Non-Linear Analysis) / (Estimated Displacement at 

Effective Modal Height) for Different Vp/Vn and Mc/Mb Ratios 

of the 6-Story Idealized Building

Vp/Vn

ΣΜc/ΣΜb 0.6 0.8 1.0 1.2

0.6 0.79 0.81 0.90 1.00

0.8 0.79 0.81 0.89 1.00

1.0 0.79 0.81 0.88 0.98

1.2 0.85 0.80 0.81 0.91

1.4 1.03 0.90 0.85 0.83

1.6 1.18 1.03 0.94 0.87

1.8 1.30 1.15 1.02 0.95
H-4 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

It was of interest to establish whether building lateral strength would affect 

the accuracy of displacement calculations. The preferred method to carry out 

this investigation would be to design several buildings with different lateral 

strengths and observe the effect on displacement estimation. For the present 

study, however, an alternative approach was used that made use of readily 

available data. Specifically, a building frame was subjected to ground 

motions scaled to progressively increasing intensity, and the displacements 

obtained from nonlinear dynamic analysis for each scaling factor were 

compared with the results of Equation H-1. The process was repeated for 

each of 44 different earthquake ground motions from FEMA P-695 (FEMA, 

2009). The results are presented as a function of the effective demand to 

capacity ratio, μstrength, defined as μstrength = SaW/ Vy, where Vy equals the base 

shear strength calculated from nonlinear static analysis under lateral loads 

distributed in an inverted triangular pattern. Figure H-2 presents a sample of 

the results. 

ΣΜc/ΣΜb=0.60 ΣΜc/ΣΜb=0.80 ΣΜc/ΣΜb=1.00 ΣΜc/ΣΜb=1.20

(a) (b) (c) (d)

ΣΜc/ΣΜb=1.40 ΣΜc/ΣΜb=1.60 ΣΜc/ΣΜb=1.80

(e) (f) (g)

Figure H-2 Ratio of (maximum displacement at effective modal height of non-linear analysis) / (estimated 

displacement at effective modal height) for different μstrength values. 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 Actual Displ. / Estimated Displ. 

 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 g p 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 g p 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 g p 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 g p 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 g p 

1 2 3 4 5 6 7 8 9 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

 Rindex

 

Each plotted point in Figure H-2 corresponds to a single earthquake ground 

motion at a particular scaling factor. The actual value of μstrength in each case 

is truncated to an integer value for plotting (the integer values are designated 

Rindex in Figure H-2). The red broken curve represents the mean of the 

results, and the green broken curves represent mean plus and minus one 
FEMA P-2018 H: Development of Procedures to H-5

Estimate Story Drift Demands

standard deviation of the results. The results indicate that, for most of the 

cases, Equation H-1 provides a conservative estimate of the expected 

maximum displacement at the effective modal height. The accuracy of the 

displacement estimation improves as the ratio of column to beam strengths 

increases.

H.3 Studies of the Story Drift Demand

H.3.1 Basic Procedure to Calculate Story Drift Demand

The basic procedure to calculate story drift demand is to use the assign a 

fraction of the total SDOF drift δeff to various stories based on the 

configuration and strength characteristics of the building, that is, story drift 

demand, δx, of story x is defined as:

eff

x x sx eff

eff

h

h

δ

δα δ

  =   ≤    

(H-2)

where:

αx = coefficient to modify story drifts at story x for building 

configuration and strength characteristics, and

hsx = height of story x

Values of αx are determined based on: (a) results of inelastic analyses of 

numerical models of multi-story buildings; and (b) judgment of the project 

team. The remainder of this section presents representative findings from the 

inelastic analyses.

H.3.2 Bare Frames

The values of coefficient α were explored for a series of uniform planar 4- to 

12-story frames having nearly equal story height in every story, designed to 

have strength closely matching the demands associated with a load 

combination comprising: (a) gravity load; and (b) lateral load equal to 0.1W

distributed in an inverted triangular load pattern. They were subjected to a 

series of 44 far-field ground motions with scaling factors gradually increased 

until collapse was obtained. Collapse was defined as either side-sway 

collapse when the maximum story drift ratio exceeded 10% or vertical 

collapse when more than 50% of the columns of a story failed from shearinduced axial load failure. Values of α were mined for a ground motion 

scaling factor slightly less than the factor required to achieve collapse.
H-6 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

(a) (b)

(c) (d)

Figure H-3 Alpha factor story profiles for different variations of the 4-story idealized building. 

1

2

3

4

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=0.60

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

1

2

3

4

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=0.80

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

1

2

3

4

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=1.00

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

1

2

3

4

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=1.20

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

Figure H-4 Alpha factor mean value at 1st story for different variations of the 

4-story idealized building. 

0.00

0.50

1.00

1.50

2.00

2.50

0.6 0.8 1 1.2 1.4 1.6 1.8

a1

ΣΜc/ΣΜb

Vp/Vn=0.60

Vp/Vn=0.80

Vp/Vn=1.00

Vp/Vn=1.20
FEMA P-2018 H: Development of Procedures to H-7 

Estimate Story Drift Demands

(a) (b)

(c) (d)

Figure H-5 Alpha factor story profiles for different variations of the 8-story idealized building.

1

2

3

4

5

6

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Story

Alpha Factor

Vp/Vn=0.60

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

1

2

3

4

5

6

7

8

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=0.80

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

1

2

3

4

5

6

7

8

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=1.00

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

1

2

3

4

5

6

7

8

0.00 0.50 1.00 1.50 2.00 2.50

Story

Alpha Factor

Vp/Vn=1.20

ΣΜc/ΣΜb=0.60

ΣΜc/ΣΜb=0.80

ΣΜc/ΣΜb=1.00

ΣΜc/ΣΜb=1.20

ΣΜc/ΣΜb=1.40

ΣΜc/ΣΜb=1.60

ΣΜc/ΣΜb=1.80

Figure H-6 Alpha factor mean value at 1st story for different variations of the 

8-story idealized building. 

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.6 0.8 1 1.2 1.4 1.6 1.8

a1

ΣΜc/ΣΜb

Vp/Vn=0.60

Vp/Vn=0.80

Vp/Vn=1.00

Vp/Vn=1.20

Vp/Vn=0.60

Vp/Vn=0.80

Vp/Vn=1.00

Vp/Vn=1.20

For taller frames, failures for some ground motions occur in the first story 

while failures for different ground motions occur in upper stories. The latter 

failures occur due to apparent higher-mode effects. Because failure can 
H-8 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

occur in one of several stories, the mean drift ratio for any story ends up 

being dominated by several collapse realizations in which collapse occurs in

other stories. Thus, although the alpha value correctly represents the mean, it

does not provide a good indication of the story drift for those realizations in 

which collapse occurs in that story. To better understand this behavior, 

values of α were recalculated for each story considering only those cases in 

which that story was the one that collapsed. The mean values for α are 

provided in Table H-3.

Table H-3 Mean Values for αα Factor for the 1st Story only for a 6-story 

Idealized Building with Critical 1st Story

Vp/Vn

ΣMc/ΣMb 0.6 0.8 1 1.2

0.8 2.56 2.04 1.91 1.93

1.2 2.16 1.53 1.55 1.69

1.8 1.75 1.61 1.46 1.34

Values of α were also explored for frames with weak stories at the first level 

or at other levels. For example, the 6-story building described previously

was modified by increasing the strength of all the stories except the critical

story by 50%. Two cases where explored. In the first case the critical story 

was located in the 1st story of the building, while in the second case the 

critical story was located in the 4th story.

For the frame with the critical first story, most of the inelastic deformation 

was concentrated in the first story for all combinations of variables, with 

results similar to those reported previously. For the frame with a critical

fourth story, most of the inelastic deformation was concentrated in the fourth 

story (Figures H-7 through H-9).

Studies were also carried out to explore effects of inadequate lap length for 

column longitudinal reinforcement and light transverse reinforcement. 

Damage at such locations is likely to result in rapid loss of moment 

resistance at the location of the lap splice.

To study this behavior, a strength-degrading plastic hinge was introduced at 

assumed locations of lap splices in the model buildings. The inadequate lap 

splicing conditions were modeled according to the experimental results 

provided by Melek and Wallace (2004). The backbone rotational behavior of 

the plastic hinge modeling the inadequate lap splicing conditions is shown in 

Figure H-10.
FEMA P-2018 H: Development of Procedures to H-9 

Estimate Story Drift Demands

Vp/Vn = 0.60 Vp/Vn = 0.80

(a) (b)

Vp/Vn = 1.00 Vp/Vn = 1.20

 

(c) (d)

Figure H-7 Alpha factor story profiles for different variations of the 6-story idealized building with a critical 4th

story. 
H-10 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

ΣMc/ΣMb

Figure H-8 Alpha factor mean value at 1st story for different variations of the 

6-story idealized building with a critical 4th story. 

ΣMc/ΣMb

Figure H-9 Alpha factor mean value at 4th story for different variations of 

the 6-story idealized building with a critical 4th story. 

Figure H-10 Zero-length plastic hinge rotational behavior for 

adequate and inadequate lap splicing conditions. 
FEMA P-2018 H: Development of Procedures to H-11

Estimate Story Drift Demands

Nonlinear dynamic analyses were conducted on model frames with flexurecritical columns (Vp/Vn = 0.6) including lap splices. Frames with different 

ΣΜc/ΣΜb ranging from 0.8 to 1.6 were investigated. Figures H-11 through 

H-13 illustrate representative results for the case of lap splices introduced 

into the bottom of the 1st and 4th stories of the 8-story frame. The results 

demonstrate that, for the case of buildings with a tendency to form weak 

stories (that is, ΣΜc/ΣΜb ≤ 1.20), the lap-splice has minimal effect. On the 

other hand, for cases where the building has a tendency for a more uniform 

drift profile (that is, ΣΜc/ΣΜb > 1.20) the lap splice magnifies the drift in the 

story containing the lap splice. 

Figure H-11 Alpha factor story profiles for different variations of the 8-story building with and without 

inadequate lap-splicing conditions. (Vp/Vn = 0.6 in the above building variations)
H-12 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Figure H-12 Alpha factor story profiles for different variations of the 8-story building with and without 

inadequate lap-splicing conditions. (Vp/Vn = 0.6 in the above building variations.) 
FEMA P-2018 H: Development of Procedures to H-13

Estimate Story Drift Demands

Figure H-13 Alpha factor story profiles for different variations of the 8-story building with inadequate lapsplicing conditions at the 1st and 4th critical story. (Vp/Vn = 0.6 in the above building variations)

The main observations are as follows:

• Very little amplification occurs where Vp/Vn > 1.0. This is apparently 

because only limited yielding of the column longitudinal reinforcement 

occurs in this case, such that the lap splices seldom fail. 

• Relatively little amplification occurs for the case of ΣMc/ΣMb ≤ 1.2, 

whereas greater amplification occurs for ΣMc/ΣMb > 1.2. Apparently, the 

former case corresponds to a case for which a weak story is already 

formed because of the weak columns, such that further reduction in 

strength due to splice failure does not significantly exacerbate the story 

failure. For the latter case, the presence of the lap splice results in 

reduced moment strength at one end of the column if the column yields, 

which tends to produce a weak-story condition. However, because the 

columns are stronger than the beams, the extent of column yielding is 

reduced, such that the amplification factor again is not much affected. 
H-14 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

H.3.3 Frames and Walls

Several studies of frame-wall structures were carried out. Most of the 

analyses were inelastic static (pushover) analyses. Results were spot checked 

using inelastic dynamic analyses, with the conclusion that the static analyses 

adequately represented the key behaviors of interest. Only the static analysis 

results are shown here.

H.3.3.1 Case 1: Frame Plus One Continuous Wall

The values of coefficient α were explored for several 4- and 8-story framewall planar structures. Inelastic response in walls was restricted to inelastic 

flexure. Section H.2.2 introduced the archetype structure used for analysis of 

bare frames, also considered here. Additionally, to evaluate the sensitivity of 

values of coefficient α under variations in frame detailing, two other 

modifications of archetype frames were considered: modified frame 1 (cross 

section of first story beams assigned for all beams) and modified frame 2 

(cross section of top story beams assigned for all beams). Analyzed cases 

included a frame plus one continuous rectangular wall, as presented in Figure 

H-14. Figure H-15 shows the typical wall cross section.

Figure H-14 Schematic elevation view of the simulated 8-story frame plus 

one rectangular wall. 

Figure H-15 Typical wall cross section.
FEMA P-2018 H: Development of Procedures to H-15

Estimate Story Drift Demands

Several values of wall length Lw were considered to evaluate the influence of 

the wall stiffness and strength on values of coefficient α. Beam gravity loads 

were those applied for analysis of bare frames. In walls, a constant gravity 

force was applied at each story to obtain an axial force demand at the base of 

0.1 c g f A′ , where Ag is the wall cross-sectional area.

The values of coefficient α were estimated for each case from nonlinear 

static analysis considering an inverted triangular force pattern, increased until 

collapse was obtained. Tables H-4 to H-6 present the values of coefficient

α for 4-story frame-wall structures, where the parameter index is the ratio 

between the wall area and the total floor tributary area of the analyzed 

structure.

Table H-4 Values of Coefficient α Estimated from Pushover Analysis for a 

4-Story Archetype Frame Plus One Continuous Wall

Story

Archetype Frame + Wall

Wall Length Lw (in.)

50 60 70 80 125 225 250 275 300

Index = Ag / Afloor

0.0004 0.0004 0.0005 0.0006 0.0009 0.0016 0.0018 0.0019 0.0021

1 1.0 1.0 0.9 1.0 0.9 1.0 1.0 1.0 1.0

2 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

4 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Table H-5 Values of Coefficient α Estimated from Pushover Analysis for a 

4-Story Modified Frame I Plus One Continuous Wall

Story

Modified Frame I + Wall

Wall Length Lw (in.)

50 60 70 80 125 225 250 275 300

Index = Ag / Afloor

0.0004 0.0004 0.0005 0.0006 0.0009 0.0016 0.0018 0.0019 0.0021

1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

2 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

4 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
H-16 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Table H-6 Values of Coefficient α Estimated from Pushover Analysis for a 

4-Story Modified Frame 2 Plus One Continuous Wall

Story

Modified Frame II + Wall

Wall Length Lw (in.)

50 60 70 80 125 225 250 275 300

Index = Ag / Afloor

0.0004 0.0004 0.0005 0.0006 0.0009 0.0016 0.0018 0.0019 0.0021

1 1.0 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0

2 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

4 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Figure H-16 presents a comparison between the collapse mechanism of a 

4-story bare frame and the same frame with an added 50 in. wall.

(a) (b)

Figure H-16 Collapse mechanism for a 4-story 

structure: (a) bare frame; (b) frame 

plus 50 in. wall.
FEMA P-2018 H: Development of Procedures to H-17

Estimate Story Drift Demands

Data presented in Tables H-4 to H-6 and Figure H-16 suggest that the 

presence of a short wall suffices to completely change the frame collapse 

mechanism, preventing soft story from occurring, and obtaining story drift 

ratios nearly equal to the roof drift ratio at all stories.

Tables H-7 to H-9 present the values of coefficient α for 8-story frame-wall 

structures.

Table H-7 Values of Coefficient α Estimated from Pushover Analysis for an 8-Story 

Archetype Frame Plus One Continuous Wall

Story

Archetype Frame + Wall

Wall Length Lw (in.)

50 60 70 90 100 125 175 225 275 300

Index = Ag / Afloor

0.0002 0.0002 0.0002 0.0003 0.0004 0.0004 0.0006 0.0008 0.0010 0.0011

1 0.7 0.8 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9

2 1.2 1.1 1.0 0.9 0.9 0.9 0.9 0.9 0.9 1.0

3 1.3 1.2 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0

4 1.3 1.2 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0

5 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0

6 1.1 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0

7 0.8 0.9 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.0

8 0.6 0.7 0.9 1.0 1.0 1.1 1.1 1.1 1.1 1.0

Table H-8 Values of Coefficient α Estimated from Pushover Analysis for an 8-Story 

Modified Frame I Plus One Continuous Wall

Story

Modified Frame I + Wall

Wall Length Lw (in.)

50.0 60.0 70.0 90.0 100.0 125.0 175.0 225.0 275.0 300.0

Index = Ag / Afloor

0.0002 0.0002 0.0002 0.0003 0.0004 0.0004 0.0006 0.0008 0.0010 0.0011

1 1.1 1.1 1.0 0.8 0.8 0.8 0.8 0.9 0.9 0.9

2 1.5 1.3 1.2 1.0 1.0 1.0 0.9 0.9 1.0 1.0

3 1.6 1.4 1.3 1.1 1.1 1.0 1.0 1.0 1.0 1.0

4 1.3 1.3 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0

5 1.0 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0

6 0.7 0.8 0.9 1.0 1.0 1.1 1.1 1.1 1.0 1.0

7 0.4 0.5 0.7 0.9 1.0 1.0 1.0 1.1 1.0 1.0

8 0.3 0.4 0.6 0.9 1.0 1.0 1.0 1.1 1.0 1.0
H-18 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Table H-9 Values of Coefficient α Estimated from Pushover Analysis for an 8-Story 

Modified Frame II Plus One Continuous Wall

Story

Modified Frame II + Wall

Wall Length Lw (in.)

50.0 60.0 70.0 90.0 100.0 125.0 175.0 225.0 275.0 300.0

Index = Ag / Afloor

0.0002 0.0002 0.0002 0.0003 0.0004 0.0004 0.0006 0.0008 0.0010 0.0011

1 1.2 0.9 1.0 0.9 0.9 0.9 0.9 0.9 0.9 0.9

2 1.5 1.3 1.2 1.1 1.0 1.0 1.0 1.0 1.0 1.0

3 1.5 1.4 1.2 1.1 1.1 1.0 1.0 1.0 1.0 1.0

4 1.4 1.4 1.2 1.1 1.1 1.0 1.0 1.0 1.0 1.0

5 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0

6 0.7 0.8 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0

7 0.4 0.6 0.8 0.9 1.0 1.0 1.0 1.0 1.0 1.0

8 0.3 0.4 0.7 0.9 0.9 1.0 1.0 1.0 1.0 1.0

According to Tables H-7 to H-9, 8-story frames require a wall longer than 50 

inches in length to obtain all values of coefficient α close to 1. 

H.3.3.2 Case 2: Frame Plus Two Continuous Walls 

For this case, the values of coefficient α were determined for several 4- and 

8-story frame-wall planar structures, considering only the archetype frame

plus two rectangular, flexure-controlled continuous walls. Figure H-17 

shows a schematic elevation view of one of the analyzed structures. 

Considering cases including only walls with equal cross section, previously 

presented in Figure H-15. As before, constant gravity forces are applied at 

each story to obtain an axial force demand of 0.1 c g f A′ at the base of each 

wall, and the distributed gravity loads in beams are those used before for the 

analysis of bare frames.

Figure H-17 Schematic elevation view of the simulated 4-story frame plus 

two rectangular walls.

Only a few cases are presented here to demonstrate that two short walls, 50 

in. length, suffice to obtain all values of coefficient α equal to 1. Tables 

H-10 and H-11 present the calculated values from nonlinear static analysis. 
FEMA P-2018 H: Development of Procedures to H-19

Estimate Story Drift Demands

Table H-10 Values of Coefficient α Estimated from Pushover Analysis for 

a 4-Story Archetype Plus Two Continuous Walls

Story

Archetype Frame + 2 Continuous Walls

Wall Length Lw (in.)

50 60 70

1 0.9 1.0 1.0

2 1.0 1.0 1.0

3 1.0 1.0 1.0

4 1.0 1.0 1.0

Table H-11 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus Two Continuous Walls

Story

Archetype Frame + 2 Continuous Walls

Wall Length Lw (in.)

50 60 70

1 1.0 1.0 1.0

2 1.1 1.0 1.0

3 1.1 1.0 1.0

4 1.0 1.0 1.0

5 1.0 1.0 1.0

6 1.0 1.0 1.0

7 0.9 1.0 1.0

8 0.9 1.0 1.0

H.3.4 Frames with Walls Discontinuous in the First Story

This section presents the values of coefficient α for several 4- and 8-story 

frame-wall planar structures, considering the archetype frame plus two walls 

of equal cross section. One of the walls is continuous and the other one is 

discontinuous in the first story, where two non-ductile columns (18×18 in. 

cross section with 1% longitudinal steel ratio) support it. Figure H-18

presents and schematic elevation view of one of these cases.

Regarding gravity loads, the beams and the continuous wall are treated as in 

the previous sections. For the discontinuous wall, a constant gravity force is 

applied at each story to obtain an axial force demand at each of the 

supporting columns of 0.15 c g f A′ , where Ag is the column area.
H-20 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Figure H-18 Schematic elevation view of the simulated 8-story frame plus 

two rectangular walls, one discontinuous in the first story. 

Tables H-12 and H-13 present the values of coefficient α calculated for these 

cases.

Table H-12 Values of Coefficient α Estimated from Pushover Analysis for 

a 4-Story Archetype Plus One Continuous Wall and One 

Discontinuous Wall in the First Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.)

50 60 70 80 90 100

1 1.0 1.0 1.0 1.0 1.0 1.0

2 1.0 1.0 1.0 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0 1.0 1.0

4 1.0 1.0 1.0 1.0 1.0 1.0

Table H-13 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Discontinuous Wall in the First Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.)

50 60 70 80 90 100

1 1.0 1.0 1.0 1.0 1.0 1.0

2 1.0 1.0 1.0 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0 1.0 1.0

4 1.0 1.0 1.0 1.0 1.0 1.0

5 1.0 1.0 1.0 1.0 1.0 1.0

6 1.0 1.0 1.0 1.0 1.0 1.0

7 1.0 1.0 1.0 1.0 1.0 1.0

8 1.0 1.0 1.0 1.0 1.0 1.0
FEMA P-2018 H: Development of Procedures to H-21

Estimate Story Drift Demands

For this case two 50 in. walls suffice to obtain a collapse mechanism with 

constant story drift ratio equal to the roof drift ratio. However, when one of 

the walls is discontinuous and supported by two nonductile columns, collapse 

is driven by capacity loss in the column below the discontinuous walls that is 

being compressed by lateral loading. Figure H-19 presents one of these cases 

(4-story frame plus two 50 in. walls), where one of the supported columns 

experienced sudden strength loss at roof drift ratio of 2.5%.

(a) (b)

Figure H-19 8-story frame plus two 50 in. walls building, one discontinuous

and supported by discontinuous columns: (a) axial force versus 

drift ratio; (b) bending moment versus drift ratio.

Analyses also included cases where the discontinuous wall was supported by 

two columns detailed to result in ductile axial force-displacement behavior, 

as might be anticipated in a column with modern details or a column that has 

been retrofitted by external jacketing. These cases showed a considerable 

improvement in the structural performance of these columns, as presented in 

Figure H-20, where the sudden strength loss is not observed. 
H-22 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

(a) (b)

Figure H-20 8-story frame plus two 50 in. walls building, one discontinuous

and supported by ductile columns: (a) axial force versus drift 

ratio; (b) bending moment versus drift ratio.

H.3.5 Frames with Walls Discontinuous in Upper Stories

In this section, values of coefficient α are calculated for frame-wall 

structures that comprise the archetype frame plus two walls of equal cross 

section, where one of the walls is discontinuous in an upper story. Different 

cases are studied to evaluate the sensitivity of values of coefficient α under 

several structural configurations. Both walls have an axial force demand due 

to gravity load of 0.1 c g f A′ at the base. Gravity forces in beams are those 

described in previous sections.

Figure H-21 Schematic elevation view of the simulated 8-story frame plus 

two rectangular walls, one discontinuous in upper story. 

Tables H-14 to H-23 present the values of coefficient α calculated for these 

cases.
FEMA P-2018 H: Development of Procedures to H-23

Estimate Story Drift Demands

Table H-14 Values of Coefficient α Estimated from Pushover Analysis for 

a 4-Story Archetype Plus One Continuous Wall and One Wall 

That Ends in the Third Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 1

50 60 70 80 90 100 150 200

1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8

2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1

3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1

4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1

Table H-15 Values of Coefficient α Estimated from Pushover Analysis for 

a 4-Story Archetype Plus One Continuous Wall and One Wall 

That Ends in the Second Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 2

50 60 70 80 90 100 150 200

1 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.8

2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1

3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1

4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1

Table H-16 Values of Coefficient α Estimated from Pushover Analysis for 

a 4-Story Archetype Plus One Continuous Wall and One Wall 

That Ends in the First Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 3

50 60 70 80 90 100 150 200

1 1.0 0.9 0.8 0.8 0.5 0.4 0.3 0.3

2 1.0 1.0 1.1 1.1 1.2 1.2 1.2 1.2

3 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.3

4 1.0 1.0 1.1 1.1 1.2 1.3 1.3 1.3
H-24 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Table H-17 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Wall That Ends in the Seventh Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 1

70 80 90 100

1 0.8 0.9 0.9 0.9

2 1.0 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0

4 1.0 1.0 1.0 1.0

5 1.1 1.1 1.0 1.0

6 1.1 1.1 1.0 1.0

7 1.0 1.0 1.0 1.0

8 1.0 1.0 1.0 1.0

Table H-18 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Wall That Ends in the Sixth Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 2

70 80 90 100

1 0.9 0.9 0.9 0.7

2 1.0 1.0 1.0 0.8

3 1.0 1.0 1.0 1.0

4 1.0 1.0 1.0 1.1

5 1.0 1.0 1.0 1.1

6 1.0 1.0 1.0 1.1

7 1.0 1.0 1.0 1.1

8 1.0 1.0 1.0 1.1
FEMA P-2018 H: Development of Procedures to H-25

Estimate Story Drift Demands

Table H-19 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and one 

Wall That Ends in the Fifth Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 3

70 80 90 100

1 0.6 0.9 0.9 0.8

2 0.8 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0

4 1.1 1.0 1.0 1.0

5 1.1 1.0 1.0 1.0

6 1.2 1.0 1.0 1.0

7 1.2 1.0 1.0 1.0

8 1.1 1.0 1.0 1.0

Table H-20 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Wall That Ends in the Fourth Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 4

70 80 90 100

1 0.8 0.9 0.9 0.8

2 0.9 1.0 1.0 1.0

3 1.0 1.0 1.0 1.0

4 1.0 1.0 1.0 1.0

5 1.1 1.0 1.1 1.0

6 1.1 1.0 1.1 1.0

7 1.0 1.0 1.1 1.0

8 1.0 1.0 1.0 1.0
H-26 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Table H-21 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Wall That Ends in the Third Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 5

70 80 90 100

1 0.3 0.7 0.9 0.8

2 0.6 0.9 1.0 1.0

3 0.8 1.0 1.0 1.0

4 1.1 1.0 1.0 1.0

5 1.3 1.1 1.0 1.1

6 1.4 1.1 1.0 1.1

7 1.3 1.1 1.0 1.0

8 1.2 1.1 1.0 1.0

Table H-22 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Wall That Ends in the Second Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 6

70 80 90 100

1 0.0 0.1 0.1 0.1

2 0.1 0.1 0.2 0.1

3 1.1 1.1 1.1 1.1

4 1.4 1.4 1.3 1.4

5 1.4 1.4 1.4 1.4

6 1.4 1.4 1.4 1.4

7 1.4 1.4 1.4 1.4

8 1.3 1.4 1.4 1.4
FEMA P-2018 H: Development of Procedures to H-27

Estimate Story Drift Demands

Table H-23 Values of Coefficient α Estimated from Pushover Analysis for 

an 8-Story Archetype Plus One Continuous Wall and One 

Wall That Ends in the First Story

Story

Archetype Frame + Continuous Wall + Discontinuous Wall

Wall Length Lw (in.) Dn = 7

70 80 90 100

1 0.0 0.2 0.0 0.0

2 0.6 0.8 0.7 0.8

3 1.3 1.1 1.2 1.2

4 1.3 1.2 1.2 1.2

5 1.3 1.3 1.2 1.2

6 1.3 1.3 1.2 1.2

7 1.2 1.2 1.2 1.2

8 1.2 1.2 1.2 1.2

These limited analyses show that, for the studied 4-story building, ending the 

discontinuous wall in the second story or above did not have an appreciable

effect in the values of coefficient α. However, when the discontinuous wall 

ended in the first story, for 90 in. wall or longer, the collapse mechanism 

changed and it occurred above the first story. For 8-story buildings, similar 

behavior was clear for discontinuous walls ending in the second story or 

below, for 70 in. walls or above.

