Assessing Seismic Performance 

of Buildings with 

Conf guration Irregularities 

Calibrating Current Standards and Practices 

FEMA P-2012 / September 2018 

FEMA P-2012

Assessing Seismic Performance of Buildings 

with Configuration Irregularities: 

Calibrating Current Standards and Practices

Prepared by 

APPLIED TECHNOLOGY COUNCIL

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

www.ATCouncil.org

Prepared for

FEDERAL EMERGENCY MANAGEMENT AGENCY

Mai (Michael) Tong, Project Officer

Farzad Naeim, Subject Matter Expert 

Washington, D.C. 

ATC MANAGEMENT AND OVERSIGHT

Jon A. Heintz, Program Executive, Program Manager

Veronica Cedillos, Project Manager

Ayse Hortacsu, Project Manager

PROJECT TECHNICAL COMMITTEE

Michael Valley (Project Technical Director) 

Curt Haselton 

Charlie Kircher

Laura Lowes

Rafael Sabelli

Thomas Sabol 

PROJECT REVIEW PANEL

Greg Deierlein

Larry Fahnestock

James Harris

Conrad Hohener 

John Hooper 

Ryan Kersting 

Roberto Leon* 

*ATC Board Contact 

WORKING GROUP MEMBERS

Kamal Ahmed

Dustin Cook 

Jared DeBock

Sara Essila

Katie Fitzgerald 

Heavenz Kaur

Kristijan Kolozvari

Dawn Lehman

Nasser Marafi

Diana Nishi

Josh Pugh

Ricardo Roldan 

Negin A. Tauberg 

Tsenguun Tsoqbadrakh

September 2018 
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 images: Partial collapse of a commercial building with a vertical irregularity in the 1995 Kobe earthquake, courtesy of 

Charlie Kircher (top left); severe damage to first story of Olive View Hospital in the 1971 San Fernando earthquake (NISEE, 

1971a; bottom left); hillside home with tall cripple walls that have failed, courtesy of Los Angeles Department of Building and 

Safety (bottom right); example of soft-story multi-family wood residential building collapse in the 1989 Loma Prieta earthquake

(FEMA; top right). 
FEMA P-2012 Foreword iii

Foreword

The National Earthquake Hazards Reduction Program (NEHRP) at Federal 

Emergency Management Agency (FEMA) has a responsibility to help

translate and implement new knowledge and research results to increase

seismic hazard resilience nationwide. One of the effective ways to fulfill this 

responsibility is through FEMA NEHRP sponsored problem-focused studies 

to use new research results and tools for developing practical solutions and

needed information suitable for implementation in national standards and 

codes. This FEMA document summaries a problem-focused study on 

seismic performance of buildings with configuration irregularities. It is one 

of many FEMA technical resource documents to help improve seismic 

design practices, it is also to support public education and awareness for

critical issues related to seismic safety of buildings. 

Most buildings in the United States have some irregularities, which are 

known to influence building seismic performances. Under ASCE/SEI 7-16, 

Minimum Design Loads and Associated Criteria for Buildings and Other 

Structures, restrictions are imposed on configuration irregularities in high 

seismic regions. In order to update and simplify the relevant design 

requirements and restrictions, it is necessary to conduct a comprehensive 

assessment of seismic performance of buildings with configuration 

irregularities. This study provides the needed assessment of ASCE/SEI 7-16 

requirements and triggers for restrictions on irregularities. Consequently, the 

findings and recommendations will lead to improvements to specific code 

requirements for irregularities and better knowledge on the subject matter. 

FEMA is greatly appreciative of the Applied Technology Council (ATC), the 

Project Technical Committee, and the Project Review Panel for the

development of this invaluable technical resource document and 

dissemination of the key findings. FEMA is also thankful to the project 

workshop participants for their scrutiny and valuable comments to the 

reported findings. The national standards and codes provide the basic 

protection for buildings against natural hazard impacts. As we call for all 

at-risk communities to adopt and enforce current national standards and 

codes, it is important to ensure that the standards and codes are based on best 

engineering knowledge, and validated new technology and information. We 

are pleased to see that this report is already receiving broad attention among 
iv Foreword FEMA P-2012

earthquake engineering professionals, and some of the recommended code 

changes are under consideration by consensus committees such as the 

NEHRP Provisions Update Committee and ASCE 7 Seismic Subcommittee. 

National Earthquake Hazards Reduction Program (NEHRP)

Federal Emergency Management Agency 
FEMA P-2012 Preface v 

Preface 

In 2014, the Applied Technology Council (ATC), with funding from the 

Federal Emergency Management Agency (FEMA) under Task Order 

Contract HSFE60-12-D-0242, commenced a series of projects (ATC-123, 

ATC-123-1, ATC-123-2, and ATC-123-3) to quantitatively evaluate current

code triggers for structural irregularities, the impact on performance from 

structural irregularities, and the effectiveness of relevant code provisions.

Irregularities are a common occurrence in buildings in the United States. 

Some of these irregularities are defined in existing standards, such as 

ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for 

Buildings and Other Structures (ASCE, 2017a), ASCE/SEI 41-17, Seismic 

Evaluation and Retrofit of Existing Buildings (ASCE, 2017b), ACI 318-14, 

Building Code Requirements for Structural Concrete (ACI, 2014), and 

ANSI/AISC 341-16, Seismic Provisions for Structural Steel Buildings

(AISC, 2016).

Although irregularities are known to influence seismic performance, the 

triggers in the current design codes for vertical and horizontal irregularities 

had not been quantitatively evaluated to determine their effectiveness in 

providing the collapse performance target. NIST GCR 13-917-23, 

Development of NIST Measurement Science R&D Roadmap: Earthquake 

Risk Reduction in Buildings (NIST, 2013), identified the need to 

systematically evaluate irregularity triggers and requirements in all Seismic 

Design Categories as an important priority research topic. 

This multi-year project (collectively referred to as the ATC-123 Project) 

calibrated quantitative triggers and related design requirements in relevant 

codes and standards, primarily ASCE/SEI 7-16. The ATC-123 Project 

conducted analysis work on four of the structural irregularities codified in 

ASCE/SEI 7-16—torsional stiffness irregularity (H1), soft story irregularity 

(V1), mass irregularity (V2), and weak story irregularity (V5)—and 

investigated other configuration issues, including torsional strength 

irregularity (H6), limitations of current strong-column/weak-beam 

requirements (V6), increased collapse potential due to gravity-induced lateral 

demand (V7), and wall discontinuity (V8). 
vi Preface FEMA P-2012

ATC is indebted to the leadership of Michael Valley, Project Technical 

Director, and to the members of the ATC-123, ATC-123-1, ATC-123-2, and 

ATC-123-3 Project Teams for their efforts in developing this report. The 

Project Technical Committee (PTC) consisting of Curt Haselton, Charlie 

Kircher, Laura Lowes, Rafael Sabelli, and Thomas Sabol, managed and 

performed the technical development efforts. Kamal Ahmed, Dustin Cook, 

Jared DeBock, Sara Essila, Katie Fitzgerald, Heavenz Kaur, Kristijan 

Kolozvari, Dawn Lehman, Nasser Marafi, Diana Nishi, Josh Pugh, Ricardo 

Roldan, Negin Tauberg, and Tsenguun Tsoqbadrakh, as Working Group 

members, conducted the design, analysis, and quality assurance work under 

the leadership and supervision of the PTC. The Project Review Panel, 

consisting of Greg Deierlein, Larry Fahnestock, James (Jim) Harris, Conrad 

(Sandy) Hohener, John Hooper, Ryan Kersting, and Robert Leon (ATC 

Board Contact), provided technical review, advice, and consultation at key 

stages of the work. A workshop of invited experts, in addition to the Project 

Review Panel, was convened to obtain feedback on the draft report and the 

Project Technical Committee considered input from this group to finalize the 

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

provided in the list of Project Participants.

ATC also gratefully acknowledges Mai (Mike) Tong (FEMA Project Officer)

and Farzad Naiem (FEMA Subject Matter Expert) for their input and 

guidance in the preparation of this document. Veronica Cedillos and Ayse 

Hortacsu managed the project and Carrie Perna provided report production 

services.

Veronica Cedillos Jon A. Heintz

ATC Director of Projects ATC Executive Director 
FEMA P-2012 Table of Contents vii

Table of Contents

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

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

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

List of Tables ..............................................................................................xxv 

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

1.1 Background .............................................................................. 1-1 

1.2 Overview of Irregularities Considered ..................................... 1-2 

1.3 Target Audience ....................................................................... 1-3 

1.4 Content and Organization ......................................................... 1-3 

2. Overview of Irregularities ............................................................... 2-1 

2.1 Literature Search ...................................................................... 2-2 

2.1.1 Observed Performance of Irregular Buildings ............ 2-3 

2.1.2 Treatment of Configuration Irregularities in Codes 

and Standards ............................................................ 2-12 

2.1.3 Published Research on Irregularities ......................... 2-15 

2.2 Performance Concerns for Irregularities and Corresponding 

Code Requirements ................................................................ 2-19 

2.3 Treatment of Irregularities in this Report ............................... 2-25 

3. Archetype Design, Modeling, and Analysis Approach ................. 3-1 

3.1 Scope of Analytical Studies ..................................................... 3-1 

3.2 Archetype Configurations and Designs .................................... 3-4 

3.2.1 Steel Moment Frame Archetypes ................................ 3-5 

3.2.2 Reinforced Concrete Moment Frame Archetypes ....... 3-8 

3.2.3 Reinforced Concrete Shear Wall Archetypes ............ 3-10 

3.3 Structural Modeling of Archetype Buildings ......................... 3-12 

3.3.1 Steel Moment Frame Archetypes .............................. 3-13 

3.3.2 Reinforced Concrete Moment Frame Archetypes ..... 3-17 

3.3.3 Reinforced Concrete Shear Wall Archetypes ............ 3-20 

3.4 Archetype Analysis Methods ................................................. 3-23 

3.4.1 Overview of FEMA P695 Analysis Methods ............ 3-24 

3.4.2 Selection of Ground Motions .................................... 3-25 

3.4.3 Incremental Dynamic Analysis ................................. 3-26 

3.4.4 Evaluation of MCER Collapse Performance .............. 3-28 

3.4.5 Collapse Evaluation Using Absolute and Relative 

Measures of Collapse Risk ........................................ 3-29 

3.4.6 Tracking of Non-Collapse Archetype Response 

Parameters ................................................................. 3-30 
viii Table of Contents FEMA P

-2012

4. Buildings with Torsional Irregularities [H1, H6] .......................... 4-1 

4.1 Overview................................................................................... 4-1 

4.2 Objectives of Studies and Summary of Findings ...................... 4-1 

4.2.1 Objective 1: Evaluate ASCE/SEI 7-16 Torsion 

Design Provisions ........................................................ 4-2 

4.2.2 Objective 2: Propose Modifications to the 

ASCE/SEI 7-16 Seismic Torsion Provisions ............... 4-2 

4.2.3 Summary of Findings .................................................. 4-2 

4.3 Methodology to Assess Torsion Design Provisions ................. 4-3 

4.4 Archetype Design Space ........................................................... 4-5 

4.4.1 Plan Configurations ..................................................... 4-5 

4.4.2 Baseline Archetypes .................................................... 4-8 

4.4.3 Proportioning the Lateral System for Seismic 

Design ........................................................................ 4-10 

4.5 Results .................................................................................... 4-11 

4.5.1 Collapse Performance under Current Code 

Requirements ............................................................. 4-11 

4.5.2 Observations about Torsion Design Requirements ... 4-14 

4.5.3 Recommended Minimum Requirements ................... 4-15 

4.6 Conclusions and Recommendations ....................................... 4-21 

5. Concrete Wall Buildings with Vertical Irregularities [V1, V8] .... 5-1 

5.1 Overview and Summary of Findings ........................................ 5-1 

5.2 Design Procedures and Common Irregularities ........................ 5-2 

5.3 Overview of Archetype Designs ............................................... 5-4 

5.4 Modeling RC Wall Response ................................................... 5-7 

5.4.1 Methodology Validation and Comparison Studies ...... 5-7 

5.4.2 Non-Simulated Failure Modes ..................................... 5-8 

5.5 Assessment of Collapse Risk .................................................. 5-11 

5.5.1 Overview ................................................................... 5-11 

5.5.2 Results ....................................................................... 5-12 

5.6 Conclusions and Recommendations ....................................... 5-17 

6. Moment Frame Buildings with Vertical Irregularities [V1, V2, 

V5, V6, V7] ........................................................................................ 6-1 

6.1 Overview................................................................................... 6-1 

6.2 Objectives of Studies and Summary of Findings...................... 6-2 

6.2.1 Objective 1: Assess the Adequacy of 

ASCE/SEI 7-16 Vertical Irregularity Provisions ......... 6-2 

6.2.2 Objective 2: Assess the Necessity for Expanding the 

ASCE/SEI 7-16 Vertical Irregularity Provisions ......... 6-2 

6.2.3 Summary of Findings .................................................. 6-3 

6.3 Methodology to Assess Vertical Irregularity Design 

Provisions ................................................................................. 6-3 

6.4 Archetype Design Space by System ......................................... 6-4 

6.5 Studies of Weight (Mass) Irregularity [V2] .............................. 6-4 

6.5.1 Archetype Descriptions ............................................... 6-5 

6.5.2 Results ......................................................................... 6-5 

6.5.3 Conclusion and Recommendations .............................. 6-7 

6.6 Studies of Soft- and Weak-Story Irregularities [V1/V5] .......... 6-8 

6.6.1 Archetype Descriptions ............................................... 6-8 

6.6.2 Results ....................................................................... 6-10 
FEMA P-2012 Table of Contents ix

6.6.3 Conclusion and Recommendations ........................... 6-12 

6.7 Studies of Strong-Column/Weak-Beam Design 

Provisions [V6]....................................................................... 6-12 

6.7.1 Archetype Descriptions ............................................. 6-13 

6.7.2 Results ....................................................................... 6-14 

6.7.3 Conclusion and Recommendations ........................... 6-17 

6.8 Studies of Gravity-Induced Lateral Demands [V7] ................ 6-17 

6.8.1 Previous Studies ........................................................ 6-17 

6.8.2 Archetype Descriptions ............................................. 6-18 

6.8.3 Results ....................................................................... 6-18 

6.8.4 Limitations of the GILD Studies ............................... 6-20 

6.9 Overview of Conclusions and Recommendations .................. 6-21 

6.9.1 Weight (Mass) Irregularity [V2] ............................... 6-22 

6.9.2 Soft/Weak Story Irregularity [V1/V5]....................... 6-22 

6.9.3 Strong-Column/Weak-Beam [V6] ............................ 6-23 

6.9.4 Gravity-Induced Lateral Demand [V7] ..................... 6-23 

7. Discussion of Other Irregularities [H2, H3, H4, H5, V3, V4, 

V8] ...................................................................................................... 7-1 

7.1 Reentrant Corner [H2] Irregularity ........................................... 7-1 

7.2 Diaphragm Discontinuity [H3] Irregularity .............................. 7-5 

7.3 Out-of-Plane Offset [H4] and In-Plane Discontinuity [V4] 

Irregularities ............................................................................. 7-7 

7.3.1 Impact of Out-Of-Plane and In-Plane 

Discontinuities in RC Wall Buildings ......................... 7-8 

7.4 Nonparallel System [H5] Irregularity ..................................... 7-10 

7.5 Vertical Geometric [V3] Irregularity...................................... 7-11 

7.6 Wall Discontinuity [V8] Irregularity ...................................... 7-11 

7.6.1 Discontinuities Associated with Initiation or 

Termination of Stacked Openings in Walls ............... 7-12 

7.6.2 Discontinuities Associated with Increased Wall 

Area to Capture Forces Introduced by New 

Structural Elements ................................................... 7-13 

8. Recommended Improvements ......................................................... 8-1 

8.1 Codes and Standards ................................................................ 8-1 

8.1.1 NEHRP Recommended Provisions and 

ASCE/SEI 7-16 ........................................................... 8-1 

8.1.2 ASCE/SEI 41-17 ......................................................... 8-6 

8.2 Future Studies and Development.............................................. 8-6 

8.2.1 Explicit Collapse Assessment Improvements ............. 8-6 

8.2.2 Design Sensitivity Studies ........................................... 8-7 

8.2.3 Strong-Column/Weak-Beam Requirements ................ 8-8 

8.2.4 More Detailed Considerations ..................................... 8-8 

Appendix A: Torsion Studies .................................................................. A-1

A.1 Development and Validation of Simplified 3D Models .......... A-1 

A.1.1 Nonlinear Backbones for Modeling the SeismicForce-Resisting System .............................................. A-1 

A.1.2 Scaling of Nonlinear Backbones ................................ A-4 

A.1.3 3D Modeling Approach .............................................. A-5 

A.1.4 Validation of Single-Story 3D Models ....................... A-5 

A.2 Torsional Strength Irregularity ................................................ A-7 
x Table of Contents FEMA P

-2012

A.3 Importance of Checking Drift and Stability Requirements 

at the Building’s Edge for Torsionally Irregular Buildings ..... A-8 

A.4 Rationale for Triggering Type 1a Torsional Irregularity 

When >75% of Strength is on One Side of the CM ................. A-9 

A.5 Application of 5% Mass Offsets to Simulate Accidental 

Torsion with Modal Response Spectrum Analysis ................ A-11 

A.6 Explanation of Why Some Trends in the Results Plots 

Double Back on Themselves ................................................. A-13 

Appendix B: Concrete Wall Studies ....................................................... B-1 

B.1 Past Investigations of Concrete Walls with Irregularities........ B-1 

B.1.1 Damage of Concrete Walls with Irregularities in 

Past Earthquakes ......................................................... B-1 

B.1.2 Quantification of Vertical Discontinuities in 

Concrete Walls Using Field Data ............................... B-6 

B.1.3 Laboratory Test Results for Concrete Walls with 

Vertical Irregularities .................................................. B-8 

B.2 Investigation of Vertical Irregularity Using Nonlinear 

Continuum Analysis .............................................................. B-10 

B.3 RC Wall Building Design Process ......................................... B-12 

B.3.1 Building Prototype .................................................... B-12 

B.3.2 Wall Design .............................................................. B-14 

B.3.3 Design of Wall Panel Zone ....................................... B-16 

B.3.4 Design of Coupling Beams ....................................... B-17 

B.3.5 RC Wall Building Design Summaries ...................... B-17 

B.4 Modeling Wall Response ....................................................... B-21 

B.4.1 ATENA ..................................................................... B-22 

B.4.2 OpenSees .................................................................. B-24 

B.5 Preliminary Analyses to Investigate Modeling Assumptions 

and Identify a Preferred Modeling Approach ........................ B-27 

B.5.1 Modeling Assumptions Employed for OpenSees 

and ATENA Analyses .............................................. B-28 

B.5.2 Pushover Analyses to Compare OpenSees and 

ATENA Models ........................................................ B-29 

B.5.3 Dynamic Analyses to Compare OpenSees 

Displacement-Based and Force-Based BeamColumn Element Models .......................................... B-31 

B.5.4 Dynamic Analyses to Compare Models Comprising 

OpenSees Displacement-Based Beam-Column 

Elements and SFI-MVLEM ...................................... B-32 

B.5.5 Identification of a Preferred Modeling Approach 

for Assessing the Impact of Vertical Irregularities 

on the Collapse Risk Posed by RC Wall 

Buildings ................................................................... B-36 

B.6 Analysis Results..................................................................... B-37 

Appendix C: Steel Moment Frame Studies ............................................ C-1 

C.1 Steel Moment Frame Baseline Designs ................................... C-1 

C.1.1 Low Seismicity Zone (SDC Bmax) – Steel Ordinary 

Moment Frame Design ............................................... C-3 

C.1.2 High Seismicity Zone (SDC Dmax) – Steel Special 

Moment Frame Design ............................................. C-12 

C.2 Summary of Steel Moment Frame Results ............................ C-25 
FEMA P-2012 Table of Contents xi

Appendix D: Concrete Moment Frame Studies .................................... D-1 