The results obtained from the static inelastic analyses were compared with 

results from the mechanism analysis of Chapter 5. For this limited set of 

archetypes, the mechanism analysis was able to identify the inelastic yielding 

mechanism of the archetype.

H.3.6 Buildings with Shear-Critical Walls

Modeling of shear critical walls is a task of ongoing investigation due to the 

complexities involved in adequately reproducing axial/flexural shear 

interactions. In this section, a simple approach is used to study the impact of 

shear critical walls that are coupled to frames, in which an elastic-perfectly 

plastic shear spring is connected in series with the beam-column flexural 

element representing the wall at a given critical story (Figure H-22). As 

shown in Figure H-22c, the horizontal drift at a given story has two 

components, a flexural deformation, δf, and a shear deformation, dv. In this 

setup, a coupled shear/flexure response is only possible for strain-hardening 

behavior at the constitutive level of each component.
H-28 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Figure H-22 Schematic elevation view of an 8-story wall with a shear critical 

story. (b) model of shear frame plus two rectangular walls, one 

discontinuous in upper story.

This model can also be thought of as a set of two springs in series as 

presented in Figure H-23a. For an elastoplastic response (Figure H-23b), in 

which the shear spring capacity is smaller than the associated shear capacity 

for flexural yielding, all the plastic demand will be concentrated in the shear 

spring. 

Figure H-23 (a) Two-spring in series model. (b) Response of each individual 

component representing flexure and shear.
FEMA P-2018 H: Development of Procedures to H-29

Estimate Story Drift Demands

The setup used to model shear critical stories in this study is based on the 

description presented above with a shear spring whose capping strength is 

given by ACI 318 provisions.

H.3.6.1 Static Response: Pushover Analyses

Figure H-22a shows an isolated cantilever wall, with a shear critical section 

at the base. Under an inverted triangular static load pattern, the minimum 

shear strength (Vsp,min) at the base to guarantee flexural failure is given by 

Equation H-3:

Vspt,min > (3/2) Mpr/Hw (H-3)

where Mpr is the expected flexural strength at the base and Hw is the height of 

the wall. For a uniform (rectangular) pattern of lateral loading, the minimum 

required shear strength increases to:

Vspr,min > 2Mpr/Hw (H-4)

Figures H-24 to H-26 describe the response of a frame-wall system with a 

wall having a shear critical cross-section at the first story. In each figure, 

plot (a) shows the building roof drift versus the base shear (pushover curve)

along with a point of interest marked with a square, plot (b) shows the 

displaced shape along with the plastic hinges formed at the noted point, plot 

(c) shows the story drift ratio (SDR) and the displaced shape at the noted

point, figure (d) shows the alpha values of the building (in red) at the noted

point along with the theoretical alpha distribution for a cantilever wall at 

yielding, (e1) shows the base reaction of each component of the frame-wall 

system, (e2) the moment-curvature relationship at the base of the wall, and 

(e3) shows the demand on the shear spring.

The only difference among the models is the strength of the shear spring at 

the first story. Variable Vns defines the provided shear strength of the wall at 

the critical section. Provided shear strength ratio, Vns/Vspr,min, are 1.5, 1.1 and 

0.5 for buildings in Figure H-24 trough to Figure H-26, respectively. It is 

worth noting that this strength is defined for an isolated cantilever wall. The 

three cases of study defined are: (i) building with a strong spring (BSS), 

where the shear spring expected to remain linear (Figure H-24); (ii) building 

with adequate shear strength (BAS), where the shear spring strength is 10% 

larger than the demand required to yield it under a rectangular load pattern in 

an isolated cantilever wall (Figure H-25); and (iii) building with a weak 

shear spring (BWS), where the wall is expected to fail in shear prior reaching 

its flexural strength (Figure H-26).

Response of the shear spring in the BSS model is linear (Figure H-24e3). 

The alpha value for the building is close to 1.0, reminding that the wall is 
H-30 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

stiff (e.g., Lw = 200 in.) and strong enough as to command the response of the 

whole structure. The first story alpha value of the building is smaller than 

1.0, following the trend of the theoretical closed-form solution of a cantilever 

wall at yielding.

Figure H-24 Response of the 8-story archetype frame-wall structure for wall 

length Lw = 200 in. with a shear critical section at the wall base. 

Simulation for a strong spring Vns/Vspr,min = 1.5 (BSS model). 

Roof drift

ratio [%]

Base shear / W [%]

Normalized height

Disp. (j) / H or 

Story drift ratio

Alpha (j) Shear Distortion

Curvature [1/in.]

Roof drift ratio [%]

Wall shear 

force [kips] Wall base moment [kip-in.] Base reaction / W [%]

elastic shear

spring

frame-wall system

isolated 

cantilever 

wall (theor.)

Plastic Hinge 

Projector

(a) (b) (c) (d)

(e1)

(e2)

(e3)

Figure H-25 Response of the 8-story archetype frame-wall structure for wall 

length Lw = 200 in. with a shear critical section at the wall base. 

Simulation for Vns/Vspr,min = 1.1 (BAS model). 

Roof drift

ratio [%]

Base shear / W [%]

Normalized height

Disp. (j) / H or 

Story drift ratio

Alpha (j) Shear Distortion

Curvature [1/in.]

Roof drift ratio [%]

Wall shear 

force [kips] Wall base moment [kip-in.] Base reaction / W [%]

frame-wall system

isolated 

cantilever 

wall (theor.)

Plastic Hinge 

Projector

shear

strength

(a) (b) (c) (d)

(e1)

(e2)

(e3)

For the BAS model, it is observed that although the shear spring strength 

ratio is larger than 1.0, the wall shear spring yields (Figure H-25e3), 

implying that coupling of the wall and the frame may result in an arm of the 

resultant forces along the wall that is closer to the base, shorter than that of a 
FEMA P-2018 H: Development of Procedures to H-31

Estimate Story Drift Demands

triangular or a rectangular load pattern (e.g., (2/3)Hw or (1/2)Hw, 

respectively). This increase in the shear force distribution along the wall 

height is likely to be more pronounced under dynamic loading due to 

apparent higher-mode effects. Figure H-25c shows that alpha values for the 

BAS model are still close to 1.0, but it is already developing drift demand 

concentration at the shear critical story.

The BWS model shows an apparent concentration of drift at the first story. 

Flexural strength at the base of the wall is not developed, and the force 

demand is concentrated in the weak shear spring (Figures H-26e2 and 

H-26e3). Figure H-26b shows a soft 1st -story forming, with alpha values 

reaching 2.0 at that location. 

Although BWS model results are expected, behavior of the BSS, and the 

BAS model need to be analyzed in the dynamic domain to account for 

apparent higher mode effect that are likely to increase the shear demand 

along the height of the wall, and may trigger shear failures not observable 

under pushover analyses. 

Figure H-26 Response of the 8-story archetype frame-wall structure for wall 

length Lw = 200 in. with a shear critical section at the wall base. 

Simulation for a weak spring Vns/Vspr,min = 0.5 (BWS model). 

Roof drift

ratio [%]

Base shear / W [%]

Normalized height

Disp. (j) / H or 

Story drift ratio

Alpha (j) Shear Distortion

Curvature [1/in.]

Roof drift ratio [%]

Wall shear 

force [kips] Wall base moment [kip-in.] Base reaction / W [%]

weak shear

spring

frame-wall system

isolated 

cantilever 

wall (theor.)

Plastic Hinge 

Projector

(a) (b) (c) (d)

(e1)

(e2)

(e3)

H.3.6.1 Dynamic Response

In this section, the wall-frame systems described above are studied under 

dynamic loading. It is of special interest to evaluate the likelihood of shear 

failure in buildings with stronger shear springs. Building models BSS, BAS, 

and BWS are evaluated under three sets of ground motions of increasing 

intensity: low hazard set (LH); intermediate hazard set (IH); and high hazard 

set (HH) (Figure H-27). 
H-32 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Figure H-28 shows the response of the building whose wall behavior is 

dominated by the shear spring (BWS model in Figure H-26). Given the 

fragile nature of the wall at the first story, responses shown only include 

those associated to the lower demand set of ground motions (e.g., LH set). 

Alpha values are separated according to the mode of failure observed into

flexure or shear. The low shear strength of the wall commands the response 

in the dynamic space as well, by failing 97% of the times in shear. 

Responses for higher demands are similar.

Figure H-27 Earthquake scenarios for shear critical models evaluation.

0.01

0.1

1

10

0.01 0.1 1

Sa [g]

Period [s]

High hazard scenario

0.01

0.1

1

10

0.01 0.1 1

Sa [g]

Period [s]

Intermediate hazard scenario

0.01

0.1

1

10

0.01 0.1 1

Sa [g]

Period [s]

Low hazard scenario

Figure H-28 Dynamic response of the BWS model under the LH set.

Alpha* = SDRmax/RDRmax

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

StoryStory

Story

Alpha Alpha Alpha

3% of flexuredominated responses

97% of shear

failures

BWS model LH set

Figure H-29 through H-31 show the response of the building whose wall has 

“adequate” shear strength (BAS model in Figure H-27). Responses shown 

include the three levels of demand described before. In Figure H-29 it is 

observed that the response is dominated by flexure (58% of the times) for LH 

set, although plastic excitation of the shear spring is also apparent (42% of 

the runs). For higher intensity demand such as that of the IH and the HH 
FEMA P-2018 H: Development of Procedures to H-33

Estimate Story Drift Demands

sets, the plastic shear demand is observed in 67% and 86% of the analyses, 

respectively.

Figure H-29 Dynamic response of the BAS model under the LH set.

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

StoryStory

Story

Alpha Alpha Alpha

42% of shear

failures

58% of flexuredominated responses

BAS model LH set

Figure H-30 Dynamic response of the BAS model under the IH set.

Alpha* = SDRmax/RDRmax

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

Story

Story

Story

Alpha Alpha Alpha

67% of shear

failures

34% of flexuredominated responses

BAS model IH set
H-34 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Figure H-31 Dynamic response of the BAS model under the HH set.

Alpha* = SDRmax/RDRmax

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

StoryStory

Story

Alpha Alpha Alpha

86% of shear

failures

14% of flexuredominated responses

BAS model HH set

Figure H-32 through 34 show the response of the building with a shearcompetent wall. Although its shear strength is 50% larger than the demand 

required to fail the wall in flexure (under uniform loading), the BSS model 

also exhibits plastic demand on the shear spring, even at lower levels of 

demand. For this model, the proportion of shear failures is lower than that of 

the BAS model, but still fails 30 to 50% of the times in shear.

Result from the dynamic analyses allow concluding that coupling of the wall 

with the framing system, along with shear amplification due to apparent 

higher mode effects may negatively impact the response of a frame-wall 

building. In the cases presented, the wall is of sufficient length to control the 

response and result initially in values of α approximately equal to 1.0, but if 

shear failure occurs, then most of the subsequent displacement occurs in the 

story where shear failure occurs. This is, of course, an outcome of the 

relatively simple model being used for shear. 
FEMA P-2018 H: Development of Procedures to H-35

Estimate Story Drift Demands

Figure H-32 Dynamic response of the BSS model under the LH set.

Alpha* = SDRmax/RDRmax

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

Story

Story

Story

Alpha Alpha Alpha

30% of shear

failures

70% of flexuredominated responses

BSS model LH set

Figure H-33 Dynamic response of the BSS model under the IH set.

Alpha* = SDRmax/RDRmax

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

Story

Story

Story

Alpha Alpha Alpha

30% of shear

failures

70% of flexuredominated responses

BSS model IH set
H-36 H: Development of Procedures to FEMA P-2018

Estimate Story Drift Demands

Figure H-34 Dynamic response of the BSS model under the HH set.

Alpha* = SDRmax/RDRmax

Flexural yielding

dominated runs

Shear yielding

dominated runs

All reponses Response discrimination

Story

Story

Story

Alpha Alpha Alpha

50% of shear

failures

50% of flexuredominated responses

BSS model HH set

To explore the impact in overall building response of shear critical walls with 

a weak section upstairs, three models where constructed with the same shear 

spring strengths as described above, but locating the shear critical section at

the third story. Responses of these structures are presented in Figure H-32 

for the three set of ground motions of various intensities. In this setup, the 

distinction between flexural- or shear-dominated responses is more difficult 

to assess, therefore, all responses are combined in each case. Nevertheless, 

the median response helps understand the influence of the shear strength in 

the global behavior of the buildings. For example, the building with the 

strong spring (BSS model) is not affected much by the presence of a shear 

weakness upstairs. On the other hand, the BWS model is highly influenced 

by the weak capacity at all level of seismic demand, showing displacement 

demand concentration at the third story. Response of the building with 

adequate strength (BAS model) shows some impact of the shear plastic 

deformation for higher levels of demand, but median alpha values are still 

close to 1.0 at the third story. 
FEMA P-2018 H: Development of Procedures to H-37

Estimate Story Drift Demands

Figure H-35 Dynamic response of the BWS, BAS and the BSS models under 

the LH, IH, and HH sets.

0 1 2 3

1

2

3

4

5

6

7

8

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

8

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

8

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

Alpha = SDRmax/RDRmax

Story

0 1 2 3

1

2

3

4

5

6

7

Alpha = SDRmax/RDRmax

Story

BSS

Model BAS 

Model BWS

Model

LH Set IH Set HH Set

Alpha Alpha Alpha

Story Story Story

median
FEMA P-2018 I: Torsional Studies I-1 

Appendix I

Torsion Studies 

I.1 Introduction

The perception that torsion problems are a significant contributor to collapse 

risk has been shaped by building collapses in past earthquakes, such as the 

CTV building in Christchurch, New Zealand in 2011, as well as a large 

number of other cases observed in New Zealand and other earthquakes over 

the past several decades (Canterbury Earthquakes Royal Commission, 2012). 

The goal of the studies conducted herein is to avoid excessive conservatism

in identification of buildings with torsion problems, while quantifying the 

potentially negative impact of torsion, when present, on the collapse risk 

evaluation for the purposes of this methodology. 

The studies described in this appendix aim to quantify the displacement 

amplification experienced by columns and walls in torsionally irregular 

buildings. This amplification is included in the evaluation procedures of 

columns and walls in Chapters 7 and 8. In addition, the studies identify the 

following conditions: (1) when torsion is negligible and is not expected to 

significantly influence collapse risk; and (2) when torsion is so significant 

such that the building can be classified as Exceptionally High Risk (so-called 

“Extreme Torsion”). 

Torsional irregularity is quantified using the Torsional Ratio (TR), which is a 

strength-based assessment of the ratio of torsional demand to capacity. The 

Torsional Ratio is used to predict a displacement amplification factor for 

frame-wall buildings (Chapter 7) and, occasionally, for bearing wall 

buildings (Chapter 8). It is also used, together with information about 

building strength, to identify buildings that have Extreme Torsion. The Wall 

Index (defined in Appendix D) is also used to identify cases where torsion 

can be neglected. Torsional effects are neglected entirely for pure frame 

structures (Chapter 6), since these buildings are unlikely to have a 

configuration that would induce enough torsion to change the collapse risk. 

The study presented in this appendix builds on torsion studies presented in 

earlier versions of this document. Together, the results are used to develop 

the procedures outlined in this document. 
I-2 I: Torsional Studies FEMA P-2018

I.2 Identify Critical Stories

The severity of torsion is quantified by the torsional ratio, TR, at the critical 

story. In this methodology, TR is defined as the torsional demand, TD, of the 

critical story, x, divided by the torsional capacity, TC, of the critical story: 

Dx

Cx

T TR

T = (I-1)

Torsional demand, TD, is directional, and must be calculated for each 

direction of earthquake loading:

TDx = Vpxe (I-2)

where:

Vpx = plastic shear capacity of the critical story;

e = eccentricity between the center of mass and the center of strength 

in the direction perpendicular to the direction of earthquake 

loading; e may not be taken as less than 5% of the overall plan 

dimension perpendicular to the direction of earthquake loading 

(i.e., 0.05L); 

L = maximum plan dimension perpendicular to the direction of 

earthquake loading.

The center of rotation is taken as the center of strength. The coordinates of 

the center of strength, ( ) x y, , are calculated in each direction as the 

summation of the products of frame/wall line location and frame/wall

strengths, divided by the summation of frame/wall strengths, as shown in

Figure I-1: 

1

1

f

f

n

i pfi

i

n

pfi

i

xV

x

V

=

=

=

∑

∑

, 1

1

f

f

n

i pfi

i

n

pfi

i

y V

y

V

=

=

=

∑

∑

(I-3)

Figure I-1 is an illustration of dimensions to be used in computing the center 

of strength. Geometries are shown for only one frame, but the process needs 

to be repeated for all of the frames and wall lines as suggested by the 

summation in Equation I-3. The example uses the bottom left corner as the 

reference point for computing frame locations. Note that accidental torsion 

is not considered in this computation, except that e has a minimum value. 
FEMA P-2018 I: Torsional Studies I-3

Figure I-1 Illustration of the calculation of the center of strength for an 

example frame line, using the bottom left corner as the 

reference location; this computation would be repeated for 

each frame/wall line in the structure.

Torsional capacity, TC, is calculated considering the capacity of frame/wall

lines in all orientations, and thus is the same regardless of the direction of 

loading considered:

1

f n

Cx fi pfi

i

T RV =

= ∑ (I-4)

where:

Rfi = is the orthogonal distance between the frame/wall line i and the 

center of strength (as shown in Figure I-2); 

Vpfi = is the plastic capacity of frame/wall line i; and

nf = is the number of frame/wall lines in story x, considering all those 

that resist torsion, regardless of orientation

Figure I-2 illustrates the torsional capacity computation, considering a 

building with two frame lines in orthogonal directions. These calculations 

would be repeated for all of the frame/wall lines in a building. 
I-4 I: Torsional Studies FEMA P-2018

Figure I-2 Illustration of the calculation of torsional capacity.

I.3 Simulation of Collapse of Torsionally-Sensitive 

Buildings

The procedures developed here to account for buildings with torsional 

irregularities are based on nonlinear dynamic simulation of collapse of 

torsionally-irregular buildings. This section discusses the buildings analyzed 

and the simulation models employed. 

I.3.1 Buildings Analyzed

The torsion assessment is based on variations of a real structure that have 

varying degrees of torsional irregularity. The 8-story real structure that 

provides the basis for these archetypes experienced larger than design 

seismic loading in the 2011 Christchurch NZ earthquake, and was designed

using pre-1974 ACI design codes (Marcilla et al., 2017). The structure 

experienced significant damage, and reconnaissance studies (Canterbury 

Earthquakes Royal Commission, 2012; Marcilla et al., 2017) found that 

torsion was a contributor to this damage. In this study, the configuration of 

this building was varied systematically investigate the influence of torsion on 

collapse risk. 

The study investigates 15 8-story buildings with the same floor plan, as 

shown in Figure I-3. The structures vary in terms of the location and length 

of the added reinforced concrete wall, such that they range from a symmetric 

pure frame building, to a building with extreme torsion behavior due to a 

large eccentrically placed wall. Each wall building with an eccentric wall 

has a comparison symmetric case with the same length wall placed at the 

center of the plan (i.e., a comparison case of equivalent lateral strength). 
FEMA P-2018 I: Torsional Studies I-5 

Story heights of 10 ft. are consistent throughout the height of the structure. 

All columns are 18 in. square with eight #6 rebar placed symmetrically. Tie 

spacing is 6 in. over the height of the columns. All beams are 8 in. by 30 in. 

and have two #7 rebar placed at the top and two at the bottom. These designs 

differ somewhat from the original structure and ensure that the structures

have a Mc/Mb ratio of 0.85 at every location, indicating that moment failure 

will occur in the columns before the beams. All columns in the modeled 

building have a Vp/Vn ratio of 0.63, indicating the expected failure mode is 

flexure. (Although shear critical columns are not directly considered in this 

study, the columns fail flexurally in are brittle manner, such that flexural 

degradation occurs at low drifts and the columns are expected to experience a 

rapid reduction of post peak strength not dissimilar from a shear failure.) 

Wall designs vary from model to model. Shorter walls are 8 in. thick with #8 

rebar spaced at 8 in. on center in both the vertical and horizontal directions. 

Larger walls (Case D and beyond) are 12 in. thick and have additional rows 

of #8 longitudinal reinforcing bars over a length of 0.15L at each end of the 

wall. The walls are assumed not to have clearly defined boundary elements. 

Figure I-3 summarizes the characteristic of the cases analyzed, including the 

Wall Index (WI) from Equation 5-1, and Torsional Ratio (TR) from Equation 

7-7. The period (Tx) represents the period in the x (shaking) direction, 

obtained from eigenvalue analysis of the building model. Since the periods 

vary slightly between the torsional and the symmetric cases, the mean value, 

considering both the torsional and the symmetric buildings, is reported. 

Figure I-3 Buildings analyzed in torsional study, showing variation in Torsional Ratio due the length of the 

walls. Each irregular case has a corresponding symmetric case. All properties are the same in the 

symmetric and torsional cases, except for the location of the wall and the Torsional Ratio.
I-6 I: Torsional Studies FEMA P-2018

I.3.2 Modeling

The building is modeled in three dimensions as shown in Figure I-4. 

Column, beam and wall elements are modeled with force-based distributed 

plasticity fiber elements. In the fiber elements, the concrete fibers are 

assigned the Kent-Scott-Park stress strain model, assuming no tensile 

strength (Kent and Park, 1971). The steel material is defined in tension in as 

a tri-linear curve that follows modeling recommendations in FEMA P-695 

(NIST, 2010c), as shown in Figure I-5, considering strain hardening and steel 

fracture. The backbone of the steel model in compression considers buckling

in both columns and walls, which depends on the tie spacing. The 

parameters for the buckling model follow the Dhakal model, which is based 

on experimental results and finite element models of buckling of reinforcing 

bars (Dhakal and Maekawa, 2002). The length of the plastic hinge is 

determined from recommendations by Paulay and Priestley (1992), and is 

used to define the location of the integration points and weighting scheme 

such that the response is regularized (i.e., not dependent on the number of 

elements). Regularization is consistent with the discussion in Appendix L. 

Floor diaphragms are modeled as rigid by the use of nodal constraints, and 

the base is fixed. Beam-column joints are not explicitly modeled. The 

models assume 2% Raleigh damping at the 1st and 3rd mode periods. Each 

element definition utilized a P-delta geometric transformation.

Figure I-4 Diagram of 3D models used for torsional simulation.
FEMA P-2018 I: Torsional Studies I-7

Figure I-5 Steel material behavior used in fiber models. 

I.3.3 Analysis Procedures

Each building is excited in the in-plane direction of the walls. Shaking in the 

analysis is considered in only one dimension for consistency with this 

methodology’s procedures which analyze buildings separately in each 

orthogonal direction. The analysis uses both horizontal recordings of the 22

far-field pairs of ground motions defined in the FEMA P-695 document 

(FEMA, 2009), for a total of 44 individual analyses. 

Each building is assessed using incremental dynamic analysis, in which the 

ground motions are scaled until collapse occurs. Ground motions are scaled 

by the spectral acceleration of the first-mode period of the building. 

For this study, collapse is defined as occurring when displacement demand 

on at least 25% of the columns has reached or exceeded 1% story drift. This 

drift is not constant over the plan of the building, due to torsion. The force 

displacement curves in Figure I-6 show how a collapse criteria of 1% drift 

was determined from initial sensitivity studies. This figure shows the force 

displacement response of two columns (with the locations shown on the 

figure). These responses indicate that these flexurally-dominated columns 

experience a dramatic loss in capacity around 1% drift, such that the column 

is not contributing significantly to the lateral capacity of the building beyond 

that point. 

Incremental dynamic analysis was carried out for each of the buildings 

illustrated in Figure I-3. 
I-8 I: Torsional Studies FEMA P-2018

Figure I-6 Response of columns in a torsionally-irregular building model, showing how the 1% story 

drift collapse definition was determined. 

I.3.4 Detailed Results for Selected Buildings

Figure I-7 and I-8 provide the pushover and incremental dynamic analysis 

results for Case E. The pushover shows the disaggregated wall and frame 

strengths, and the total system strength. For Case E, the wall is somewhat 

stronger than the frame systems, and the failure of the columns is controlling 

the post-peak response. This behavior is consistent with most of the other 

cases examined. However, for cases where the wall strength is much greater 

than the strength of the frame and the building is symmetric, then building 

failure is dependent on wall failure. 

Figure I-7 Pushover results for case E, deaggregated to 

show contributions from frame and wall lines. 

Figure I-8 provides an example of the dynamic analysis results that are used 

to develop the recommendations in this appendix. These results show that 

symmetric cases are generally able to withstand larger ground motion 

intensities (spectral accelerations) before reaching collapse than the torsional 

buildings. For Case E, the median collapse capacity at a period of 0.66 s is 
FEMA P-2018 I: Torsional Studies I-9 

2.3g for the symmetric building, which is 30% larger than the median 

collapse capacity for the torsional building.