D.1 Concrete Moment Frame Baseline Designs ............................ D-1 

D.1.1 Low Seismicity Zone (SDC Bmax) – RC Ordinary 

Moment Frame Design ............................................... D-2 

D.1.2 High Seismicity Zone (SDC Dmax) – RC Special

Moment Frame Design ............................................... D-7 

D.2 Summary of Reinforced Concrete Moment Frame Results... D-18 

Appendix E: Results of Quality Control Review ....................................E-1 

E.1 Overview of Quality Control Review ....................................... E-1 

E.2 Results from Quality Control Review ...................................... E-1 

E.2.1 Torsional Studies ......................................................... E-1 

E.2.2 Concrete Shear Wall Studies ....................................... E-2 

E.2.3 Steel Moment Frame Studies ...................................... E-3 

E.2.4 Concrete Moment Frame Studies ................................ E-4 

Appendix F: Global Behavior of Buildings with Mass Irregularity 

[V2] .................................................................................................... F-1 

F.1 Background .............................................................................. F-1 

F.2 Expanded Design Space and Assessment Method ................... F-2 

F.2.1 Expanded Design Space .............................................. F-2 

F.2.2 Assessment Method for Global Behavior.................... F-6 

F.3 Findings .................................................................................... F-7 

F.4 Recommendations .................................................................... F-8 

Appendix G: Story Stiffness and Strength Calculation ........................ G-1 

G.1 Background ............................................................................. G-2 

G.2 Calculation of Story Stiffness .................................................. G-3 

G.2.1 Simple Hand Calculations and Their Limitations ...... G-3 

G.2.2 SEAOC Story Drift Ratio Method ............................. G-6 

G.2.3 Apparent Story Stiffness Method ............................... G-7 

G.3 Calculation of Story Strength .................................................. G-8 

G.4 Recommendations ................................................................... G-9 

G.4.1 Calculation of Story Stiffness ..................................... G-9 

G.4.2 Calculation of Story Strength ..................................... G-9 

Appendix H: Steel Systems Not Specifically Detailed for Seismic 

Resistance ......................................................................................... H-1 

H.1 Background ............................................................................. H-1 

H.2 Configuration........................................................................... H-2 

H.3 Proportioning ........................................................................... H-2 

H.3.1 Strong-Column/Weak-Beam Requirement ................ H-2 

H.3.2 Panel Zone Proportioning ........................................... H-2 

H.3.3 Connection Design Philosophy .................................. H-3 

H.4 Member Local Buckling and Lateral Bracing 

Requirements ........................................................................... H-3 

H.5 Less Stringent Material Specifications and Inspection 

Requirements ........................................................................... H-4 

Symbols ........................................................................................................ I-1 

Glossary ...................................................................................................... J-1 
xii Table of Contents FEMA P-2012

References .................................................................................................. K-1 

Project Participants ................................................................................... L-1 
FEMA P-2012 List of Figures xiii

List of Figures

Figure 2-1 Examples of URM building collapse in the 1983 

Coalinga earthquake, the 1987 Whittier earthquake, and 

the 1989 Loma Prieta earthquake ...................................... 2-4 

Figure 2-2 Example of non-ductile concrete frame building collapse 

at the Veterans Administration (VA) complex in the 

1971 San Fernando earthquake; including total collapse 

of 4 of 26 buildings............................................................ 2-5 

Figure 2-3 Examples of soft-story multi-family wood residential 

building collapse in the 1989 Loma Prieta earthquake 

and in the 1994 Northridge earthquake.............................. 2-5 

Figure 2-4 Photographs of severe damage and collapse of buildings 

of the Olive View Hospital due to the 1971 San 

Fernando earthquake.......................................................... 2-7 

Figure 2-5 Photograph showing severe leaning and incipient 

collapse of a 2-story mixed-use building in Kobe City ..... 2-8 

Figure 2-6 Partial collapse of a 6-story commercial building with a 

torsional irregularity .......................................................... 2-9 

Figure 2-7 Partial collapse of a 12-story commercial building with 

plan and vertical irregularities ......................................... 2-10

Figure 2-8 Coupled walls in upper stories do not continue to lower 

story ................................................................................. 2-11

Figure 2-9 A change in the wall section from the upper to lower 

story results in a loss of wall area and localization of 

flexural yielding............................................................... 2-12

Figure 2-10 Horizontal irregularities................................................... 2-20

Figure 2-11 Vertical irregularities....................................................... 2-21

Figure 3-1 Building elevations for steel moment frames .................... 3-6 

Figure 3-2 Seismic Design Category D steel building floor plans...... 3-6 

Figure 3-3 Seismic Design Category B steel building floor plans ...... 3-6 

Figure 3-4 Plan and elevation of the RC moment frame 

archetypes........................................................................ 3-10 
xiv List of Figures FEMA P-2012

Figure 3-5 Building prototype plans for 8-story buildings and 

12-story buildings designed for Dmax and Bmax spectra..... 3-11 

Figure 3-6 Schematic of a lumped plasticity nonlinear frame 

model................................................................................ 3-14 

Figure 3-7 Modified Ibarra Krawinkler Deterioration Model............ 3-15 

Figure 3-8 Example cyclic behavior of a W30×108 RBS beam 

with composite slab action ............................................... 3-15 

Figure 3-9 Example cyclic behavior of a W14×193 column ............. 3-16 

Figure 3-10 Idealized panel zone shear force deformation 

relationship....................................................................... 3-17 

Figure 3-11 Backbone properties of the Ibarra et al (2005) material 

model................................................................................ 3-18 

Figure 3-12 Example hysteretic properties of a 30 in. by 26 in. RC 

column with low axial load ratio...................................... 3-18

Figure 3-13 Example hysteretic properties of a RC OMF joint with 

axial load ratio of 0.11, 4000 psi concrete, joint area of 

378 in.

2

, and effective beam depth of approximately 13 

inches................................................................................ 3-19

Figure 3-14 Schematic of OpenSees RC wall building model ............ 3-21 

Figure 3-15 OpenSees model configurations for walls with and 

without openings.............................................................. 3-21 

Figure 3-16 Nonlinear 1D cyclic material models............................... 3-23 

Figure 3-17 Regularization of concrete material response using 

mesh dependent length..................................................... 3-23 

Figure 3-18 Far-field record set response spectra normalized by 

peak ground velocity ........................................................ 3-26 

Figure 3-19 Incremental dynamic analysis response plot of spectral 

acceleration versus maximum story drift ratio................. 3-28 

Figure 3-20 Collapse IDA, Baseline 12-story RC SMF ...................... 3-31

Figure 3-21 Interstory Drift Ratio (IDR), Baseline 12-story RC 

SMF.................................................................................. 3-31

Figure 4-1 Torsional Irregularity Ratio................................................ 4-4 

Figure 4-2 Plan view of the baseline archetype configuration, and a 

generic configuration ......................................................... 4-5 
FEMA P-2012 List of Figures xv

Figure 4-3 Illustration of archetype configurations............................. 4-6 

Figure 4-4 Illustration of “Mixed” archetype configurations.............. 4-7 

Figure 4-5 Illustration of “three-sided” archetype configurations....... 4-8 

Figure 4-6 Collapse resistance relative to the baseline for short 

code-conforming archetypes............................................ 4-12 

Figure 4-7 Collapse resistance relative to the baseline for mid-rise 

code-conforming archetypes............................................ 4-12 

Figure 4-8 Trends in collapse resistance for mid-rise archetypes 

with torsional effects neglected in the design process..... 4-14

Figure 4-9 Collapse resistance relative to the baseline for short 

archetypes designed with the proposed minimum 

standards .......................................................................... 4-17 

Figure 4-10 Collapse resistance relative to the baseline for mid-rise 

archetypes, designed with the proposed minimum 

standards .......................................................................... 4-18

Figure 4-11 Collapse resistance relative to the baseline for mixed 

system archetypes, designed with the proposed 

minimum standards.......................................................... 4-18

Figure 5-1 Vertical wall-system configurations.................................. 5-2 

Figure 5-2 Common wall cross-sectional configurations.................... 5-3 

Figure 5-3 Core wall versus distributed planar and flanged walls ...... 5-3 

Figure 5-4 Idealized building elevations ............................................. 5-5 

Figure 5-5 Typical response of slab-column connections................... 5-9 

Figure 5-6 Drift of slab-column connections..................................... 5-10

Figure 5-7 Base shear versus roof drift for 8-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure ......................................................................... 5-13 

Figure 5-8 Earthquake intensity at design period, Sa, versus 

maximum interstory drift for 8-story walls designed for 

Dmax spectrum using the ASCE/SEI-16 ELF 

procedure ......................................................................... 5-14 

Figure 5-9 Impact of vertical irregularity and building height on 

ACMR for walls designed for Dmax demands using 

ASCE/SEI 7-16 ELF procedure....................................... 5-16 
xvi List of Figures FEMA P-2012

Figure 5-10 Impact of vertical irregularity and building height on 

ACMR for walls designed for Dmax demands using 

ASCE/SEI 7-16 MRSA procedure................................... 5-17

Figure 5-11 Impact of vertical irregularity and building height on 

ACMR for walls designed for Bmax demands using 

ASCE/SEI 7-16 ELF procedure ....................................... 5-17

Figure 6-1 Mass irregularity per ASCE/SEI 7-16................................ 6-5 

Figure 6-2 V2 mass irregularity........................................................... 6-6 

Figure 6-3 Interstory drift profile at increments of MCE for the 

3-story MRSA designed steel building with a MR = 3.0 

at the 3rd Floor .................................................................... 6-6 

Figure 6-4 Comparison of ELF and MRSA design forces for a 

20-story RC frame building with a mass irregularity at 

the third story ..................................................................... 6-7 

Figure 6-5 Soft story irregularity per ASCE/SEI 7-16......................... 6-9 

Figure 6-6 Weak story irregularity per ASCE/SEI 7-16...................... 6-9 

Figure 6-7 V1/V5 soft/weak story ..................................................... 6-10

Figure 6-8 V1 weak story .................................................................. 6-11 

Figure 6-9 V1 weak story overstrenth................................................ 6-12 

Figure 6-10 Weak-column/strong-beam.............................................. 6-13 

Figure 6-11 V6 strong-column/weak-beam......................................... 6-15 

Figure 6-12 V6 stepped SCWB ratio, 12-story RC SMF .................... 6-16

Figure 6-13 V6 strong-column/weak-beam......................................... 6-16 

Figure 6-14 Gravity-induced lateral demand ....................................... 6-18 

Figure 6-15 V7 gravity-induced lateral loading with design for 

GILD ................................................................................ 6-19

Figure 6-16 V7 gravity-induced lateral loading without design for 

GILD ................................................................................ 6-20

Figure 6-17 Mean interstory drift at MCE of the poorest performing 

GILD designed and un-designed irregular buildings....... 6-20

Figure 7-1 Example of reentrant corner............................................... 7-2 
FEMA P-2012 List of Figures xvii

Figure 7-2 Comparison of reentrant corner examples as 

proportioned in ATC-3-06 Commentary and drawn to 

scale ................................................................................... 7-2 

Figure 7-3 Impact considering dimensions of plan offsets about both 

axes in identifying reentrant corner irregularity ................ 7-4 

Figure 7-4 Diaphragm discontinuity comprising 50% of the gross 

floor area drawn to scale .................................................... 7-5 

Figure 7-5 Walled buildings classified as irregular due to out-ofplane and in-plane offset of the wall system...................... 7-8 

Figure 7-6 Vertical wall discontinuities potentially constituting an 

irregularity ....................................................................... 7-12 

Figure A-1 Backbone properties of the baseline archetypes 

representing short, mid-rise, and RC wall type 

buildings............................................................................ A-2 

Figure A-2 Backbone properties for lines of lateral resistance 

representing the “wall” and “frame” that make up the 

mixed system .................................................................... A-3 

Figure A-3 Cyclic properties of the short baseline backbone.............. A-4 

Figure A-4 Effects of scaling strength and stiffness of the nonlinear 

backbones, illustrated with the short archetype ................ A-4 

Figure A-5 Plan view of a single story model including placement 

of leaning columns, mass offset, and SFRS ...................... A-5 

Figure A-6 Trends in collapse resistance of 2:1 aspect ratio single 

asymmetric archetypes with increasing eccentricity, but 

no re-proportioning of the SFRS for torsion demands...... A-6 

Figure A-7 Trends in collapse resistance of 2:1 aspect ratio 

symmetric archetypes with increasing torsional 

irregularity, but no re-proportioning of the SFRS for 

torsion demands................................................................ A-6 

Figure A-8 Relative collapse resistance of symmetric short 

archetypes having strength irregularities due to lower 

DCR on one side of the center of mass............................. A-8 

Figure A-9 Relative collapse resistance of symmetric mid-rise 

archetypes having strength irregularities due to lower 

DCR on one side of the center of mass............................. A-8 
xviii List of Figures FEMA P-2012

Figure A-10 Trends in collapse resistance for mid-rise archetypes 

proportioned according to ASCE/SEI 7-16 to resist 

seismic forces, but with a redundancy of 1.0 and 

drift/stability checks performed at the CM, rather than 

the edge of the building..................................................... A-9 

Figure A-11 Trends in collapse resistance for short 3-sided variants

designed with all of the recommended torsion 

provisions from Chapter 4, except that torsional 

irregularity is determined only by TIR ............................ A-10

Figure A-12 Trends in collapse resistance for mid-rise 3-sided 

variants designed with all of the recommended torsion 

provisions from Chapter 4, except that torsional 

irregularity is determined only by TIR ............................ A-10 

Figure A-13 Trends in collapse resistance for mixed system 

variants designed with all of the recommended torsion 

provisions from Chapter 4, except that torsional 

irregularity is determined only by TIR ............................ A-11

Figure A-14 Collapse performance of symmetric archetypes 

designed with modal analysis and accidental torsion 

applied directly by offsetting the mass ± 5% of the 

perpendicular building dimension in the structural 

model............................................................................... A-12

Figure A-15 Illustration of how the torsional irregularity ratio 

computed in ASCE/SEI 7-16 Table 12.3-1 varies with 

plan aspect ratio and eccentricity .................................... A-13 

Figure B-1 Coupled walls in upper stories do not continue to lower 

story................................................................................... B-2 

Figure B-2 A change in the wall section from the upper to lower 

story results in a loss of wall area and localization of 

flexural yielding ................................................................ B-3 

Figure B-3 Vertical discontinuity(ies) in coupled walls...................... B-3 

Figure B-4 Damage to building sustained during the 1989 Loma 

Prieta earthquake............................................................... B-4 

Figure B-5 Damage to “column” at wall discontinuity in a 20-story 

high-rise building .............................................................. B-5 

Figure B-6 Discontinuities observed in walls in Chilean buildings 

and corresponding damage................................................ B-7 

Figure B-7 Wall configurations and designs used for ATENA 

analyses to investigate the impact of opening location ... B-11
FEMA P-2012 List of Figures xix

Figure B-8 Normalized base shear stress versus drift at the 

effective height ................................................................ B-11

Figure B-9 Story stiffness calculation................................................ B-12

Figure B-10 Building prototypes.......................................................... B-13

Figure B-11 Typical wall section and assumed strain distribution ...... B-15

Figure B-12 Forces in the panel zone................................................... B-17 

Figure B-13 Wall response histories as measured and as simulated 

using OpenSees and ATENA specimen RW1 – bar 

fracture failure.................................................................. B-23 

Figure B-14 OpenSees model configurations for walls with and 

without openings.............................................................. B-25 

Figure B-15 OpenSees model configuration for RC wall building...... B-25 

Figure B-16 Nonlinear 1D cyclic material models .............................. B-27 

Figure B-17 Regularization of concrete material response using 

mesh dependent length..................................................... B-27 

Figure B-18 Base shear versus drift at effective height for 8-story 

walls as simulated using ATENA, OpenSees DBE, and 

SFI-MVLEM models....................................................... B-30 

Figure B-19 Earthquake spectral acceleration at the design period 

of the structure, Sa, versus maximum interstory drift 

for the 8-story continuous wall building designed for 

Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure ......................................................................... B-31 

Figure B-20 Earthquake intensity at design period, Sa, versus 

maximum interstory drift for 8-story RC wall building 

with opening at 1st story resulting in 50% stiffness loss 

and designed for Dmax spectrum using the ASCE/SEI 

7-16 ELF procedure ......................................................... B-32 

Figure B-21 Simulated response quantities for models comprising 

SFI-MVLEM and displacement-based beam-column 

element responses for collapse-level of shaking.............. B-33 

Figure B-22 Comparison of SFI-MVLEM and displacement-based 

beam column element IDA results for selected ground 

motion .............................................................................. B-35

Figure B-23 Comparison of SFI-MVLEM and displacement-based 

IDA analysis results for 8-story RC wall building 

without openings.............................................................. B-35 
xx List of Figures FEMA P-2012

Figure B-24 Comparison of SFI-MVLEM and displacement-based 

IDA analysis results for 8-story archetype with opening 

at the first floor................................................................ B-36 

Figure B-25 Base shear versus roof drift for 8-story walls designed 

for Dmax spectrum using the ASCE/SEI7-16 ELF 

procedure......................................................................... B-40 

Figure B-26 Base shear versus roof drift for 8-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 MRSA 

procedure......................................................................... B-41 

Figure B-27 Base shear versus roof drift for 12-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-42 

Figure B-28 Base shear versus roof drift for 12-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 MRSA 

procedure......................................................................... B-43 

Figure B-29 Earthquake intensity at design period, Sa, versus 

maximum inter-story drift for 8-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-44 

Figure B-30 Earthquake intensity at design period, Sa, versus 

maximum interstory drift for 8-story walls designed for 

Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-45 

Figure B-31 Earthquake intensity at design period, Sa, versus 

maximum inter-story drift for 12-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-46 

Figure B-32 Earthquake intensity at design period, Sa, versus 

maximum inter-story drift for 12-story walls designed 

for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-47 

Figure B-33 Earthquake intensity at design period, Sa, versus 

maximum interstory drift for 8-story walls designed for 

Bmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-48 

Figure B-34 Earthquake intensity at design period, Sa, versus 

maximum interstory drift for 12-story walls designed 

for Bmax spectrum using the ASCE/SEI 7-16 ELF 

procedure......................................................................... B-49
FEMA P-2012 List of Figures xxi

Figure B-35 Impact of vertical irregularity and building height on 

ACMR for walls designed for Dmax demands using 

ASCE/SEI 7-16 ELF procedure....................................... B-50

Figure B-36 Impact of vertical irregularity and building height on 

ACMR for walls designed for Dmax demands using 

ASCE/SEI 7-16 MRSA procedure................................... B-50

Figure B-37 Impact of vertical irregularity and building height on 

ACMR for walls designed for Bmax demands using 

ASCE/SEI 7-16 ELF procedure....................................... B-50

Figure C-1 Baseline steel moment frame building elevations.............. C-2 

Figure C-2 Baseline SDC Dmax steel moment frame building plans .... C-2 

Figure C-3 Baseline SDC Bmax steel moment frame building plans..... C-2 

Figure C-4 Baseline SDC Bmax steel moment frame building typical 

3-story elevation ................................................................ C-5 

Figure C-5 Baseline SDC Bmax steel moment frame building typical 

3-story plan ........................................................................ C-5 

Figure C-6 Baseline SDC Bmax steel moment frame building typical 

9-story elevation ................................................................ C-8 

Figure C-7 Baseline SDC Bmax steel moment frame building typical 

9-story plan ........................................................................ C-8 

Figure C-8 Baseline SDC Bmax steel moment frame building 

typical 20-story elevation................................................. C-10

Figure C-9 Baseline SDC Bmax steel moment frame building 

typical 20-story plan ........................................................ C-10

Figure C-10 Reduced beam section profiles ........................................ C-13 

Figure C-11 Baseline SDC Dmax steel moment frame building 

typical 3-story elevation................................................... C-15 

Figure C-12 Baseline SDC Dmax steel moment frame building 

typical 3-story plan .......................................................... C-15 

Figure C-13 Baseline SDC Dmax steel moment frame building 

typical 9-story elevation................................................... C-17 

Figure C-14 Baseline SDC Dmax steel moment frame building 

typical 9-story plan .......................................................... C-17 

Figure C-15 Baseline SDC Dmax steel moment frame building 

typical 20-story elevation................................................. C-20 
xxii List of Figures FEMA P-2012

Figure C-16 Baseline SDC Dmax steel moment frame building 

typical 20-story plan........................................................ C-20 

Figure D-1 Baseline RC moment frame building typical 4-story 

elevation ............................................................................ D-2 

Figure D-2 Baseline RC moment frame building typical 4-story 

plan.................................................................................... D-2 

Figure D-3 Baseline RC moment frame building typical 12-story 

elevation ............................................................................ D-4 

Figure D-4 Baseline RC moment frame building typical 12-story 

plan.................................................................................... D-5 

Figure D-5 Baseline RC moment frame building typical 4-story 

elevation ............................................................................ D-7 

Figure D-6 Baseline RC moment frame building typical 4-story 

plan.................................................................................... D-7 

Figure D-7 Baseline RC moment frame building typical 8-story 

elevation ............................................................................ D-9 

Figure D-8 Baseline RC moment frame building typical 8-story 

plan.................................................................................... D-9 

Figure D-9 Baseline RC moment frame building typical 12-story 

elevation .......................................................................... D-11 

Figure D-10 Baseline RC moment frame building typical 12-story 

plan.................................................................................. D-11 

Figure F-1 Expanded design space for assessment of global 

behavior of buildings with mass irregularity...................... F-2 

Figure F-2 Member sizes for the 20-story steel SMF baseline 

archetype ............................................................................ F-4 

Figure F-3 Member sizes for the 10-story steel SMF baseline 

archetype ............................................................................ F-5 

Figure F-4 Member sizes for the 3-story steel SMF baseline 

archetype ............................................................................ F-5 

Figure F-5 Cantilever-type response of RC SW archetypes ................ F-6 

Figure F-6 Shear-type response of steel SMF archetypes.................... F-6 

Figure F-7 3-story RC SW, irregular mass at Level 2, story shear 

ratios................................................................................... F-9 
FEMA P-2012 List of Figures xxiii

Figure F-8 3-story RC SW, irregular mass at Level 2, story 

moment ratios .................................................................. F-10

Figure F-9 20-story RC SW, irregular mass at Level 2, story 

moment ratios .................................................................. F-10

Figure F-10 20-story SMF, irregular mass at Level 2, story moment 

ratios ................................................................................ F-11

Figure F-11 20-story RC SW, irregular mass at Level 8, story shear 

ratios ................................................................................ F-11

Figure F-12 20-story RC SW, irregular mass at Level 8, story 

moment ratios .................................................................. F-12

Figure F-13 20-story SMF, irregular mass at Level 8, story shear 

ratios ................................................................................ F-12

Figure F-14 20-story SMF, irregular mass at Level 14, story shear 

ratios ................................................................................ F-13

Figure F-15 20-story SMF, irregular mass at Level 14, story 

moment ratios .................................................................. F-13

Figure F-16 20-story SMF, irregular mass at Level 14, mass 

ratio = 3............................................................................ F-14

Figure F-17 20-story SMF, irregular mass at Level 14, mass 

ratio = 5............................................................................ F-14

Figure F-18 20-story SMF, irregular mass at Level 14, mass 

ratio = 10.......................................................................... F-15

Figure F-19 20-story RC SW, irregular mass at Level 14, story 

shear ratios....................................................................... F-15

Figure F-20 20-story RC SW, irregular mass at Level 14, story 

moment ratios .................................................................. F-16

Figure F-21 10-story RC SW, irregular mass at Level 5, story shear 

ratios ................................................................................ F-16

Figure F-22 10-story RC SW, irregular mass at Level 5, story 

moment ratios .................................................................. F-17

Figure F-23 20-story RC SW, irregular mass at Level 14, mass 

ratio = 3............................................................................ F-17

Figure F-24 20-story RC SW, irregular mass at Level 14, mass 

ratio = 5............................................................................ F-18

Figure F-25 20-story RC SW, irregular mass at Level 14, mass 

ratio = 10.......................................................................... F-18
xxiv List of Figures FEMA P-2012

Figure F-26 10-story RC SW, irregular mass at Level 5, mass 

ratio = 3 ............................................................................ F-19

Figure F-27 10-story RC SW, irregular mass at Level 5, mass 

ratio = 5 ............................................................................ F-19

Figure F-28 10-story RC SW, irregular mass at Level 5, mass 

ratio = 10 .......................................................................... F-20

Figure G-1 Design space for story stiffness calculations..................... G-2 

Figure G-2 Stiffness comparisons and correlations for steel moment 

frames ................................................................................ G-5 

Figure G-3 Stiffness comparisons and correlations for concrete 

shear walls......................................................................... G-6 
FEMA P-2012 List of Tables xxv

List of Tables

Table 2-1 Structural Irregularities in U.S. Codes and their 

Treatment in this Report .................................................... 2-1 

Table 2-2 Code Requirements for Horizontal Structural 

Irregularities, by Seismic Design Category ..................... 2-24 

Table 2-3 Code Requirements for Vertical Structural 

Irregularities, by Seismic Design Category ..................... 2-25 

Table 3-1 Systems Used to Study Structural Irregularities ................ 3-2 

Table 3-2 Parameters Varied in Designs and Detailed Analytical 

Studies ................................................................................ 3-3 

Table 3-3 Metrics Monitored in Detailed Analytical Studies ............ 3-4 

Table 3-4 Overview of Baseline Steel Moment Frame Building 

Designs............................................................................... 3-7 

Table 3-5 Common Design Values Used for Steel Moment Frame 

Designs............................................................................... 3-7 

Table 3-6 Example Baseline Design Summary .................................. 3-7 

Table 3-7 Overview of Baseline RC Moment Frame Building 

Designs............................................................................... 3-8 

Table 3-8 Common Design Values Used for RC Moment Frame 

Designs............................................................................... 3-8 

Table 3-9 Example Baseline Design Summary .................................. 3-9 

Table 3-10 Overview of Baseline RC Wall Building Designs ........... 3-11 

Table 3-11 Common Design Values Used for RC Wall Designs ...... 3-12 

Table 3-12 Mean Stripe Results at Selected Intensities, Baseline 12 

Story RC SMF ................................................................. 3-31 

Table 4-1 Design Properties of Baseline Archetypes ....................... 4-10 

Table 4-2 Recommended Modifications for ASCE/SEI 7-16 to 

Achieve Minimum Torsion Design Requirements 

Resulting in Adequate Collapse Resistance for a Broad 

Range of Building Configurations ................................... 4-16 

Table 5-1 Design Space for RC Wall Buildings ................................ 5-4 
xxvi List of Tables FEMA P-2012

Table 5-2 RC Wall Building Periods and Base Shear Demands ........ 5-5 

Table 5-3 Design Properties for RC Walls ......................................... 5-6 

Table 5-4 Collapse Probabilities for RC Wall Building Archetypes 

Designed for the Dmax Spectra for the Case of Collapse 

at Maximum Story Drifts in Excess of 5% ...................... 5-15 

Table 5-5 Collapse Probabilities for RC Wall Building Archetypes 

Designed for the Bmax Spectrum for the Case of 

Collapse at Maximum Story Drifts in Excess of 5%........ 5-16 

Table 6-1 Weight (Mass) Irregularity Archetype Space ..................... 6-5 

Table 6-2 Soft/Weak Irregularity Archetype Space ........................... 6-9 

Table 6-3 SCWB Archetype Space .................................................. 6-14 

Table 6-4 GILD Archetype Space .................................................... 6-18 

Table A-1 Model Information for Baseline Archetypes ..................... A-3 

Table A-2 Differences in Strength and Stiffness Required When 

5% Mass Offsets are Used in Lieu of Static Accidental 

Torsion Moments for Torsionally Irregular Symmetric 

Archetype Buildings ........................................................ A-12 

Table B-1 Summary of Parameters Used in the Design and 

Analysis ........................................................................... B-17 

Table B-2 Summary of Parameters Used in the Design and 

Analysis ........................................................................... B-18 

Table B-3 Summary of Parameters Used in the Design and 

Analysis ........................................................................... B-19 

Table B-4 Summary of Parameters Used in the Design and 

Analysis ........................................................................... B-20 

Table B-5 Collapse Probabilities for RC Wall Building 

Archetypes Designed for the Dmax Spectrum for the 

Case of Collapse at Maximum Story Drifts in Excess 

of 10% ............................................................................. B-38 

Table B-6 Collapse Probabilities for RC Wall Building 

Archetypes Designed for the Bmax Spectrum for the 

Case of Collapse at Maximum Story Drifts in Excess 

of 10% ............................................................................. B-39 

Table C-1 Typical Design Loading .................................................... C-3 

Table C-2 Low Seismicity Zone Seismic and Wind Design 

Values ................................................................................ C-4 
FEMA P-2012 List of Tables xxvii

Table C-3 V0030101 Baseline ............................................................C-6 

Table C-4 V0030102 Baseline ............................................................C-6 

Table C-5 V0030103 Baseline ............................................................C-6 

Table C-6 V0030104 Baseline ............................................................C-7 

Table C-7 V0030105 Baseline ............................................................C-7 

Table C-8 V0030106 Baseline ............................................................C-7 

Table C-9 V0090101 Baseline ............................................................C-9 

Table C-10 V0090102 Baseline ............................................................C-9 

Table C-11 V0200101 Baseline .......................................................... C-11 

Table C-12 V0200102 Baseline .......................................................... C-12 

Table C-13 High Seismicity Zone Seismic and Wind Design 

Values .............................................................................. C-14 

Table C-14 Reduced Beam Section Profiles Used in SDC Dmax 

Buildings .......................................................................... C-14 

Table C-15 V0300201 Baseline .......................................................... C-15 

Table C-16 V0300202 Baseline .......................................................... C-16 

Table C-17 V0300203 Baseline .......................................................... C-16 

Table C-18 V0300204 Baseline .......................................................... C-16 

Table C-19 V0900201 Baseline .......................................................... C-18 

Table C-20 V0900202 Baseline .......................................................... C-18 

Table C-21 V0900203 Baseline .......................................................... C-19 

Table C-22 V0900204 Baseline .......................................................... C-19 

Table C-23 V02002011 Baseline ........................................................ C-21 

Table C-24 V02002012 Baseline ........................................................ C-22 

Table C-25 V02002021 Baseline ........................................................ C-23 

Table C-26 V02002022 Baseline ........................................................ C-24 

Table C-27 Steel Moment Frame Results ........................................... C-25 

Table D-1 Summary of Baseline Reinforced Concrete Frame 

Archetypes ........................................................................ D-1 
xxviii List of Tables FEMA P-2012

Table D-2 Common Design Values Used for All RC MF 

Designs .............................................................................. D-2 

Table D-3 Design Values – 4-Story RC OMF Baseline ..................... D-3 

Table D-4 4-Story RC OMF Baseline Design Summary: 

V104201 ............................................................................ D-4 

Table D-5 Design Values – 12-Story RC OMF Baseline ................... D-5 

Table D-6 12-Story RC OMF Baseline Design Summary: 

V112201 ............................................................................ D-6 

Table D-7 Design Values – Baseline 4-Story RC SMF ..................... D-7 

Table D-8 4-Story RC SMF Baseline Design Summary: 

V104101 ............................................................................ D-8 

Table D-9 Design Values – 8-Story RC SMF Baseline ..................... D-9 

Table D-10 8-Story RC SMF Baseline Design Summary: 

V108101 .......................................................................... D-10 

Table D-11 Design Values – 12-Story RC SMF Baseline ................. D-12 

Table D-12 12-Story RC SMF Baseline Design Summary: 

V112101 .......................................................................... D-13 

Table D-13 Design Values – 20-Story RC SMF Baseline ................. D-14 

Table D-14 20-Story RC SMF Baseline ELF Design Summary: 

V120101 .......................................................................... D-14 

Table D-15 20-Story RC SMF Baseline MRSA Design Summary: 

V120301 .......................................................................... D-16 

Table D-16 Reinforced Concrete Moment Frame Results ................. D-18 

Table F-1 System Properties for Expanded Design Space ................. F-3 
FEMA P-2012 1: Introduction 1-1 

Chapter 1 

Introduction

This report documents the work and findings of the ATC-123 Project, 

Improving Seismic Design of Buildings with Configuration Irregularities, a 

multi-year study funded by the Federal Emergency Management Agency 

(FEMA) under the National Earthquake Hazards Reduction Program 

(NEHRP). The primary purpose of the project was to facilitate improvement 

of irregularity-related design requirements of: FEMA P-1050-1, NEHRP 

Recommended Seismic Provisions for New Buildings and Other Structures

(FEMA, 2015); ASCE/SEI 7-16, Minimum Design Loads and Associated 

Criteria for Buildings and Other Structures (ASCE, 2017a); and ASCE/SEI 

41-17, Seismic Evaluation and Retrofit of Existing Buildings (ASCE, 2017b). 

1.1 Background

It is commonly accepted that structural configuration irregularities can affect 

seismic performance. For the purposes of this report, a structural irregularity 

is defined as an aspect of configuration that detrimentally affects a structure’s 

performance during an earthquake leading to an unacceptable reduction in 

collapse safety or increase in damage. Generally, there are three remedies 

for such irregularities, as follows:

• Remove the irregularity from the design;

• Address the irregularity using an analytical approach; or

• Resolve the irregularity through a design approach (e.g., by changing the 

proportioning). 

U.S. codes and standards, such as ASCE/SEI 7, ASCE/SEI 41, ACI 318, 

Building Code Requirements for Structural Concrete, and AISC 341, Seismic 

Provisions for Structural Steel Buildings contain requirements related to 

structural configuration, which tie prohibitions, analysis requirements, and 

design requirements to various triggers. The irregularity-related 

requirements found in codes and standards generally reflect the best 

judgment of practitioners and academics based primarily on anecdotal 

observations and fairly simple linear static and linear dynamic analyses, 

without explicit consideration of collapse probability. 
1-2 1: Introduction FEMA P-2012

In the last decade, a methodology to validate building system performance 

and response parameters for use in seismic design was developed. That 

methodology, reported in FEMA P695, Quantification of Building Seismic 

Performance Factors (FEMA, 2009) has been accepted as the rational basis 

for establishing global seismic performance factors, including the response 

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

the deflection amplification factor (Cd) used for design of new seismic-forceresisting systems in accordance with U.S. model building codes and related 

standards. To date, most investigations of system performance using the 

FEMA P695 methodology have focused on classes of buildings without 

significant configuration irregularities.

1.2 Overview of Irregularities Considered

This report summarizes work conducted under the ATC-123 Project to 

quantitatively evaluate current building code triggers, the influence of 

structural irregularities on seismic building performance (in terms of collapse 

probability), and the effectiveness of relevant code provisions. The objective 

of the studies conducted under this project was to inform and improve U.S. 

codes and standards so that structures with configuration irregularities have a 

level of safety against collapse in an earthquake that is comparable to that for 

regular structures. The project focuses primarily on design requirements for 

new buildings, with limited consideration of the treatment of irregularities for 

existing buildings. 

With a focus on irregularities that have detrimentally affected structural 

performance in past earthquakes or that are common in current construction

trends, the project considered 12 classes of structural configuration 

irregularities identified in current U.S. codes and standards and two new 

classes as follows:

• Torsional stiffness

• Reentrant corner

• Diaphragm discontinuity 

• Out-of-plane offset 

• Nonparallel system

• Torsional strength

• Soft story

• Weight [mass]

• Vertical geometric
FEMA P-2012 1: Introduction 1-3 

• In-plane discontinuity

• Weak story

• Weak-column/strong-beam 

• Two new classes of irregularity: gravity-induced lateral demand and wall 

discontinuities

Treatment of these irregularities by the project ranges from explicit 

quantitative collapse evaluation (using the FEMA P695 methodology) to a 

general discussion of the most critical issues.

The structural systems addressed in this report include moment frames (both 

steel and reinforced concrete), reinforced concrete shear walls, combinations 

thereof, and simplified treatment of wood frame shear wall buildings. 

1.3 Target Audience

This report is written and organized to facilitate the transfer of project 

findings to: (1) the FEMA-sponsored Building Seismic Safety Council 

(BSSC) NEHRP Provisions Update Committee; (2) the ASCE/SEI 7 Seismic 

Subcommittee; and (3) the ASCE/SEI 41 Committee. The work and findings 

of the ATC-123 Project are also of value to other engineering practitioners 

and researchers interested in building design and code development. 

1.4 Content and Organization

Chapter 2 provides an overview of structural configuration irregularities, 

including observations of performance in past earthquakes, treatment of 

irregularities in the building codes of various countries, and a summary of 

key findings from earlier research. Each type of irregularity is illustrated, 

and key performance concerns are discussed briefly. 

Chapter 3 describes the approach used to design, model, and analyze the 

building archetypes used to evaluate the impact of configuration irregularity 

on collapse resistance.

Chapter 4 summarizes analytical studies of torsional stiffness and torsional 

strength irregularities. Those studies are used to assess the effectiveness of 

current code requirements related to torsional irregularities and to identify

corresponding recommended improvements. 

Chapter 5 addresses concrete shear wall buildings with vertical irregularities. 

The impact of openings in the lowest one or two stories of mid-rise buildings 

on their collapse resistance is investigated using a variety of software 

platforms and model types. 
1-4 1: Introduction FEMA P-2012

Chapter 6 summarizes analytical studies of five aspects of vertical 

configuration—soft story irregularity, weight (mass) irregularity, weak story 

irregularity, strong-column/weak-beam provisions, and gravity-induced 

lateral demand—using reinforced concrete and structural steel moment frame 

buildings. Some of the studies also compare the performance of buildings 

designed using the equivalent lateral force procedure with those designed 

using the modal response spectrum analysis method. 

Chapter 7 discusses the triggers and design consequences for several 

irregularities that were not the subject of extensive analysis in the course of 

the ATC-123 Project, including reentrant corners, diaphragm discontinuity, 

out-of-plane offset, nonparallel systems, vertical geometric, in-plane 

discontinuity, and wall discontinuity. Recommendations are made so the 

treatment of these irregularities can be more consistent with observed 

performance and the evolution of the related design requirements.

Chapter 8 summarizes recommended improvements for the seismic design of 

buildings with configuration irregularities and identifies areas for future 

study. 

Appendices A through D provide more detailed information and results of

the work reported in Chapters 4 through 6. Appendix E describes quality 

control review work conducted for each of the analytical studies. Appendix 

F documents a series of supplemental analyses performed to test the 

generality of observations made regarding the use of the equivalent lateral 

force procedure for buildings with mass irregularity. Appendix G provides 

recommendations for the calculation of story stiffness and story strength, 

which are used to assess soft story and weak story irregularities and to 

determine the redundancy factor. Appendix H provides a discussion and 

some general conclusions regarding steel systems not specifically detailed for 

seismic resistance.

A glossary of definitions and list of symbols used throughout this report, 

along with a list of references, are provided at the end of this report. 
FEMA P-2012 2: Overview of Irregularities 2-1 

Chapter 2 

Overview of Irregularities

Structural irregularities are a common occurrence due to the configuration of

buildings to meet architectural and functional needs. Some of these 

irregularities are defined in existing standards, such as ASCE/SEI 7-16, 

Minimum Design Loads and Associated Criteria for Buildings and Other 

Structures (ASCE, 2017a); ASCE/SEI 41-17, Seismic Evaluation and 

Retrofit of Existing Buildings (ASCE, 2017b); ACI 318-14, Building Code 

Requirements for Structural Concrete (ACI, 2014); and ANSI/AISC 341-16, 

Seismic Provisions for Structural Steel Buildings (AISC, 2016). Table 2-1 

lists these irregularities and their treatment in current U.S. standards. (This 

report uses the item numbers that appear in Table 12.3-1 and Table 12.3-2 of 

ASCE/SEI 7-16 with H or V prepended to indicate class of irregularity—

horizontal or vertical.) Table 2-1 also indicates how each irregularity is

treated in this project, where “Analysis” indicates an explicit assessment of 

collapse probability using the FEMA P695 method. 