Figure I-8 Incremental dynamic analysis results for Case E, showing response of the building with the 

symmetrically-placed wall and the asymmetrically-placed wall, and the lower collapse capacity of 

the torsionally-irregular building. 

I.3.5 Normalization of Results for Comparison between 

Buildings

Figure I-9 summarizes the median collapse capacities for all the buildings 

analyzed. For the purposes of this comparison, we recalculate the spectral 

accelerations such that all values are reported at the same period. 

Figure I-9 shows that, for Cases A-C, there is negligible difference in the 

collapse resistance of the torsional and symmetric cases; for Cases E-G there 

is an increasing difference in behavior between the torsional and symmetric 

cases, with the torsionally-irregular buildings indicating lower collapse 

resistance. 

Figure I-10 examines the collapse results for the torsional buildings (bottom 

row in Figure I-3). For this purpose, the collapse capacity of each building is 

normalized by the strength of the building, i.e., μStrength, permitting 

comparison across buildings with different wall lengths and, accordingly 

different lateral strengths; the x-axis is represented as the torsional ratio. 

Each set of points connected by a dashed line represents a different percentile 

on the collapse fragility curve. The normalized median collapse points are 

shown in turquoise. The points corresponding to the 30th and 70th percentiles 

are also highlighted to clarify later discussions.
I-10 I: Torsional Studies FEMA P-2018

Figure I-9 Median collapse capacities of all the building 

cases analyzed in this study. Refer to Figure 

I-3 for a diagram of each case.

Figure I-10 Collapse fragility for the torsionally-irregular buildings 

shown in Figure I-3, plotted in terms of μStrength. 

I.4 Extreme Torsion

The Extreme Torsion provision identifies those buildings that have torsion 

that is so significant the building is classified as Exceptionally High Seismic 

Risk without more detailed calculation. 

Extreme torsion is defined as those buildings that are found to have more

than 70% probability of collapse in the dynamic simulations of building 

response, according to the results plotted in Figure I-10 and repeated in 

Figure I-11. We focus on that region of the plot where torsion has a 

significant influence on collapse (i.e., TR > 0.8). Buildings with TR = 0.8 

and μStrength > 5 have a simulated collapse probability greater than 0.70. As

TR increases beyond 0.8, indicating even greater torsional irregularity, the 
FEMA P-2018 I: Torsional Studies I-11

μStrength required to cause collapse is smaller (i.e., smaller excitation relative 

to base shear strength will cause collapse). For TR > 1, the torsional 

amplification factor, AT, is not well defined, and any building with this TR, 

regardless of strength is judged to have a high collapse probability. This 

“collapse prone” region is shown in Figure I-11 and labeled as Extreme 

Torsion. These buildings are judged to be Exceptionally High Seismic Risk. 

Figure I-11 Buildings that are define to have “Extreme Torsion” are shown 

in the shaded area, identifying cases that may exceed 70% 

collapse probability. The “weak building line” defines when 

μStrength > 5.5, which indicates buildings that are Exceptionally 

High Risk due to being exceptionally weak (Appendix E). 

I.5 Neglecting Torsion

In frame-wall buildings, even those that have some torsional irregularity, 

torsion may not significantly influence response. For these buildings, the 

analyst may neglect the torsional amplification factor in computation of drift 

demands on columns due to the small expected effect of torsion on building 

risk. This section describes the results used to identify those buildings for 

which torsion is not significant. 

To define those situations in which we can neglect torsion we return to Cases 

A-C, where the difference in collapse capacity between symmetric and

torsional cases is shown to be negligible, as plotted in Figure I-9 and Figure

I-12. These results identify the region (TR < 0.4) for which torsion is not

expected to be significant.

Note that the TR limit illustrated in Figure I-12 is effective at identifying 

cases where torsion does not significantly influence collapse risk, but the 

calculation of TR is cumbersome. Figure I-13 is the same as Figure I-12, 

except the x-axis has been replaced by the wall index (WI). Figure I-14 

shows that buildings with WI < 0.006 are not expected to have significant 

enough torsion effects to warrant detailed analysis of torsional amplification 
I-12 I: Torsional Studies FEMA P-2018

of drift demands on columns. We note that the WI is the same regardless of 

where the walls are found in the building. This analysis suggests that a 

frame-wall building with WI < 0.006, regardless of how the walls are 

configured, does not have sufficient torsional irregularity to substantially 

alter the collapse outcome. Like the frame buildings, these frame-wall 

buildings with relatively small amounts of walls are not expected to be 

vulnerable to torsion. 

Figure I-12 Buildings for which torsional effects can be neglected are shown 

in the shaded area as a function of the torsional ratio. Buildings 

that fall in the shaded area were shown to have negligible 

difference in behavior between symmetric and torsional models.

Figure I-13 Buildings for which torsional effects can be neglected are shown 

in the shaded area as a function of the wall index. Buildings that 

fall in the shaded area were shown to have negligible difference 

in behavior between symmetric and torsional models.
FEMA P-2018 I: Torsional Studies I-13 

I.6 Torsional Amplification

I.6.1 Torsional Amplification Overview

All other frame-wall and wall buildings will require a full torsional analysis. 

Buildings for which the torsional analysis is needed are defined by Figure 

I-14. 

Figure I-14 Buildings that are required to undergo a full torsional analysis 

are defined by the shaded area.

I.6.2 Extraction of Torsional Amplification from Analytical 

Models

Buildings that qualify for torsional analysis require that the displacement

demand on columns are amplified beyond the story displacement demand to 

account for torsion. To obtain the displacement amplification from the 

analysis, Equation I-5 is used. 

AT,max = ( )

( )

Edge

Story

max

max

δ

δ (I-5)

Here, max(δEdge) is the maximum displacement experienced at the edge of the 

building in the time history analysis. max(δStory) is the maximum 

displacement experienced at the center of strength. This calculation is 

illustrated in Figure I-15. Torsional amplification values are computed for 

each ground motion at each scale level considered in the dynamic analysis. 
I-14 I: Torsional Studies FEMA P-2018

Figure I-15 Column drift amplification due to torsion is the 

multiplier required to convert story drift to edge drift.

The accuracy of the torsional amplification factor being extracted from the 

models depends on e, the distance between the center of mass and the center 

of strength. Here, we compare hand calculated estimates of e to the e

extracted from the model result, and compared to results obtained by analysis 

of simple 3D portal frame (Figure I-16). 

Figure I-16 3D portal frame used to examine estimates of e. 

Figure I-17 illustrates the difference in e when hand calculated using either 

center of stiffness (Equation I-7) or strengths from mechanism calculations 

(Equation I-6), compared to e extracted from the pushover of a simplified 3D 

portal frame analytical model. At small lateral load levels, the building 

rotates about its center of stiffness. However, as the load level increases and 

the building response becomes nonlinear, the system begins to rotate about 

the center of strength from the hand calculations. Since we are trying to 

determine the nonlinear performance of a building just before collapse, then 

using a strength based eccentricity is an appropriate choice. The strengths 

used are determined from mechanism analysis.

Σ

Σ

i pfi

pfi

y V

y V = (I-6)

Σ

Σ

i pfi

pfi

y K

y K = (I-7)
FEMA P-2018 I: Torsional Studies I-15 

Figure I-17 Difference between stiffness based eccentricity and strength based eccentricity 

compared to eccentricity extracted from a model 3D portal frame with a wall on 

one side. 

I.6.3 Torsional Amplification Results

The median torsional amplification values obtained from the models at the 

scale level corresponding to “collapse” are shown in Figure I-18, and are 

compared to the torsional amplification equation proposed in this document

(Equation 7-6 and I-8). For TR < 1 the equation for torsional amplification 

factor fits the data well. However, for buildings with a TR > 1, the equation 

may under predict the drift demand; these buildings are defined as having 

Extreme Torsion. Buildings with TR > 0.4 do not require torsional 

amplification to be used in analysis.

AT,max = eTR (I-8) 

Figure I-18 Torsional amplification curve. AT,max defines 

the drift amplification on the edge of the 

building relative to the drift demand at the 

center of strength. 
I-16 I: Torsional Studies FEMA P-2018

I.6.4 Torsional Amplification Calculations in Each Column

After the torsional amplification is determined, the torsional amplification of 

the drift at each column is determined by geometry (and as illustrated in

Figure I-19). At the edge farthest away from the center of strength of the 

building (i.e., the weak or flexible side of the building), the amplification is 

equal to the maximum amplification. At the center of strength, the 

amplification is 0, and it varies linearly in plan to the maximum value. On 

the side of the building closest to the center of strength (strong or stiff side), 

the amplification is taken as 1.0, as shown in Figure I-20. 

Figure I-19 Illustration of torsional amplifications computed for earthquake 

loading in the N-S direction. The amplification in each column 

depends on the location of the column.

I.7 Comparison of Results to Other Torsion Studies

Figure I-20 compares the collapse capacities obtained from this study to 

analysis of torsionally-critical buildings conducted for the ATC-123 Project

by DeBock (2017). As we did here, DeBock (2017) simulates building with 

an array of torsional layouts ranging from symmetric to highly torsional. The 

differences are that here we examine non-ductile pre-1980 concrete building 

behavior, while the DeBock (2017) buildings are representative code 

compliant ductile structures. To model these structures, DeBock (2017) 

represented the lateral resisting system of code compliant systems with two 

frame lines acting in each horizontal direction at various locations, modeled 

with hysteretic springs capturing the response of each line of resistance at 

each story. Two subsets of the buildings from DeBock (2017) study are 

included for comparison here: those low-rise buildings that are code 

compliant and those low-rise buildings that are code compliant and designed 
FEMA P-2018 I: Torsional Studies I-17

to have proportional strength and stiffness. We compare to the low-rise 

buildings because they have periods close to the buildings considered in this 

study. 

The DeBock (2017) results are superimposed on the results from this study in

Figure I-20, reporting the median collapse capacities on the collapse fragility 

results obtained in this study. In most cases, the median collapse capacities 

(normalized by strength) fall between the 30th and 70th percentile curves from 

the results of this study, showing relatively good agreement. At high 

torsional levels, the DeBock (2017) results have relatively higher collapse 

capacities, due to the additional design requirements in modern seismic codes 

when torsional irregularities are significant (DeBock et al., 2014). 

TR 

Figure I-20 Collapse capacities from buildings analyzed by DeBock (2017), 

compared to the results of this study. 
FEMA P-2018 J: Determination of Drift Factors J-1 

Appendix J 

 Determination of Drift Factors 

J.1 Overview

In this methodology, the fraction of the story drift that is taken by the critical 

component is denoted γ. For example, during seismic excitation, the story 

drift demand in a frame structure is resisted by beams and columns. During 

elastic (or near elastic) response, the drift demand is distributed between 

beams and columns in proportion to their relative stiffnesses. During 

nonlinear response, drift tends to concentrate in the components of the 

building that have yielded (or experienced some other physical damage that 

leads to a significant reduction in component stiffness and degradation of 

response). γ quantifies this drift concentration in particular components. 

This appendix shows how the values of γ were determined for cases where 

columns are critical (J.2), where slab-column or beam corner connections are 

critical (J.3), and where walls or wall segments are critical (J.4).

J.2 Drift Factor for Critical Columns 

J.2.1 Buildings Analyzed

For frame and frame-wall buildings the values of γ were obtained from 

dynamic analysis of models of six-story reinforced concrete frame buildings, 

subjected to a suite of 44 ground motions. The flexural and shear properties 

of the columns in the buildings were varied between models to obtain a broad 

data set capable of capturing the values of γ for buildings with varying 

characteristics.

J.2.2 Results

If the building is responding in the nonlinear range, the portion of the drift 

taken by the column, γ, depends on the relative strength of the columns and 

the beams framing into a joint (or relative strength of columns and slabcolumn connection framing into a joint). This is because the drift tends to 

concentrate in the weaker element. To extract values of γ from the nonlinear 

models, the portion of drift taken by the columns was read from lumpedplasticity, nonlinear springs which were present at beam and column ends in 

the nonlinear models. The maximum ratio of column drift to total story drift 

was taken from the analysis in which the ground motion was scaled to a 
J-2 J: Determination of Drift Factors FEMA P-2018

spectral acceleration value corresponding to incipient collapse. Results were 

then averaged over all of the ground motions to obtain the values shown in 

Figure J-1. In Figure J-1, each point represents the results obtained from 

analysis of a 6-story building with a uniform ratio of column to beam 

strength at every joint, and a uniform ratio of column shear capacity to 

flexural capacity in every column. The portion of drift taken by the column 

during nonlinear response depends on both the ratio of column to beam 

strength, ΣMc/ΣMb, and the ratio of column shear capacity controlled by 

flexure to column shear capacity controlled by shear, Vp/Vn. 

Figure J-1 Portion of drift taken by the column, γ, during 

nonlinear response from incremental dynamic

analysis of selected 6-story buildings.

To simplify the calculation of γ in the nonlinear range, the value of γ was 

taken to be linear with respect to relative strength of the columns and the 

beams framing into a joint. This relationship is shown in Figure J-2. Note 

that for ΣMc/ΣMb greater than 1.4, γ should be taken as 0.6. Limited analyses 

were conducted for larger ΣMc/ΣMb ratios.

Figure J-2 Portion of drift taken by the column, γ, assuming a 

linear relationship with ΣMc/ΣMb. 
FEMA P-2018 J: Determination of Drift Factors J-3

Failure to consider γ is conservative because it assumes all of the drift is 

taken by the column.

J.3 Drift Factor for Critical Slab-Column Connections and 

Beam-Column Corner Connections

If the slab-column connection is found to be the critical component, γ, will be 

taken as 1.0. This is because the drift capacities for connections are based on 

the entire connection subassembly, considering the deformation of the 

slab/beam, connection, and column. Therefore, there is no need to separate 

the drift attributable to these different components.

J.4 Drift Factor for Critical Wall and Wall Segments

In frame-wall and wall buildings, the story drift is the same as the drift in the 

wall. For this reason, for critical walls and wall segments, the drift factor, γ, 

is taken as 1.0.
FEMA P-2018 K: Archetype Building Analysis Methods K-1

Appendix K

Archetype Building Analysis 

Methods

K.1 Introduction

This Appendix presents the methods considered for analysis of archetype 

structures including bare frames and frame plus walls combinations. The 

included methods are: nonlinear static analysis, incremental dynamic 

analysis, dynamic analysis for hazard consistent ground motions, and 

3-dimensional dynamic analysis for torsion studies.

K.2 Nonlinear Static Analysis

Nonlinear static analyses (pushover) were performed in structural systems 

composed of one frame plus different wall configurations to identify the 

influence of the walls in the building strength, the plastic collapse 

mechanism, and the story drift demands at collapse. The structures were 

subjected to an inverted triangular load pattern. For studies of the effect of 

wall shear strength on building response, some of the nonlinear static 

analyses were conducted using lateral forces that were uniformly distributed 

over height. Selected results from the analyzed cases are presented in 

Appendix H.

The software OpenSees was used as analysis platform. It was not possible to 

obtain a unique set of parameters for nonlinear analysis that provides the best 

results for all structures. Therefore, all the cases were analyzed several times 

under different parameters (tolerances, controlled horizontal DOF, nonlinear 

analysis algorithm, and others). Nonlinear analysis algorithms included 

Newton, Modified Newton and Krylov-Newton. Detailed description of 

nonlinear fiber models considered in this study can be found in appendix L. 

Analysis results were post-processed in the software MATLAB.

K.3 Incremental Dynamic Analysis

Incremental dynamic analyses (Vamvatsikos and Cornell, 2002) were 

employed to assess the collapse potential of shear- and flexure-dominated 

bare frames models and for the analysis of selected frame-wall structures. 

This analysis methodology uses a set of seed ground motions which are 

scaled progressively to perform response history analyses of the structural 
K-2 K: Archetype Building Analysis Methods FEMA P-2018

model under consideration. For each scaling factor, each ground motion has 

an associated intensity measure (IM) value and a corresponding peak 

structural response of interest, referred to as an engineering demand 

parameter (EDP). The ground motion scaling factor is incremented until a 

response threshold is surpassed for each ground motion. At the end of the 

analysis process, each EDP of interest is associated to a distribution of IM 

values. Figure K-1 shows an example of the IDA results, along with the 

estimation of two points of the corresponding fragility curve of certain EDP 

level. The process consists of counting the proportion of IM realizations of 

ground motion that result in the EDP level under consideration. A lognormal 

distribution is usually fitted to the empirical probability function estimated 

(Baked, 2015). 

EDP (e.g. Roof drift ratio, RDR)

IM (e.g. 

Sa(T1))

EDP level of interest

N reco

saj

sak

edp

GRDR(rdr│imj) ≡ P r RDR ≥ rdr Sa T1 = saj = 2

N

GRDR rdr imk = N

N = 1

IM levels of 

evaluation

Figure K-1 IDA results and corresponding fragility curve 

estimation (adapted from Haindl et al., 2015).

IM (e.g. Sa(T1))

saj sak

P r RDR

≥ rdr

Sa T1 = sa

2/N

0

1

saj+1

Pr(saj+1)

Fit lognormal 

distribution

Collapse was defined for the smallest input motion required to achieve either 

one of the following two limit states: (1) maximum story drift ratio 

exceeding 10% of story-height; or (2) shear or axial failure in more than 50% 
FEMA P-2018 K: Archetype Building Analysis Methods K-3 

of the columns in any story. A suite of 22 pairs of far-field ground motions 

was selected, for a total of 44 ground motions. The output of the analysis is 

the relation between the spectral acceleration (at the first-mode period T1 of 

the building) and maximum story drift ratio for a given ground motion 

record.

Figure K-2 shows a typical output from an IDA analysis of a single building 

model. Each line in the figure represents the response of the building model 

to a single ground motion record scaled to increasing intensity. Note that the 

curves begin to flatten out at maximum story drift ratio of approximately 

0.03 to 0.04, suggesting that the structure becomes unstable at around this 

story drift ratio. The collapse risk of each building model was obtained from 

statistics on the IDA results. In this study, collapse performance was 

evaluated using the probability of collapse as a function of the ground motion 

intensity level, defined in terms of Sa(T1). The collapse probabilities in terms 

of Sa(T1) were assumed to be log-normally distributed. Figure K-3 shows 

collapse fragility relations. 

Figure K-2 Incremental Dynamic Analysis (IDA) curves for 

an 8-story modern code design building model 

(Vu/Vn = 0.6, ΣΜnc/ ΣΜnb = 1.2). 

In incremental dynamic analysis a single-record provides a single measure of 

how collapse occurs for that one ground motion record. To measure the 

variability in the dynamic response, multiple IDA analyses are done using 

different ground motions. After the IDA procedure has been completed for 

each seed ground motion, post-processing of the results is required to 

develop the fragility curve of the specified model. A first step is to 

established the empirical cumulative distribution function (CDF) of 

probability of collapse as a function of ground motion intensity. Then, a 
K-4 K: Archetype Building Analysis Methods FEMA P-2018

lognormal distribution is fit to the collapse data points. The lognormal 

collapse fragility is defined by two parameters, which are the logarithmic 

mean (μln) and the standard deviation (σln). This study considered only the 

record-to-record collapse (aleatory) uncertainty. Modeling (epistemic) 

uncertainties were not considered. Also, the effect of spectral shape of the 

considered ground motions in the estimation of the probability of collapse 

was not considered. 

Figure K-3 Collapse fragility functions for the “modern code design” 

building models (Vu/Vn = 0.6, ΣMnc/ΣMnb = 1.2). 

K.4 Dynamic Analyses with Hazard-Consistent Ground 

Motions

Some studies of frame-wall structures used dynamic analyses with hazardconsistent ground motions. Hazard consistency in ground motion selection 

allows assigning rates of occurrence to each time series used in nonlinear 

dynamic analyses. Assigned rates are defined based on spectral shape and 

intensity. Under the assumption that structural responses have the same rate 

of occurrence as the uniform excitation that generate them, a hazardconsistent set of ground motions allows estimating the risk of engineering 

demand parameters (EDP) of interest. Figure K-4 shows data for a set of 

ground motions selected based on the Conditional Scenario Spectra (CSS)

Methodology (Arteta and Abrahamson, 2017) for a site of high seismicity in

the West Coast of the United States. 

The CSS is a set of ground motions with assigned rate of occurrence that 

represents the hazard at a site over a period of 100,000 years. The selection 

procedure for the CSS is based on targeting several Conditional Mean 

Spectra (CMS) (Baker, 2011) with corresponding variability at increasing 

return periods. These CMSs are anchored at a given period to Uniform 
FEMA P-2018 K: Archetype Building Analysis Methods K-5 

Hazard Spectra (UHS) that are estimated from the hazard curves at a site, 

which are typically estimated by means of a Probabilistic Seismic Hazard 

Analysis (PSHA). This ensures that the selected ground motions have the 

proper spectral shape at all intensities of selection, thus allowing recovery of 

the hazard according to Equation K-1: 

v(Sa(T) > z) = ( ) ( ) #

, ,

1

recordings

CS i a i

i

Rate H S T z =

∑ − (K-1) 

where Sa,i(T) is the spectral acceleration of the i

th recording, z is a test level, 

H is the Heaviside function (for example, H(x) = 1 for x > 0 and H(x) = 0 for 

x ≤ 0); and RateCS,i is the assigned rate of occurrence to each ground motion. 

Figure K-4 Scenario spectra: (a) 402 scenario spectra (5% 

damped); (b) assigned rate of occurrence for 

each spectrum of the CSS (after Arteta and 

Abrahamson, 2017).

10-2 100 10-2

10-1

100

101

Spectral acceleration, [g]

0 200 400

10-10

10-8

10-6

10-4

10-2

Rate of occurrence

Period, [s] Spectrum index

Spectral acceleration, [g]

Rate of occurrence

(a) (b)

Figure K-5 compares the hazard recovered from the CSS with target hazard 

curves (estimated in a PSHA) of a site in a high seismicity site. The target 

and recovered hazard curves are shown for hazard levels from 10-2 to 10-5 at 

three different periods. 

Figure K-5 Hazard curves at different periods 

recovered with the CSS set.

0.00001

0.0001

0.001

0.01

0.01 0.1 1

Annual rate of being exceeded

Spectral acceleration, [g]

T=2.5s T=1.7s T=0.55s

υ=2.5x10-4

υ=1x10-3

Target (Y.B. site)

Recovered from CSS
K-6 K: Archetype Building Analysis Methods FEMA P-2018

The risk of response parameters of interest, such as story drift ratio (SDR) or 

roof drift ratio (RDR), can be readily estimated using Equation K-2, which 

has the same functional form as Equation K-1: 

#

,

1

()( ) ( )

recordings

CS i

i

λ edp v EDP d Rate H EDP d =≡ >= ∑ − (K-2) 

where vEDP(EDP > d) is the annual frequency with which demand level d is 

exceeded, and, as before, H(EDP – d) is either 1 or 0, per the Heaviside 

function H, depending on whether the EDP from time series i exceeds level 

d. 

The seismic behavior of frame-wall systems was assessed using the 

Conditional Scenario Spectra methodology. To illustrate the type of data 

available after analyzing structural systems with the CSS, Figure K-6 shows 

the response of two 8-story reinforced concrete building models, one whose 

lateral load resisting system comprises a bare frame, and the other having in 

addition a competent flexural wall. Figure K-6a compares the response of 

the pushover curves of the structures, showing an apparent improved 

response of the frame-wall system with respect to the bare frame. Figure 

K-6b shows maximum roof drift ratio versus rate of occurrence relationships. 

Figure K-6 Static and dynamic response of two 

8-story buildings: (a) pushover curves; 

(b) maximum roof drift ratio versus rate of 

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.01 0.02 0.03 0.04

Normalized base shear 

(Vb/W)

Roof displacement/ Total height

Flexural Wall-Frame

Bare Frame

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

0.5 5

Rate of ocurrance

Maximum RDR [%]

Frame w/ wall

Bare Frame

(a)

(b)

occurrence.
FEMA P-2018 K: Archetype Building Analysis Methods K-7 

Reduction of the data in Figure K-6b through Equation K-2 allows estimating 

the annual rate of exceedance of any EDP of interest. Figure K-7 shows risk 

curves for the maximum roof drift ratio of the aforementioned structures. A 

feature of the graph worth noting feature is that it offers an objective 

platform to compare system performances at various levels of return periods. 

In the example shown, the wall-frame system shows an apparent 

(measurable) improved behavior with respect to the bare frame system at any 

return period over 75 years. 

Figure K-7 Risk curves of maximum roof drift ratio for two 

8-story buildings.

0.00001

0.0001

0.001

0.01

0.1

0.1 1 10

Annual frequency of 

exceedance

Maximum RDR [%]

Wall-Frame System

Bare Frame

TR=75 yrs

TR=500 yrs

TR=2,500 yrs

Because of the broad range of intensities covered, the CSS is an adequate set 

to study building behavior in the elastic and the inelastic range of response. 

This allows construction of fragility curves, with the advantage that the 

spectral accelerations used as predictor are also hazard-consistent. Figure 

K-8a shows a scatter plot of spectral acceleration at the fundamental period,

Sa(T1), versus maximum roof drift ratio for the bare frame system described 

above. The data are organized by Sa, and probabilities of exceeding certain 

demand levels can be estimated (Figure K-8b). Typically, a lognormal 

cumulative density function is fitted to the empirical data. Fragility curves 

also allow comparing building responses at different levels of demand 

(Figure K-8c).

The same data presented above, can also be analyzed to estimate dynamic 

alpha values at various levels of seismic demand. Figure K-9 shows the 

transition of alphas values from those of an archetype bare-frame 4-story 

building (Figure K-9a) to those of frame-wall structures with walls of 

increasing length (e.g., Lw = 50 in. and Lw = 80 in., Figures K-9b and K-9c, 

respectively). It is observed that as the walls grow in length, the mean alpha 

distributions tend to one. 
K-8 K: Archetype Building Analysis Methods FEMA P-2018

Figure K-8 Fragility curves construction: (a) scatter plot of raw data; 

(b) fragility curve construction; (c) fragilities comparison. 

0

0.2

0.4

0.6

0.8

1

0.0 1.0 2.0 3.0

P(RDR>6% I Sa = y)

Sa (T1)

0 1 2 3

0

2

4

6

Sa(T1)

MAX RDR [%]

0.00

0.25

0.50

0.75

1.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Pr(IDR > j I Sa(T1)=y)

Sa(T1), [g]

Wall-Frame System

Bare Frame

(a) (b)

(c)

j = 6%

j = 2%

j = 0.5%

Fitted lognormal CDF

Figure K-9 Dynamic alphas, 4-story building: (a) bare frame archetype; 

(b) frame coupled to a wall with Lw = 50 in.; (c) frame coupled 

to a wall with Lw = 80 in.

Bare Frame

Alpha

Story

0 1 2 3 0 1 2 3 0 1 2 3

Frame + Wall 

Lw=50 in.

Frame + Wall 

Lw=80 in.

(a) (b) (c)
FEMA P-2018 K: Archetype Building Analysis Methods K-9 

Figures K-10 shows the transition of alphas values from those of an 

archetype bare-frame 8-story building (Figures K-10a) to those of frame-wall 

structures with walls of increasing length (e.g., Lw = 50 in. and Lw = 100 in., 

Figures K-10b and K-10c, respectively). It is observed how the alpha values 

transition from a distribution with large concentrations in the bare frame (due 

to a weak story upstairs) to a more uniform distribution with alpha values 

close to one and smaller for a frame-wall system with a wall of length Lw = 

100 in. 

Figure K-10 Dynamic alphas, 8-story building: (a) bare frame archetype; 

(b) frame coupled to a wall with Lw = 50 in.; (c) frame coupled 

to a wall with Lw = 100 in.

Bare Frame

Alpha

Story

0 1 2 3 0 1 2 3 0 1 2 3

Frame + Wall 

Lw=50 in.

Frame + Wall 

Lw=100 in.

(a) (b) (c)

K.5 Dynamic Analyses for Torsion Studies

Incremental dynamic analyses were employed for the torsion studies. 

However, for the torsion studies, models were three-dimensional. In this 

study, seismic excitation was applied to the 3D models in only one horizontal 

direction at a time. This decision was made for consistency with the ATC-78 

methodology, which looks at response in the two orientations of the building 

separately before combining to obtain a building rating. The IDA thus 
K-10 K: Archetype Building Analysis Methods FEMA P-2018

proceeds as described above using the same 22 pairs of far-field ground 

motions, with each ground motion applied separately for a total of 44 

separate analyses.

In the torsion studies, collapse was defined as occurring when displacement 

demand on at least 25% of the columns reached or exceeded 1% story drift. 

The columns used in that study were brittle, and this collapse state 

corresponded to the loss of shear capacity, and likely gravity-load bearing

capacity, of an entire frame line. More details and illustrations are provided 

in Appendix I.
FEMA P-2018 L: Frame and Wall Modeling Procedures L-1

Appendix L

Frame and Wall Modeling 

Procedures

L.1 Introduction

This Appendix describes modeling procedures for gravity and seismic 

analyses of bare frames and frame-wall combinations.

L.2 Bare Frames Models

Buildings were modeled using two-dimensional structural frames. Thus, 

biaxial interaction associated with simultaneous loading in two plan 

directions was not represented. The mathematical model is an assemblage of 

line beam-column elements, representative of the stiffness of beams and 

columns, connected to beam-column joints and to fixed supports at the base. 

To approximate flexibilities of beam-column joints, the joints were modeled 

as rigid, with dimensions equal to d/2, where d is the effective depth of the 

connected beam and column. Diaphragms were modeled as rigid in their 

plane. P-Delta formulation was employed to account for non-linear 

geometry effects. For dynamic analyses, Rayleigh damping was employed, 

with parameters adjusted to achieve 2% of critical damping at the initial firstand third-mode periods.

Buildings with different ratios of shear demand to shear capacity, Vu/Vn, were 

modeled. Thus, failure of structural components could be initiated due to 

either flexure or shear. It was assumed that shear failure does not dominate 

member failure where Vu/Vn < 0.7. Thus, only flexural failure was modeled 

for this case. Where Vu/Vn ≥ 0.7, the possibility of having shear failure or 

shear induced axial failure was also considered by explicitly modeling 

nonlinearities associated with flexural, shear, and axial failure (Galanis and 

Moehle, 2015).

A concentrated plasticity approach was used to model both beams and 

columns. By this approach, the plasticity of the elements is represented by a 

nonlinear rotational spring with hysteretic rules assigned at the ends of a 

linear elastic beam-column element, with effective (cracked) stiffness 

properties. For those cases where shear and axial failure was likely, 
L-2 L: Frame and Wall Modeling Procedures FEMA P-2018

horizontal and vertical springs were also connected in series with the linear 

elastic element. 

L.2.1 Building with Flexure-Controlled Columns

For the cases where Vu/Vn < 0.7, non-linear flexural response was modeled 

using the concentrated plasticity approach, where a flexural linear-elastic 

member is connected to two plastic hinges at the ends (Figure L-1). 

Figure L-1 Beam column element with concentrated 

flexural plasticity at the ends (after Galanis 

and Moehle, 2015).

The inelastic rotational spring response follows the Clough model, using 

hysteresis implemented in OpenSees by Ibarra et al. (2005), This model uses 

a post-peak negative slope to model strain-softening behavior associated with 

degradation of the flexural resisting mechanism. The model also 

incorporates cyclic strength degradation (Figure L-2). 

Figure L-2 Backbone and cyclic response rule of the rotational 

spring representative of the flexural plastic hinge 

region (after Galanis and Moehle, 2015). 

Seven parameters are required to control the response of the beam-column 

element: [My, Mc/My, θcap,pl, θpc, λ, c]; where My is the nominal moment 

strength according to ACI 318-11 (2011) provisions; ratio Mc/My was 

assumed to be equal to 1.2. The values of λ, c, θcap,pl and θpc were estimated 
FEMA P-2018 L: Frame and Wall Modeling Procedures L-3 

using the equation in Haselton et al. (2007) but re-calibrated to exclude the 

cases for which shear or flexure-shear failure were reported. 

L.2.2 Building with Shear-Critical Columns

For the cases where Vu/Vn > 0.7, shear failure may occur, possibly followed 

by axial failure. The Elwood and Moehle (2008) model introduced to 

simulate this behavior was adopted here. Flexural response is modeled using 

a lumped plasticity model, similar to the model used for flexure-controlled 

behavior. Two additional springs are added at the top of each column 

member to model shear and axial failure (Figure L-3). 

Figure L-3 Limit state shear-axial-spring material introduced (after Galanis and Moehle, 

2015).

The shear spring is linearly-elastic until the shear failure strength. For larger 

drifts, the post-peak response of the shear spring follows a linear softening. 

The onset of shear failure is defined as a function of the story drift ratio of 

the column. In its original definition, the model was restricted so that shear 

failure only occurs after flexural yielding. For this work, the model was 

updated such that shear failure could be initiated prior to flexural yielding. 

L.3 Modeling Criteria of Frame-Wall Systems

In older construction, reinforced concrete walls were sometimes added for 

lateral resistance but they were also added as stair case enclosures, as 

firewalls, and/or as partitions. Consequently, the configuration, location, and 

reinforcement are not always ideal for lateral force resistance. These walls 
L-4 L: Frame and Wall Modeling Procedures FEMA P-2018

can resist a significant portion of the overall story shear because of their 

inherent lateral stiffness and strength. Additionally, interaction with 

structural frames may result in moment demand distribution along the height 

of the wall that may produce yielding at multiple elevations. It is necessary 

to use models that enable development of these varied yielding mechanisms. 

This section presents the modeling approach selected to simulate walls 

interacting with older frames.

L.3.1 Frame-Wall Definition

To study the response of a shear wall in a frame-wall system, a lightly 

reinforced concrete wall is coupled to a ductile frame using rigid links. 

Figure L-4 presents the 8-story structure, which comprises a 4-bay ductile 

frame, braced by a 260 in. wall. 

Figure L-4 Elevation and wall reinforcement detailing of the frame-wall structure used for this 

study. 

100'

horizontal reinforcement

ρt = 0.0025

lw=260"

concentrated reinforcement

Asbe = (200/fy)tw(0.8lw)

lw=260" tw=10"

distributed reinforcement

ρl = 0.0025

1 1

2 2

Sec. 2-2

Sec. 1-1

dist. reinforcement

ρl = 0.0025

22"x32"

32"x32"

32"x32" 22"x32"

1

2

3

4

5

6

7

8

13'

12' typ.

tw=10"
FEMA P-2018 L: Frame and Wall Modeling Procedures L-5

For the frame, concrete is assumed normal weight (γc = 150 lb/ft3) with 

nominal strength cf ′ = 6 ksi and reinforcing steel with nominal yielding 

strength of fy = 60 ksi. Columns are 32 × 32 in. with longitudinal steel ratios 

(total area of steel to gross area ratio) ρmin = 1.00% and transverse steel ratio 

with Av / bs > 0.87%, where Av is the total area of transverse reinforcement 

within distance s of two adjacent layers and b is the core dimension of 

column. Beams are 22 × 32 in. with longitudinal steel ratios (area of tension 

reinforcement divided by web width and effective depth) ranging from ρ = 

0.39 to 0.54% and transverse steel ratios Av / bs > 0.63%. Given the adequate 

framing detailing, shear failure is not expected in the frame; therefore, shear 

in beams and columns is modeled as elastic. The shear wall was detailed 

following recommendation of (ACI Committee-318, 1977) with longitudinal 

and transverse reinforcement ratio of 0.25%. Additionally, the bottom half 

of the wall has boundary reinforcement with area As,be = (200 / fy) tw (0.8lw ), 

where fy = 60 ksi, tw = 10 in. is the thickness of the wall and lw = 260 in. is its 

length. The concrete of the wall is normal weight with cf ′ = 4.5 ksi and it is 

assumed that no confinement is provided by the transverse reinforcing steel. 

The axial load at the base of the wall is assumed to be 0.1Ag cf ′ and decreases 

proportionally to the height.

L.3.2 Wall Modeling Approach for Frame-Wall Systems

Force-based nonlinear beam-column elements with concentrated plasticity at 

the ends were used to model all structural elements of the frame (Scott and 

Fenves, 2006). This modeling technique allows selecting the span of 

plasticity spread by allowing the selection of a plastic hinge length. Fiber 

sections assigned to the plastic hinge regions simulate material nonlinearities 

while accounting for moment-axial load interaction.

Distributed plasticity formulation offers a flexible platform for modeling 

structural walls because the location of the critical section cannot be 

predicted prior to the analysis. Three main formulations of distributed 

plasticity elements are: the force-based, the displacement-based, and the 

mixed formulation (Scott and Hamutçuoğlu, 2008). In this study, we 

selected the force-based nonlinear beam-column element with distributed 

plasticity (Spacone et al., 1996).

Computational implementation of the force-based elements requires selection 

of a numerical integration method. Three quadrate (or integration) rules

were considered in this study: (i) Gauss-Lobatto; (ii) Gauss-Legendre; and 

(iii) Gauss-Radau.
L-6 L: Frame and Wall Modeling Procedures FEMA P-2018

To test the impact of different quadrature rules in the response of the forcebased element, a cantilever wall with the geometry, material characteristics, 

and reinforcement layout of that in Figure L-4 was programmed in 

OpenSees. Figure L-5 shows the geometry of the mathematical model. The 

centerline of the element representing the wall coincides with the centroid of 

the cross section and does not migrate with the neutral axis location. 

Concrete was modeled as unconfined using the stress-strain relationship 

proposed in Kent and Park (1971) as modified by Scott et al. (1982) to 

include the tensile behavior of concrete. The hysteretic behavior of concrete 

under stress reversal was modeled according to Mohd Yassin (1994), 

including gradual degradation of stiffness under unloading and reloading in 

compression (Spacone et al., 1996). The longitudinal reinforcing steel stressstrain behavior was assumed to be bilinear with isotropic strain hardening 

(Filippou et al., 1983) but modeled with a hysteretic material as implemented 

by Scott and Filippou in OpenSees. 

Figure L-5 Nonlinear force-based element with distributed plasticity 

formulation for the wall.

load pattern

f c'

f c

Unconfined concrete

material model

0.01Es

Strain hardening steel

material model

fs

Es

f y

εs

εc

elastic rigid

elements

Fiber section @ IPs

FBE w/ Dist. Plasticity

A physical interpretation often given to the weights of the quadrature rules 

used in the formulation of distributed plasticity elements is related to the 

spread of plasticity within the element. For softening behavior, it is expected 

that the inelastic demand over the element concentrates on a single 

integration point. In flexure, this results in high curvature demand at the 

section level, which results in a reduced total deformation capacity of the 

element. To test the impact of this behavior, three wall models were 

constructed using the Gauss-Lobatto integration rules (i.e., with integration 

points at the ends of the element) with increasing number of integration 

points: Np = 3, 4 and 5 (models GLo3, GLo4 and GLo5). It was of interest to 

test if the reduced length (weights) of the external integration point impacted 

the behavior of the wall at a global and at a section level. A fourth wall 
FEMA P-2018 L: Frame and Wall Modeling Procedures L-7

model was also constructed by mixing the Gauss-Radau integration rule with 

2 integration points for the first story and Gauss-Legendre rule with 3 

integration points for the rest of the elements (model GRa2GLe3). The ideas 

behind this integration point scheme are: (i) using the quadrature rule with 

the largest weight at the end of the first story element allows representing the 

spread of plasticity at the critical section (base) over a larger, more 

meaningful length (approximately 0.15lw), while still maintaining accuracy; 

(ii) using a more accurate integration rule, such as the Gauss-Legendre, for 

the rest of the wall element, where integration points at the ends of each story 

are not necessary, allows reducing the total number of integration points, 

hence the running cost.

Pushover analyses were conducted over the aforementioned models using 

two different load patterns of lateral force: an inverted triangular load pattern 

with horizontal forces proportional to the height of each floor and a similar 

triangular load pattern with a reversed force at the roof. The latter pattern 

simulates interaction with the framing system, and generates large moment 

demand in the sections above the wall midheight.

Figures L-6 through L-9 show the pushover curves under the triangular load 

pattern. Two critical sections are observed along the height of the wall: one 

at the base and another at the moment capacity discontinuity above the fourth 

story. The pushover curve shape is similar for all models but the onset of 

softening occurs at lower roof drift ratios for lower values of the weight of 

the first integration point. Four instances in the force-displacement relation 

of the wall are isolated to study the moment and curvature demand 

distribution along its length: (i) cracking capacity (red markers); (ii) first 

yield (green markers); (iii) onset of concrete crushing (cyan markers); and 

(iv) 3.5% roof drift ratio (blue markers). Moments and curvature values 

depicted were obtained at each integration point along the height of the wall 

and are plotted at the relative distance within each element according to the 

selected integration rule.

Moment distribution along the height of the wall is similar for all models. 

The curvature figures show that all the models are able to spread the 

plasticity above the critical integration point (i.e., above the first IP in the 

first and fifth story). Curvature distribution along the height of the wall is 

similar for all models while the wall remains elastic. Inelastic curvature 

demand follows a parabolic shape within the first story element (which 

contains the critical section). Elements with larger number of IPs model this 

distribution in a smoother manner. The downside to this is that, for larger 

roof displacements, much of the inelastic curvature demand is concentrated

within the first IP which has a smaller associated physical length (weight).
L-8 L: Frame and Wall Modeling Procedures FEMA P-2018

Figure L-6 Wall response under triangular load pattern for Gauss-Lobatto 

rule with three integration points. 

0 0.01 0.02 0.03 0.04 0

50

100

150

200

250

300

350

400

Roof displacement / Wall height

Base Shear [kips]

0 1 2 3

x 105

0

200

400

600

800

1000

Moment [kip-in.]

Height along hw [in.]

0 2 4

x 10-5

0

200

400

600

800

1000

Curvature [1/in.]

GLo3

cracking

onset of yielding

onset of cracking

3.5% roof 

drift ratio

Figure L-7 Wall response under triangular load pattern for Gauss-Lobatto 

rule with four integration points. 

0 0.01 0.02 0.03 0.04

0

50

100

150

200

250

300

350

400

Roof displacement / Wall height

Base Shear [kips]

GLo4

0 1 2 3

x 105

0

200

400

600

800

1000

Moment [kip-in.]

Height along hw [in.]

0 2 4

x 10-5

0

200

400

600

800

1000

Curvature [1/in.]

Figure L-8 Wall response under triangular load pattern for Gauss-Lobatto 

rule with five integration points. 

0 0.01 0.02 0.03 0.04

0

50

100

150

200

250

300

350

400

Roof displacement / Wall height

Base Shear [kips]

0 1 2 3

x 105

0

200

400

600

800

1000

Moment [kip-in.]

Height along hw [in.]

0 2 4

x 10-5

0

200

400

600

800

1000

Curvature [1/in.]

GLo5
FEMA P-2018 L: Frame and Wall Modeling Procedures L-9 

Figure L-9 Wall response under triangular load pattern for Gauss-Radaue

rule with two integration points in the first story and three 

Gauss-Legendre integration points upstairs. 

0 0.01 0.02 0.03 0.04

0

50

100

150

200

250

300

350

400

Roof displacement / Wall height

Base Shear [kips]

0 1 2 3

x 105

0

200

400

600

800

1000

Moment [kip-in.]

Height along hw [in.]

0 2 4

x 10-5

0

200

400

600

800

1000

Curvature [1/in.]

GRa2GLe3

Figure L-10 shows the pushover curves under the triangular load pattern with 

a load reversal at the roof level for the GRa2GLe3 model. Curvatures shown 

are for two levels of magnification and show that the model is able to model 

curvature sign change within the length of a single element and the parabolic 

nature of the curvature distribution given the moment distribution along the 

element length.

Figure L-10 Wall response under triangular load pattern with a reversed load at the roof

for Gauss-Radaue rule with 2IPs at the first story, and 3 Gauss-Legendre IPs 

upstairs. 

0 0.01 0.02 0.03 0.04 0.05

0

100

200

300

400

500

600

700

800

Roof displacement / Wall height

Base Shear [kips]

GRa2GLe3

-1 0 1 2 3

x 105

0

200

400

600

800

1000

Moment [kip-in.]

Height along hw [in.]

-1 0 1

x 10-4

0

200

400

600

800

1000

Curvature [1/in.]

0 2 4

x 10-6

0

200

400

600

800

1000

Curvature [1/in.]

Figure L-11a shows the roof drift ratio at which the first three states of 

response (e.g., cracking, yielding, and crushing) occurred for each model. 

Figure L-19b shows, in logarithmic space, the curvature demand at the first 

IP of the wall for different levels of roof drift ratio. This is normalized by the 

curvature at the onset of yielding, obtained from a moment-curvature 
L-10 L: Frame and Wall Modeling Procedures FEMA P-2018

analysis of the critical section, under the axial load at the base. The momentcurvature ductility demand relation of the section at the base is presented in 

Figure L-11c. The curvature ductility demand is defined as the curvature 

divided by the yielding curvature. 

Figure L-11 Normalized curvature demand at the first integration point 

(critical section at the base) for the inverted triangular load 

pattern. 

0.07% 0.07% 0.07% 0.07%

0.53% 0.54% 0.56% 0.53%

1.43%

1.15%

1.05%

1.72%

0

0.005

0.01

0.015

0.02

GLo3 GLo4 GLo5 GRa2GLe3

Roof displacement / Wall height

Cracking

Yielding

Crushing

0.87 0.77 0.85 0.80

4.86

7.34 10.35

4.09

20.49

37.07

59.76

14.52

42.71

81.80

134.22

29.31

0.1

1

10

100

GLo3 GLo4 GLo5 GRa2GLe3

Curvature / Yielding curvature

RDR =0.5%

RDR =1%

RDR =2%

RDR =3.5%

(a)

(b)

0

50000

100000

150000

200000

250000

300000

0 5 10 15 20

Moment, [kip-in.]

Curvature ductility demand

(c)

It is concluded that after the onset of yielding, the limitation of displacement 

capacity for larger numbers of IP is apparent. The onset of crushing 

produces differences in roof drift capacity as large as 60% (GRa2GLe3 vs 

GLo5). This is supported by the fact that even for very low levels of roof 

drift ratio (e.g., 0.5%) the curvature demand at the critical section can differ 

by a factor as large as 2.5 (GLo5/GRa2GLe3) among the models. For larger 

roof drift ratios (e.g., 3.5%), this ratio doubles. The moment-curvature 

relation shows that the wall has limited ductility capacity, and some 

integration rules might produce demands at the critical section past 

meaningless physical values. This can be solved with material 

regularization, to account for the size of the integration points. This requires 

additional effort to estimate fracture energy of the constitutive models and is 

outside the scope of this report. 
FEMA P-2018 L: Frame and Wall Modeling Procedures L-11

In view of the preceding, and to keep local demands within tolerable values, 

the integration scheme used for the ATC-78 project to model walls is the 

GRa2GLe3, which has the lowest number of integration points along the wall 

length, hence requiring shorter computation times, yet maintaining adequate 

accuracy for the numerical integration of deformations and the stiffness 

matrix at the element level.

L.3.3 Frame Modeling Approach for Frame-Wall Systems

The modeling approach of frame-wall systems mainly focused on identifying 

how walls of different characteristics modified the global response of the 

coupled system. Therefore, the framing portion of the model followed a 

simpler approach than that described above in Section L.2.

Force-based nonlinear beam-column elements with concentrated plasticity at 

the ends were used to model all structural elements (Scott and Fanver, 2006),

without modeling shear failure or shear-induced axial failure. Fiber sections 

assigned to the plastic hinge regions simulate material nonlinearities while 

accounting for moment-axial load interaction. For nonlinear dynamic 

analyses, mass and stiffness-proportional Rayleigh damping was used to 

simulate the energy dissipation characteristics of the building that is not 

accounted for by the nonlinear behavior of the structural elements. The 

Rayleigh damping coefficients were established to achieve a damping ratio 

of ζ = 2.5% at periods corresponding to the first and third translational 

vibration modes of the linear model. Calculated periods for the nonlinear 

models were obtained after applying the vertical load, such that some initial 

service level cracking is accounted for. P-Delta effects were accounted for in 

the formulation of the columns.
FEMA P-2018 M: Column Shear Strength M-1 

Appendix M 

Column Shear Strength 

M.1 Column Shear Strength Equation

The column shear strength equations adopted in this methodology are based on 

the equations specified in ASCE/SEI 41, except for the way widely spaced 

shear reinforcement is considered. ASCE/SEI 41 defines transverse 

reinforcement to be 100% effective in contributing to the shear strength term Vs

for spacing-to-effective-depth ratios s/d ≤ 0.75, to be 0% effective for s/d ≥ 1.0, 

with effectiveness linearly interpolated between these limits. In contrast, this 

methodology considers transverse reinforcement to be fully effective for any 

spacing.

The shear strength expression in this methodology was adopted after a review 

of the original data set that served as a basis for the ASCE/SEI 41 expression 

(Sezen and Moehle, 2004). Figure M-1 plots the results. Solid circles 

correspond to strength ratios Vtest/Vn based on this methodology (identified as 

ATC-78 in the figure), while open circles correspond to strength ratios Vtest/Vn

based on ASCE/SEI 41. The data points plot atop one another for s/d ≤ 0.75, 

and begin to diverge for s/d ≥ 0.75. The data suggest that the expression in this 

methodology remains suitably conservative for wider hoop spacing.

Figure M-1 Column shear strength (data from Sezen and Moehle, 2004). 

Older building codes permitted tie spacing as large as the greatest of: (a) 16 

times the longitudinal bar diameter; (b) 48 times the tie bar diameter; and 

(c) the least dimension of the column. Consequently, tie spacing sometimes 

approached the column gross cross-sectional dimension, which exceeds 

effective depth d. The shear strength expression in this methodology is 

intended to permit the engineer to count on that reinforcement in calculating Vs. 
FEMA P-2018 N: Development of Wall Drift Capacities N-1

Appendix N

Development of Wall Drift 

Capacities

N.1 Introduction

In this methodology, wall drift capacities at axial failure are used to compute 

the wall ratings, which are then used to compute story and building ratings. 

This appendix first presents an approach to determine the expected failure 

mode for reinforced concrete (RC) structural walls, i.e., whether a wall is 

flexure- or shear-controlled, and it then describes the details of the 

development of drift capacities at axial failure for both flexure- and shearcontrolled walls. The drift capacities are based on wall test data filtered from 

a database of more than 1000 wall tests (i.e., UCLA-RCWalls) developed by 

Abdullah and Wallace (2018a). The drift capacities given in this appendix 

are at axial failure, unless noted otherwise.

N.2 Expected Wall Behavior and Failure Mode

For the purpose of deriving the wall drift capacities, it is important to 

distinguish between flexure-controlled (slender) walls and shear-controlled 

walls/piers (low-rise squat walls/piers), as they have different lateral load 

resisting mechanisms and thus different behavior expectations. Currently, 

unlike RC column, there is no consensus approach to quantitatively define 

flexure- and shear-controlled walls. ASCE/SEI 41-17 Section C10.7.1 

defines slender and squat walls as walls with aspect ratio (hw/lw) > 3.0 and 

< 1.5, respectively. Walls with intermediate aspect ratios are defined as 

flexure-shear-controlled walls. ACI 318-14 defines slender walls as walls 

with hw/lw > 2.0. However, as well be shown in the next paragraph, shearflexure strength ratio (Vn,ACI /V@Mn) is a better indicator of the expected wall 

behavior and failure mode than aspect ratio (or shear span ratio). Therefore, 

a different approach was used in this methodology, which is based on shear 

and flexural strength ratio. This approach is similar to that used for columns 

in this methodology and in ASCE/SEI 41-17.

A recently developed database (known as UCLA-RCWalls) by Abdullah and 

Wallace (2018a) that contains detailed information and test results from more 

than 1000 wall tests reported in literature was used to define the criterion for 

distinguishing flexure- and shear-controlled walls. The database includes the 
N-2 N: Development of Wall Drift Capacities FEMA P-2018

reported failure modes of the wall tests. When recording the failure modes in 

the database, the authors made sure that the reported failure mode in the 

reference documents matches the observed behavior and damage. 

The database was filtered to obtain a dataset of 990 walls with flexure, shear, 

or flexure-shear failure modes. Walls with failure modes due to insufficient 

lap-splices or anchorages of longitudinal reinforcement were not included. 