Table 2-1 Structural Irregularities in U.S. Codes and their Treatment in this Report

Structural Irregularities Codified in Treatment in this Report

H1. Torsional (stiffness) irregularity ASCE/SEI 7-16 Analysis

H2. Reentrant corner irregularity ASCE/SEI 7-16 Discussion

H3. Diaphragm discontinuity irregularity ASCE/SEI 7-16 Discussion

H4. Out-of-plane offset irregularity ASCE/SEI 7-16 Discussion

H5. Nonparallel system irregularity ASCE/SEI 7-16 Discussion

H6.(1) Torsional strength irregularity ASCE/SEI 41-17 Analysis

V1. Soft story irregularity ASCE/SEI 7-16 Analysis

V2. Weight (mass) irregularity ASCE/SEI 7-16 Analysis

V3. Vertical geometric irregularity ASCE/SEI 7-16 Discussion

V4. In-plane discontinuity ... irregularity ASCE/SEI 7-16 Discussion

V5. Weak story irregularity ASCE/SEI 7-16 Analysis

V6.(1) Story mechanism: weak-column/strong-beam ACI 318-14, ANSI/AISC 341-16 Analysis

V7.(1) Gravity-induced lateral demand Analysis

V8.(1) Wall discontinuity Limited analysis

(1) The designations “H6” and “V6”–“V8” are used in order to extend the ASCE/SEI 7-16 code designations to additional 

irregularities addressed in this report. 
2-2 2: Overview of Irregularities FEMA P-2012

Although irregularities are known to influence seismic performance, the 

triggers in the current design codes for vertical and horizontal irregularities 

are based on the judgment of code writers, not clearly demonstrated 

differences in structural performance, and have not yet been quantitatively 

evaluated. An exception is a Building Seismic Safety Council (BSSC) 

project on Simplified Seismic Design Procedures that found torsional 

irregularity triggers to have little effect on the collapse risk for Seismic 

Design Category (SDC) B buildings, resulting in a code change proposal to 

eliminate the requirement in areas of low seismic hazard (DeBock et al., 

2014). The need to systematically evaluate other irregularity triggers and 

requirements in all Seismic Design Categories has been identified as a highly 

important priority for conducting further research activities in the NIST GCR 

13-917-23 report, Development of NIST Measurement Science R&D 

Roadmap: Earthquake Risk Reduction in Buildings (NIST, 2013). 

The tools for quantitative evaluation of the influence of structural 

irregularities and associated irregularity triggers on collapse performance are 

available (e.g., the FEMA P695 report, Quantification of Building Seismic 

Performance Factors (FEMA, 2009)). During development of FEMA P695

and numerous follow-on projects, the methodology set forth in the FEMA 

P695 report was used to investigate the collapse performance of a number of 

different seismic-force-resisting systems (SFRSs) against the quantitative 

collapse and overall risk performance criteria of ASCE/SEI 7-10 for life 

safety. In these studies, seismic-force-resisting systems were assumed to be 

regular in configuration. Similar work has not yet been conducted for 

systems with horizontal and vertical irregularities.

2.1 Literature Search

Phase I of the ATC-123 Project included a review of reported performance of 

irregular buildings in past earthquakes—with particular focus on the 1971 

San Fernando, 1989 Loma Prieta, 1994 Northridge, 1995 Kobe, 2010 Maule, 

and 2011 Christchurch events. Also reviewed was the treatment of 

configuration irregularities in codes and standards throughout the world, 

including the codes used in Canada, Europe, New Zealand, Japan, China, 

Mexico, Venezuela, Panama, Costa Rica, and Chile. The literature search 

also included review of scores of prior studies of structural irregularities and 

related metrics and triggers, and analytical methods to quantify or assess 

such irregularities. 
FEMA P-2012 2: Overview of Irregularities 2-3 

2.1.1 Observed Performance of Irregular Buildings

The ATC-123 Project included a review of reported performance of irregular 

buildings in past earthquakes. Findings concerning earthquake-related 

fatalities and causes of structural collapse are summarized below. 

2.1.1.1 Earthquake-Related Fatalities

In general, earthquake-related fatalities are attributed to the performance of 

structures subjected to ground motion or ground failure, including 

medical-related deaths such as heart failure brought on by the earthquake, 

fire following, or tsunami. Deaths due to ground motion or ground failure 

are due primarily to injuries sustained because of building (or bridge) 

collapse.

Of the estimated 1,687 fatalities in U.S. earthquakes between 1900 and 2000, 

573 are related to ground motion or failure, 640 to fire following, and 474 to 

tsunami. (This estimate does not reflect recent studies that suggest that the 

“official” 800 deaths in the 1906 San Francisco earthquake should be 3,000 

deaths.) The relatively few number of earthquake fatalities in recent U.S. 

earthquakes (less than 200 deaths since 1970) reflects both good fortune (i.e., 

only moderate magnitude earthquakes have occurred off hours or away from 

the center of the areas of densest population), as well as the generally good 

earthquake resistance of U.S. (California) buildings. Larger magnitude 

events closer to the center of dense urban areas would be expected to cause a 

much greater loss of life due to collapse of vulnerable buildings such as those 

which have a significant structural irregularity.

For instance, the 6,434 fatalities in the 1995 Kobe earthquake, which is one 

of the most significant events to affect an urban region of modern 

construction, were primarily due to building collapse. More than 82,000 

buildings collapsed in the 1995 Kobe earthquake, with building collapse rates 

of approximately 21% for sites within 5 km of the fault rupture and 1.2% for 

sites greater than 5 km from fault rupture (AIJ, 1995). 

2.1.1.2 Causes of Structural Collapse

Recent U.S. Earthquakes

Since 1970, roughly one-half of the approximate 200 deaths in United States 

earthquakes are due to building collapse, and virtually all of these deaths 

occurred due to collapse of buildings of either unreinforced masonry (URM) 

or non-ductile concrete material (i.e., materials no longer permitted for 

construction in seismic regions) and/or of irregular structural configuration 

(e.g., soft-story light-frame wood buildings). 
2-4 2: Overview of Irregularities FEMA P-2012

Figure 2-1, Figure 2-2, and Figure 2-3 are photos showing examples of 

collapse of the most vulnerable types of U.S. construction in past 

earthquakes. Vulnerable construction includes URM buildings (Figure 2-1), 

non-ductile reinforced concrete buildings (Figure 2-2), and soft/weak story 

wood frame buildings (Figure 2-3). Collapse of these three types of 

buildings caused over 70 of the approximate 100 deaths due to building 

collapse in U.S. earthquakes since 1970. These building types are either no 

longer permitted in regions of moderate or high seismicity (i.e., URM 

buildings) or, presumably, current seismic code provisions (ASCE/SEI 7-16) 

have adequately addressed issues of element ductility (e.g., for reinforced

concrete buildings) or irregular configuration (e.g., soft/weak story wood 

buildings). 

 

(a) (b)

 

(c) (d) 

Figure 2-1 Examples of URM building collapse in the (a) 1983 Coalinga earthquake (NISEE, 1983); 

(b) the 1987 Whittier earthquake (NISEE, 1987), and (c, d) the 1989 Loma Prieta 

earthquake (photos courtesy of the U.S. Geological Survey and Bill Lovejoy of the Santa

Cruz Sentinel, respectively). 5 deaths (San Francisco, photo c) and 3 deaths (Santa Cruz, 

photo d) out of 15 building collapse-related deaths occurred due to out-of-plane failure of 

URM walls in the 1989 Loma Prieta earthquake. 
FEMA P-2012 2: Overview of Irregularities 2-5 

Figure 2-2 Example of non-ductile concrete frame building collapse at the Veterans Administration 

(VA) complex in the 1971 San Fernando earthquake; including total collapse of 4 of 26 

buildings. 47 of the 58 deaths in the 1971 San Fernando earthquake occurred at the 

VA complex. Photo courtesy of the U.S. Geological Survey. 

 

(a) (b)

 

(c) (d) 

Figure 2-3 Examples of soft-story multi-family wood residential building collapse in the 1989 

Loma Prieta earthquake (a, b) and in the 1994 Northridge earthquake (c, d). 16 of the 

20 building collapse-related deaths in the 1994 Northridge earthquake occurred in the 

Northridge Meadows apartment complex (c). Photos (a) and (d) are from NISEE 

(1989; 1994); photos (b) and (c) are courtesy of EERI.
2-6 2: Overview of Irregularities FEMA P-2012

With respect to the cause of collapse and hence occupant fatality, failure of 

URM buildings (Figure 2-1) is typically associated with out-of-plane failure 

of bearing walls, especially at wall-to-diaphragm connections, and not related 

to structural irregularity. It might be noted that URM buildings could have a 

structural irregularity, but the building would still be more vulnerable due to 

out-of-plane wall failure. With respect to non-ductile concrete buildings, 

structural irregularity likely contributed to at least some of the collapse 

damage at the VA complex (Figure 2-2); however, like URM buildings, other 

factors are the primary cause of failure. With respect to soft/weak story 

wood buildings, by definition, collapse of these buildings is directly related 

to their soft/weak story irregularity.

In the case of the Olive View Hospital, vertical stiffness (strength) 

irregularity caused first floor collapse of the Community Mental Health 

Building and nearly caused collapse of the main building of the Olive View 

hospital. The hospital was staffed with 98 employees and had 606 patients at 

the time of the earthquake, but there were only three earthquake fatalities 

(i.e., 2 medical-related deaths and 1 death due to collapse of a stairwell). 

There were no deaths in the Community Mental Health Center, which was 

unoccupied (off hours) at the time of the earthquake. Arguably, the number 

fatalities in the Olive View Hospital complex could have been comparable to 

(or greater) than the 47 fatalities at the VA complex given the near collapse 

of the main building and first floor collapse of the unoccupied Community 

Mental Health Building.

Figure 2-4 shows photos of damage to buildings at the Olive Hospital caused 

by the 1971 San Fernando earthquake. Damage includes extreme distortion 

and near collapse of the “soft-story” moment-frame columns of the lower 

floors of the five-story main building of Olive View Hospital (Figure 2-4a, 

2-4c). Columns at the lower levels had large ductile capacity due to spiral 

reinforcement (as shown in Figure 2-4c) and collapse would likely have 

occurred without such reinforcement. There was complete collapse of the 1st

floor of the two-story Community Mental Health Building (Figure 2-4d). In 

this case, lateral deflection was concentrated at the 1st-floor level due in part 

to masonry walls at the 2nd floor limiting 2nd-floor lateral deflection and 

effectively creating a soft/weak 1st story. 
FEMA P-2012 2: Overview of Irregularities 2-7 

Olive View Hospital, Main Building Olive View Hospital Complex, 1971 MW 6.6 San Fernando EQ

 

 

 (a) (b)

Olive View Hospital, Main Building

 

Olive View Hospital, Community Mental Health Building 

 

 (c) (d) 

Figure 2-4 Photographs of severe damage and collapse of buildings of the Olive View Hospital due to 

the 1971 San Fernando earthquake. Photos from NISEE (1971a; 1971b; 1971c; 1971d, 

respectively).

1995 Kobe Earthquake 

Most of the buildings that collapsed in the 1995 Kobe earthquake were of 

older construction that had the following three attributes: (1) weak lateral 

system; (2) non-ductile material; and (3) irregular structural configuration—

conditions no longer permitted, or subject to greater penalties, by the 

Japanese building code (since 1981). 

Smaller commercial and mixed-use Japanese buildings are typically 2-story 

and 3-story structures common to denser urban areas. The first floor is often 

used for the family business with the family living upstairs. Typically, 

several businesses (families) occupy different units of the same building. 

These buildings are typically made of wood, similar to low-rise residential 

construction, or light-gage steel. It is common for these buildings to have a 

soft/weak first story and significant torsional response since the first floor 

will typically have large openings (and no wall) on the street-side of the 

building. Figure 2-5 shows severe leaning and incipient collapse of a mixeduse building in Kobe City typical of damage to these types of buildings.
2-8 2: Overview of Irregularities FEMA P-2012

Incipient collapse of a 2-story 

mixed-use building

Figure 2-5 Photograph showing severe leaning and incipient collapse of a 2-story mixed-use 

building in Kobe City. Photo courtesy of Charlie Kircher. 

Mid-rise Japanese buildings are 3-stories to 60 meters in height and are used 

for both residential (apartments) and commercial occupancies. They are 

constructed of steel framing or reinforced concrete (RC), or a combination of 

a steel frame encased in reinforced concrete (SRC). In older SRC buildings, 

the steel frame may not continue up the full building height of the building 

creating a hidden strength discontinuity at an upper floor. Japanese mid-rise 

buildings are the building type most similar to U.S. buildings. And, like the 

seismic provisions of the U.S. building codes, the seismic provisions of the 

Japanese building code have changed substantially over time (often for the 

same reasons).

In 1981, the Japanese building code was completely revised to incorporate a 

sophisticated two-phase design approach that retained traditional methods as 

the first phase of design for safety and serviceability during medium 

earthquake motions, and added a new, second phase of design for safety 

against severe ground shaking. As part of the new approach, vertical 

stiffness irregularity is checked using a “rigidity factor” and torsional 

irregularity is checked using an “eccentricity factor.” Structures deemed to 

be irregular have more stringent design requirements; the underlying concept 

is to encourage use of regular configurations.
FEMA P-2012 2: Overview of Irregularities 2-9 

Differences in the performance of buildings of different design vintages is 

apparent in the tagging data compiled by engineers from Obayashi 

Corporation who inspected 332 buildings that their company had designed 

and constructed in Kobe since about 1950 (Obayashi, 1995). Over 50 

percent of buildings designed before 1982 were assigned a yellow or red tag, 

whereas less than 10 percent of the buildings designed after 1982 were 

assigned a yellow or red tag. No post-1982 buildings collapsed, and it is 

likely that some the post-1982 buildings that were assigned a red tag (8 

buildings) reflect damage due to nonstructural systems, rather than structural 

damage.

Figure 2-6 and Figure 2-7 are photographs of collapse damage to older midrise buildings with vertical and/or horizontal irregularities, including 

information about building type, configuration, and collapse failure 

mechanism when known. These buildings are representative of more 

common types of collapse damage observed in older mid-rise buildings. 

Figure 2-6 Partial collapse of a 6-story commercial building (Chou Ward) with a torsional 

irregularity. The building was a reinforced concrete structure with perimeter 

shear walls on two orthogonal sides of the building and gravity framing on the 

other two orthogonal sides of the building. The torsional irregularity caused 

the building to rotate during the earthquake. As the building rotated, large 

displacement of the gravity frames at the corner away from the stiffer walls 

exceeded frame capacity causing failure of columns and collapse or sagging of 

floors above. Photo courtesy of Charlie Kircher. 

Partial collapse of a 6-story 

commercial building
2-10 2: Overview of Irregularities FEMA P-2012

Figure 2-7 Partial collapse of a 12-story commercial building (Sannomiya 

District) with plan and (presumed) vertical irregularities. The 

building was a 12-story reinforced concrete shear wall structure 

with perimeter shear walls on three sides. Shear walls were 

lightly reinforced. The torsional irregularity caused the building 

to rotate as well as displace laterally during the earthquake. As 

the building displaced and rotated, the capacity of gravity 

framing was exceeded and the building partially collapsed at the 

4th floor on the side of the building facing the street (i.e., side 

without walls), most likely due to a vertical irregularity at this 

level although the source of the irregularity could not be 

confirmed. Photo courtesy of Charlie Kircher. 

Partial collapse of a 12-story 

commercial building
FEMA P-2012 2: Overview of Irregularities 2-11

2010 Maule Earthquake

Evaluation of buildings damaged during the 2010 M8.8 Maule earthquake 

identified a number of building system design and configuration issues that 

could be expected to result in poor earthquake performance. These issues 

include discontinuities in walls; coupling of walls via slabs, beams, and 

spandrels; wall demands induced by nonstructural elements; and wall axial 

demands. These issues are described in detail in Appendix D of NIST GCR 

14-917-25, Recommendations for Seismic Design of Reinforced Concrete 

Wall Buildings Based on Studies of the 2010 Maule, Chile Earthquake 

(NIST, 2014), and addressed in Birely (2012). The following provides a 

brief description of the building configuration issues considered to be most 

highly correlated with earthquake damage.

Many of the RC wall buildings damaged during the 2010 Maule earthquake 

were observed to have significant vertical discontinuities in walls that were 

primary elements of the lateral load resisting system. Figure 2-8 and Figure 

2-9 show vertical discontinuities in which a significant length of wall is lost 

from an upper to a lower story. Appendix D of NIST GCR 14-917-25 

discusses vertical discontinuities in detail and provides vertical discontinuity 

data for the Chilean buildings that were studied. 

Section B.1.1 provides more detailed information on observed damage 

particular to concrete walls with irregularities in past earthquakes, including 

the 2010 Maule earthquake. 

Figure 2-8 Coupled walls in upper stories do not continue to lower story 

(Plaza del Rio Building, Concepción, Chile). Photo courtesy of 

Ken Elwood. 
2-12 2: Overview of Irregularities FEMA P-2012

Figure 2-9 A change in the wall section from the upper to lower story results in a loss of wall 

area and localization of flexural yielding (Plaza del Rio Building, Concepción, 

Chile). Photo courtesy of Ken Elwood.

2.1.2 Treatment of Configuration Irregularities in Codes and 

Standards

2.1.2.1 U.S. Codes and Standards

The 1976 Uniform Building Code (International Conference of Building 

Officials, 1976) contains the first explicit treatment of structural 

“irregularities” in a U.S. building code. Section 2312(e)3, reads as follows:

“Structures having irregular shapes or framing systems. The 

distribution of the lateral forces in structures which have highly irregular 

shapes, large differences in lateral resistance or stiffness between 

adjacent stories or other unusual structural features shall be determined 

considering the dynamic characteristics of the structure.” 

This requirement was added at the recommendation of the Seismology 

Committee of the Structural Engineers Association of California (SEAOC) 

based on “observation of earthquake damage” (SEAOC, 1975). The 

commentary suggests that “due to the infinite variations of irregularities that 

can exist, the impracticality of establishing definite parameters and rational 

rules for the application of this Section are readily apparent.” It goes on to 

identify four “categories of buildings or conditions that are deserving of 

special design consideration,” as follows:
FEMA P-2012 2: Overview of Irregularities 2-13

• Buildings with irregular configuration in plan or in the vertical 

dimension. 

• Buildings with abrupt changes in lateral resistance within any level or 

between adjacent levels.

• Buildings with abrupt changes in lateral stiffness within any level or 

between adjacent levels.

• Unusual or novel structural features. 

The SEAOC commentary also provides guidance for each of the four 

categories.

The ATC-3 project sought “to present, in one comprehensive document, 

current state-of-knowledge in the fields of engineering seismology and 

engineering practice as it pertains to seismic design and construction of 

buildings” (ATC, 1978). Project participants included design professionals, 

researchers, federal agency representatives, staffs from model code 

organizations, and representatives from state and local governments 

throughout the United States. The resulting report includes a provision that 

“buildings which have an approximately symmetrical geometric 

configuration and which have the building mass and seismic resisting system 

nearly coincident shall be classified as regular.” Buildings would be 

classified as irregular where they have plan or vertical configuration as 

follows: 

• Plan irregularity

o The building does not have an approximately symmetrical geometric 

configuration or has re-entrant corners with significant dimensions.

o There is the potential for large torsional moments because there is 

significant eccentricity between the seismic resisting system and the 

mass tributary to any level.

o The diaphragm at any single level has significant changes in strength 

or stiffness.

• Vertical irregularity

o The building does not have an approximately symmetrical geometric 

configuration about the vertical axes or has horizontal offsets with 

significant dimensions.

o The mass-stiffness ratios between adjacent stories varies 

significantly.
2-14 2: Overview of Irregularities FEMA P-2012

In subsequent years, revisions were made to the Uniform Building Code, the 

NEHRP Recommended Provisions, ASCE/SEI 7, ASCE/SEI 31/41, ACI 318, 

and ANSI/AISC 341 to expand the list of irregularities, provide specific 

triggering thresholds, and prescribe related analysis, design, and detailing 

requirements—based on observed performance, ongoing research, and the 

consensus process.