The results are presented in Figure N-1, where Vn,ACI is the nominal wall 

shear strength computed from ACI 318-14 Equation 18.10.4.1 using tested 

material strengths, V@Mn is the shear strength associated with the 

development of wall nominal flexural strength (Mn) at concrete compressive 

strain of 0.003 using sectional analysis and tested material strengths, and VTest

is the peak base shear obtained during the test. From this figure, it is clear 

that all shear-controlled walls (i.e., walls failed in diagonal tension or 

compression) have shear-flexure strength ratio Vn,ACI /V@Mn < 1.0, and most 

flexure-controlled walls have Vn,ACI /V@Mn ≥ 1.0. Walls that fail in shear 

sliding at the base mainly have Vn,ACI /V@Mn ≥ 1.0 because shear friction 

strength should be used instead of ACI 318-14 Equation 18.10.4.1 to 

compute nominal shear strength, Vn. Walls with failure modes reported as 

flexure-shear (i.e., yielded in flexure but failed in shear) are mainly scattered 

between 0.5 < Vn,ACI /V@Mn < 1.5. Therefore, in this methodology, walls with 

Vn,ACI /V@Mn < 1.0 are classified as shear-controlled walls, and walls with 

Vn,ACI /V@Mn ≥ 1.0 are classified as flexure-controlled walls. 

Figure N-1 Definition of flexure-controlled and shear-controlled walls

based on results from a dataset of 990 wall tests. 
FEMA P-2018 N: Development of Wall Drift Capacities N-3 

N.3 Drift Capacity of Poorly Detailed Flexure-Controlled 

Walls

The UCLA-RCWalls database was used to obtain a dataset of poorly detailed 

walls in which deformation at axial failure is reported or complete loss of 

lateral strength was observed due to out-of-plane instability or concrete 

crushing in both the boundary zones and the web. A reduced dataset of 80

wall tests was identified that satisfied the following requirements:

• Walls exhibiting flexure failure mode, i.e., Vn,ACI /V@Mn ≥ 1.0 

• Walls tested under quasi-static, reversed cyclic loading

• Walls with one or two curtains of web vertical and horizontal 

reinforcement

• Walls with ratio of provided-to-required (per ACI 318-14 Section 18.10.6.4) 

area of boundary transverse reinforcement, Ash,provided/Ash,required ≤ 0.7, or ratio 

of vertical spacing of boundary transverse reinforcement to minimum 

diameter of longitudinal boundary reinforcement, s/db ≥ 8.0. 

Figure N-2 Histograms of the reduced dataset of 80 flexure-controlled 

walls.

Histograms for various dataset parameters for the 80 wall tests are shown in

Figure N-2, where ( ) / P Af g c′ is the sustained axial load used during the test 

normalized by concrete compressive strength ( ) cf ′ and gross concrete area 

(Ag), and M/(Vlw) is the ratio of base moment-to-base shear normalized by 

wall length (lw), b is the width of compression zone, and c is the depth of 

neutral axis corresponding to concrete compressive strain of 0.003. Since 

this methodology is applied to older buildings constructed prior to 

development of modern building codes (i.e., pre-1971), wall tests that do not 

satisfy the design and detailing requirements of ACI 318-14 for special 

structural walls are used to develop the drift capacities.
N-4 N: Development of Wall Drift Capacities FEMA P-2018

Abdullah and Wallace (2018b) studied the drift capacity of flexure-controlled 

walls with special boundary elements at 20% lateral strength loss and found 

that wall drift capacity correlates well with a slenderness parameter λb = 

lwc/b2

, which is the product of the ratio of wall neutral axis depth-to-width of 

the compression zone, c/b, and the ratio of the wall length-to-width of the 

compression zone, lw/b. This slenderness parameter considers the impact of 

concrete and reinforcement material strengths, axial load, wall cross-section 

geometry, and quantities and distributions of longitudinal reinforcement at 

the wall boundaries and in the web. 

After studying the reduced dataset shown in Figure N-2, it was found that 

λb = lwc/b2 also correlates well with wall drift capacity at loss of axial load 

carrying capacity. Although the axial load is included in the λb parameter 

through depth of neutral axis, c, it was found that the level of axial load has a 

significant impact on post-strength loss deformation capacity. Figure N-3 

shows the variation of drift capacity at axial collapse as a function of λb and

/ P Af g c′ . Application of linear regression analyses for the dataset of 80 

tests, including the variables that significantly impact lateral drift capacity

(i.e., λb and / P Af g c′), resulted in the following predictive equation for drift 

capacity (DC) at axial failure: 

(%) 3.85 3.5 0.75% 30

b

g c

P DC

A f

λ

= −− ≥′ (N-1) 

where λb = lwc/b2

 should not be taken more than 60. Results from Figure N-3 

and Equation N-1 are presented in a tabular format in Figure N-4. 

Figure N-3 Variation of drift capacity at axial failure as a function 

of λb and / ′ g c P Af . 
FEMA P-2018 N: Development of Wall Drift Capacities N-5 

Figure N-4 Drift capacity at axial failure for poorly detailed flexurecontrolled walls. Drift capacity values in this figure should be

multiplied by a factor of 1.25 for flexure-controlled walls with 

spirally reinforced boundary columns (see Section N.7.1).

Figure N-5 presents a comparison of predicted drift capacities from Equation 

N-1 and Figure N-4 with experimentally obtained drift capacities at axial 

failure from the dataset of 80 wall tests, with a mean of 1.02 to 1.03 and 

coefficient of variation (COV) of 0.20 to 0.23.

(a) Equation N-1 (b) Figure N-5 

Figure N-5 Comparison of predicted drift capacities from Equation N-1 and 

Figure N-4 with experimentally obtained drift capacities.

In Figure N-4 and Equation N-1, the depth of neutral axis, c, can be 

computed from sectional analysis of the wall using the expected material 

properties and the sustained gravity load. Alternatively, Equation N-2 can be 

used to compute an approximate c (Abdullah and Wallace, 2018c), which is 

derived based on data from 696 walls in the UCLA-RCWalls database with 

/ P Af g c′ > 0 and different cross-sectional shapes. 

1 2

w g c

c P k k

l Af

= + ′ (N-2) 
N-6 N: Development of Wall Drift Capacities FEMA P-2018

where values of k1 and k2 are obtained from Table N-1. Figure N-6 compares 

the depth of neutral axis computed from Equation N-2 with that computed 

from detailed sectional analysis using as-tested material properties.

Table N-1 Neutral Axis Depth (c) Parameters Used in Equation N-2

Wall Cross-Section Shape k1 k2 Mean COV

Rectangular 0.10 1.2 1.04 0.17

Barbell 0.03 1.4 1.05 0.27

T-, L-shaped, and flanged; flange in 

compression 0.03 0.7 1.00 0.30

T-, L-shaped, and half-barbell; web in 

compression 0.20 2.0 1.01 0.24

Figure N-6 Comparison of neutral axis depth, c, computed from 

Equation N-2 with that from detailed sectional analysis.

N.4 Drift Capacity of Shear-Controlled Walls/Piers

As noted previously, shear-controlled walls are defined as walls with shearflexure strength ratio Vn,ACI /V@Mn < 1.0. The limited available literature was 

reviewed to identify parameters that primarily control drift capacity at axial 

failure. Wallace et al. (2008) developed an axial collapse model for lightly 

reinforced wall piers under axial load based on a shear-friction model. They 

found that in addition to axial load, the amount of wall web reinforcement 

provided had a significant impact on drift capacity at axial failure. Looi et al. 

(2017) showed that drift capacity of heavy reinforced squat walls is primarily 

a function of axial load ratio. 

Similar to flexure-controlled walls/piers, the UCLA-RCWalls database was 

filtered to obtain shear-controlled wall tests for which the deformation at loss 

of axial load-carrying capacity is reported, which resulted in a subset of 33 

wall tests. 
FEMA P-2018 N: Development of Wall Drift Capacities N-7 

Drift Capacities of the wall tests are plotted against / P Af g ′ in Figure N-7 

for two levels of provided minimum wall web reinforcement ratio (i.e., the 

least of the vertical and horizontal reinforcement ratio). From this figure, it 

is clear that axial load has a significant impact on drift capacity, and that 

there is only a moderate trend for wall web reinforcement ratio, which could 

be due to limited data for walls with web reinforcement ratios < 0.0025. 

Therefore, the impact of web reinforcement ratio was ignored herein as 

shown in Figure N-8, perhaps until further data become available. 

Figure N-7 Drift capacity of shear-controlled walls/piers as a 

function of / ′ g c P Af and minimum web reinforcement

ratio. 

Figure N-8 Drift capacity of shear-controlled walls/piers as a 

function of / ′ g c P Af with a natural log fit.
N-8 N: Development of Wall Drift Capacities FEMA P-2018

A logarithmic fit through the data results in the following predictive equation 

for drift capacity (DC) at axial failure (Figure N-8): 

DC(%) 0.65 ln( ) PAf g c =− × ′ (N-3) 

Alternatively, a bi-linear curve through data could be used, as shown in 

Figure N-9, which can be expressed with the following expressions: 

DC(%) 2.5 10 for 0.1

DC(%) 1.75 2.6 for 0.1

g c g c

g c g c

P P

Af Af

P P

Af Af

= − ≤ ′ ′

= − > ′ ′

(N-4) 

Figure N-9 Drift capacity of shear-controlled walls/piers as a function 

of / ′ g c P Af with a bi-linear fit.

Table N-2 Drift Capacity for Shear-Controlled Walls/Piers at Axial Collapse

P/Agf′c Drift Capacity, DC (%)(1)

0.0 2.50

0.05 1.95

0.10 1.40

0.20 1.13

0.30 0.87

0.40 0.60

0.50 0.35 

(1) Drift capacity values in this table should be multiplied by a factor of 1.5 for 

shear-controlled walls with spirally reinforced boundary columns (see Section 

N.7.2).
FEMA P-2018 N: Development of Wall Drift Capacities N-9

The results of Equation N-4 are presented in a tabulated format in Table N-2. 

Figure N-10 presents a comparison of predicted drift capacities from 

Equation N-4 with experimentally obtained drift capacities at axial failure

from the dataset of 33 shear-controlled wall/pier tests, with a mean and COV 

of 1.03 and 0.19, respectively. 

Figure N-10 Comparison of predicted drift capacities 

from Equation N-4 with experimentally 

obtained drift capacities at axial failure.

N.5 Drift Capacity of Walls with Inadequate Lap Splices

Review of test results from 10 wall tests that lost lateral strength due to 

inadequate lap-splice of longitudinal reinforcement (Bimschas, 2010; 

Hannewald et al., 2013; Elnady, 2008; Jeon and Park, 2016; Paterson and 

Mitchell, 2003; Woods, 2017) revealed that the bond failure of a lap-splice 

could actually increase deformation capacity, and that loss of axial loadcarrying capacity is unlikely. This is because once the splice fails, the wall 

becomes very flexible and rocks back and forth as a rigid body when 

subjected to lateral loads. Therefore, walls with inadequate lap-splices are 

treated as walls without lap-splices, and the impact of the presence of lap 

splices is essentially ignored in determining the wall drift capacity at axial 

failure. However, the potential for overturning instability due to failure of 

lap-splices should be evaluated (Wallace et al., 2012). 

N.6 Drift Capacity of Walls with L-Shaped, T-Shaped, and

Half-Barbell Cross-Sections

In the case of walls with asymmetric cross-sections, such as T-shaped, 

L-shaped, and half-barbell cross-sections (Figure N-11), drift capacity should 

be evaluated in both directions of loading (i.e., flange in compression and 
N-10 N: Development of Wall Drift Capacities FEMA P-2018

web in compression) and the larger value should be used to determine the 

wall rating. This is because in cases with a large b, where the barbell or 

flange of the wall is in compression, drift capacity is likely to be relatively 

large (low λb). In such cases, it is unlikely that the wall will lose axial load 

carrying capacity because the flange or the barbell may remain largely intact 

and thus could carry the axial load if the web becomes heavily damaged

(Figure N-12). 

Figure N-11 Examples of asymmetric wall cross-sections.

(a) T-shaped (b) Half-barbell 

(Thomson and Wallace, 1995) (Takahashi et al., 2013)

Figure N-12 Damage in walls with asymmetric wall cross-sections.

N.7 Drift Capacity of Walls Spirally Reinforced Columns 

at the Boundary Regions

Use of walls with barbell shaped cross-sections (i.e., walls with a thin web 

and large columns at boundary regions) was common in pre-1971, low-rise

and medium-rise, concrete buildings. Typically, boundary columns have 

spiral transverse reinforcement spaced at, or smaller than, 3 inches center-tocenter (Bertero et al., 1975). It is believed that such walls perform better 

than walls with non-spirally reinforced boundary elements, and, therefore, 

larger drift capacities are assigned to them.

The UCLA-RCWalls database was filtered to identify walls with boundary 

columns reinforced with spiral hoops with or without intermediate legs of 

crossties, and 14 flexure-controlled walls and 28 shear-controlled walls were 

identified. One important limitation of these tests, which were mostly 

completed in the 1990s and earlier, is that they are not tested to axial 

collapse. Some have been tested to peak strength, and others have been

tested to some level of lateral strength degradation. In the absence of 
FEMA P-2018 N: Development of Wall Drift Capacities N-11

experimental data for axial collapse of walls with spirally reinforced 

columns, the drift capacities at axial collapse suggested in the following 

sections are judged to be appropriate.

N.7.1 Flexure-Controlled Walls with Spirally Reinforced Columns

For the 14 flexure-controlled walls, test results show that the damage 

includes bar fracture, and in some cases cover spalling of the boundary 

columns and concrete crushing in the columns and web next to the columns. 

Figure N-13 shows drift capacity of the dataset at 20% lateral strength loss, 

which ranges from 2.0 to 5.0% on average (blue dots). This is because the 

closely spaced spirals prevent early strength degradation due to bar buckling 

and concrete core crushing. It is noted that since the width of compression 

zone, b, is relatively large, lwc/b2 is equal, or smaller, than 15. Abdullah and 

Wallace (2018c) found that walls with lwc/b2

 < 30 can exhibit moderate to 

significant post-20% strength loss deformation capacity. Therefore, drift 

capacity of flexure-controlled walls with spirally reinforced columns at axial 

failure is taken as drift capacity of non-spirally reinforced walls increased by 

25%, as shown in Figure N-13. That is, the results presented in Figure N-4 

are increased by 25% for walls with spirally reinforced columns.

Figure N-13 Drift capacity of flexure-controlled walls with spirally 

reinforced boundary columns.

N.7.2 Shear-Controlled Walls with Spirally Reinforced Columns

For the 28 shear-controlled walls, test results show that the damage usually 

includes crushing the concrete in the thinner web, and in some cases spalling 

concrete cover of the columns, as seen in Figure N-14. However, the core of 

the boundary columns appears to be perfectly intact and can, therefore, 
N-12 N: Development of Wall Drift Capacities FEMA P-2018

support the axial load on the wall after the web is crushed. Figure N-15 

shows drift capacity of the dataset at either peak strength or 20% lateral 

strength loss. After the web is crushed, it is possible that the wall becomes 

more flexible and can deform significantly before the columns fail in a 

sliding shear failure mode along the crushed plane. Therefore, the drift 

capacity of shear-controlled walls with spirally reinforced boundary columns 

at axial failure is taken as the drift capacity of non-spirally reinforced walls 

increased by 50%, as shown in Figure N-15. That is, the results presented in 

Table N-2 are increased by 50% for walls with spirally reinforced columns.

(a) Imanishi, 1996 (b) Kabeyasawa and Matsumoto, 1994

(c) Saitoh et al., 1990 (d) Hines et al., 2002

Figure N-14 Damage of shear-controlled walls with spirally reinforced 

boundary columns at some level of lateral strength loss.
FEMA P-2018 N: Development of Wall Drift Capacities N-13

Figure N-15 Drift capacity of shear-controlled walls with spirally 

reinforced boundary columns. 
FEMA P-2018 O: Studies on Infilled Frames O-1

Appendix O

Studies on Infilled Frames

O.1 Introduction

Masonry infill panels are commonly treated as non-structural elements in

analysis and design. However, past earthquakes and laboratory studies have 

demonstrated that infills can increase the strength and stiffness of the

structure considerably, but they can also induce large forces on the bounding 

frame leading to significant damage, even when subjected to moderate 

ground shaking (EERI, 1994; EERI, 1999; Brando et al., 2015). As a result, 

concrete buildings with masonry infill walls are considered rather vulnerable 

when subjected to seismic forces. The seismic assessment of existing 

concrete buildings with infills is a challenging task, especially for structures 

with non-ductile reinforcing details, due to the interaction between the infills 

and the bounding frame. This interaction can alter the load-transfer 

mechanism, and cause the brittle shear failure of concrete elements. The 

goal of the studies conducted herein is to develop reliable, yet efficient, 

guidelines for the evaluation of the collapse potential of buildings classified 

as infilled concrete frames. The proposed guidelines follow the assessment 

approach developed for frame and frame-wall buildings.

The studies discussed in this appendix focus on existing concrete structures 

with masonry infill walls in the perimeter and bare concrete columns in the 

interior. Such structures are commonly found in the US and house a variety 

of uses including hotels, theaters, and warehouses. The studies in this 

appendix utilize assessment guidelines in ASCE 41-17 (Martin and Stavridis,

2017; 2018) and a recently proposed modeling framework for these buildings 

(Bose et al., 2018).

The guidelines developed here for infilled frames are included in the 

evaluation procedures discussed in Chapters 4, 5, and 9. These procedures 

include the estimation of the plastic mechanism, the shear strength of the 

critical story, the effective period that allows the estimation of the seismic 

drift demand, and the rating of the columns and the critical story. In 

addition, the effects of openings in the infill panels on strength and column 

shear failures is quantified.
O-2 O: Studies on Infilled Frames FEMA P-2018

O.2 Simulation of Collapse of Buildings Infilled with Solid 

Infills

The procedures developed here to evaluate infilled buildings are based on 

nonlinear dynamic simulations of the seismic response of a set of prototype

reinforced concrete buildings with masonry infill panels representing the 

buildings stock in the U.S. This section discusses the design details of the 

prototype structures, the numerical models, and the results of the nonlinear 

analyses.

O.2.1 Details of the Prototype Buildings

The prototype structures considered in this study are based on an actual

6-story warehouse that has infilled bays at the perimeter, and non-infilled

interior columns. This is thought to be representative of the building stock of 

this type found in California. The elevation of the building and a typical 

floor plan are shown in Figure O-1. This 6-story building, the prototype 

3-story structure designed by Stavridis (2009) to represent construction 

practice of 1920s, and the design guidelines used in 1930s (Caughey, 1933), 

are the basis for the design of one 8-story and five 4-story buildings. The 

main features of these prototype structures are summarized in Table O-1. 

Besides the number of stories, the effect of the relative strength of the infill 

to that of the interior columns is examined, as well as the effect of a noninfilled weak first story. 

Table O-1 Details of the Archetype Models Considered in This Study to 

Evaluate Seismic Behavior of Infilled Buildings

Model

ID

Infill 

Compressive 

Strength

fm’

(ksi)

Infill 

Cohesion

C

(psi)

Infill 

Thickness

(in)

Interior 

Column 

Shear 

Strength

(kips)

Number of 

Stories

Non-Infilled 

Story

M1 1.4 45 12

48

4 

No

M2 0.8 30 8 

M3 0.4 22 8 

M4 1.4 45 12 24

M5 1.4 45 12 102 8 

M6 0.4 22 8 48 8 First Story

To limit the variables between the buildings, all buildings have the floor plan 

shown in Figure O-2a and uniform story heights of 11 ft. The dimensions 

and design details of the concrete members of the two bottom stories of the 

4-story prototypes are shown in Figure O-2b. The beam details (B1 and B2) 

are consistent throughout the height of the structures for all buildings as the 
FEMA P-2018 O: Studies on Infilled Frames O-3 

tributary areas and gravity loads that governed the design in that era do not 

change. The column sizes and reinforcement details vary along the height 

according to the warehouse drawings. The column details of the eight-story 

prototype are summarized in Table O-2. Stories 5-8 in the table reflect the 

design details of the 4-story prototypes. Tie spacing is 16 in. over the height 

of the columns for all the structures to represent the non-ductile detailing of 

old concrete buildings.

(a) front view elevation (a) typical floor plan

Figure O-1 Building details of the six-story San Diego warehouse with infilled RC frames. 

C1 B1

C2 B2

(a) floor plan of archetypes (b) design details

Figure O-2 Floor plans of the prototype structures and design details of the columns and the 

beams of the first two stories of the 4-story prototype. 
O-4 O: Studies on Infilled Frames FEMA P-2018

Model M-1 is the baseline model for this study. The masonry compressive 

strength, number of wythes (or wall thickness), and cohesion, of the infill 

walls are varied in the models M2 and M3, with the strongest infill in M1 

representing a triple-wythe brick masonry and the weakest infill in M3 

representing a double-wythe wall of hollow clay tiles. Model M4 has the 

same material properties as that of M1, however, the interior columns are 

weak with half the lateral resistance of the columns in Table O-2. The 

8-story prototype, M5, has the strongest infill, similar to M1. Model M6 has 

the infill from the bottom story of the M3 model removed to represent 

buildings with weak infill and open ground stories. The masonry and 

concrete material properties are those measured through in-situ and 

laboratory tests in a structure of this type in El Centro, California 

(Yousefianmoghadam and Stavridis, 2016). 

Table O-2 Column Dimensions and Design Details of the Prototypes

Stories

Column Dimensions (in.) Reinforcement Details

Interior Exterior Interior Exterior

8-S1 30.0 28.0 20#11 16#11

8-S2 28.0 26.0 18#11 14#11

8-S3 26.0 24.0 18#10 14#10

8-S4 23.0 21.0 16#9 12#9

8-S5 / 4-S1 21.0 18.5 14#8 10#8

8-S6 / 4-S2 18.5 17.0 12#8 8#8

8-S7 / 4-S3 18.0 16.0 14#7 10#7

8-S8 / 4-S4 18.0 16.0 14#7 10#7

O.2.2 Development of Numerical Models

Three-dimensional numerical models of M1-M6 are developed using beamcolumn elements for the RC members and diagonal truss elements for the 

infill walls. The struts are calibrated using a recently proposed framework 

for the nonlinear simulation of infilled RC buildings (Bose et al., 2018). 

According to this framework, the backbone force-displacement response for 

each infilled bay is estimated based on the anticipated failure pattern 

following the methodology proposed by Martin and Stavridis (2017; 2018) 

for frames with solid infill panels, now adopted by ASCE 41-17. The 

obtained backbone curves for a typical infilled bay in the ground floor of 

each building are illustrated in Figure O-3a. The backbone curves for M4 are 

the same as those of M1. To account for the deterioration of the buildings, 

the initial stiffness is reduced to 40% (ACI, 2011b). 
FEMA P-2018 O: Studies on Infilled Frames O-5

The envelop force-displacement responses are used to calibrate the struts 

representing the masonry infill panels according to the methodology 

proposed by Bose et al. (2018). This modeling method for the struts does not 

account explicitly for the shear-dominated failure patterns of infilled frames. 

However, the backbone curves used to calibrate the struts take into account 

the anticipated failure mechanisms, including the aforementioned brittle 

shear failures. An example of a calibrated strut model for Model M1 is 

shown in Figure O-3b, while the material properties for concrete and 

masonry for all models are presented in Table O-3. 

The interior columns of the buildings are not infilled. Therefore, a uniaxial 

material model combined with shear axial springs developed by Elwood 

(2005) is used to capture the response of the interior RC columns during 

shear and axial load failure. 

Table O-3 Calibrated Concrete and Strut Properties of the Models’ Elements

Panels

Peak 

Compressive 

Strength

MPa (ksi)

Residual 

Strength

MPa (ksi)

Tensile 

Strength

MPa (ksi)

Strain at 

Peak 

Strength

Strain at 

Residual 

Strength

Strut

Width

mm (in)

Tension 

Softening 

Stiffness

MPa (ksi) Lamda*

Concrete 24.1 (3.5) 2.4 (0.35) 3.4 (0.5) 0.003 0.006 - 431 (62.5) 0.1 Masonry

M1 9.6 (1.4) 0.4 (0.06) 3.2 (0.5) 0.0007 0.0011 9.2 431 (62.5)

0.1

M2 5.5 (0.8) 0.8 (0.12) 1.8 (0.3) 0.0013 0.0023 15.6 258 (37.5)

M3 2.8 (0.4) 0.3 (0.04) 0.9 (0.1) 0.0016 0.0023 25.0 86 (12.5)

M5 24.1 (3.5) 2.4 (0.35) 3.4 (0.5) 0.0012 0.0022 11.8 431 (62.5)

* ratio between unloading slope and initial slope at onset of residual strength

(a) envelop curves estimated using ASCE 41-17 (b) calibration of struts of M1

Figure O-3 Lateral force-drift ratio curves for the infilled bays and calibration of struts. 

Once the diagonal struts simulating the effect of the masonry panels and the 

shear axial springs are calibrated, the three-dimensional model of the entire 

building is assembled, as shown in Figure O-4. The floor diaphragms are 
O-6 O: Studies on Infilled Frames FEMA P-2018

assumed to be rigid, and all structures are fixed at their base. The damping 

of the structure is modeled using the Rayleigh formulation, considering 3% 

of critical damping for the first two modes.

Figure O-4 Three-dimensional numerical 

model with infill struts. 

O.2.3 Nonlinear Time-History Analyses

Each building model is subjected to pushover analyses in the two principal 

directions independently to evaluate its strength and stiffness. The nodes 

over each slab are constrained to the node at the centroid of the each floor for 

this purpose. These master nodes are subjected to monotonically increasing 

triangular load pattern along the height during a displacement-controlled 

analysis in the direction of interest. 

The three-dimensional numerical models of the buildings are then excited 

with two components of the ground motions to account for the effects of 

bidirectional dynamic loading. Each building is subjected to incremental 

dynamic analyses using the horizontal components of the 22 far-field pairs of 

ground motions defined in the FEMA P-695 document (FEMA, 2009). The 

ground motion intensities are gradually increased until collapse, which is 

considered to occur: (i) when a small increase of the ground motion intensity 

results in drastic increase of the inter-story drift ratio; or (ii) when the inter 

story drift exceeds 1.5%. This limit for infilled frames is determined based 

on the tests conducted by Gao et al. (2018) and Stavridis et al. (2012). The 

six prototype structures were also dynamically analyzed with all the infills 

removed to obtain the bare frame response. In that case, the second collapse 

criterion is adjusted so that collapse is considered to occur when the drift 

demand reaches or exceeds 3.0%.
FEMA P-2018 O: Studies on Infilled Frames O-7

O.2.4 Detailed Results for Prototype Buildings

The results from the monotonic pushover analyses of models M1 to M5 are 

presented in Figure O-5a., while the peak base shear strength reached by 

each model and the corresponding bare frame is reported in Table O-4. As 

expected, the infills increase the strength of the buildings, with the most 

dramatic increase reported for models M1 and M4 which have strong infills 

(CMU). From Figure O-5a, it can be observed that the numerical models 

reach the peak strength at a very low drift ratio, prior to a sudden loss in 

strength. This loss of strength is followed by gradual increase of the shear 

resistance. The first peak is reached when the infills in the exterior bays 

reach their peak strength. At that point, the interior bare columns only 

contribute a fraction of their peak shear capacity, which they reach at 

considerably larger drifts as indicated in Figure O-5b. The figure presents 

the disaggregated contributions of the interior and the exterior frames for 

models M1, and M3. For Model M4, which has weaker interior columns, 

this post-peak increase in strength is not as drastic compared to model M1

due to the limited strength of the interior columns. In summary, in all cases, 

the exterior frames determine the peak resistance, while the bare columns in 

the interior frames govern the post-peak response.