In addition to the 10 irregularities addressed in ASCE/SEI 7-16 (identified as 

H1-H5 and V1-V5 in this report), ASCE/SEI 41-17 identifies a torsional 

strength irregularity, which is identified as H6 in this report. 

U.S. design standards for concrete (ACI 318-14) and steel (ANSI/AISC 

341-16) regulate moment frame proportioning to avoid weak-column/strongbeam systems to reduce the likelihood of the premature formation of a story 

mechanism; that type of configuration is identified as V6 in this report.

2.1.2.2 International Codes

This project reviewed the treatment of configuration irregularities in building 

codes applicable in Canada, Europe, Japan, China, Mexico, Venezuela, 

Panama, Costa Rica, and Chile. The following is a summary:

• The building code in Canada is similar to that of the U.S. Specifically, 8 

of the 10 ASCE/SEI 7-16 irregularities are defined, excluding re-entrant 

corners and diaphragm discontinuity [H2 and H3]. In response to recent 

architectural trends to include sloping columns in large-scale 

construction, the National Building Code of Canada (National Research 

Council of Canada, 2015) triggers that configuration as a gravity-induced 

lateral demand irregularity based on recent analytical studies (Dupuis et 

al., 2014); this report uses the designation V7 for this condition. 

• Section 4 of Eurocode 8 provides commentary-like guidance on good 

design, which states that it is good practice to have a regular structure. 

Table 4.1 in Eurocode 8 provides a method for choosing an analysis 

approach (European Committee for Standardization, 2004). It uses 

analysis methods and strength requirements to address irregularities.

• The New Zealand building code is similar to ASCE/SEI 7. MacRae and 

Deam (2009) compiled a series of papers summarizing the thinking of 

the New Zealand engineering community on irregularities before the 

2010 Christchurch earthquake. 

• The Japanese building code was summarized in a paper by Aoyama 

(1981). According to this paper, the guidance provided is that the 

building design should be simple, short, and regular—to avoid an 

elaborate design process. Rigidity and eccentricity factors determine if 
FEMA P-2012 2: Overview of Irregularities 2-15

the building is sufficiently regular to avoid more elaborate design. The 

detailed calculations prescribed in the Japanese building code differ from 

those in ASCE/SEI 7, but the conditions addressed roughly correspond to 

V1b (extreme soft story irregularity) and H1 (torsional stiffness 

irregularity).

• The building code in China is similar to that in the U.S. Specifically, 7 

of the 10 ASCE/SEI 7-16 irregularities are defined, excluding out-ofplane offset, nonparallel system, and weight (mass) irregularities [H4, 

H5, and V2] (Ministry of Construction of the People’s Republic of China 

and the State Quality Supervision and Quarantine Bureau, 2001). 

• The building code in Mexico defines structural regularity and severe 

irregularity, but not irregularity per se (ISCDF, 2004). The consequence 

of an irregularity is a decrease in the R-factor (i.e., an increase in design 

base shear). 

• The Venezuelan building code defines vertical and plan irregularities 

similar to those in the U.S., but adds items for excessive slenderness, 

short column effects, flexible diaphragms, and columns disconnected 

from diaphragms (FUNVISIS, 2001). The consequence is on values of 

design factors, not the use of a different analysis approach. 

• The building code in Panama includes the 10 categories of irregularities 

defined in ASCE/SEI 7-16 (Junta Técnica de Ingeniería y Arquitectura, 

2004).

• The building code in Costa Rica includes the 10 categories of 

irregularities defined in ASCE/SEI 7-16, but adds a torsional irregularity 

where the first torsional mode has a longer period than one (or both) of 

the fundamental translational modes in the two orthogonal horizontal 

directions (CFIA, 1986). 

• The Chilean building code does not explicitly address irregularities. 

2.1.3 Published Research on Irregularities

The project reviewed recent research on irregularities. In addition to papers 

for individual studies, the paper by De Stefano and Pintucchi (2008) is “a 

review of research on seismic behavior of irregular building structures since 

2002,” which summarizes findings from scores of studies between 2002 and 

2008. None of the research reviewed addresses reentrant corner (H2), 

diaphragm discontinuity (H3), out-of-plane offset (H4), nonparallel system 

(H5), torsional strength (H6), or in-plane discontinuity (V4) irregularity. 

Key observations from the reviewed research for the addressed irregularities 

follow. 
2-16 2: Overview of Irregularities FEMA P-2012

Torsional (stiffness) irregularity [H1]. A horizontal torsional irregularity 

is a function of the distribution of a structure’s stiffness and mass at a given 

floor level. Specific ASCE/SEI 7-16 regulations pertaining to torsional 

(stiffness) irregularities are triggered if the deflection on one side of the story 

is greater than 1.2 times the average deflection of that story along the same 

axis where a load with 5% eccentricity from the story’s center of mass is 

applied (the 5% eccentricity measured with respect to a building’s dimension 

perpendicular to the direction of applied load). Out of all the irregularities to 

be studied in this project, torsional irregularity is the most previously studied 

irregularity. There has been much research using single-story analytical 

models to quantify the effects of torsional irregularities, and, in recent years, 

there has been a push to study the effects of nonlinearity on the torsional 

behavior of structures. Studies using simplified single-story models seem to 

show little difference between elastic and plastic effects of torsional 

irregularities, but several studies (e.g., Stathopoulos and Anagnostopoulus, as 

summarized by De Stefano and Pintucchi, 2008) using 3D multi-story 

models seem to contradict previous studies and find that torsional 

irregularities have greater effect the more nonlinear the model becomes. In 

all of these studies, there is a general expression of need to perform more 

research on the effects of torsional irregularities on nonlinear behavior using 

more advanced 3D multi-story models. There have also been several studies 

looking into the effects of accidental torsion requirements with torsional 

irregularities. In DeBock et al. (2014) it was concluded that the accidental 

torsion requirements in ASCE/SEI 7-16 for the equivalent lateral force (ELF) 

design procedure significantly impact collapse resistance only for structures 

with moderate to high torsional irregularity. It was also concluded in that 

study that the torsional amplification factor (Ax) as well as drift limits on 

building edges (rather than at the center of mass) are significant in preventing 

building collapse for torsionally irregular buildings in high seismic zones. 

Soft story irregularity [V1]. According to ASCE/SEI 7-16, soft story 

irregularities occur where a given story has a stiffness less than 70% of the 

story above or less than 80% of the average stiffness of the 3 stories above. 

In Michalis et al. (2006), it was shown through analytical models of 9-story 

steel moment frames that soft story irregularities have the largest effect on 

collapse capacity where the soft story occurs at one of the first three stories. 

Where the soft story is more towards the middle or top of the structure, the 

study showed that it has little effect on collapse capacity. Even though this 

study found that soft story irregularities have an effect, both this study and 

other studies have shown that the weak story aspects of a vertical irregularity 

are more important than the soft story aspect of such an irregularity. 
FEMA P-2012 2: Overview of Irregularities 2-17

Weight (mass) irregularity [V2]. As defined in ASCE/SEI 7-16, weight 

irregularity occurs where the effective mass of one story is greater than 150% 

of that of an adjacent story. The effects of mass irregularities on 9-story steel 

moment frame buildings were studied by Michalis et al. (2006). It was found 

that mass irregularity had a similar but inverse effect to that of a soft story 

irregularity. The degree to which mass affects collapse capacity was shown 

to be similar to that of a soft story, but placement effects were inverse. 

Where the mass irregularity occurred on the top floor, it had the greatest

effect; where it occurred on the middle or lower floors, it had little effect on 

collapse capacity. Both mass and soft story irregularities had less effect on 

collapse than a weak story irregularity in the Michalis et al. (2006) study. 

Other studies (Magliulo et al., 2002; Tremblay and Poncet, 2005) have also 

noted that vertical mass eccentric buildings perform well in seismic events. 

Vertical geometric irregularity [V3]. As defined in ASCE/SEI 7-16 

vertical geometry irregularities occur where the horizontal dimension of the 

seismic-force-resisting system on any story is greater than 130% of that on 

the adjacent story. A common example of vertical geometry irregularity is 

story setback. A 2004 study by Tena-Colunga (as summarized by De 

Stefano and Pintucchi, 2008) found that buildings with vertical setback 

performed well as long as there was adequate redundancy in the lateral 

system, but systems without redundancy and with vertical setback performed 

poorly. Several other studies mention the variability observed in studies on 

setback, and that more research is needed to better understand this 

irregularity. 

Weak story irregularity [V5]. As defined in ASCE/SEI 7-16 weak story 

irregularities occur where the story lateral strength is less than 80% of that of 

the story above. As mentioned before, it was shown in the study by Michalis 

et al. (2006) that weak story irregularities have much larger effect on collapse 

capacity than mass or soft story irregularities. The effect seems to be the 

greatest where the weak story is near the bottom of the structure, causing the 

largest decrease in collapse capacity. However, there is a benefit to 

structural performance at levels of ground motion farther away from 

collapse. A fuse effect is created and the damage is concentrated in the 

weakened story, protecting the upper stories from damage. In general 

Michalis et al. (2006) conclude that the effects of vertical irregularities are 

not well understood and modern building codes are overly conservative 

where it comes to mass and soft story irregularities. FEMA P-807, Seismic 

Evaluation and Retrofit of Multi-Unit Wood-Frame Buildings With Weak 

First Stories (FEMA, 2012a), provides useful information for the seismic 
2-18 2: Overview of Irregularities FEMA P-2012

evaluation and retrofit of multi-unit wood-frame buildings with weak first 

stories.

Story mechanism: weak-column/strong-beam [V6]. Weak-column/strongbeam occurs where the moment capacity of the column in the lateral force 

resisting system is weaker than that of the beam. Previous work studying the 

effects of a weak-column/strong-beam on building performance has shown 

that the ratio of column to beam strength has a large impact on the collapse 

safety of the building, and that the impact differs for various height buildings 

(Haselton et al., 2011). This study by Haselton et al. only included 4-story 

and 12-story reinforced concrete frame buildings, so further study on this 

topic is warranted. 

Gravity-induced lateral demand [V7]. Gravity-induced lateral demand 

irregularity occurs where the vertical members of the gravity system are 

sloped and subject the lateral system to a continuous lateral load. Dupuis et 

al. (2014) describes the issue and reports the results of analyses to quantify 

this effect for concrete shear walls buildings. As a result of that study, the 

2015 edition of the National Building Code of Canada introduces a new 

irregularity class to address gravity-induced lateral demands. 

Wall discontinuity [V8]. Wall discontinuity occurs where there is an abrupt 

discontinuity or large variance of stiffness along the height of a shear wall. 

This may occur above or below a multi-story stack of openings or at building 

setbacks and major changes in the overall layout of walls. Naeim et al. 

(1990) and Moehle (2015) describe the mechanics of such discontinuities. 

NIST (2014) describes poor performance in the 2010 Maule, Chile 

earthquake as a result of such irregularities.

MacRae and Deam (2009) summarizes an effort in New Zealand to quantify 

the effect of different amounts and types of irregularity on structures 

designed using their implementation of the equivalent lateral force method in 

their loading standard. As such, it addresses relatively simple structures. 

The research addresses relationships between the amount of irregularity 

versus changes in behavior to assess when structural irregularities could be 

ignored as well as the magnitude of demand change due to these 

irregularities. It was concluded that diaphragm flexibility is unlikely to 

increase seismic force demand in most structures due to the increase in the 

building’s period and the resulting decrease in spectral acceleration. The 

report presents a simplified method to assess the resulting increase in 

displacement using an amplifier based on a diaphragm flexibility ratio. 
FEMA P-2012 2: Overview of Irregularities 2-19

For more information on past laboratory test results related to concrete walls 

with vertical irregularities, see Section B.1.3. 

2.2 Performance Concerns for Irregularities and 

Corresponding Code Requirements

Figure 2-10 and Figure 2-11 illustrate all 14 irregularities identified in this 

report. The notation in the figures is consistent with that in ASCE/SEI 7-16 

and common U.S. practice, as follows:

• DCR = demand/capacity ratio

• K = stiffness

• M = mass

• Mc = column moment capacity 

• Mb = beam moment capacity

• Q = demand or capacity action 

• ∆ = story drift

Performance concerns for these irregularities include additional 

proportioning considerations (such as amplified global or local loads or 

drifts), specific detailing issues (such as at collectors, connectors, or joints), 

and the possible need for additional analysis considerations (such as 

dynamic, 3-dimensional, bi-directional, or nonlinear). As noted in Section 

C12.3.2 of ASCE/SEI 7-16: 

“most seismic design provisions were derived for buildings that have 

regular configurations, but earthquakes have shown repeatedly that 

buildings that have irregular configurations suffer greater damage. This 

situation prevails even with good design and construction. 

There are several reasons for the poor behavior of irregular structures. In 

a regular structure, the inelastic response, including energy dissipation 

and damage, produced by strong ground shaking tends to be well 

distributed throughout the structure. However, in irregular structures, 

inelastic behavior can be concentrated by irregularities and can result in 

rapid failure of structural elements in these areas. In addition, some 

irregularities introduce unanticipated demands into the structure, which 

designers frequently overlook when detailing the structural system. 

Finally, the elastic analysis methods typically used in the design of 

structures often cannot predict the distribution of earthquake demands in 

an irregular structure very well, leading to inadequate design in the areas 

associated with the irregularity.”
2-20 2: Overview of Irregularities FEMA P-2012

Figure 2-10 Horizontal irregularities.
FEMA P-2012 2: Overview of Irregularities 2-21

Figure 2-11 Vertical irregularities.
2-22 2: Overview of Irregularities FEMA P-2012

A summary of key performance concerns for each irregularity is as follows:

Torsional (stiffness) irregularity [H1]. Twisting response of a building 

with this irregularity cannot be captured directly using 2-dimensional 

analysis in orthogonal plan directions. That twisting produces increased 

deformation demands at the perimeter, which could cause failure of gravity 

load resisting elements precipitating collapse. Force demands at the interface 

of horizontal and vertical elements of the seismic-force-resisting system may 

also be greater than those in a building without significant twisting response. 

Reentrant corner irregularity [H2]. The projecting wings of the floor may 

respond somewhat independently, with an opening/closing or flapping 

motion, during an earthquake. This independent response can generate 

additional demands on the horizontal and vertical elements in the seismicforce-resisting system, particularly near the reentrant corner.

Diaphragm discontinuity irregularity [H3]. Significant differences in 

stiffness between portions of a diaphragm at a level may cause a change in 

the distribution of seismic forces to the vertical components and may create 

torsional forces not accounted for in the distribution normally considered for 

a regular building. Concentration of forces at the boundaries of the openings 

must be resolved in the design. Where the triggering condition is a change in 

diaphragm stiffness from one story to the next, the apparent concern is 

redistribution of forces, which would not be captured in typical seismic 

analyses idealizing the diaphragm as fully rigid or fully flexible. 

Out-of-plane offset irregularity [H4]. The response parameters used in 

seismic design are based on the characteristics of the vertical elements of the 

seismic-force-resisting system. Where there is an out-of-plane offset, the 

horizontal elements that transfer story shears may be subjected to much 

greater demands than predicted by typical seismic analyses.

Nonparallel system irregularity [H5]. Where the vertical elements of the 

seismic-force-resisting system are not orthogonal to each other, response 

cannot be captured directly using 2-dimensional analysis in orthogonal plan 

directions. 

Torsional strength irregularity [H6]. Where inelastic response can 

concentrate on one side of a building, linear elastic analysis may not reflect 

the resulting increases in deformation on the weak side. The increased twist 

could cause lateral- or gravity-load resisting elements to fail precipitating 

collapse.

Soft story irregularity [V1]. The simple static analysis that is the basis of 

the equivalent lateral force (ELF) procedure assumes a linear displaced shape 
FEMA P-2012 2: Overview of Irregularities 2-23

leading to reasonably uniform distribution of inelastic behavior. Where one 

story is much softer than adjacent stories dynamic amplification in the 

response should be considered.

Weight (mass) irregularity [V2]. Since the ELF procedure assumes a linear 

displaced shape, the concern is that significant variations in mass could cause 

an unanticipated increase of displacement at the affected story leading to a 

concentration of inelastic response and possible collapse.

Vertical geometric irregularity [V3]. This irregularity represents a 

qualitative indicator of systems that could have a non-uniform distribution of 

stiffness or strength, for which the load pattern assumed in the ELF

procedure could be inaccurate.

In-plane discontinuity irregularity [V4]. The response parameters used in 

seismic design are based on continuous vertical elements of the seismicforce-resisting system with well distributed inelastic response. Where there 

is an in-plane discontinuity, overturning demands on the supporting elements

may be much greater than those predicted by a linear elastic analysis using 

forces reduced by the response modification coefficient, R. 

Weak story irregularity [V5]. Buildings with a weak story tend to develop 

all of their inelastic behavior and related damage at the weak story, 

increasing the likelihood of collapse. 

Story mechanism: weak-column/strong-beam [V6]. Since the response 

parameters used in seismic design assume inelastic response that extends 

across multiple stories, moment frames should be proportioned to avoid 

premature yielding of all the columns at a particular story. Where inelastic 

response can concentrate at a single story, a column failure mechanism can 

lead to collapse.

Gravity-induced lateral demand [V7]. Where the inclination of gravityload-resisting elements induces significant sustained lateral demands on the 

seismic-force-resisting system, there is concern that ground shaking could 

cause biased inelastic displacement, ratcheting in successive cycles of 

response, leading to collapse. As shown in Figure 2-11, the metric used to 

assess gravity-induced lateral demand is the ratio of gravity-induced story 

shear (QG) to story shear capacity (QV).

Wall discontinuity [V8]. Story-by-story analysis, as is commonly used in 

design of reinforced concrete walls, may not identify discontinuities that can 

concentrate damage during inelastic response. For instance, the panel zones 

within solid wall segments above and below a vertical stack of openings are 

subject to much higher stresses than simple analyses would indicate. Where 
2-24 2: Overview of Irregularities FEMA P-2012

openings are close to the end of a wall (V4 irregularity), amplified 

overturning demands may cause poor performance in the small supporting 

pier. The response parameters used in seismic design are based on 

continuous vertical elements of the seismic-force-resisting system with well 

distributed inelastic response. Where the plan form of the wall changes 

dramatically, shear lag effects for flanged sections should be included in the 

design. 

Sections 12.3.2 and 12.3.3 of ASCE/SEI 7-16 require classification of 

structures as regular or irregular, based on quantitative triggers, and set forth 

a series of requirements for irregular structures, including the analysis used 

to proportion the structure, design considerations for strength and stiffness, 

forces used in detailing, and system prohibitions. 

The irregularity-related code requirements in ASCE/SEI 7-16 depend on the 

Seismic Design Category (SDC) to which a structure is assigned, ranging 

from few requirements in SDC B to system prohibitions in SDC E and F. 

Table 2-2 and Table 2-3 summarize quantitative triggers and code 

requirements, by SDC, for all 14 irregularities considered in this report. 

Table 2-2 Code Requirements for Horizontal Structural Irregularities, by Seismic Design Category

Requirements

H1

Torsional 

(Stiffness) 

H2

Reentrant 

Corner

H3

Diaphragm 

Discontinuity

H4

Out-of-Plane 

Offset

H5

Nonparallel 

System

H6

Torsional 

Strength

Quantitative trigger

Drift ratio

> 1.2

(1.4, extreme) 

Projection

> 15% plan 

dimension 

Opening area 

> 50%

maxDCRi/ 

maxDCRj > 

1.5

Analysis

3-D analysis required B, C, D, E, F B, C, D, E, F B, C, D, E, F

ELF prohibited D, E, F

Consider orthogonal effects C, D, E, F

Nonlinear analysis required ASCE/SEI

41-17(1)

ASCE/SEI

41-17(1)

Design

Amplify accidental torsion C, D, E, F

Assess drift at perimeter C, D, E, F

Overstrength forces at 

discontinuous elements

B, C, D, E, F

Detailing

Increase collector and 

diaphragm connector forces

D, E, F D, E, F D, E, F D, E, F

Other

Extreme prohibited E, F

(1) Seismic Design Categories are not used in ASCE/SEI 41-17.
FEMA P-2012 2: Overview of Irregularities 2-25

Table 2-3 Code Requirements for Vertical Structural Irregularities, by Seismic Design Category

Requirements

V1

Soft story

V2

Weight 

(mass)

V3

Vertical 

geometric

V4

In-plane

V5

Weak 

story

V6

Weak-column/ 

strong-beam

V7

Gravityinduced 

lateral 

demand

V8

Wall 

discontinuity

Quantitative 

trigger

Stiffness 

< 70%

story above 

(60%, 

extreme); or 

< 80%

3-stories 

above (70%, 

extreme) 

Mass

> 150% 

adjacent

SFRS width

> 130% 

adjacent

Strength < 

80%

story above 

(65%, 

extreme) 

ΣMc/ ΣMb

< target value

QG/QV

> target 

value

Analysis

ELF prohibited D, E, F D, E, F D, E, F

Nonlinear 

analysis 

required

ASCE/SEI

41-17

ASCE/SEI

41-17

Design

Overstrength 

forces at

discontinuous 

elements

B, C, D, 

E, F

Detailing

Increase 

collector and 

diaphragm 

connector forces

D, E, F

Other

Prohibited E, F

Extreme 

prohibited

E, F D, E, F

2.3 Treatment of Irregularities in this Report

From among the identified conditions, structural irregularities and 

configuration issues that are most likely to lead to increased collapse 

potential were identified. Most building collapses in past earthquakes have 

been associated with excessive torsional response (H1 and/or H2), soft or 

weak stories (V1 or V5), or story mechanisms for moment frame systems 

(V6). Analytical studies to assess collapse safety explicitly for buildings 

with these irregularities were performed and are presented in this report. 

Published research suggests that mass irregularity (V2) does not necessarily 

result in increased inelastic demands, and the collapse mode is still similar to 

that for the base case (with identical mass at all stories). Analytical studies to 
2-26 2: Overview of Irregularities FEMA P-2012

assess collapse safety and global behavior of systems with this condition are 

included in this report. 

U.S. codes have not yet addressed gravity-induced lateral demands. The 

work reported in Dupuis et al. (2014), which led to provisions in the National 

Building Code of Canada, is limited to shear wall buildings and does not 

include assessment of relative collapse probability. This report includes 

analytical studies of steel and reinforced concrete moment frame systems 

with gravity-induced lateral demands (V7) to test whether it is advisable to 

add a corresponding structural irregularity to U.S. codes.

Some irregularities (H2, H3, H4, V4, V8) and configuration requirements 

(such as those for chords and collectors) reflect load path issues that are 

particularly sensitive to the specific structure, are usually associated with 

earthquake damage but not collapse, and are not well suited to quantification 

across a broad design space of archetypes. This report only includes 

discussion for these irregularities (see Chapter 7). 

As currently written, application of ASCE/SEI 7-16 Section 12.3.3.4 triggers 

global design remedies (amplification of collector and connection forces for 

the entire structure) in response to local configuration irregularities (such as 

items H2 and H3); this report recommends improvements to this code 

requirement.

Items H5 and V3 are not irregularities as defined in this report as they are not 

generally associated with poor structural performance. Instead, they are 

codified as “irregularities” since two-dimensional application of the 

equivalent lateral force procedure may not adequately characterize their 

response. The code remedy of requiring three-dimensional dynamic analysis 

is considered sufficient, so further study is not warranted. 

Other configuration-related design issues, such as distributing load in steel 

braced frame systems between tension and compression members, are best 

addressed (as currently) in the material standards. Such issues are outside the 

scope of this report.

The analytical studies focus primarily on issues related to design 

requirements for new buildings. Although some real buildings include 

multiple irregularities that could interact, the analyses of this project treat 

irregularities separately, just as they are defined independently in codes. 

Other variations in configuration, such as vertical or horizontal combinations 

of framings systems, which are treated in Sections 12.2.2 and 12.2.3 of 

ASCE/SEI 7-16, could also affect collapse probability. Except for the mixed 

system results reported in Chapter 4, such combinations are beyond the scope 

of this report. 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-1 

Chapter 3 

Archetype Design, Modeling, 

and Analysis Approach

This chapter provides an overview of the approach used to design, model, 

and analyze the building archetypes. This process was used for both the 

baseline archetypes and the variant archetypes that were used to gauge the 

effects of the various irregularities and related design provisions on building 

performance. The design, modeling, and analysis approach for the 

“simplified” three-dimensional archetypes that were used to study torsional 

irregularities is uniquely different and is described separately in Chapter 4

and Appendix A. 

3.1 Scope of Analytical Studies

For the eight classes of irregularities that were addressed analytically (H1, 

H6, V1, V2, V5, V6, V7, V8), it is necessary to make appropriate selections

of seismic-force-resisting systems (SFRSs), including quality (ordinary or 

special), building height, ground motion intensity (e.g., Seismic Design 

Category B or D), analysis method used in design, gravity load level, and 

degree of irregularity. Table 3-1 shows the SFRSs and building heights used 

to study each irregularity. Table 3-2 outlines the parameters varied in the 

designs and detailed analytical studies.

The detailed studies start with development of designs for regular “baseline” 

buildings and continue with the introduction of irregularities to the baseline 

buildings separately (as opposed to designing real buildings with multiple 

irregularities). This allows the development of a broad design space across a 

wide range of the parameters of interest, rather than a smaller set of 

anecdotal observations.

Baseline archetypes were designed using Special SFRSs for Seismic Design 

Category (SDC) D and Ordinary systems for SDC B. Initial designs (without 

configuration irregularities) were prepared in accordance with all current 

U.S. code requirements for new buildings. Modified systems were designed 

according to code requirements including requirements triggered by the 

configuration irregularity, but often ignoring prohibitions that may result due 

to the configuration irregularity (e.g., the prohibition of the equivalent lateral 

force procedure for buildings with weight (mass) irregularity). In some 
3-2 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

cases, additional designs that do not comply with irregularity-related code 

requirements were also studied. This permits assessment of both the 

significance of the irregularity to building performance and the effectiveness 

of code remedies in producing desirable changes in performance.

Table 3-1 Systems Used to Study Structural Irregularities 

Structural Irregularities

Systems for Study, # stories

RC

Moment 

Frame

RC 

Shear

Wall

Steel 

Moment 

Frame

Wood

Shear 

Wall

H1. Torsional (stiffness) 

irregularity 8, 12 8 2 

H2. Reentrant corner irregularity

H3. Diaphragm discontinuity

irregularity

H4. Out-of-plane offset 

irregularity

H5. Nonparallel system 

irregularity

H6. Torsional strength irregularity 12 2 

V1. Soft story irregularity 4,8,12, 20 8,12

V2. Weight (mass) irregularity 20 3,20

V3. Vertical geometric irregularity

V4. In-plane discontinuity

irregularity

V5. Weak story irregularity 4,8,12, 20

V6. Story mechanism: 

weak-column/strong-beam 4,8,12 3,9,20

V7. Gravity-induced lateral 

demand 12 20

V8. Wall discontinuity 8,12

Designs were completed for Seismic Design Categories Dmax and Bmax, using 

general code-defined spectra for Site Class C and Risk Category II. Site 

Class C was selected, rather than the default Site Class D, to avoid the 

stopgap requirements in Section 11.4.8 of ASCE/SEI 7-16, Minimum Design 

Loads and Associated Criteria for Buildings and Other Structures (ASCE, 

2017a), which would either complicate this general study by requiring sitespecific ground motions or bias the findings by applying the scaling 

adjustments permitted in Exception 2 of that section. Additionally, the 

FEMA P695 analysis method used in this study (FEMA, 2009) is tied to this 

target spectrum. In the collapse capacity evaluations of the building designs, 

the FEMA P695 method is used, along with the FEMA P695 far-field ground 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-3 

motion set being used for most analyses. For torsional irregularity studies, 

an additional set of FEMA P695 analyses was performed using pulse motions 

from the near-field record set.

Table 3-2 Parameters Varied in Designs and Detailed Analytical Studies

Parameter Range

Seismic Design Category (SDC)

Bmax: SDS = 0.32, SD1 = 0.132

Dmax: SDS = 1.50, SD1 = 0.60

Seismic-Force-Resisting System

(SFRS)

Reinforced Concrete Special/Ordinary Moment Frames (RC SMF and RC OMF) 

Reinforced Concrete Shear Walls (RC SW)

RC SMF + RC SW

Steel Moment Frames (SMF and OMF) 

Wood Shear Walls (simplified)

Seismic-Force-Resisting System 

quality

Ordinary

Special

Building height Low- to mid-rise for horizontal irregularities

Mid- to high-rise for vertical irregularities

Analysis method used in design Equivalent Lateral Force (ELF)

Modal Response Spectrum Analysis (MRSA)

Gravity load level Low

High

Degree of irregularity Regular to highly irregular

Designs are based on the results of modal response spectrum analysis 

(MRSA) or the equivalent lateral force (ELF) procedure found in Chapter 12 

of ASCE/SEI 7-16. These variations permit assessment of how analysis 

methods used in design may predict different performance and how designs 

informed by different analysis methods may actually perform differently. 

Where MRSA was used in design, the scaling requirements of ASCE/SEI

7-16 (to 100% of the ELF base shear) were followed. All designs use fixed 

base models, with no direct consideration of foundation flexibility, as 

permitted by Section 12.7.1 of ASCE/SEI 7-16. Generally, the designs have 

variations in proportioning and a degree of refinement or optimization that is 

representative of typical design practice. In a few cases additional designs 

with highly optimized proportioning are prepared to assess the sensitivity of 

such “barely code-conforming” conditions.

Consistent with the performance criteria outlined in Section 1.3.1.3 of 

ASCE/SEI 7-16, the MCER probability of collapse is the primary metric of 

the FEMA P695 methodology for evaluation of the collapse capacity of the 

archetype model of interest. However, the adjusted collapse margin ratio 

(ACMR) is better suited for comparing the relative collapse performance of a 

given SFRS with and without a particular irregularity. This study compares 
3-4 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

the ratio of the values of the ACMR parameter for a given SFRS with and 

without a particular irregularity to 1.0.

Although collapse is the primary metric of interest, other data were retained 

for use in this and future projects. Table 3-3 shows the metrics that were 

monitored in the detailed analytical studies performed using the FEMA P695 

method. 

Table 3-3 Metrics Monitored in Detailed Analytical Studies

Metric Detail

Collapse Simulated (analytically)

Non-simulated (inferred from other metrics)

Story drift

Floor displacement

Residual story drift

Maximum and average

 for

Floor plate and framing lines

 at

1/3 MCE, 2/3 MCE, MCE

Story twist (in three-dimensional 

models) 

Maximum and average

 at

1/3 MCE, 2/3 MCE, MCE

Floor acceleration

Floor velocity

Maximum and average

 for

Multiple points

Ductility demand Maximum and average

 at

1/3 MCE, 2/3 MCE, MCE

Relevant force-demand 

parameters

(such as column axial load and 

moment) 

Maximum and average

 at

1/3 MCE, 2/3 MCE, MCE

3.2 Archetype Configurations and Designs 

The majority of the archetype buildings are composed of three different 

SFRSs: (1) steel moment frames; (2) reinforced concrete moment frames; 

(3) reinforced concrete shear walls. The intent of the archetype designs was 

to create structural models that represent realistic modern structures. 

Therefore, design assumptions and structural properties that are considered to 

be a good representation of the common building stock and new building 

design practices were selected. Detailed information about the 

configurations of the baseline designs for each system type is given in 

Sections 3.2.1 through 3.2.3. Modifications to the baseline configurations to 

introduce configuration irregularities are outlined in this chapter, but 

described in detail in Chapters 4 through 6. The baseline designs served as a 

basis against which to compare the impact of the irregularities studied.
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-5 

3.2.1 Steel Moment Frame Archetypes

The baseline steel moment frames reflect the three building geometries 

shown in Figure 3-1, Figure 3-2, and Figure 3-3, and match the model 

buildings from Boston and Los Angeles found in Appendix B of FEMA 

355C, State of the Art Report on Systems Performance of Steel Moment 

Frames Subject to Earthquake Ground Shaking (FEMA, 2000b). Baseline 

designs for 3-, 9-, and 20-story buildings were developed for SDC Dmax and 

SDC Bmax; these are summarized in Table 3-4. Table 3-5 summarizes the 

design values used to develop the steel moment frame archetypes and Table 

3-6 documents an example 3-story special moment frame (SMF) design for 

SDC Dmax. A comprehensive discussion of the design process and resulting 

frame designs is provided in Appendix C. 

Gravity and wind loading criteria match those used in the earlier postNorthridge earthquake analyses documented in FEMA 355C. The baseline 

designs reflect ASCE/SEI 7-16 and AISC 341-10, Seismic Provisions for 

Structural Steel Buildings (AISC, 2010b), requirements. Ordinary moment 

frames (OMFs) are used for SDC Bmax and special moment frames with 

reduced-beam sections are used for SDC Dmax. 

The baseline buildings for SDC Dmax are governed by seismic forces and 

have been designed to satisfy a story drift limit of 0.02; note that Table 

12.12-1 of ASCE/SEI 7-16 allows a drift limit up to 0.025 for moment frame 

buildings four stories or less, where nonstructural components are designed 

to accommodate the extra drift, but this option was not used in the present 

study. The baseline design base shears for SDC Bmax are governed by wind 

forces from ASCE/SEI 7-16 for the 9- and 20-story buildings, while the base 

shear for the 3-story building is governed by seismic demands. Under 

service loads, the designs were checked to confirm that they satisfy a roof

drift limit of H/400 using wind forces equivalent to a 50-year mean return 

period obtained from Appendix C of ASCE/SEI 7-16. Ultimately, wind 

demands controlled the final design of all SDC Bmax buildings. 

To study the relative collapse performance of buildings with vertical 

irregularities, 108 irregular designs were created by modifying the baseline 

steel moment frame archetypes. The separate modifications were made by: 

• Increasing the mass of specific floors to introduce weight (mass) 

irregularity [V2].

• Modifying the minimum strong-column/weak-beam ratio used for design 

[V6].

• Introducing slanting columns at a given story to cause gravity-induced 

lateral demand [V7]. 
3-6 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

Chapter 6 describes in detail how each of these modifications are applied to 

the baseline archetypes and how their collapse resistance is affected as a 

result. 

Figure 3-1 Building elevations for steel moment 

frames. 

Figure 3-2 Seismic Design Category D steel building 

floor plans. 

Figure 3-3 Seismic Design Category B steel building 

floor plans. 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-7 

Table 3-4 Overview of Baseline Steel Moment Frame Building Designs 

No. 

Stories

Frame 

Detail SDC

Design 

Method

Period for Computing 

Design Forces 

(CuTa) [s]

Analytical 

Period [s](1)

3 OMF Bmax ELF, MRSA 0.86 1.75, 1.93 

3 SMF Dmax ELF, MRSA 0.74 0.97, 1.46

9 OMF Bmax ELF, MRSA 2.14 3.19, 3.19

9 SMF Dmax MRSA 1.83 3.13

20 OMF Bmax ELF, MRSA 3.98 4.23, 4.23

20 SMF Dmax MRSA 3.40 4.54

(1) The reported analytical periods are from the linear structural design models, in the 

north-south direction. Where ELF and MRSA are used, the first listed value is for ELF. 

For designs governed by wind, ELF vs MRSA does not affect the fundamental period.

Table 3-5 Common Design Values Used for Steel Moment Frame Designs

Design Property SDC Bmax SDC Dmax

Short period design spectral acceleration, SDS 0.32g 1.5g 

One-second design spectral acceleration, SD1 0.13g 0.6g

Response modification coefficient, R 3.5 8 

Deflection amplification factor, Cd 3 5.5

Story drift limit (seismic) 2% 2%

Basic wind speed (strength, Exposure B) 130 mph 110 mph

Basic wind speed (service, Exposure B) 100 mph 85 mph

Roof drift limit (wind) H/400 H/400

Risk Category II II

Floor dead load 96 psf 96 psf

Partition load (reduce by 50% for seismic mass) 20 psf 20 psf

Roof dead load 83 psf 83 psf

Roof dead load at penthouse 116 psf 116 psf

Live load 50 psf 50 psf

Roof live load 20 psf 20 psf

Table 3-6 Example Baseline Design Summary (3-Story Steel SMF) 

3-Story Steel SMF, MRSA Design, SDC Dmax

Story/ 

Floor

Columns 

Doubler 

Plates Girder

Drift (%) Moment Ratio

Exterior Interior ΔX ΔY Exterior Interior

Roof W14×159 W14×176 No W24×55 1.75 1.77 2.00 1.15

3rd W14×159 W14×176 Yes W27×94 1.86 1.88 1.89 1.09

2nd W14×159 W14×176 Yes W27×94 1.36 1.37 1.75 1.05

Note: Steel tonnage 2.81 psf (columns: 1.53 psf, beams: 1.28 psf)
3-8 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

3.2.2 Reinforced Concrete Moment Frame Archetypes

Concrete moment frame archetypes were designed to represent a modern 

commercial office structure using current design and construction practices 

for SDC Bmax and SDC Dmax, ranging from 4 to 20 stories. The baseline 

archetype design space is summarized in Table 3-7. Table 3-8 gives an 

overview of design parameters for designing the RC moment frames and

Table 3-9 documents an example 4-story RC SMF design for SDC Dmax. 

Summary design information for all RC moment frame archetypes is 

provided in Appendix D. 

Table 3-7 Overview of Baseline RC Moment Frame Building Designs 

No. 

Stories

Frame 

Detail SDC

Design 

Method

Period for Computing 

Design Forces 

(CuTa) [s]

Analytical 

Period [s](1)

4 OMF Bmax ELF 0.93 1.93

4 SMF Dmax ELF 0.81 1.12

8 SMF Dmax ELF 1.49 2.11

12 OMF Bmax ELF 2.44 4.51

12 SMF Dmax ELF 2.13 2.58

20 SMF Dmax ELF, MRSA 3.36 3.66, 3.87

(1) The reported analytical periods are from the linear structural design models. Where ELF 

and MRSA are used, the first listed value is for ELF.

Table 3-8 Common Design Values Used for RC Moment Frame Designs

Design Property SDC Bmax SDC Dmax

Short period design spectral acceleration, SDS 0.33g 1.5g 

One-second design spectral acceleration, SD1 0.13g 0.6g

Response modification coefficient, R 3 8 

Deflection amplification factor, Cd 2.5 5.5

Story drift limit (seismic) 2% 2%

Basic wind speed (strength, Exposure B) 130 mph - 

Basic wind speed (service, Exposure B) 100 mph - 

Roof drift limit (wind) H/400 - 

Floor dead load 175 psf 175 psf

Roof dead load 140 psf 140 psf

Partition load 15 psf 15 psf

Live load 50 psf 50 psf

Roof live load 20 psf 20 psf

f'c beams 4,000 psi 5,000 psi

f'c columns 4,000 psi 7,000 psi

Reinforcing steel yield strength, fy 60 ksi 60 ksi

Beam design stiffness 0.35EIg 0.35EIg

Column design stiffness 0.7EIg 0.7EIg
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-9 

Table 3-9 Example Baseline Design Summary (4-Story RC SMF)

Level

Columns 

depth × width [tie spacing]

(ρtotal , ρsh) 

Beams 

depth × width [hoop spacing]

(ρtop , ρbot , ρsh) 

Drift (%)

Moment 

ratio, 

∑Mc/∑Mb

Exterior 

Exterior Interior Exterior Interior (Interior)

4

26×22 [2.5]

(0.0110, 0.0107)

26×22 [2.5]

(0.0110, 0.0107)

24×18 [5]

(0.0081, 0.0046, 0.0044)

24×18 [5]

(0.0081, 0.0046, 0.0044)

1.2

1.16

(0.74)

3 

26×22 [2.5]

(0.0110, 0.0107)

26×22 [2.5]

(0.0165, 0.0107)

24×18 [5]

(0.0097, 0.0046, 0.0044)

24×18 [5]

(0.0097, 0.0046, 0.0044)

1.5

1.96

(1.65)

2 

30×22 [3.5]

(0.0119, 0.0102)

30×22 [3.5]

(0.0167, 0.0102)

34×20 [5]

(0.0069, 0.0048, 0.0039)

34×20 [5]

(0.0069, 0.0048, 0.0039)

1.2

1.37

(1.22)

1 

30×22 [3.5]

(0.0167, 0.0102)

30×22 [3.5]

(0.0167, 0.0102)

34×20 [5]

(0.0069, 0.0048, 0.0039)

34×20 [5]

(0.0069, 0.0048, 0.0039)

1.0

1.89

(1.44)

Notes: ρsh is the area ratio of transverse reinforcement in the column or beam hinge region. 