Figure O-6 summarizes the results from the dynamic analyses for models M1 

to M6. The median spectral accelerations at collapse of the infilled buildings 

are compared with their bare frame counterparts in Table O-5. The results 

indicate that collapse is anticipated to occur for lower values of spectral 

acceleration regardless of which of the three demand metrics (spectral 

acceleration at the initial period of the structure, spectral acceleration at a 

period of 0.5 sec, and peak ground acceleration) is considered as the masonry 

weakens from M1 to M3. This is expected as the compressive strength, mf ′ , 

of the masonry decreases from model M1 to M3. In fact, the collapse 

potential of M3 is similar to that of the corresponding bare frame, with the 

two buildings expected to collapse at a similar PGA and spectral acceleration 

at 0.5s. Therefore, the weak masonry infills of M3 do not affect the overall 

collapse potential of the frame. However, when the ground story of the 

model M3 is removed to obtain model M6, the spectral acceleration at which 

collapse is anticipated further decreases. The lack of infill in the bottom 

story of this building increases the vulnerability of the structure, and slightly 

worsens the behavior compared to the bare frame. M4 has similar material 

properties for infill as M1, but weaker interior columns. As a result, it is 

expected to collapse at significantly lower excitation level compared to M1.
O-8 O: Studies on Infilled Frames FEMA P-2018

(a) monotonic pushover analyses (b) contribution of interior and exterior frames

Figure O-5 Pushover analyses results of the models (M1 to M5) and deaggregated response of 

interior and exterior frames for models M1 and M3. 

Table O-4 Collapse Potential of the Infilled Buildings and Frame 

Counterparts

Models

Peak Base Shear Resistance (kips)

Infilled Frame Bare Frame

M1 2250

1200

M2 1819

M3 1776

M6 1200

M4 2114 1040

M5 4208 2604

Table O-5 Collapse Potential of the Infilled Buildings and Frame 

Counterparts

Models

Median Collapse Intensity (g)

Infilled Frame Bare Frame

SA[T1] SA[0.5] PGA SA[T1] SA[0.5] PGA

M1 0.89 0.77 0.40

0.54 0.62 0.30

M2 0.73 0.69 0.35

M3 0.66 0.62 0.31

M6 0.54 0.58 0.29

M4 0.72 0.70 0.36 0.45 0.60 0.28

M5 0.65 0.75 0.37 0.35 0.61 0.30
FEMA P-2018 O: Studies on Infilled Frames O-9 

M1 M2 M3

M4 M5 M6

Figure O-6 Incremental dynamic analysis results of the infilled frame models M1 to M6.

O.3 Calculation of Strength of Infilled Frame Buildings

This section discusses the procedures proposed for the estimation of the 

strength of these buildings based on the results of the nonlinear time-history 

analyses discussed in the previous section. In some cases, detailed finite 

element analyses of single bays were also run to provide further insight 

needed for the development of the proposed methodology. 

O.3.1 Default Material Properties

There is great uncertainty regarding the exact values of masonry properties 

which depend on the construction materials and practice, deterioration and 

other factors. Without in situ testing, estimating the material properties of 

masonry infills is challenging, as they tend to vary considerably. The most 

important properties are the compressive strength, cohesion, and the 

coefficient of friction. It is outside the scope of this methodology to require 

testing that would provide better estimates of these factors. Therefore, a 

table of default material property values (Table 3-1) is provided despite these 

uncertainties. 

The values for expected cohesion, friction, and f′m in Table 3-1 are based on 

values provided in NZSEE (2017), taken in the middle of the range, and 

converted from MPa to psi. These values are based on unreinforced masonry 

construction in New Zealand. Values were revised based on engineering 

judgement, through consultation with the Project Review Panel and others 

with expertise in masonry construction. Users are cautioned that it is not 

conservative to assume the weakest (worst) conditions. If more detailed 
O-10 O: Studies on Infilled Frames FEMA P-2018

information is available, it should be used in lieu of the values provided in 

Table 3-1. 

O.3.2 Plastic Mechanism of Infilled Frames

Typical displacement profiles of the prototype buildings (M1 to M6) are 

presented in Figure O-7. In each subplot, the displacement profiles at the 

instants of peak strength, peak deformation, as well as the residual 

deformation profiles are illustrated. In all cases, the selected motion

represents the intensity just before collapse, according to the collapse criteria 

discussed in Section O.2.3. It is evident from the deformation profiles that

once these structures become nonlinear, the deformation mostly concentrates 

in the first story. Therefore, it can be concluded that in case of infilled 

frames without plan or height irregularities, mechanism 1 develops and the 

first story above ground is the critical story. For buildings with an obvious 

strength irregularity along the height, the critical story may be an upper story. 

This may occur due to reduction in strength of concrete columns, infills, or 

both. In that case, mechanism 3 governs. Mechanisms 2 and 4 as described 

in Section 5.5.1 are not considered feasible options, as they are not expected 

to govern the behavior of infilled buildings with infills strong enough not to 

be ignored according to this methodology. 

M1 M2 M3 M4 M5 M6

Figure O-7 Displacement profiles of the buildings M1 to M6 just before collapse.

O.3.3 Column Effective Length

Infill panels can shorten the effective length of a column, potentially 

precipitating shear failure in a column that would otherwise fail in flexure. 

To account for these effects, in this methodology, infills are assumed to 

shorten the effective height of the adjacent columns. This shorter effective 

height must be considered in the calculation of the column shear strength 
FEMA P-2018 O: Studies on Infilled Frames O-11

ratio to determine whether flexure or shear governs the behavior. The infill 

also effectively reduces the column drift capacity in Chapter 9. 

The effective heights of the columns are defined in Table O-6 (repeated from 

Table 9-5), where lu is the clear height of the column. The recommendation

of lu/2 is based on Martin and Stavridis (2018). Although they distinguish 

between strong and weak infill in definition of effective height, here, for 

simplicity, one value is recommended. For openings that are close to the 

column, Table O-6 suggests an effective height equal to the height of the 

opening. This suggestion is based on earthquake damage, which often causes 

shear failure in columns adjacent to openings, as shown in Figure O-8. 

Table O-6 Effective Height of Columns in Infilled Frame

Effective Height of Column lu,inf

Bare column lu

Columns with infill abutting on one or 

more sides in the direction of loading lu/2

Partial height infills Clear height of the column that does not 

have abutting infill

Columns with infill with openings abutting 

on one or more sides in the direction of 

loading 

Where an opening exists within a distance 

of dop < hinf/2 of the column, the effective 

height of the column is taken as the height 

of the opening, hop. 

Otherwise, use lu/2.

Figure O-8 Damage in infill panel with opening causing shear failure in 

bounding column (Yousefianmoghadam and Stavridis, 2018). 
O-12 O: Studies on Infilled Frames FEMA P-2018

O.3.4 Classification of Infilled Frames based on Failure 

Mechanism

The infilled concrete frames are classified here in terms of the relative 

strengths of the infill and the column as strong infill or weak infill. For this 

methodology, the infill with solid panel is classified in terms of the 

anticipated failure mechanism as

• ‘strong’ relative to the frame if Vm/ Vlc > 3.0, and

• ‘weak’ otherwise

where Vlc is the shear resistance of the weakest of the two columns bounding 

the infill panel, Vm is the strength of the masonry infill calculated based on 

Equation (O-2). 

In section O.3.7 these definitions of ‘weak’ and ‘strong’ infills are revisited 

to: (a) account for openings, if present; and (b) to identify extremely weak 

infills not contributing substantially to the strength. The later are ignored 

from the strength calculations.

The effectiveness of the proposed criterion is compared with the criteria

adopted by ASCE 41-17, which are based on stiffness, by considering the 

structures considered by Martin and Stavridis (2018) for the development of 

the ASCE 41-17 methodology. The comparison of Figures O-9 and O-10

demonstrates that, with few exceptions, the proposed criteria provide 

consistent classification with ASCE 41-17. 

Figure O-9 Classification of infills based on relative stiffness of infill and bounding frame.

Figure O-10 Classification of infills based on relative strength of infill and bounding frame.
FEMA P-2018 O: Studies on Infilled Frames O-13 

O.3.5 Strength of Single Infilled Bay with Solid Panel

Detailed finite element models of the single-story single-bay frames for the 

typical infilled bays of the prototype buildings are created following a 

modeling methodology that combines the smeared-crack and interface 

elements (Stavridis and Shing, 2010). This methodology can simulate 

dominant shear and diffused flexural cracks in the concrete members, the 

crushing and tensile splitting of the masonry units, and the mixed-mode 

failure of the mortar joints. The deformed mesh of a panel from model M1 

and the lateral strength-vs.-drift curves obtained from the detailed FE models 

subjected to pushover analyses are presented in Figure O-11. 

(a) deformed mesh of panel in M1 (b) backbone curves of single-story 

single bays for all prototypes

Figure O-11 Results of detailed FE analyses single-story single bay frames for the 

prototypes structures considered here. 

As the infilled frames are loaded laterally, the internal forces are 

redistributed and the vertical load carried by the infill changes. The values of 

the vertical load carried by the infill initially, and at the instant when the peak 

vertical load is reached, are summarized in Table O-7. The values provided 

in the table are indicative of this fluctuation.

Table O-7 grav Pinf and max Pinf Values of the Models

Models PT (kips)

grav Pinf

(kips) / grav P P inf T

max Pinf

(kips) / max P P inf T

M1 130.6 83.0 0.63 91.2 0.70

M2 110.6 44.2 0.40 75.7 0.68

M3 110.6 27.6 0.25 75.7 0.68

M4 124.5 79.1 0.63 89.2 0.72

M5 299.2 126.3 0.42 199.2 0.67

The strength of a single infilled bay can be estimated according to the 

equations proposed by Martin and Stavridis (2017; 2018), which are adopted 

in the ASCE 41-17 (2017). By focusing on the structures examined here and 
O-14 O: Studies on Infilled Frames FEMA P-2018

making a series of appropriate assumptions, the following simplified 

provisions are proposed for this methodology.

Vinf,sol = ( , ) / 6 max max V P V f t n h m inf lc m inf s inf μ + ≤ ′ (O-1)

Vm = grav

inf w P AC μ + (O-2)

where, μ is the initial friction coefficient, C is the cohesion, mf ′ is the 

compressive strength of the masonry assembly, Linf is the length of the infill 

wall, hinf is the height of the infill panel, tinf is the net thickness of the panel, 

Aw is the horizontal cross-sectional area of an infill panel (tinf Linf), ns is the 

number of developed struts in the infill, equal to 1 for panels with aspect 

ratio (Linf /hinf) < 1.0 and 2 otherwise, grav Pinf is the vertical load carried by the 

infill, calculated from the total gravity load, PT, above the story of interest, max Pinf is the total axial load supported by the infill when the maximum lateral 

strength is reached. Finally, Vlc is the strength of the weaker of the two 

columns bounding the bay of interest. The calculation of Vlc considers both 

flexure- and shear-critical behavior to determine the governing value of shear 

strength. For the estimation of the flexural strength of the column, one 

should consider the reduced clear column height, defined in Table 9-5 of the 

document.

Based on Table O-7, and additional calculations not shown for conciseness, 

the initial gravity load carried by the infill can be assumed to be equal to 50% 

of the total load, PT, while the vertical load at the instant of peak lateral 

resistance can be assumed to be equal to 70% of the total vertical load, PT. 

These recommendations apply to the cases with wall lengths between 15 ft. 

and 25 ft., and for story heights between 10 ft. and 14 ft. Otherwise, the 

vertical loads can be calculated according to ASCE 41-17 Table 11-9.

The maximum shear strength of a single-bay infilled frame obtained from 

Equation O-1 and the detailed FE analyses are summarized in Table O-8 (M4 

and M6 have the same infilled frame as that of M1 and M3, respectively). 

The table indicates that the analytical equations proposed here predict the 

peak strength with sufficient accuracy.

Table O-8 Comparison of Strength of Single Infilled Bays Obtained

Models

Strength (kips) of Single Infilled Bay

Finite Element Analyses

ATC-78 Calculations 

(Equations O-1 and O-2)

M1 and M4 194.6 195.9

M2 167.1 127.3

M3 and M6 141.4 125.2

M5 289.7 282.5
FEMA P-2018 O: Studies on Infilled Frames O-15

O.3.6 Strength of Single Infilled Bay with Openings

Assessing the effect of openings on the response of infilled frames is rather 

challenging. A parametric study using nonlinear finite element models is 

conducted to examine the influence of the opening size and location within 

the masonry panel. For consistency, the frame detailing of the baseline 

model M1 (same as in M2,3,4, and 6) is used in all the analyses presented in 

this section. Four different opening sizes are considered, and the windows 

are placed in the center of the panel or eccentrically. The opening sizes and 

locations considered in the parametric study are summarized in Table O-9. 

Masonry with compressive strength of 1.4 ksi (triple wythe), 0.8 ksi (double 

wythe), and 0.4 ksi (double wythe) is considered to represent the infills in 

each of the models M1, M2 and M3, respectively. The first part of the 

nomenclature of the models indicates the opening size: O1 (60 in. × 48 in.), 

O2 (100 in. × 48 in.), O3 (124 in. × 60 in.) and O4 (148 in. × 64 in.), while 

the second part indicates the window location: M – concentrically placed 

opening which is symmetric for the two directions of loading, and two 

eccentric locations, denoted as L and R. Since the analysis is monotonic, L 

and R configurations are essentially the same structure loaded laterally from 

the two opposite directions with R representing the loading direction in 

which the longer masonry pier is on the windward side of the structure. To 

facilitate the comparison of the deformed meshes and the load distributions, 

all analyses are presented with the load applied on the left side of the 

specimen.

Table O-9 Geometric Details of the Openings Considered in the Parametric Study 

(all dimensions are in inches)

Model 

Name Opening Area

Length Height

From 

Leeward 

Column Opening

From 

Windward 

Column

From 

Top Opening

From 

Bottom

MO1-M

(60 in. × 48 in.)

11.7%

80 60 80 32 48 32

MO1-L 16 60 144 32 48 32

MO1-R 144 60 16 32 48 32

MO2-M

(100 in. × 48 in.)

19.3%

60 100 60 32 48 32

MO2-L 16 100 104 32 48 32

MO2-R 104 100 16 32 48 32

MO3-M

(124 in. × 60 in.)

30.2%

48 124 48 28 60 28

MO3-L 16 124 80 28 60 28

MO3-R 80 124 16 28 60 28

MO4-M

(148 in. × 64 in.)

38.4%

36 148 36 24 64 24

MO4-L 16 148 56 24 64 24

MO4-R 56 148 16 24 64 24
O-16 O: Studies on Infilled Frames FEMA P-2018

The deformed meshes of the FE models at 1.0% drift ratio are presented in 

Figures O-12 to O-14. It can be observed from the figures, that both the size 

and location of the openings considerably affect the failure pattern and, 

therefore, the maximum lateral force that the infilled frame can withstand. 

These observations are in agreement with earlier observations (Stavridis, 

2009), which indicate that the lengths of the piers between the opening and 

the columns determine the level of the diagonal compressive forces that can 

develop in the infill, and, eventually, affect the maximum resistance and 

failure pattern of the infilled frames. The lateral force-drift responses of the 

FE models are presented in Figure O-15. The backbone curves of the frames 

without an infill and with a solid infill are also presented for reference. The 

strength reduction of the infilled frames due to the presence of openings as a 

function of opening location and size is presented in Figures O-16 and O-17, 

respectively.

For the models with the opening close to one of the columns, the short 

masonry pier does not allow the development of the diagonal compressive 

strut. When the masonry piers are wide enough, for instance, in the case of 

smaller openings in the center of the panel, the openings do not affect the 

load-transfer mechanism significantly, as the struts can develop in a similar 

fashion as in the solid panel. However, for the larger windows, the effective 

struts could not develop even when the opening is located at the center of the 

panel due to the narrow masonry piers. Figure O-15 indicates that the lateral 

behavior of the infilled frame with opening at the middle is closer to that of 

the solid panel and gradually converges to the behavior of the bare frame as 

the opening size increases; and especially when the openings are close to one 

of the columns. 

Although this trend has been identified, its precise quantification is rather 

complex and outside the scope of this document. Hence, the strength of 

infilled frames with openings is calculated based on Equation O-3.

Vinf,op = Vinf,sol(1 – Aop/Ainf) (O-3)

where, Vinf,sol is taken from Equation O-1, Aop is the elevation area of the 

openings (Aop = ΣopLophop), hop and Lop are the height and length of the 

opening, respectively, and Ainf = Linf hinf. If Aop/Ainf > 0.6, the infills can be 

ignored for the calculation of shear strength. However, the openings, even 

when ignored in the strength calculations, should be considered in the 

column ratings for inducing possible short column effects. The comparison 

of the strengths estimated using Equation O-3 and those obtained from the 

detailed finite element analyses presented in Figure O-18, indicates that the 

proposed equation can predict the peak strength efficiently and with 

reasonable accuracy.
FEMA P-2018 O: Studies on Infilled Frames O-17 

MO1-L MO1-R MO1-R 

MO2-L MO2-R MO2-R 

MO3-L MO3-R MO3-R 

MO4-L MO4-R MO4-R 

Figure O-12 Deformed meshes at 1.0% drift of panels with openings for ′

m

f = 0.4 ksi. 

MO1-L MO1-R MO1-R 

\

MO2-L MO2-R MO2-R 

MO3-L MO3-R MO3-R 

MO4-L MO4-R MO4-R 

Figure O-13 Deformed meshes at 1.0% drift of panels with openings for ′

m

f = 0.8 ksi. 
O-18 O: Studies on Infilled Frames FEMA P-2018

MO1-L MO1-R MO1-R 

MO2-L MO2-R MO2-R 

MO3-L MO3-R MO3-R 

MO4-L MO4-R MO4-R 

Figure O-14 Deformed meshes at 1.0% drift of panels with openings for ′

m

f = 1.4 ksi. 

(a) ′

m

f = 0.4 ksi

(b) ′

m

f = 0.8 ksi

(c) ′

m

f = 1.4 ksi

Figure O-15 Lateral force-vs.-drift behavior of the infilled panels with openings of different size and 

locations.
FEMA P-2018 O: Studies on Infilled Frames O-19

Figure O-16 Strength reduction of infilled frames as a function of opening location compared to the frame 

with a solid panel.

Figure O-17 Strength reduction of infilled frames as a function of opening area compared to the frame 

with a solid panel.

Figure O-18 Comparison of strength of infilled bays with openings obtained from Equation O-3 and 

detailed FE analyses in FEAP.

O.3.7 When to Ignore Infills in Strength

As indicated by the results of incremental dynamic analyses in Section O.2.4,

the collapse potential of the model M3, which incorporates double wythe

masonry panels with a low compressive strength, fm

′ , of 0.4 ksi, is similar to

that of the corresponding bare frame. Based on this observation, it can be 

concluded that the masonry infill in Model M3 is weak enough to not affect

the behavior of the building frame in terms of its collapse potential. The 

strength ratio of the infill and bounding frame is 1.4 for M3. Hence, this 

value of the strength ratio is adopted here as a criterion to define an infill that

can be ignored in the strength calculations (Vm/Vlc < 1.4). This observation 

together with Equation O-3 results in Table O-10 which provides guidance as

to the classification of infilled frames (with and without openings) in terms

of their contribution to the lateral resistance. 
O-20 O: Studies on Infilled Frames FEMA P-2018

Since the collapse potential of M3 is similar with or without the infills in the 

perimeter bays, the strength of a solid panel with the masonry properties 

same as model M3 (141 kips) is considered as the criteria to ignore infills for 

strength. Therefore, panels with openings that have strength less than 141 

kips can be ignored for strength calculations. The criterion proposed here is 

consistent with the detailed FE analyses summarized in Table O-11, with 

very few exceptions, marked in red in the table.

Table O-10 Classification of Infill in Each Infilled Bay

Ratio of Masonry Panel to 

Column Strength

Infill 

Classification Implication

  −     ≥

op

m inf

lc

A V A

V

1

3 Strong Panel requires full 

consideration

.

  −     > ≥

op

m inf

lc

A V A

V

1

3 1 4 Weak Panel requires full 

consideration

.

  −     <

op

m inf

lc

A V A

V

1

1 4

Very weak due to 

opening(1)

Neglect in strength 

calculations, but consider for 

column rating

Vm/Vlc < 1.4 Ineffective Panel can be ignored 

throughout this methodology

(1) This case also applies when Aop/Ainf > 0.6, but not Vm/Vlc < 1.4, or if Aop/Ainf > 0.2 with 

an opening within 2 ft. of the column. 

Table O-11 When Infill Panels with Openings Can Be Ignored for Calculation of Strength? 

Model ID

Analytical Calculations FEAP Results

Can Ignore?

Aop/Ainf

(%) Vm, op (kips) Vm,op/Vlc

Vinf 

(kips)

Eff. Vinf

(kips) Vinf,sol

fm' = 0.40 ksi

M-O1-L 

0.117

57 1.2 115

115

141

Yes

M-O1-R 57 1.2 132

M-O1-M 57 1.2 140 140 yes 

M-O2-L 

0.193

52 1.1 111

111 yes M-O2-R 52 1.1 116

M-O2-M 52 1.1 126 126 yes 

M-O3-L 

0.302

45 1.0 101

101 yes M-O3-R 45 1.0 103

M-O3-M 45 1.0 108 108 yes 

M-O4-L 

0.384

40 0.9 96

96 yes M-O4-R 40 0.9 96

M-O4-M 40 0.9 102 102 yes 
FEMA P-2018 O: Studies on Infilled Frames O-21 

Table O-11 When Infill Panels with Openings Can Be Ignored for Calculation of Strength? 

(continued) 

Model ID

Analytical Calculations FEAP Results

Can Ignore?

Aop/Ainf

(%) Vm, op (kips) Vm,op/Vlc

Vinf 

(kips)

Eff. Vinf

(kips) Vinf,sol

fm' = 0.80 ksi

M-O1-L 

0.117

83 1.8 125

125

167

yes M-O1-R 83 1.8 142

M-O1-M 83 1.8 150 150 no 

M-O2-L 

0.193

76 1.6 114

114 yes M-O2-R 76 1.6 130

M-O2-M 76 1.6 135 135 yes

M-O3-L 

0.302

66 1.4 114

114 yes M-O3-R 66 1.4 120

M-O3-M 66 1.4 128 128 yes 

M-O4-L 

0.384

58 1.2 105

105 yes M-O4-R 58 1.2 106

M-O4-M 58 1.2 113 113 yes 

fm' = 1.40 ksi

'M-O1-L 

0.117

172 3.6 150

150

194.61

no M-O1-R 172 3.6 180

M-O1-M 172 3.6 191 191 no 

M-O2-L 

0.193

157 3.3 137

137 yes M-O2-R 157 3.3 157

M-O2-M 157 3.3 164 164 no 

M-O3-L 

0.302

136 2.9 131

131 yes M-O3-R 136 2.9 139

M-O3-M 136 2.9 146 146 no 

M-O4-L 

0.384

120 2.5 120

120 yes M-O4-R 120 2.5 126

M-O4-M 120 2.5 145 144.77 no 

O.3.8 Calculation of Story-Shear Strength

As indicated in Section O.2.4, the exterior infilled frames reach their peak 

strength at significantly lower drift ratios compared to the interior columns, 

which are not infilled. The different drift ratios at which the various

components reach their strength are depicted in Figure O-19 for models M1 

(strongest infill) and M3 (weakest infill). The figure indicates that when the 

exterior frames reach their peak strength, the interior frames have reached 

only 40% of their peak strength in the case of M1 and 80% in M3. This 

difference is expected as M1 has much stronger infill ( mf ′ = 1.40 ksi and 3 
 

 

 

 

 

 

wythes) compared to M3 ( fm 

′ = 0.40 ksi and 2 wythes), and as a result it 

reaches its peak strength at significantly lower drift. 

This observation indicates that when estimating the strength of buildings 

with infilled frames in the perimeter and bare columns in the interior, only a 

fraction of the interior columns’ strength should be considered when 

estimating the peak shear strength of the critical story. This fraction depends 

on the drift at which the exterior frames reach peak resistance, as indicated in 

Figure O-19. Based on these observations, the story-shear strength is 

calculated for the critical story based on Equation O-4. 

n inf n n c wall 

Vpx = ∑Vinf,op + β ∑Vncx + ∑Vnw,i (O-4) i=1 i=1 i=1 

where, ninf is the number of infilled bays at the critical story, nwall is the 

number of structural concrete walls, nc is the total number of interior columns 

that do not have infill panels abutting either side of the column in the 

direction of loading and the columns in the exterior frames next to infills 

whose strength is ignored. For each column, Vnc may be governed by the 

columns, or slab-column or beam strength, whichever is lower. 

Model Contribution of noninfilled columns 

M1 0.41 

M2 0.85 

M3 0.80 

M4 0.45 

M5 0.84 

Figure O-19 Contribution of non-infilled columns at the peak strength of infilled frames. 

The β-factor determines the contribution of the non-infilled columns to the 

total strength. It is a function of the drift at which the strongest infilled frame 

reaches its peak shear resistance (i.e., the minimum of the Δpeak values 

computed for all of the infilled bays at the critical story in each loading 

direction). Δpeak can be evaluated based on the ASCE 41-17 provisions, 

which are also provided in Chapter 5 of this methodology. As shown in 

Figure O-19, β varies linearly from 0.4 to 0.9 for Δpeak from 0.15% to 0.4%, 

and it is equal to 0.9 for Δpeak > 0.4%. 

The maximum base shear for each prototype computed using Equation O-4 is 

compared to the strength estimated by the pushover analyses in Table O-12 

obtained following the ASCE 41-17 framework and its extension by Bose et 

O-22 O: Studies on Infilled Frames FEMA P-2018 
FEMA P-2018 O: Studies on Infilled Frames O-23 

al. (2018). The comparison indicates that the proposed equation, though 

simple, provides a good estimate of the strength of the structures obtained 

from more sophisticated nonlinear analysis.

Table O-12 Collapse Potential of the Infilled Buildings and Frame 

Counterparts

Models

Base Shear Strength (kips)

Pushover Analyses Equation O-4 

M1 2250 2261

M2 1819 1789

M3 1776 1757

M6 1200 1274

M4 2114 2101

M5 4208 4156

O.4 Estimation of Effective Periods

The effective fundamental period is the period which, when used with 

Equation 9-1 and an elastic response spectrum with 5% critical damping, can 

yield the peak displacement the structure will experience at, or close to, 2/3 

of its height (here the displacement of the 4th floor is selected for the 4-story 

buildings, and the displacement of the 7th floor story is selected for the 

8-story prototype). This period cannot be obtained with an eigenvalue 

analyses or other analytical methods. Hence, a parameter sweep is conducted 

varying the effective period (Te) from 0.01s to 10s to calculate δeff and 

compare it with the 4th floor displacement for models M1 to M4, M6 and the 

7th floor displacement for model M5. As shown in Figure O-20, the effective 

period increases with increasing excitation level and induced damage. 

As this method focuses on the prediction of collapse, the effective period 

corresponding to the collapse initiation (i.e., peak drift of 1.5%) is considered 

here and the effective periods summarized in Figure O-21 are obtained. The 

figure indicates that the effective periods of the infilled frames at collapse

can be related to the effective period (Te,bare) of the bare frame (Equation 

5-17), adjusted by the ratio of strengths of the infilled frame to that of the 

bare frame (Vp1/Vp1,bare) using Equation (O-5). For an infilled frame system, 

Vp1/Vp1,bare shall not be taken greater than 2.0.

Te = 1

,

1,

1.6 0.6 p

e bare

p bare

V

T

V

    −

 

(O-5)
 

M1 M2 M3 

M4 M5 M6 

Figure O-20 Variation of Te with increase in seismic excitation of the infilled frame models M1 to M6. 

Figure O-21Estimation of effective period of 

infilled frames. 

O.5 Determination of Story-Drifts

The estimation of effective period, Te, according to Equation O-5 facilitates 

the calculation of global effective seismic demand, δeff, based on Equation 

9-1. The story drift demand, δx, is calculated based on Equation 9-4 which

uses the α-factors to modify the story drifts considering the number of stories

in a building and the yield mechanism. The displacement profiles of models

M1 to M6 at collapse are normalized such that the δ (4th 

eff floor displacement

in the 4-story buildings and the 7th floor in M5) is equal to 1, and are

presented in Figure O-22. The figures present the median normalized

displacement profiles. The fractions of δeff concentrated in the bottom story

for the infilled buildings are summarized in Table O-13. It can be observed

O-24 O: Studies on Infilled Frames FEMA P-2018 
 

 

from the table that the displacement at the first story of the models varies 

from 81 to 98% of δeff. In addition, the maximum and the minimum values 

indicate that there is small variability in the values. For consistency with the 

other structural systems, the coefficient α is determined according to Table 

9-1. This table is similar to Table 7-1 developed for shear wall buildings, 

which assumes the drift demand at the critical story is 0.8 times the effective 

global drift demand. 

 

M1 M2 M3 M4 M5 M6 

Figure O-22 Normalized displacement profile of the infilled frame buildings with δeff = 1.0. 

Table O-13 Fraction of the Drift Demand in the First Story 

Models Min of 22 GMs Max of 22 GMs Median 

M1 0.91 0.96 0.94 

M2 0.92 0.97 0.95 

M3 0.92 0.95 0.94 

M4 0.90 0.96 0.93 

M5 0.81 0.91 0.85 

M6 0.93 0.98 0.96 

O.6 Impact of Infill on Column Ratings 

The rating of the building in this methodology is based on ratings of critical 

components (e.g., columns, walls, slab-column connections), which are used 

to determine the story and building ratings. Infill panel walls are not 

considered critical components and therefore are not rated. The effect of 

infill panels on column shear failure is considered by shortening the effective 

height of the column. In addition, infill panels can support substantial 

gravity loads, essentially preventing collapse of columns even if they are 

failed in shear. An example of this phenomenon is shown in Figure O-23. 

In this methodology, the ability of infill to carry gravity loads is considered 

by applying a reduction in the column rating (indicating a better performing 

column) if infill is likely to be intact and load bearing at the drift levels under 

consideration, as shown in Table 9-8. Two factors are considered in 

evaluating an infill’s capacity to bear gravity loads. First, panels that are 

FEMA P-2018 O: Studies on Infilled Frames O-25 
very slender (high hinf/tinf) are likely to fail out of plane and,therefore, are not 

expected to carry vertical loads following a damaging earthquake. Two 

limits on hinf/tinf are proposed. hinf/tinf of 25 is based on FEMA 273. The 

value of hinf/tinf of 35 is based on test results from Angel et al. (1994). 

Second, panels that have experienced large in-plane deformations are also 

unlikely to carry significant gravity loads. The limits on in-plane 

deformations are based on studies by Martin and Stavridis (2017; 2018), 

which quantified the deformation at which residual strength is reached for 

infilled frame bays with various configurations. The reduction in column 

rating applied is based on judgment. 

O-26 O: Studies on Infilled Frames FEMA P-2018 

 

 

 

 

Figure O-23 Damage to an infilled frame building, showing 

severely damaged columns, but no collapse. Infill 

panels are likely carrying significant portion of the 

gravity loads (Bose et al., 2017). 
FEMA P-2018 Symbols P-1 

Symbols

a site class factor, or coefficient for calculation of neutral axis depth of 

a wall

Ab area of an individual reinforcing bar, in2

Abase area of the base of a structure, ft2

Af total area of floors above the story under consideration, ft2

Ag gross area of concrete section, in2

Ainf area of infill panel, in elevation, ft2

Aj effective cross-sectional area of a joint, in2

Aop area of openings in infill panel, in elevation, ft2

As area of longitudinal tension reinforcement, in2

Asb total area of main slab bottom reinforcement passing through, or 

anchored within, a column cage, in2

AT, max maximum torsional amplification factor 

AT torsional amplification factor

Av area of shear or transverse reinforcement within spacing s, in2

Aw area of webs and associated boundary elements in structural walls in 

a story in the direction under consideration, ft2

Aw,inf horizontal cross-sectional area of infill panel, in2 or ft2

b plastic rotation at loss of gravity load-carrying ability (from 

ASCE/SEI 41), or coefficient for calculation of neutral axis depth of 

a wall

bc overall width of a column in the direction perpendicular to shear, 

inches 

BR building rating 

bw web width (or thickness) of a beam, column, or wall segment, inches

wb′ web width of a beam, excluding portions of the web that extend 

beyond the width of a column, inches 
P-2 Symbols FEMA P-2018

c neutral axis depth in wall, feet or inches 

C expected cohesion of masonry mortar joint, psi 

C1 modification factor to relate expected maximum inelastic 

displacement to displacement calculated for linear elastic response

C2 modification factor to represent the effect of pinched hysteresis 

shape, cyclic stiffness degradation, and strength deterioration on 

maximum displacement response 

Cm effective mass factor

CMU concrete masonry unit 

COV the standard deviation of all column ratings at a story divided by the 

weighted mean column rating at that story 

CR column rating

CRadj adjusted average column rating in a story 

 the mean column rating for all columns in the story 

Cvx vertical distribution factor for story forces

Cw coefficient for effective fundamental period of frame-wall structures

d effective depth or the distance from extreme compression fiber to 

centroid of longitudinal tension reinforcement, inches

dop distance between opening in infill panel and the nearest column, 

inches or feet

DCR(avg) average value of DCRx over the height of the building 

DCR(max) maximum value of DCRx over the height of the building

DCRx relative demand-to-capacity ratio for story x 

e real (inherent) eccentricity between the center of mass and the 

center of strength, feet

Ec modulus of elasticity of concrete, psi

cf ′ specified compressive strength of concrete, psi

ce f ′ expected compressive strength of concrete, psi

fcol fraction of gravity loads supported by columns in a story 

f′m expected compressive strength of the masonry assembly

fy specified yield strength of reinforcement, psi or ksi

fye expected yield strength of reinforcement, psi or ksi

CR
FEMA P-2018 Symbols P-3 

fwall fraction of gravity loads in a story supported by wall

g acceleration of gravity, in/sec2

G limit state function defining failure of a column

hb overall depth of a beam, inches 

hc overall dimension of a column in the direction of shear, inches

heff effective height of the building, taken as the height from the base to 

the centroid of lateral forces (same as the effective height of an 

equivalent single-degree-of-freedom system), feet or inches

hi, hx height from the base of the building to level i or level x, feet

hinf height of the infill panel, inches or feet

hn height from the base of the building to the highest level of the 

seismic force-resisting system, feet or inches

hop height of opening in an infill panel, inches or feet 

hsx height of story x

hx height from the base of a building to level x

hw height of shear wall, feet; clear height of wall segment, inches 

Ie effective moment of inertia of a concrete section, in4

Ig moment of inertia of gross concrete section about centroidal axis, 

neglecting reinforcement, in4

k factor related to ductility demand for computing column shear 

strength

Ke effective stiffness of a building, k/in

linf height of an equivalent cantilever column, from the face of a joint to 

the point of inflection (or zero moment), inches 

ln clear span of beam measured face-to-face of supports, inches 

lu clear height of a column, inches or feet

lu,inf clear height of a column with abutting infill on either side in the 

direction of loading, inches or feet 

lw length of shear wall or wall segment, inches or feet

L overall building plan dimension, or plan dimension between the 

outermost frame columns in a story, feet 

Linf length of the infill panel, inches or feet
P-4 Symbols FEMA P-2018

Lop length of opening in an infill panel, inches or feet 

L1 longer dimension between the edge of the building and the center of 

strength 

L2 shorter dimension between the edge of the building and the center of 

strength

McB flexural strength at the bottom of a column, kip-inches 

McT flexural strength at the top of a column, kip-inches 

Mn expected flexural strength of a column, wall, or beam, calculated 

using expected material properties and strength reduction factor (φ) 

equal to 1.0, kip-inches 

Mnb flexural strength of a beam, in mechanism calculations, kip-inches 

Mnc flexural strength of a column, in mechanism calculations, kip-inches 

Mnj flexural strength of beam-column, slab-column, beam-wall, and slabwall connections (joints), in mechanism calculations, kip-inches 

Mns moment transfer strength of slab-column connections, in mechanism 

calculations, kip-inches 

Mnw flexural strength of a wall, in mechanism calculations, kip-inches 

MOT overturning moment at the base of a building, kip-feet

MOTi overturning resistance provided by an individual frame in a building, 

kip-feet

ΣMc summation of column expected flexural strengths, kip-inches 

ΣMb summation of beam expected flexural strengths, kip-inches 

n number of levels or number of stories in a building

nc number of interior columns that do not have abutting infill panels on 

either in the direction of loading

ncol number of columns in story x

nf number of frame or wall lines in story x

ninf number of infilled bays at the critical story

ns number of struts developed in an infill panel 

nwall number of walls in story x

pf probability of column drift demand exceeding column drift capacity 

P total column axial load, kips
FEMA P-2018 Symbols P-5 

PD axial load due to tributary dead loads, kips

Peq axial load due to earthquake overturning effects, kips 

Pg axial load due to gravity effects, kips or pounds 

grav Pinf vertical load initially supported by an infill panel, kips

PL axial load due to unreduced tributary live loads, kips

max Pinf vertical load supported by an infill panel when the maximum 

(lateral) strength is reached, kips

POT axial load due to earthquake overturning effects on corner columns, 

kips

PT total gravity load above story under consideration, kips 

Radj adjusted average of column ratings in a story

Ravg weighted average column rating for all columns in the story, where 

the average is weighted by the gravity load taken by each column

Rfi perpendicular distance from frame or wall line to the center of 

strength (for torsion), feet

s spacing of transverse reinforcement, inches 

Sa spectral acceleration at the effective fundamental period of the 

building, percentage of g

Sa, collapse spectral acceleration at collapse at the effective fundamental period 

of the building, percentage of g

Sd spectral displacement at the effective fundamental period of the 

building 

SR story rating 

SS mapped spectral response acceleration parameter at short periods, 

percentage of g 

S1 mapped spectral response acceleration parameter at a period of one 

second, percentage of g

SXS site class adjusted spectral response acceleration parameter at short 

periods, percentage of g 

SX1 site class adjusted spectral response acceleration parameter at a 

period of one second, percentage of g 

tinf net thickness of infill panel, inches or feet
P-6 Symbols FEMA P-2018

Tbare upper bound period of an infilled frame evaluated without any infill 

panels, s 

TCx torsional capacity of story x, kip-feet

TDx torsional demand at story x, kip-feet 

Te effective fundamental period of a building, seconds 

TR torsional ratio at the critical story

v shear stress, psi

Vb expected shear strength of a beam, kips

Vc punching shear strength of concrete 

Vinf,solid strength of single infilled bay with solid infill, kips

Vinf,open strength of single infilled bay adjusted for openings, kips

Vg unfactored gravity shear demand, kips 

Vlc strength of the weaker of the two columns bounding an infill panel of 

interest, kips

Vm shear strength of a single masonry infill panel, kips 

Vn expected shear strength of a column, wall, or beam, kips or pounds 

Vnc shear strength of a column, in mechanism calculations, kips 

Vnj expected joint shear strength, kips or pounds 

Vnw shear strength of a wall, in mechanism calculations, kips

Vp column capacity-limited (plastic) shear strength, pounds or kips

Vpf plastic shear capacity of a frame or wall line, kips or pounds 

VpMx column shear capacity controlled by flexure in story x, kips

Vp1 plastic mechanism base-shear strength at story 1, kips or pounds 

Vp1,bare plastic mechanism base-shear strength of an infilled frame evaluated 

without infill panels, kips 

Vpx plastic mechanism shear strength at story x, kips or pounds 

Vrx relative story shear demand at story x, kips or pounds

Vy effective yield strength of a structure, kips or pounds

W total effective seismic weight of a building, kips

Wx effective seismic weight above story x, kips 

WI wall index
FEMA P-2018 Symbols P-7 

WR wall rating

WSI wall strength index

wx portion of the total effective seismic weight tributary to level x, kips 

x, y distance from center of strength to column or wall line of interest, 

feet

x story under consideration 

αx coefficient to modify story drifts at story x for building configuration 

and strength characteristics

α ratio of post-yield stiffness to initial effective stiffness before yield

α′ coefficient to modify story drifts at a given story for building 

configuration, recalculated from α considering only the simulations 

in which the story collapsed 

β reliability index for a given column (Appendix A) 

β contribution of frame elements to the total strength of an infilled 

frame system

γ drift factor representing the fraction of story drift affecting the 

critical component

δeff global displacement demand of an equivalent single degree-offreedom system, inches 

δcol column drift demand, inches

δx story drift demand at story x, inches 

δx1 story drift demand at story x amplified for P-delta effects, inches

δy yield displacement at the roof of a building, inches 

ΔC drift capacity of a column, slab-column connection, beam-column 

corner connection, wall, or vertical wall segment, inches or percent

ΔD adjusted column drift demand, inches 

median drift capacity of a particular column, inches

 median drift demand on a particular column, inches

Δpeak drift at which the peak strength of the infilled bays is reached, 

percent 

Δres drift at onset of residual strength for infilled bays, inches or feet

φ strength reduction factor 
P-8 Symbols FEMA P-2018

λ modification factor for lightweight concrete

μ expected initial friction coefficient of masonry mortar joints 

μstrength global demand-to-capacity ratio

θc column plastic rotation capacity, radians 

ρn transverse reinforcement ratio of a wall

ρt shear reinforcement ratio of a column 

σln,∆C standard deviation of the drift capacity (in log space)

σln,∆D standard deviation of the drift demand (in log space) 
FEMA P-2018 References Q-1 

References

Abdullah, S.A., and Wallace, J.W., 2018a, “UCLA-RCWalls database for 

reinforced concrete structural walls,” Proceedings, 11th National 

Conference in Earthquake Engineering, Earthquake Engineering 

Research Institute, Los Angeles, California. 

Abdullah, S.A., and Wallace J.W., 2018b, “Drift capacity of RC structural 

walls with special boundary elements,” ACI Structural Journal, 

accepted for publication, 33pp.

Abdullah, S.A., and Wallace J.W., 2018c, “A reliability-based design 

methodology for RC structural walls with special boundary 

elements,” ACI Structural Journal, submitted for review and 

possible publication, May 4, 2018, 33pp.

ACI, 1977, Building Code Requirements for Reinforced Concrete, ACI 

318-77, American Concrete Institute, Detroit, Michigan.

ACI, 2008, Guide to Durable Concrete, ACI 201.2R-08, American Concrete 

Institute, Farmington Hills, Michigan.

ACI, 2011, Building Code Requirements for Structural Concrete and 

Commentary, ACI 318-11, American Concrete Institute, Farmington 

Hills, Michigan.

ACI, 2011b, Guide for Seismic Rehabilitation of Existing Concrete Frame 

Buildings and Commentary, ACI 369R-11, American Concrete 

Institute, Farmington Hills, Michigan.

ACI, 2014, Building Code Requirements for Structural Concrete and 

Commentary, ACI 318-14, American Concrete Institute, Farmington 

Hills, Michigan.

Angel, R., Abrams, D.P., Shapiro, D., Uzarski, J., Webster, M., 1994, 

Behavior of Reinforced Concrete Frames with Masonry Infills, Civil 

Engineering Studies—Structural Engineering Research Series No. 

589, University of Illinois, Urbana-Champaign, Illinois.

Arteta, C.A., and Abrahamson, N.A., 2017, “Methodology based on 

conditional scenario spectra to estimate engineering demand 
Q-2 References FEMA P-2018

parameter risk,” Proceedings, 16th World Conference on Earthquake 

Engineering, Santiago, Chile.

ASCE, 2003, Seismic Evaluation of Existing Buildings, ASCE/SEI 31-03, 

American Society of Civil Engineers, Structural Engineering 

Institute, Reston, Virginia.

ASCE, 2007, Seismic Rehabilitation of Existing Buildings, ASCE/SEI 41-06, 

American Society of Civil Engineers, Structural Engineering 

Institute, Reston, Virginia.

ASCE, 2010, Minimum Design Loads for Buildings and Other Structures, 

ASCE/SEI 7-10, American Society of Civil Engineers, Structural 

Engineering Institute, Reston, Virginia.

ASCE, 2013, Seismic Evaluation and Retrofit of Existing Buildings, 

ASCE/SEI 41-13, American Society of Civil Engineers, Structural 

Engineering Institute, Reston, Virginia.

ASCE, 2017a, Minimum Design Loads and Associated Criteria for Buildings 

and Other Structures, Provisions, ASCE/SEI 7-16, American 

Society of Civil Engineers, Structural Engineering Institute, Reston, 

Virginia.

ASCE, 2017b, Seismic Evaluation and Retrofit of Existing Buildings, 

ASCE/SEI 41-17, American Society of Civil Engineers, Structural 

Engineering Institute, Reston, Virginia.

Aslani, H., 2005, Probabilistic Earthquake Loss Estimation and Loss 

Disaggregation in Buildings, Ph.D. Dissertation, Stanford 

University, Stanford, California.

ATC, 2000, Database on the Performance of Structures Near Strong-Motion 

Recordings: 1994 Northridge Earthquake, ATC-38, Applied 

Technology Council, Redwood City, California.

ATC, 2011, Identification and Mitigation of Seismically Hazardous Older 

Concrete Buildings: Interim Methodology Evaluation, ATC-78, 

Applied Technology Council, Redwood City, California.

ATC, 2012, Evaluation of the Methodology to Select and Prioritize Collapse 

Indicators in Older Concrete Buildings, ATC-78-1, Applied 

Technology Council, Redwood City, California.

ATC, 2013, Seismic Evaluation for Collapse Potential of Older Concrete 

Frame Buildings, ATC-78-2, Applied Technology Council, 

Redwood City, California.
FEMA P-2018 References Q-3 

ATC, 2015, Seismic Evaluation of Older Concrete Frame Buildings for 

Collapse Potential, ATC-78-3, Applied Technology Council, 

Redwood City, California.

ATC, 2016, Seismic Evaluation of Older Concrete Frame and Shear Wall 

Buildings for Collapse Potential, ATC-78-4, Applied Technology 

Council, Redwood City, California.

ATC, 2016, Seismic Evaluation of Older Concrete Frame, Wall, and FrameWall Buildings for Collapse Potential, ATC-78-5, Applied 

Technology Council, Redwood City, California.

ATC, 2017, Seismic Evaluation of Older Concrete Frame, Frame-Wall, and 

Bearing Wall Buildings for Collapse Potential, ATC-78-6, Applied 

Technology Council, Redwood City, California.

Baker, J.W., 2011, “Conditional mean spectrum: Tool for ground-motion 

selection,” Journal of Structural Engineering, Vol. 137, No. 3, pp. 

322-331, doi:10.1061/(Asce)St.1943-541x.0000215.

Baker, J.W., 2015, “Efficient analytical fragility function fitting using 

dynamic structural analysis,” Earthquake Spectra, Vol. 31, No. 1, 

pp. 579-599, doi:10.1193/021113eqs025m.

Beres, A., White, R.N., and Gergely, P., 1992, Seismic Performance of 

Interior and Exterior Beam-to-Column Joints Related to Lightly 

Reinforced Concrete Frame Buildings: Detailed Experimental 

Results, NCEER-92-0007, National Center for Earthquake 

Engineering Research, State University of New York, Buffalo, New 

York.

Berry, M., Parrish, M., and Eberhard, M., 2004, PEER Structural 

Performance Database User’s Manual, Version 1.0, Pacific 

Earthquake Engineering Research Center, University of California, 

Berkeley, California. 

Bimschas, M., 2010, Displacement-Based Seismic Assessment of Existing 

Bridges in Regions of Moderate Seismicity, Ph.D. Dissertation, 

Institute of Structural Engineering, Swiss Federal Institute of 

Technology Zurich.

Blume, J.A., Newmark, N.M., and Corning, L.M., 1961, Design of Multistory Reinforced Concrete Buildings for Earthquake Motions, 

Portland Cement Association, Chicago, Illinois.
Q-4 References FEMA P-2018

Bose, S., Martin, J., Stavridis, A., 2018, “Simulation framework for infilled 

RC frames subjected to seismic loads,” Earthquake Spectra (under 

review).

Bose, S., Nozari, A., Mohammadi, M.E., Stavridis, A., Babak, M., Wood, 

R.L., Gillins, D., and Barbosa, A., 2016, “Structural assessment of a 

school building in Sankhu, Nepal damaged due to torsional response 

during the 2015 Gorkha earthquake,” Proceedings, A Conference 

and Exposition on Structural Dynamics of Multiphysical Systems: 

From Active Materials to Vibroacoustics, 34th IMAC, Orlando, 

Florida.

Bose, S., Nozari, A., Stavridis, A., and Moaveni, B., 2017, “Nonlinear 

modeling of the seismic performance of a building at Sankhu Nepal 

during the 2015 Nepal Earthquake,” Proceedings, 16th World 

Conference on Earthquake Engineering, Santiago, Chile.

Brando, G., Rapone, D., Spacone, E., Barbosa, A., Olsen, M., Gillins, D., 

Soti, R., Varum, H., Arede, A., Vila-Pouca, N., Furtado, A., Oliveira, 

J., Rodriges, H., Stavridis, A., Bose, S., Faggella, M., Gigliotti, R., 

and Wood, R.L., 2015, Reconnaissance report on the 2015 Gorkha 

earthquake effects in Nepal 2015, XVI Congegno ANIDIS, 

L’AQUILA, Italy.

Canbolat, B.B., and Wight, J.K., 2008, “Experimental investigation on 

seismic behavior of eccentric reinforced concrete beam-column-slab 

connections,” ACI Structural Journal, Vol. 105, No. 2, pp. 154-162.

Canterbury Earthquakes Royal Commission, 2012, Final Report, Canterbury 

Earthquakes Royal Commission, Christchurch, New Zealand, 

http://canterbury.royalcommission.govt.nz/Commission-Reports. 

Caughey, R.A., 1933, Reinforced Concrete, Edwards Brothers Inc., Ann 

Arbor, Michigan.

Ciampi, V., and Carlesimo, L., 1986, “A nonlinear beam element for seismic 

analysis of structures,” Proceedings, 8th European Conference on 

Earthquake Engineering, Lisbon, Portugal.

DeBock, D.J., Liel, A.B., Haselton, C.B., Hooper, J.D., and Henige, R.A., 

2014, “Importance of seismic design accidental torsion requirements 

for building collapse capacity,” Earthquake Engineering and 

Structural Dynamics, Vol. 43, No. 6, pp. 831-850. 

DeBock, D.J., 2017, New Studies on Effects of Torsional Irregularities, 

ATC-123 Project unpublished manuscript, Applied Technology 

Council, Redwood City, California.
FEMA P-2018 References Q-5 

De Souza, R.M., 2000, Force-based Finite Element for Large Displacement 

Inelastic Analysis of Frames, Ph.D. Dissertation, University of 

California, Berkeley, California.

Dhakal, R., and Maekawa, K., 2002, “Modeling for postyield buckling of 

reinforcement,” Journal of Structural Engineering, Vol. 128, No. 9, 

pp. 1139-1147. 

EERI, 1996, “Northridge earthquake of January 17, 1994 reconnaissance 

report,” Earthquake Spectra, Vol. 12, No. S1.

EERI, 2000, “Kocaeli, Turkey earthquake of August 17, 1999 reconnaissance 

report,” Earthquake Spectra, Vol. 16, No. S1.

Ellingwood, B., Galambos, T.V., MacGregor, J.G., and Cornell, C.A., 1980, 

Development of a Probability Based Load Criterion for American 

National Standard A58, National Bureau of Standards, Special 

Publication 577, Washington, D.C.

Elnady, E.M.M., 2008, Seismic Rehabilitation of RC Structural Walls, Ph.D. 

Dissertation, McMaster University, Hamilton, Ontario, Canada.

Elwood, K.J., 2004, “Modelling failures in existing reinforced concrete 

columns,” Canadian Journal of Civil Engineering, Vol. 31, No. 5, 

pp. 846-859.

Elwood, K.J., 2005, “Modeling failures in existing reinforced concrete 

columns,” Canadian Journal of Civil Engineering, Vol. 31, No. 5, 

pp. 846-859.

Elwood, K.J. and Eberhard, M.O., 2009, “Effective stiffness of reinforced 

concrete columns,” ACI Structural Journal, Vol. 106, No.4, 

pp. 476-484.