All dimensional units are in inches (e.g., column and beam sizes).

Story heights of the baseline RC moment frames are 15 feet at the first story 

and 13 feet at all other stories. Each has a 120 ft. by 120 ft. footprint with six 

bays in each direction and moment frames along the perimeter (see Figure 

3-4). For simplicity, only three “typical” bays of the six-bay frame from one 

side of the building were designed and modeled. This is accomplished by 

designing a three-bay frame for half of the tributary weight and mass of the 

six-bay moment frame, except that overturning forces in the end columns are 

reduced to reflect the overturning forces in a six-bay frame. Since the 

nonlinear analysis models are two-dimensional, end columns were designed 

for uniaxial bending only—allowing for consistency between the design and 

analysis approaches. The concept of making a three-bay representation of a 

six-bay moment frame is consistent with the approach taken for analyzing 

RC moment frames in the original FEMA P695 studies (FEMA, 2009). 

To study the relative collapse performance of buildings with vertical 

irregularities, 106 irregular designs were created by modifying the baseline 

RC moment frame archetypes. The separate modifications were made by: 

• Increasing the mass of specific floors to introduce weight (mass) 

irregularity [V2].

• Adjusting story heights and strengths to introduce soft/weak story 

irregularities [V1/V5].

• Modifying the minimum strong-column/weak-beam ratio used for design 

[V6].
3-10 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

• Introducing slanting columns at a given story to cause gravity-induced 

lateral demand [V7]. 

Chapter 6 describes in detail how each of these modifications are applied to 

the baseline archetypes and how their collapse resistance is affected as a 

result. 

Figure 3-4 Plan and elevation of the RC moment frame archetypes.

3.2.3 Reinforced Concrete Shear Wall Archetypes

A set of five baseline RC wall designs were created, representing both 

special RC walls designed for SDC Dmax, as well as ordinary RC walls

designed for SDC Bmax (Table 3-10). The designs cover two heights: 8 and 

12 stories and are intended to represent a modern commercial office structure 

using current design and construction practices. Story heights are identical to 

the RC moment frame baselines—15 ft. at the first story and 13 ft. at all other 

stories. The archetypes employ a 120 ft. by 120 ft. footprint, (example 

shown in Figure 3-5). For 8-story buildings, lateral loads are resisted by two 

independent planar walls in each of two orthogonal directions; for 12-story 

designs, lateral loads are resisted by four (shorter) independent planar walls 

in each of two orthogonal directions. For Dmax designs, earthquake demands 

control strength design, and wall length was determined by earthquake 

strength requirements; for Bmax designs, wind demands control strength 

design, and wall length is controlled by earthquake drift limits. For all 

designs, walls are located such that the centers of stiffness and mass 

coincide. 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-11 

Table 3-10 Overview of Baseline RC Wall Building Designs 

Model ID

Number of 

Stories

Wall 

Detailing SDC

Analysis 

Procedure

8-D-0-0-ELF 8 Special Dmax ELF

8-D-0-0-MRSA 8 Special Dmax MRSA

8-B-0-0-ELF 8 Ordinary Bmax ELF

12-D-0-0-ELF 12 Special Dmax ELF

12-B-0-0-ELF 12 Ordinary Bmax ELF

(a) 8-story building (b) 12-story building

Figure 3-5 Building prototype plans designed for Dmax and Bmax spectra for (a) 8-story buildings and (b) 12-

story buildings. Wall length shown is for Dmax designs; wall length is 20 ft. for Bmax designs. 

All RC wall building archetypes are designed according to ASCE/SEI 7-16

for concrete shear walls that are part of the building frame system; (i.e., R = 6 

for special walls and R = 5 for ordinary walls). Four baseline archetypes 

were designed using the ELF procedure and an additional baseline design 

was created using the MRSA from Chapter 12 of ASCE/SEI 7-16. Walls 

with vertical irregularities were designed using both the ELF and MRSA 

procedures. Table 3-11 gives an overview of the common design properties

that were used for the RC wall building designs. Summary design 

information for each archetype is in Appendix B. 

To study the relative collapse performance of buildings with vertical 

irregularities, 19 irregular designs were created by modifying the archetype

baselines discussed above. The baseline archetypes were modified to include

stiffness irregularities resulting from openings located in the 1st, 1st and 2nd, 

and 5th (8-story buildings) or 8th (12-story buildings) stories. Openings were 
3-12 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

sized to reduce story stiffness to 75% or 50% of the stiffness of the baseline 

building. Specifics for the designs analyzed for each irregularity appear 

Chapter 5. 

Table 3-11 Common Design Values Used for RC Wall Designs

Design Property SDC Bmax SDC Dmax

Short period design spectral acceleration, SDS 0.33g 1.5g 

One-second design spectral acceleration, SD1 0.13g 0.6g

Response modification coefficient, R 5 6 

Deflection amplification factor, Cd 4.5 5 

Story drift limit (seismic) 2% 2%

Basic wind speed (strength, Exposure B) 110 mph - 

Basic wind speed (service, Exposure B) 85 mph - 

Roof drift limit (wind) H/400 - 

Floor dead load 175 psf 175 psf

Roof dead load 140 psf 140 psf

Partition load 15 psf 15 psf

Live load 50 psf 50 psf

Roof live load 20 psf 20 psf

Concrete compressive strength, f’c 5000 psi 5000 psi

Reinforcing steel yield strength, fy 60 ksi 60 ksi

Wall stiffness used for MRSA 0.5EIg 0.5EIg

3.3 Structural Modeling of Archetype Buildings 

Nonlinear structural models of the archetype buildings were developed to 

perform dynamic analysis and assess collapse resistance. The following 

sections describe the methods used to model the steel moment frame (Section 

3.3.1), RC moment frame (Section 3.3.2), and RC wall (Section 3.3.3)

building systems. Each of these systems were modeled with twodimensional planar models for conducting nonlinear dynamic analyses in 

OpenSees. 

Building mass tributary to moment frames and walls are lumped at the joint 

nodes and wall nodes, respectively. For analysis, an expected mass of 1.05 

times the dead weight was considered. Raleigh damping, anchored to the 

first and third modes of vibration, was implemented; however, the stiffness 

proportional damping was applied only to linear elements, in order to avoid 

unintended damping forces that may develop in nonlinear elements 

(Charney, 2008). The steel and concrete models had damping ratios of 2% 

and 5% of critical, respectively. 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-13 

For all models, the gravity system was represented by a linear elastic P-Delta

leaning column, in order to model the destabilizing second-order geometric 

effects, but without adding any strength or stiffness from the gravity system. 

The P-Delta leaning column provided no lateral resistance and was

connected to SFRS elements via stiff axial-only elements. Inclusion of the 

P-Delta leaning column enabled simulation of base moment demand and 

story shear associated with gravity load acting through large lateral 

displacements. Geometric nonlinearity was simulated using the “Linear with 

P-Delta” transformation rules in OpenSees. 

Gravity loads were applied to the SFRS elements and to the P-Delta column, 

based on the tributary areas of each. Per FEMA P695, the load combination 

representing expected gravity loads, 1.05D + 0.25L, was used to compute the 

vertical load effects. Gravity loads directly carried by the frames were

distributed on the beams. Gravity loads carried by the wall were determined 

by the tributary area assigned to the wall. The remaining gravity load, which 

is carried by the building’s gravity system, was applied to the P-Delta

leaning column.

3.3.1 Steel Moment Frame Archetypes

3.3.1.1 System Modeling

Steel moment frames were modeled as recommended in NIST GCR 

17-917-46v2, Guidelines for Nonlinear Structural Analysis for Design of 

Buildings, Part IIa – Steel Moment Frames (NIST, 2017). Nonlinear models 

of the moment frame archetype buildings were constructed in OpenSees

using the lumped plasticity method. The lumped plasticity models consist of 

linear elastic beam and column elements, joined by nonlinear elements where 

plastic deformations are expected to concentrate, as depicted in Figure 3-6. 

Nonlinear behavior was simulated with plastic hinges at the ends of beams 

and columns and in the joint panel zones as well. In the 3-story steel 

moment frames, the rotational stiffness of the foundation was modeled with a 

rotational spring that approximates a grade-beam; however, it had 

significantly higher stiffness than the first-story columns, so column behavior 

was similar to what would be observed for a fixed base condition. The 9- 

and 20-story steel frames have basement levels below the first story, and the 

column connection at the bottom of the basement was modeled as pinned (it 

is also designed as pinned).
3-14 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012Leaning (P-

∆) 

column

Elastic beam/ 

column

Nonlinear 

plastic 

hinge

Nonlinear 

joint element

Figure 3-6 Schematic of a lumped plasticity nonlinear frame model

(without basement levels). 

3.3.1.2 Modeling of Beam and Column Components

Nonlinear beam and column hinges were modeled with the Modified Ibarra 

Krawinkler Deterioration Model in OpenSees (Ibarra et al., 2005; Lignos and 

Krawinkler, 2009), illustrated in Figure 3-7. Initial backbone properties were

calculated with the equations recommended by Chapter 4 of NIST GCR 

17-917-46v2 and cyclic deterioration parameters were computed from 

Lignos and Krawinkler (2011). For calculating the nonlinear properties of 

the beams and columns, the actual yield strength of the steel was assumed to 

be 10% higher than the nominal yield strength (per NIST GCR 17-917-46v2

recommendations). Properties of the beams that were used to determine the 

monotonic backbone are as follows: (1) the expected material yield strength;

(2) plastic section modulus (Z); (3) web and flange depth-to-thickness ratios;

(4) the ratio of beam depth to effective length; (5) composite action; and (6) 

potential for lateral torsional buckling. Additionally, backbone properties of 

the reduced beam sections (RBSs) were modified to account for plastic hinge 

offsets. That is, strength was increased and rotation capacity decreased to 

account for the actual hinges occurring at the location of the reduced beam 

section rather than the face of the joint (where they are modeled).
Figure 3-7 Modified Ibarra Krawinkler Deterioration 

Model (Image from Lignos et al., 2011). 

Composite action was not considered for the design of the beams, but it was 

considered in the nonlinear analysis, because steel moment frames are 

commonly connected to a diaphragm. The controlling mechanism for 

composite action of the slabs is yielding of the shear studs, which are 

assumed to be 3⁄4-inch diameter, 65 ksi steel, placed at 12 inches on center. 

Composite action was also considered for computing the effective moment of 

inertia of the linear beam elements. Plastic hinge behavior of an example 

beam is illustrated in Figure 3-8. 

Figure 3-8 Example cyclic behavior of a W30×108 RBS beam with 

composite slab action. Moment increase (and rotation 

decrease) to account for plastic hinge offsets in the actual 

building are approximately 12%. 

Plastic hinge behavior of an example column is illustrated in Figure 3-9. The 

monotonic backbone properties of the column hinges were computed 

according to Chapter 4 of NIST GCR 17-917-46v2. Column backbones tend 

FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-15 
to be more ductile and deteriorate less quickly because they are more 

compact than the beams. An additional factor that was used for determining 

column hinge strengths is the ratio of the expected axial load to the yield 

axial load (Pg/Py), which affects both strength and rotation capacity. 

However, axial load ratios of the perimeter frame columns tend to be low 

(Pg/Py < 0.1), so axial load effects are generally small. 

Figure 3-9 Example cyclic behavior of a W14×193 column. 

Ultimate rotation (not shown on figure) is 0.15 radians. 

3.3.1.3 Modeling of Joint Panel Zones 

Plastic deformation of the joint panel zones is expected to occur in the steel 

moment frames, particularly the ordinary moment frames. Panel zones were 

modeled with the Joint2D element (Altoontash, 2004) in OpenSees with 

nonlinear behavior idealized as trilinear without cyclic deterioration or 

isotropic hardening, based on Gupta and Krawinkler (1999). Figure 3-10 

illustrates the idealized relationship between panel zone shear force and 

distortion. Panel zone moment (M) and shear (V) are related as follows: 

 M = Vdb

in which db is the depth of the beam. The yield shear force (Vy) is given as 

follows: 

Vy = 0.60Fydctp

in which Fy is the expected steel yield strength, dc is the depth of the column, 

and tp is the thickness of panel zone. The yield distortion of the panel (γy) 

was computed as follows: 

F

  y

y G 3

in which G is the modulus of rigidity of steel. The fully plastic shear 

strength occurs at a distortion four times γy and was determined as follows: 

3-16 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-17 

1

2

c cf

p y

b cp

3b t

V V

ddt

 

= +  

 

in which bc and tcf are the width and thickness of the column flange. The 

strain hardening parameter (α) was taken as 1.5%. 

Figure 3-10 Idealized panel zone shear force deformation 

relationship (Gupta and Krawinkler, 1999). 

3.3.2 Reinforced Concrete Moment Frame Archetypes

3.3.2.1 System Modeling

Reinforced concrete moment frames were modeled with the lumped 

plasticity method. They use the same elements as the steel moment frames

(i.e., linear beam-columns, nonlinear plastic hinges, nonlinear joint elements, 

as shown in Figure 3-6), but with material models calibrated to simulate RC 

moment frame behavior. Like the 3-story steel frames, the rotational 

stiffness of the foundation was modeled with a rotational spring that 

approximates a grade-beam and footing; however, it had significantly higher 

stiffness than the first-story columns, so column behavior was closer to what 

would be observed for a fixed base condition. 

3.3.2.2 Modeling of Beam and Column Components

Nonlinear beam and column hinges were idealized with trilinear backbones 

having peak-oriented hysteretic response and cyclic deterioration, using the 

model developed by Ibarra et al. (2005), shown in Figure 3-11. The 

backbone and hysteretic properties of the nonlinear beam-column hinges 

were computed from empirical relationships developed by Haselton et al. 

(2008) based on the design properties of the beams and columns (i.e., 

concrete strength, element dimensions, axial load ratio, and reinforcement 

detailing). The expected axial load ratio was used to calibrate column hinge 

backbones, but it was not updated throughout the analysis, therefore dynamic 
axial-flexure interaction effects were ignored. This simplification should 

minimally affect the performance for two reasons: (1) the columns tend to 

have axial load ratios less than 0.2; and (2) increases in axial force at one end 

of the frame coincides with decreases in axial force at the other end, so axial 

load effects at the two ends of a frame counteract one another. An example 

hysteresis of a concrete column is shown in Figure 3-12. 

Flexural stiffness of the linear beam-column elements was computed using 

an effective moment of inertia based on empirical equations recommended 

by Haselton et al. (2008). The effective moment of inertia can range from 

35% to 80% of the gross moment of inertia and depends upon member 

dimensions and axial load ratio. 

Figure 3-11 Backbone properties of the Ibarra et al. (2005) 

material model (Image from Ibarra et al., 2005). 

Figure 3-12 Example hysteretic properties of a 30 in. by 26 in. RC column 

with low axial load ratio. Total longitudinal reinforcement ratio 

and shear reinforcement ratio are 0.014 and 0.01, respectively. 

3-18 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012 
3.3.2.3 Modeling of Joint Panel Zones 

Joint panel zones were modeled with the Joint2D element (Altoontash, 2004) 

in OpenSees. The panel zones were modeled as linear for the RC SMFs, 

because special detailing requirements relating to the size, confinement, and 

reinforcement of joints are expected to prevent joint failure. Ordinary 

moment frame joints were modeled with the pinched Ibarra material model 

(Ibarra et al., 2005). Nonlinear properties of the joints were determined 

using a procedure developed by Lowes and Altoontash (Lowes et al., 2004; 

Altoontash, 2004), which is the same procedure used for OMF joints in 

FEMA P695. A detailed summary and background for the procedure for 

determining OMF joint properties is documented by Liel (2008). 

Strength of the OMF joints were computed according to ACI 318-14, 

Building Code Requirements for Structural Concrete (ACI, 2014), using the 

joint area and concrete strength. Initial stiffness was based on the secant 

stiffness to 40% yield (effective stiffness). The hardening stiffness was set at 

4% of the effective stiffness, and the pinch point at 25% of the maximum 

historic stress and rotation. The cyclic deterioration parameter was set to the 

same value that is computed for the beam-columns. The rotation capacity to 

peak strength was set as 0.010 radians and 0.015 radians for exterior and 

interior joints, respectively, based on recommendations by Moehle et al. 

(2006). Figure 3-13 shows the cyclic properties of an example RC OMF 

joint. 

Figure 3-13 Example hysteretic properties of a RC OMF joint with 

axial load ratio of 0.11, 4000 psi concrete, joint area of 

378 in.2

, and effective beam depth of approximately 13 

inches. 

FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-19 
3-20 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

3.3.3 Reinforced Concrete Shear Wall Archetypes

3.3.3.1 System Modeling

Nonlinear models of the RC wall buildings were constructed using three 

different methods in OpenSees. They were also modeled by finite elements 

with ATENA, but for validation purposes only. Brief descriptions of the 

modeling methods are provided here, and detailed descriptions are provided 

in Appendix B. 

Collapse simulations of RC wall buildings were performed with the 

OpenSees models, because of their computational efficiency. The three 

methods by which RC walls were modeled in OpenSees are: (1) force-based 

beam-column elements (FBE) with fiber-type section models and the 

distributed plasticity modeling approach developed by Pugh et al. (2015); 

(2) displacement-based beam-column elements (DBE) with fiber-type section 

models and the distributed plasticity modeling approach developed by Pugh 

et al. (2015) and updated by Marafi et al. (2018); and (3) the shear-flexureinteraction multi-vertical line-element model (SFI-MVLEM) developed by 

Kolozvari et al. (2015a,b, 2018). The final collapse assessment results 

reported in Chapter 5 are obtained using method two in the preceding list—

displacement-based beam-column elements with the Pugh et al. (2015) 

approach.

The modeling approaches developed by Pugh et al. (2015) and Marafi et al. 

(2018) employ regularization of material softening to achieve mesh-objective 

simulation of strength loss; by doing this, the effective size of the plastic 

hinge region (which essentially maps the material strain capacities to the 

element plastic deformation capacities) is controlled and is not arbitrarily 

affected by the details of the mesh size, even after the onset of negative 

stiffness. These have been verified using a large database of planar and nonplanar wall tests, to provide accurate, mesh-objective, simulation of onset of 

strength loss, which is required for accurate assessment of collapse risk. 

The SFI-MVLEM employs the fixed-strut angle approach (Orakcal et al., 

2012) to characterize the biaxial constitutive response of the two-dimensional 

RC panel fibers that compose the SFI-MVLEM (Orakcal et al., 2004). 

Axial-shear coupling is achieved within each two-dimensional fiber through

the two-dimensional RC panel constitutive model. 

Figure 3-14 shows an idealization of the OpenSees model of a baseline 8-

story RC wall building, which includes a single vertical line of nonlinear 

force-based beam-column elements to represent a wall, in addition to the line 

of elastic elements defining the P-Delta leaning column. The wall is fixed at 

its base. 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-21 

One force-based element with five fiber sections OR six 

displacement-based elements, each with five fiber sections 

OR six SFI-MVLEMs each with one fiber section

Figure 3-14 Schematic of OpenSees RC wall building model.

3.3.3.2 Modeling of Walls using Fiber Elements

The force-based and displacement-based beam-column elements represent 

nonlinear flexural response of the wall via fiber-type section models that 

comprise nonlinear confined and unconfined concrete and reinforcing steel 

fibers. Concrete and steel material model response was defined using 

standard material models and were modified using the regularization method 

proposed by Pugh et al. (2015). A linear moment distribution and constant 

axial load distribution along the length of the element was assumed, where

flexure and shear response was decoupled in element formulation. Fibertype section models employed approximately 150 fibers along the in-plan 

length of the wall. Figure 3-15 shows the element layout for walls with and 

without openings.