Elwood, K.J., Matamoros, A.B., Wallace, J.W., Lehman, D.E., Heintz, J.A., 

Mitchell, A.D., Moore, M.A., Valley, M.T., Lowes, L.N., Comartin, 

C.D., and Moehle, J.P., 2007, “Update to ASCE/SEI 41 concrete 

provisions,” Earthquake Spectra, Vol. 23, No. 3, pp. 493-523.

Elwood, K.J., and Moehle, J.P., 2005, “An axial capacity model for sheardamaged columns,” ACI Structural Journal, Vol. 102, No. 4, 

pp. 578-587.

Elwood, K.J., and Moehle, J.P., 2008, “Dynamic shear and axial-load failure 

of reinforced concrete columns,” Journal of Structural Engineering, 

Vol. 134, No. 7, pp. 1189-1198, doi:10.1061/(Asce)0733-9445(2008)

134:7(1189).
Q-6 References FEMA P-2018

FEMA, 1998, Evaluation of Earthquake Damaged Concrete and Masonry 

Wall Buildings, FEMA 306, prepared by the Applied Technology 

Council for the Federal Emergency Management Agency, 

Washington, D.C.

FEMA, 2000, Prestandard and Commentary for the Seismic Rehabilitation 

of Buildings, FEMA 356, prepared by the American Society of Civil 

Engineers for the Federal Emergency Management Agency, 

Washington, D.C.

FEMA, 2009, Quantification of Building Seismic Performance Factors, 

FEMA P-695, prepared by the Applied Technology Council for the 

Federal Emergency Management Agency, Washington, D.C.

FEMA, 2012, Seismic Performance Assessment of Buildings, Methodology, 

and Implementation, FEMA P-58, prepared by the Applied 

Technology Council for the Federal Emergency Management 

Agency, Washington, D.C.

FEMA, 2016, Rapid Visual Screening of Buildings for Potential Seismic 

Hazards: A Handbook, Third Edition, FEMA P-154, prepared by the 

Applied Technology Council for the Federal Emergency 

Management Agency, Washington, D.C.

FEMA, 2018, Seismic Performance Assessment of Buildings, Methodology, 

and Implementation, FEMA P-58 (Second Edition), prepared by the 

Applied Technology Council for the Federal Emergency 

Management Agency, Washington, D.C.

Filippou, F.C., Popov, E.P., and Bertero, V.V., 1983, Effects of Bond 

Deterioration on Hysteretic Behavior of Reinforced Concrete Joints, 

UCB/EERC-83/19, University of California, Berkeley, California.

Galanis, P.H., and Moehle, J., 2015, “Development of collapse indicators for 

risk assessment of older-type reinforced concrete buildings,” 

Earthquake Spectra, Vol. 31, No. 4, pp. 1991-2006, doi:10.1193

/080613EQS225M.

Gao, X., Stavridis, A., Bolis, V., and Preti, M., 2018, “Experimental study on 

the seismic performance of non-ductile RC frames infilled with 

sliding subpanels,” Proceedings, 11th National Conference on 

Earthquake Engineering, Los Angeles, California.

Ghannoum, W.M., 2017, “Updates to modeling parameters and acceptance 

criteria for non-ductile and splice-deficient concrete columns,” 

Proceedings, 16th World Conference on Earthquake Engineering, 

Santiago, Chile.
FEMA P-2018 References Q-7 

Ghannoum, W.M., and Matamoros, A.B., 2014, Nonlinear Modeling 

Parameters and Acceptance Criteria for Concrete Columns, 

American Concrete Institute, ACI Special Publication 297, 

Farmington Hills, Michigan.

Ghannoum, W.M., and Sivaramakrishnan, B., 2012a, “ACI 369 Rectangular 

Column Database: Network for Earthquake Engineering Simulation 

(NEES),” https://nees.org/resources/3658. 

Ghannoum, W.M., and Sivaramakrishnan, B., 2012b, “ACI 369 Circular 

Column Database: Network for Earthquake Engineering Simulation 

(NEES),” https://nees.org/resources/3659. 

Goel, R., and Chopra, A.K., 1997a, Vibration Properties of Buildings 

Determined from Recorded Earthquake Motions, Earthquake 

Engineering Research Center, University of California, UCB/EERC97/14, Berkeley, California.

Goel, R., and Chopra, A.K., 1997b. “Period formulas for moment-resisting 

frame buildings,” Journal of Structural Engineering, Vol. 123, No. 

11, pp. 1454-1461.

Goel, R., and Chopra, A.K., 1998, “Period formulas for concrete shear wall 

buildings,” Journal of Structural Engineering, Vol. 124, No. 4, 

pp. 426-433.

Gogus, A., and Wallace, J.W., 2015, “Fragility assessment of slab-column 

connections,” Earthquake Spectra, Vol. 31, No. 1, pp. 159-177. 

Haindl, M., Hube, M., and Arteta, C.A., 2015, “Seismic Performance 

Assessment of a Reinforced Concrete Shear Wall House,” VII 

Congreso Nacional de Ingenieria Sismica, Bogota, Columbia.

Hannewald, P., Bimschas, M., and Dazio, A., 2013, Quasi-Static Cyclic Tests 

on RC Bridge Piers with Detailing Deficiencies, Institut fur 

Baustatik und Konstruktion, Bericht Nr. 352, ETH Zurich, Zürich, 

Switzerland.

Haselton, C.B., Liel, A.B., Lange, S., and Deierlein, G.G., 2007, BeamColumn Element Model Calibrated for Predicting Flexure Response 

Leading to Global Collapse of RC frame Buildings, PEER Report 

2007/03, Pacific Earthquake Engineering Research Center, 

University of California, Berkeley, California.

Hassan, W.M., 2011, Analytical and Experimental Assessment of Seismic 

Vulnerability of Beam-Column Joints without Transverse 
Q-8 References FEMA P-2018

Reinforcement in Concrete Buildings, Ph.D. Dissertation, University 

of California, Berkeley, California. 

Henkhaus, K., 2010, Axial Failure of Vulnerable Reinforced Concrete 

Columns Damaged by Shear Reversals, Ph.D. Dissertation, Purdue 

University, West Lafayette, Indiana.

Hines, E.M., Seible, F., and Priestley, M.J.N., 1999, Seismic Performance of 

Hollow Rectangular Reinforced Concrete Piers with Highly 

Confined Corner Elements—Phase I: Flexural Tests, and Phase II: 

Shear Tests, Structural Systems Research Project 99/15, University 

of California, San Diego, California.

ICBO, 1967, Uniform Building Code, International Council of Building 

Officials, Whittier, California.

ICBO, 1976, Uniform Building Code, International Council of Building 

Officials, Whittier, California.

Ibarra, L.F., Medina, R.A., and Krawinkler, H., 2005, “Hysteretic models 

that incorporate strength and stiffness deterioration,” Earthquake 

Engineering and Structural Dynamics, Vol. 34, No. 12, pp. 1489-

1511, doi:10.1002/eqe.495.

Imanishi, T., 1996, “Post-yield behavior of multistory reinforced concrete 

shear walls subjected to bilateral deformations under axial loading,” 

Proceedings, 11th World Conference on Earthquake Engineering, 

Acapulco, Mexico.

Joh, O., Goto, Y., and Shibata, T., 1991, “Behavior of Reinforced Concrete

Beam-Column Joints with Eccentricity,” Design of Beam-Column 

Joints for Seismic Resistance, SP-123, American Concrete Institute, 

Farmington Hills, Michigan. 

Jeon, S.H., and Park, J.H., 2016, “Experimental assessment of numerical 

models for reinforced concrete shear walls with deficient details,” 

Journal of the Earthquake Engineering Society of Korea, Vol. 20, 

No. 4, pp. 211-222.

Johnston, R.G., 1973, “Veterans Administration Hospital,” San Fernando, 

California, Earthquake of February 9, 1971, Vol. I, Pt. B, N.A. 

Benfer and J.L. Coffman, Editors, L.M. Murphy, Scientific 

Coordinator, National Oceanic and Atmospheric Administration, 

Washington, D.C. 

Kabeyasawa, T., and Matsumoto, K., 1992, “Tests and analyses of ultra-high 

strength reinforced concrete shear walls,” Proceedings, 10th World 
FEMA P-2018 References Q-9 

Conference on Earthquake Engineering, Madrid, Spain, pp. 3291-

3296.

Kent, D.C., and Park, R., 1971, “Flexural members with confined concrete,” 

Journal of the Structural Division, Vol. 97, No. 7, pp. 1969-1990.

Kleinbaum, D.G., and Klein, M, 2005, Survival Analysis: A Self-Learning 

Text, Springer Science + Business Media, Inc., New York, New 

York. 

LaFave, J.M., Bonacci, J.F., Burak, B., and Shin, M., 2005, “Eccentric beamcolumn connections,” Concrete International, Vol. 27, No. 9, 

pp. 58-62. 

Lew, H.S., Leyendecker, E.V., and Dikkers, R.D., 1971, Engineering Aspects 

of the 1971 San Fernando Earthquake, National Bureau of 

Standards, Building Science Series 40, Washington, D.C. 

Li, Y., Elwood K.J., and Hwang S.-J., 2014, Assessment of ASCE/SEI 41 

Concrete Column Provisions using Shaking Table Tests, American 

Concrete Institute, ACI Special Publication 297, Farmington Hills, 

Michigan.

Looi, D.T.W., Su, R.K.L., Cheng, B., and Tsang, H.H., 2017, “Effects of 

axial load on seismic performance of reinforced concrete walls with 

short shear span,” Engineering Structures, Vol. 151, pp. 312-326.

Luco, N., Mori, Y., Funahashi, Y., Cornell, A., and Nakashima, M, 2003, 

“Evaluation of predictors of non-linear seismic demands using 

‘fishbone’ models of SMRF buildings,” Earthquake Engineering and 

Structural Dynamics, Vol. 32, pp. 2267–2288, doi:10.1002/eqe.331.

Lynn, A., 1999, Seismic Evaluation of Existing Reinforced Concrete Building 

Columns, Ph.D. Dissertation, University of California, Berkley, 

California. 

Marcilla, T., Uma, S.R., and Liel, A., 2017, “Critical structural weaknesses 

exposed in older RC wall-frame structures during the Christchurch 

earthquakes,” Proceedings, 16th World Conference on Earthquake 

Engineering, Santiago, Chile.

Martin, J., and Stavridis, A., 2017, “Simplified method to assess lateral 

resistance of infilled reinforced concrete frames,” Proceedings, 16th 

World Conference on Earthquake Engineering, Santiago, Chile.

Martin, J., Stavridis, A., 2018, “Lateral resistance of infilled RC frames,” 

Bulletin of Earthquake Engineering (under review).
Q-10 References FEMA P-2018

Melchers, R.E., 1999, Structural Reliability Analysis and Prediction, Second 

Edition, John Wiley and Sons Ltd., West Sussex, England.

Melek, M., and Wallace, J.W., 2004, “Cyclic behavior of columns with short 

lap splices,” ACI Structural Journal, Vol. 101, No. 6, pp. 802-811.

Moehle, J., 2014, Seismic Design of Reinforced Concrete Buildings, 

McGraw-Hill, New York, New York. 

Mohd Yassin, M.H., 1994, Nonlinear Analysis of Prestressed Concrete 

Structures under Monotonic and Cyclic Loads, Ph.D. Dissertation, 

University of California, Berkeley, California. 

Mori, Y., and Ellingwood, B.R., 1993, “Reliability-based service-life 

assessment of aging concrete structures,” Journal of Structural 

Engineering, Vol. 119, No. 5, pp. 1600-1621.

Murphy, L. M., Steinbrugge, K. V., and Duke, C. M., 1973, “The San 

Fernando earthquake,” San Fernando, California, Earthquake of 

February 9, 1971, Vol. I, Part A, L.M. Murphy, Scientific 

Coordinator, National Oceanic and Atmospheric Administration, 

Washington, D.C.

MSJC, 2013, Building Code Requirements and Specification for Masonry 

Structures, TMS 402/ACI 530/ASCE 5 and TMS 602/ACI 530.1/

ASCE 6, Masonry Standards Joint Committee (MSJC) of The 

Masonry Society, Boulder, Colorado; the American Concrete 

Institute, Farmington Hills, Michigan; and the American Society of 

Civil Engineers, Reston, Virginia.

NEES, 2010, Mitigation of Collapse Risk in Older Concrete Buildings, 

Grand Challenge Research, Pacific Earthquake Engineering 

Research Center and the Network for Earthquake Engineering 

Simulation, http://peer.berkeley.edu/grandchallenge/index.html, last 

accessed November 5, 2014. 

NIST, 2010a, Concrete Model Building Subtypes Recommended for Use in 

Collecting Inventory Data, NIST GCR 10-917-6, prepared by the 

Building Seismic Safety Council for the National Institute of 

Standards and Technology, Gaithersburg, Maryland.

NIST, 2010b, Program Plan for the Development of Collapse Assessment 

and Mitigation Strategies for Existing Reinforced Concrete 

Buildings, NIST GCR 10-917-7, prepared by the NEHRP 

Consultants Joint Venture, a partnership of the Applied Technology 

Council and the Consortium of Universities for Research in 
FEMA P-2018 References Q-11 

Earthquake Engineering, for the National Institute of Standards and 

Technology, Gaithersburg, Maryland.

NIST, 2010c, Evaluation of the FEMA P-695 Methodology for 

Quantification of Building Seismic Performance Factors, NIST GCR 

10-917-8, prepared by the NEHRP Consultants Joint Venture, a 

partnership of the Applied Technology Council and the Consortium 

of Universities for Research in Earthquake Engineering, for the 

National Institute of Standards and Technology, Gaithersburg, 

Maryland.

NIST, 2014, Review of Past Performance and Further Development of 

Modeling Techniques for Collapse Assessment of Existing

Reinforced Concrete Buildings, NIST GCR 14-917-28, prepared by 

the NEHRP Consultants Joint Venture, a partnership of the Applied 

Technology Council and the Consortium of Universities for 

Research in Earthquake Engineering, for the National Institute of 

Standards and Technology, Gaithersburg, Maryland.

NZSEE, 2017, Seismic Assessment of Existing Buildings, New Zealand 

Society of Earthquake Engineering, http://www.eq-assess.org.nz. 

Paterson, J., and Mitchell, D., 2003, “Seismic retrofit of shear walls with 

headed bars and carbon fiber wrap,” Journal of Structural 

Engineering, Vol. 129, No. 5, pp. 606–614.

Paulay T., and Priestley M.J.N., 1992, Seismic Design of Reinforced 

Concrete Masonry Buildings, John Willey & Sons, New York, USA.

Pessiki, S.P., Conley, C.H., Gergely, P., and White, R.N., 1990, Seismic 

Behavior of Lightly-Reinforced Concrete Column and Beam-Column 

Joint Details, NCEER-90-0014, National Center for Earthquake 

Engineering Research, State University of New York, Buffalo, New 

York.

Renouard, F., 2014, Evaluation of a Methodology to Assess the Collapse Risk 

of Older Reinforced Concrete Buildings, M.S. Thesis, University of 

California, Berkeley. 

Saitoh, F., Kuramoto, H., and Minami, K., 1990, “Shear behavior of shear 

walls using high strength concrete,” Summaries of Technical Papers 

of Annual Meeting, Architectural Institute of Japan, pp. 605-606 (in 

Japanese). 

Scott, B.D., Park, R., and Priestley, M.J.N., 1982, “Stress-strain behavior of 

concrete confined by overlapping hoops at low and high strain rates,” 
Q-12 References FEMA P-2018

ACI Journal Proceedings, Vol. 79, No. 1, pp. 13-27, 

doi:10.14359/10875.

Scott, M.H., and Fenves, G.L., 2006, “Plastic hinge integration methods for 

force-based beam-column elements,” Journal of Structural 

Engineering, Vol. 132, No. 2, pp. 244-252, doi:10.1061/(Asce)0733

-9445(2006)132:2(244).

Scott, M.H., and Hamutçuoğlu, O.M., 2008, “Numerically consistent 

regularization of force-based frame elements,” International Journal 

for Numerical Methods in Engineering, Vol. 76, No. 10, 

pp. 612-1631, doi:10.1002/nme.2386.

Sezen, H., and Moehle, J.P., 2004, “Shear strength model for lightly 

reinforced concrete columns,” Journal of Structural Engineering, 

Vol. 130, No. 11, pp. 1692-1703, doi:10.1061/(ASCE)0733

-9445(2004)130:11(1692).

Sozen, M.A., 2014, “Surrealism in facing the earthquake risk,” Seismic 

Evaluation and Rehabilitation of Structures, Vol. 26, pp. 1-13.

Spacone, E., Filippou, F.C., and Taucer, F.F., 1996, “Fibre beam-column 

model for non-linear analysis of R/C frame: Part I. Formulation,” 

Earthquake Engineering and Structural Dynamics, Vol. 25, 

pp. 711-725.

Stavridis, A., 2009, Analytical and Experimental Study of Seismic 

Performance of Reinforced Concrete Frames Infilled with Masonry 

Walls, Ph.D. Dissertation, University of California, San Diego, 

California. 

Stavridis, A., Koutromanos, I., and Shing, P., 2012, “Shake‐table tests of a 

three‐story reinforced concrete frame with masonry infill walls,” 

Earthquake Engineering and Structural Dynamics, Vol. 41, No. 6, 

pp. 1089-1108.

Stavridis, A., and Shing, P., 2010, “Finite element modeling of nonlinear 

behavior of masonry-infilled RC frames,” Journal of Structural 

Engineering, Vol. 136, No. 3, pp. 285-296.

Takahashi, S., Yoshida, K., Ichinose, T., Sanada, Y., Matsumoto, K., 

Fukuyama, H., and Suwada, H., 2013, “Flexural drift capacity of 

reinforced concrete wall with limited confinement,” ACI Structural 

Journal, Vol. 110, No. 1, pp. 95-104.

Thomsen, J.H., and Wallace, J.W., 1995, Displacement-Based Design of 

Reinforced Concrete Structural Walls: Experimental studies of walls 
FEMA P-2018 References Q-13 

with rectangular and T-shaped cross sections, Report No. CU/CEE95/06, Department of Civil and Environmental Engineering, 

Clarkson University, Potsdam, New York.

Vamvatsikos, D., and Cornell, C.A., 2002, “Incremental dynamic analysis,”

Earthquake Engineering and Structural Dynamics, Vol. 31, No. 3, 

pp. 491-514, doi:10.1002/eqe.141. 

Wallace, J.W., Elwood, K.J., and Massone, L.M., 2008, “Investigation of the 

axial load capacity for lightly reinforced wall piers,” Journal of 

Structural Engineering, Vol. 134, No. 9, pp. 1548-1557.

Wallace, J.W, Massone, L.M., Bonelli, P., Dragovich, J., Lagos, R., Luders, 

C., and Moehle, J., 2012, “Damage and implications for seismic 

design of RC structural wall buildings,” Earthquake Spectra, 

Vol. 28, No. S1, pp. 281-289.

Wang, T.Y., Betero, V.V., and Popov, E.P., 1975, Hysteretic Behavior of 

Reinforced Concrete Framed Walls, Report No. EERC 75-23, 

Earthquake Engineering Research Center, University of California, 

Berkeley, California.

Woods, C., and Matamoros, A., 2010, “Effect of longitudinal reinforcement 

ratio on the failure mechanism of R/C columns most vulnerable to 

collapse,” Proceedings, 9th U.S. National and 10th Canadian 

Conference on Earthquake Engineering, Toronto, Canada.

Woods, J.E., Lau, D.T., Cruz-Noguez, C.A., and Shaheen, I.K., 2017, 

“Repair of earthquake damaged squat reinforced concrete shear walls 

using externally bonded CFRP sheets,” Proceedings, 16th World 

Conference on Earthquake Engineering, Santiago, Chile.

Yousefianmoghadam, S., and Stavridis, A., 2016, “Nonlinear response of a 

dynamically tested two story infilled RC structure at different 

damage levels,” Proceedings of 2nd Huixian International Forum on 

Earthquake Engineering for Young Researchers, Beijing, China.
FEMA P-2018 Project Participants R-1 

Project Participants

FEMA Emergency Management Agency

Michael Mahoney (Project Officer)

Federal Emergency Management Agency

400 C Street, SW 

Washington, DC 20472 

Robert D. Hanson (Technical Monitor) 

Federal Emergency Management Agency

5885 Dunabbey Loop 

Dublin, Ohio 43017

Applied Technology Council

Jon A. Heintz (Project Manager) 

Applied Technology Council

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065

Project Technical Committee 

William T. Holmes (Project Technical Director)

Rutherford + Chekene

375 Beale Street, Suite 310 

San Francisco, California 94105 

Abbie Liel 

University of Colorado, Boulder 

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

ECOT 441, UCB 428 

Boulder, Colorado 80309 

Michael Mehrain

Mehrain Naeim International, Inc.

100 Spectrum Center Drive, Suite 900 

Irvine, California 92618

Jack P. Moehle

University of California, Berkeley

Dept. of Civil and Environmental Engineering 

3444 Echo Springs Road 

Lafayette, California 94549

Peter Somers 

Magnusson Klemencic Associates

1301 Fifth Avenue, Suite 3200 

Seattle, Washington 98101 

Project Review Panel

Terry Lundeen (Chair)

Coughlin Porter Lundeen, Inc. 

801 Second Avenue, Suite 900 

Seattle, Washington 98104 

Michael Cochran

Thornton Tomasetti

4551 Glencoe Avenue, Suite 350 

Marina del Rey, California 90292

Gregory G. Deierlein

Stanford University

Dept. of Civil and Environmental Engineering 

318 Parkside Drive 

Palo Alto, California 94306 

Ken Elwood 

The University of Auckland

Dept. of Civil and Environmental Engineering 

3 Grafton Road 

Auckland, New Zealand
R-2 Project Participants FEMA P-2018

Josh Gebelein

Parsons 

100 West Walnut Street, C4-03-01

Pasadena, California 91124

Laura N. Lowes

University of Washington

Dept. of Civil and Environmental Engineering

233C More Hall, Box 352700

Seattle, Washington 98195

Khalid Mosalam

University of California, Berkeley

Structural Engineering, Mechanics, and Materials 

Civil and Environmental Engineering

723 Davis Hall

Berkeley, California 94720

Robert Pekelnicky

Degenkolb Engineers

375 Beale Street, Suite 500

San Francisco, California 94105

Pui-Shum (Benson) Shing

University of California, San Diego

Dept. of Structural Engineering

9500 Gilman Drive, MC0085

La Jolla, California 92093

Bill Tremayne

Holmes Structures

235 Montgomery Street

San Francisco, California 94104

Fred Turner

1516 40th Street

Sacramento, California 95819

John W. Wallace

University of California, Los Angeles

Dept. of Civil and Environmental Engineering

5731 Boelter Hall

Los Angeles, California 90095

Working Group Members

Saman A. Abdullah

University of California, Los Angeles

2541 Boelter Hall

Los Angeles, California 90095

Carlos Arteta

Universidad del Norte

Km.5 Vía Puerto Colombia, Of. 8-28K

Barranquilla, Colombia

Supratik Bose

University at Buffalo

82 Springville Avenue

Buffalo, New York 14226

Panagiotis Galanis

University of California, Berkeley

760 Davis Hall

Berkeley, California 94720

Cody Harrington

University of Colorado, Boulder

ECOT 441, UCB 428

Boulder, Colorado 80309

Travis Marcilla

University of Colorado, Boulder

4362 Ohio Street

San Diego, California 92104

Pablo Parra

Universidad Adolfo Ibáñez

Avenida Quebrada de Macul #8600 

Santiago, Chile

Siamak Sattar 

National Institute of Standards and Technology

Engineering Laboratory (MS 8604)

100 Bureau Drive 

Gaithersburg, Maryland 20899

Andreas Stavridis

University at Buffalo

Dept. of Civil, Structural, and Environ. Engin.

224 Ketter Hall

Buffalo, New York 14260

Duy Vu To

University of California, Berkeley

15662 Jefferson Street

Midway City, California 92655
FEMA P-2018 Project Participants R-3

Trial Evaluation Participants

Brandow & Johnston, Inc.

Josh Gebelein

700 South Flower Street, Suite 1800

Los Angeles, California 90017

Coughlin Porter Lundeen, Inc.

Terry Lundeen, Rebecca Hix Collins, and 

Alex Barnes

801 Second Avenue, Suite 900

Seattle, Washington 98104

Degenkolb Engineers (Los Angeles)

Daniel Zepeda and Garrett Hagen

300 South Grand Avenue, Suite 3850

Los Angeles, California 90071

Degenkolb Engineers (San Francisco)

Insung Kim

375 Beale Street, Suite 500

San Francisco, California 94105

Gilsanz Murray Steficek LLP

Ramon Gilsanz, Joe Mugford, and Yuxing Yang

129 W 27th Street

New York, New York 10001

Holmes Structures

Nina Mahjoub and Dion Marriott

523 West 6th Street, Suite 1122

Los Angeles, California 90014

IDS Group

Rami Elhassan, David Pomerleau, and 

Yangbo Chen

1 Peters Canyon Road, Suite 130

Irvine, California 92606

Murphy Burr Curry, Inc.

David Murphy and Pak Hui

85 Second Street

San Francisco, California 94105

Nishkian Chamberlain

Craig Chamberlain, Jack Hadjian, and

Eugene Ungermann

3710 S. Robertson Blvd., Suite 220

Culver City, California 90232

Rutherford + Chekene

Afshar Jalalian, Brett Lizundia, Lawrence Burkett, 

and Francisco, Parisi

375 Beale Street, Suite 310

San Francisco, California 94105

Simpson Gumpertz & Heger

Kevin O’Connell

1055 W. Seventh Street, Suite 2500

Los Angeles, California 90017

Thornton Tomasetti

Chukwuma G. Ekwueme

4551 Glencoe Avenue, Suite 350

Marina del Rey, California 90292

Thornton Tomasetti (Los Angeles)

Albert Chen, Jeffrey Shoemaker, and 

Mark Ellis

707 Wilshire Blvd., Suite 4450 

Los Angeles, California 90017

Thornton Tomasetti (San Francisco)

Jaime Neilson

650 California Street, Suite 1400

San Francisco, California 94108

University of California, Los Angeles

John W. Wallace, Sofia Gavridou, and 

Elham Moore

5731 Boelter Hall

Los Angeles, California 90095

University of Washington

Dawn Lehman and Jakob Sumearll

214B More Hall, Box 352700

Seattle, Washington 98195

ZFA Structural Engineers

Mark Moore and Ryan Bogart

100 Bush Street, Suite 1850

San Francisco, California 94104
FEMA P-2018 

Catalog No. 18233-1