Figure 3-15 OpenSees model configurations for walls with and without openings. 

One force-based 

element OR six 

displacement-based 

elements OR six SFIMVLEM elements
3-22 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

Concrete and steel material response models used in the SFI-MVLEM were 

calibrated such that the SFI-MVLEM predicted drift capacities for the wall 

designs that were equal to those predicted using models comprising 

distributed-plasticity beam-column elements.

3.3.3.3 Material Constitutive Models for Concrete and Rebar

Concrete response was simulated using the OpenSees Concrete02 material 

model. In compression, this model represents a quadratic response to peak 

strength with linear deterioration to a residual compressive strength. In 

tension, the model represents a linear response history to tensile strength with 

linear strength loss to zero tensile capacity. Tensile strength for unconfined 

and confined concrete was defined as 4 cf ′ psi; regularization of post-peak 

response in tension was not required as concrete cracking did not result in 

section or element softening. Unconfined concrete was assumed to reach 

peak strength at a strain of -0.002 in./in.; confined concrete strength and 

strain at maximum strength were defined using the model by Saatcioglu and 

Razvi (1992). Per the recommendations of per the recommendations of Pugh 

et al. (2015) and Marafi et al. (2018), concrete post-peak response was 

defined by the unconfined or confined concrete crushing energy and a meshdependent length; this was required to ensure that simulation of onset of 

strength loss was accurate and did not depend on mesh size. Concrete 

residual strength was defined as 20% of peak strength for confined concrete 

and 10% of peak strength for unconfined concrete. 

For reinforcing steel, the OpenSees Steel02 model was used. Reinforcing 

steel was assumed to lose compressive and tensile strength, due to buckling, 

at the regularized strain at which concrete strength deteriorates to the residual 

compressive strength. 

Figure 3-16 shows concrete and steel material model response under cyclic 

loading. Figure 3-17 shows regularization of concrete and steel response 

using unconfined, Gfc, and confined concrete, Gfcc, crushing energies and LIP, 

which is the element length associated with the fiber section in which the 

material model is used. Note that the red ‘X’ in Figure 3-17 shows the strain 

at which reinforcing steel loses strength due to buckling. 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-23 

(a) (b)

Figure 3-16 Nonlinear 1D cyclic material models. (a) Yassin cyclic concrete model, which employs the 

monotonic Modified Kent-Park model (Yassin, 1994; Scott et al., 1982) as presented by Orakcal 

and Wallace (2006). Note that compressive stress-strain is positive. (b) Menegotto-Pinto-Filippou 

reinforcing steel model (Filippou et al., 1983) as presented by Orakcal and Wallace (2006). 

Figure 3-17 Regularization of concrete material response using mesh 

dependent length. Note that steel buckling occurs at ε20u and ε20c. 

(Figure adapted from Pugh et al., 2015) 

(a) unconfined concrete (b) confined concrete 

compression envelope compression envelope

X 

Reinforcing steel 

buckling

X 

Reinforcing steel 

buckling

3.4 Archetype Analysis Methods

The nonlinear analysis methods of FEMA P695 were used to investigate 

archetype response and collapse performance. The FEMA P695

methodology was developed to provide a rational basis for determining 

global seismic performance factors, including the response modification 

coefficient (R factor), the system overstrength factor (Ω0), and the deflection 

amplification factor (Cd) that, when properly implemented in the seismic 

design process, will result in “equivalent safety against collapse in an 

earthquake, comparable to the inherent safety against collapse intended by 

current seismic codes, for buildings with different seismic-force-resisting 

systems” (FEMA, 2009). The primary acceptance criterion of FEMA P695 is 

that the SFRS be shown to have not more than a ten percent probability of 
3-24 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

collapse conditioned on MCER ground motions (i.e., conditional collapse 

criterion subsequently adopted by ASCE/SEI 7-10).

The FEMA P695 methodology is intended for use with United States model 

building codes and resource documents to set minimum acceptable criteria 

for new SFRSs seeking adoption by seismic codes. The methodology also 

provides a basis for evaluation of current code-approved SFRSs for their 

ability to achieve intended seismic performance objectives, and to improve 

design requirements for current SFRSs to better achieve these objectives, the 

subject application of the methodology for the work summarized in this 

report. 

The FEMA P695 report provides a complete methodology for establishing 

and documenting seismic performance factors of new SFRSs, including 

collecting requisite system information (e.g., test data), developing 

performance groups of representative archetypes, developing designs of 

archetypes, developing analytical models of archetype designs, analyzing the 

nonlinear response of archetype models to failure, evaluating the MCER

collapse performance of archetype models from the results of the nonlinear 

response analyses, documenting results, and peer reviewing the entire 

process. The studies described in this report selectively used the analysis and 

collapse evaluation methods of FEMA P695 to calculate nonlinear response 

behavior and collapse performance of specific building archetypes modeled 

with and without irregularities. 

3.4.1 Overview of FEMA P695 Analysis Methods 

The FEMA P695 methodology relies on collapse simulation through 

nonlinear dynamic response history analysis. Analysis methods are 

rigorously and unambiguously defined by the FEMA P695 methodology, 

including the specification (selection and scaling) of ground motion records 

to be used in dynamic response history analysis of nonlinear models. FEMA 

P695 intentionally excludes nonstructural components and structural 

elements not part of the SFRS from archetype models of a new SFRS seeking 

adoption by seismic codes, although the analysis methods are generally 

applicable to all building elements subject only to availability of test data

required to establish model properties. Similarly, FEMA P695 does not 

require modeling of potential building irregularities, although the analysis 

methods are generally applicable to archetype models with irregular 

configurations. 

FEMA P695 analysis methods include: (1) nonlinear static (pushover) 

analysis to determine post-yield displacement capacity expressed in terms of 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-25 

the period-based system ductility parameter (μT); and (2) incremental 

dynamic analysis (IDA) to calculate median collapse capacity expressed in 

terms of a corresponding value of response spectral acceleration ( ˆ

CT S ) at the 

elastic, fundamental-mode, period, T, of the archetype model of the system of 

interest. The collapse margin ratio (CMR) is defined as the value of median 

collapse response spectral acceleration divided by the value of MCER

response spectral acceleration at the elastic period (SMT) used as the basis for 

design of the archetype model (i.e., CMR = ˆ

CT S /SMT). The larger the value of 

the CMR, the lower the probability of collapse. The adjusted collapse margin 

ratio (ACMR) is the value of the CMR adjusted by the spectrum shape factor 

(SSF) to account for the inherent “rareness” of MCER ground motions (i.e., 

ACMR = SSF × CMR). The SSF accounts for the post-yield elongation of the 

elastic period based on the value of the system ductility parameter. The 

larger the value of the system ductility parameter, the larger the adjustment 

(increase) in the value of the CMR and the lower the probability of collapse. 

It should be noted that, for the comparisons between collapse performance of 

irregular archetypes and baseline archetypes presented in Chapters 4-6, 

irregular archetypes are assigned the same SSF as their corresponding 

baseline archetypes. 

3.4.2 Selection of Ground Motions

The FEMA P695 methodology provides two sets of ground motion records 

for collapse assessment using nonlinear dynamic analysis—the far-field 

record set and the near-field record set. The far-field record set includes 22

component pairs of horizontal ground motions from sites located greater than 

or equal to 10 km from fault rupture. The near-field record set includes 28

component pairs of horizontal ground motions recorded at sites less than 10 

km from fault rupture. The record sets do not include the vertical component 

of ground motion since this direction of earthquake shaking is generally not 

considered of primary importance for collapse evaluation and is not required 

for nonlinear dynamic analysis. The far-field record set is used by this study

for nonlinear response calculations and collapse evaluations.

The far-field ground motion record set is composed of strong-motion records

(i.e., records with PGA > 0.2g and PGV > 15 cm/s) from all large magnitude 

(M > 6.5) events in the PEER NGA West1 Database (PEER, 2006). Large

magnitude events dominate collapse risk and generally have longer durations 

of shaking, which is important for collapse evaluation of nonlinear degrading 

models. The ground motion sets include records from soft rock and stiff soil 

sites (predominantly Site Class C and D conditions) and from shallow crustal 

sources (predominantly strike-slip and thrust mechanisms). To avoid event 

bias, no more than two of the strongest records are taken from each 
3-26 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

earthquake. Figure 3-18 shows the 44 individual response spectra (i.e., 22 

records, 2 components each), the median response spectrum, and spectra 

representing response at +1- and +2-standard deviations of the far-field 

record set.

0.01

0.1

1

10

0.01 0.1 1 10

Period (seconds)

Spectral Acceleration (g)

Median Spectrum - Far-Field Set

+ 1 LnStdDev Spectrum - FF Set

+ 2 LnStdDev Spectrum - FF Set

Figure 3-18 Far-field record set response spectra normalized by 

peak ground velocity (Figure 6-3 of FEMA P695; 

FEMA, 2009). 

The far-field record set provides a fully-defined set of records for use in a 

consistent manner to evaluate collapse of all possible types of SDC B, C, and 

D systems located in any seismic region. The FEMA P695 methodology 

uses actual earthquake records (in contrast to artificial or synthetic records) 

recognizing that regional variation of ground motions would not be 

addressed. Large magnitude events are rare and few existing earthquake 

ground motion records are strong enough to collapse large fractions of 

modern, code-compliant buildings. In the United States, strong-motion 

records date back to the 1933 Long Beach earthquake, with only a few 

records obtained from each event until the 1971 San Fernando earthquake. 

3.4.3 Incremental Dynamic Analysis

FEMA P695 methods utilize IDA to determine median collapse capacity of 

the archetype model of interest. Median collapse capacity is the value of 

response spectral acceleration, ˆ

CT S , at the fundamental-mode period, T, at 

which the archetype model has a 50 percent probability of collapse. For 

defining ˆ

CT S , the fundamental period is limited by the ASCE/SEI 7-16 upper 

bound equation T ≤ CuTa. 

Median collapse capacity is determined by applying the far-field set of 22 

records (2 components each) to the model incrementally scaled from 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-27

relatively low to relatively high values of response spectral acceleration. For 

a given ground motion, an archetype is assumed to have collapsed when 

either the analysis will not converge (often due to loss of stability) or an 

engineering demand parameter (EDP) such as interstory drift ratio (IDR) 

exceeds a predetermined threshold for which the building is expected to lose 

its capability to carry vertical loads. In some cases, the analytical model may 

still be stable, but the building is considered collapsed because of a nonsimulated mode of failure (e.g., a failure mode that is not explicitly modeled, 

such as failure of the gravity system). Conceptually, median collapse 

capacity is the value of response spectral acceleration at which 22 of the 44 

analyses effect collapse of the archetype model. To avoid potential problems 

with interpolation of discrete data, fitted median values of responses were

estimated by fitting a lognormal curve to the 44 collapse data.

Figure 3-19 is an example plot from FEMA P695 that is used to illustrate the 

FEMA P695 methodology for determining collapse resistance from IDA. 

For collapse evaluation of two-dimensional (planar) archetype models, each 

of the 44 far-field components (i.e., 22 records, 2 components each) are 

individually applied to the model generating 44 values of response and 

collapse data at each increment of ground motion intensity. For collapse 

evaluation of three-dimensional archetype models, the 22 far-field records 

(two components each) are applied to the archetype model in two orthogonal

orientations (e.g., NS-EW and EW-NS orientations of components) also 

generating 44 values of response and collapse data at each increment of 

ground motion intensity. However, the CMR based on median collapse 

intensity, SCT

ˆ , is multiplied by 1.2 when three-dimensional archetypes are 

used to evaluate collapse capacity (i.e., CMR3D = 1.2CMR2D). Adjustment of 

the CMR for three-dimensional analyses is required by Section 6.4.5 of 

FEMA P695 to achieve parity with two-dimensional analyses.

In this study, spectral acceleration of a ground motion was defined as the 

geometric mean spectral acceleration of its two horizontal components. This 

is a modification to the FEMA P695 approach, which first normalizes the 

entire ground motion set to have the same peak ground velocity (to obtain the 

“cloud” of response spectra in Figure 3-18), and then defines spectral 

acceleration as the geometric mean spectral acceleration of the cloud (scaled 

all together). Scaling on geometric mean of individual ground motions, 

rather than cloud-scaling, has relatively inconsequential effects on estimates 

of ˆ

CT S ; although, it does result in an underestimation of record-to-record 

variability, particularly for nonductile buildings. However, since FEMA 

P695 recommends a standard record-to-record variability of β = 0.4, there is 

no need to compute it from IDA. 
3-28 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

Figure 3-19 Incremental dynamic analysis response plot of 

spectral acceleration versus maximum story drift 

ratio (FEMA, 2009).

While evaluation of median collapse capacity requires only the identification 

of the ground motion intensity at which 22 of the 44 analyses effect collapse, 

the studies described in this report also tracked values of other key response 

parameters (e.g., peak story drift ratio and peak floor acceleration) over a 

broad range of ground motion intensities, as described in Section 3.4.6. 

3.4.4 Evaluation of MCER Collapse Performance

The probability of collapse as a function of ground motion intensity (at the 

period, T, of archetype model) is assumed to be lognormally distributed with 

an adjusted median, ˆ

ACT S (i.e., ACMR × SMT), and a lognormal standard 

deviation, βTOT, that accounts for total collapse uncertainty related to: 

(1) record-to-record variability; (2) design requirements (for the SFRS of 

interest); (3) test data (used to establish nonlinear properties); and 

(4) modeling methods, as described in Section 7.3 of FEMA P695. 

Reasonably well-defined archetype models have total collapse uncertainty 

values of βTOT = 0.50 – 0.60; βTOT = 0.50 was used as the default in this study. 

Note that the comparisons presented in Chapters 4-6 of this study are based 

on ACMR, not the probability of collapse for an MCER ground motion level, 

so they are insensitive to the total collapse uncertainty parameter, βTOT; this is 

discussed further in Section 3.4.5.
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-29

3.4.5 Collapse Evaluation Using Absolute and Relative 

Measures of Collapse Risk

Both the collapse probability for MCER ground motions and the ACMR

values are tracked for each archetype building in this study. This section 

discusses both of these performance metrics and explains why the relative 

comparisons of ACMR values between irregular archetypes and a 

corresponding regular baseline archetype was used as the primary measure of 

performance (used in Chapters 4-6).

The MCER probability of collapse is the primary metric of the FEMA P695

methodology for evaluation of the collapse capacity of the archetype model 

of interest as well as the parameter used by ASCE/SEI 7-10 to define 

anticipated reliability of the structure to resist total or partial collapse (e.g., 

see Table C.1.3.1b of ASCE/SEI 7-10). The MCER collapse probability 

represents an absolute measure of collapse risk that may not be the best 

metric for comparing the relative collapse performance of a given SFRS with 

and without a particular irregularity for the following reasons. The MCER

collapse probability is very sensitive to the value βTOT (i.e., total collapse 

uncertainty) when the MCER collapse probability is low (e.g., less than 10 

percent) and relatively insensitive to the value βTOT when the MCER collapse 

is near the median. For the purpose of comparing the collapse performance 

of a given SFRS with and without a particular irregularity, it is desirable to 

have a metric that is not sensitive to total collapse uncertainty. Arguably, the

SFRS of interest has the same (or nearly the same) value of total collapse

uncertainty with and without the irregularity, since individual uncertainties 

associated with design requirements, testing, and modeling are similar. The 

ACMR provides a more suitable metric that is independent of collapse

uncertainties and is linearly related to the value of MCER ground motions 

used as the basis for design and collapse evaluation. 

The ACMR parameter is an absolute measure of median collapse resistance,

values of which necessarily vary for different SFRSs and corresponding

configurations. That is, values of the ACMR parameter will be different for 

archetype models of different SFRSs and corresponding configurations even 

when those SFRSs are seismic code compliant and, in concept, should have 

the same, acceptably low, MCER collapse probability. For the purpose of 

comparing the relative collapse performance of a given SFRS with and 

without a particular irregularity, it is deemed useful to compare the ratio of 

the values of the ACMR parameter for a given SFRS with and without a 

particular irregularity to 1.0 (i.e., compare ACMRirregular / ACMRbaseline to 1.0). 

Thus, the collapse performance of a given SFRS with and without a 

particular irregularity would be considered the same if the ratio of the ACMR
3-30 3: Archetype Design, Modeling, and Analysis Approach FEMA P-2012

values is 1.0, even if the ACMR parameter is relatively small or large (e.g., 

ACMRirregular / ACMRbaseline of 1.5/1.5 versus 2.0/2.0 versus 2.5/2.5). If the 

ratio of ACMR values is less than 1.0, that would indicate that the presence of 

the irregularity has caused a decrease in the building collapse resistance.

While the ratio ACMRirregular / ACMRbaseline is the primary metric for 

evaluating the effects that configuration irregularities (and the accompanying 

design requirements, where applicable) have on collapse resistance, the 

MCER probability of collapse was still monitored in this study. In some 

cases, where the MCER probability of collapse was extremely low, a larger 

reduction of ACMRirregular / ACMRbaseline was considered acceptable, due to the 

overall low collapse risk of the archetype design group. An additional use of 

computing the MCER probability of collapse was to provide a sanity check 

for the design and modeling approaches in this study; values of MCER for the 

baseline archetypes generally should (and did) fall within a range that is 

consistent with prior studies (e.g., 1%-15% for SDC Dmax designs, as seen in 

FEMA P695). 

3.4.6 Tracking of Non-Collapse Archetype Response Parameters

Nonlinear dynamic analyses were conducted on all models across the design 

space by applying the FEMA P695 far-field ground motions at increasing 

intensities until collapse (i.e., incremental dynamic analysis). The majority 

of the results presented in this report focus on collapse and IDR (e.g., Figure

3-20 and Figure 3-21). A number of other engineering demand parameters 

(EDPs) were tracked as well, including residual story drift ratios, roof drift 

ratio, residual roof drift ratio, peak floor accelerations and velocities, and 

peak column axial forces.

Each of the aforementioned EDPs are recorded for a broad range of 

intensities, up to the point of collapse. The set of EDPs for a given ground 

motion intensity is referred to as a “stripe.” As an example, Table 3-12

reports stripes at three key levels of ground motion intensity for the 12-story 

baseline RC special moment frame (SMF) designed for SDC Dmax: 1/3 MCE, 

2/3 MCE, and MCE. Note that the maximum story drift for this example

archetype building is 0.015 under design level motions (due to some 

conservatism in the design process), which is similar to the median drift at 

2/3 MCE of 0.018. 

The EDPs selected for tracking at each stripe level were selected by the 

project team that developed this report. In addition to providing detailed 

information to support the results of the study, these data are intended to also 

be made available for other future uses. It should be noted that these data are 
FEMA P-2012 3: Archetype Design, Modeling, and Analysis Approach 3-31 

non-collapse cases and they are not adjusted for spectral shape effects, so the 

reported values are likely to overestimate the response in cases where the 

ground motion demands have favorable spectral shapes (i.e., “high epsilon” 

cases) (as summarized in Appendix B of FEMA P695; FEMA, 2009). 

Figure 3-20 Collapse IDA, Baseline 12-story RC SMF.

Figure 3-21 Interstory Drift Ratio (IDR), Baseline 12-story 

RC SMF.

Table 3-12 Mean Stripe Results at Selected Intensities, Baseline 12 Story RC SMF

Engineering Demand Parameter 1/3 MCE 2/3 MCE MCE 

Fraction collapsed 0.00 0.02 0.20

IDR max all stories 0.011 0.018 0.028

IDR residual max all stories 0.003 0.007 0.017

Roof drift ratio (RDR) max 0.005 0.008 0.012

RDR residual max 0.001 0.003 0.006

Peak floor acceleration (PFA) max all stories, g 0.306 0.592 0.807

Peak floor velocity (PFV) max all stories, in./s 141 302 412

Peak column axial force max all columns, kips 1,031 1,072 1,071

Column shear force abs max all columns, kips 205 236 248

Column moment abs max all columns, kip-in. 16,410 21,438 22,837

FEMA P-2012 4: Buildings with Torsional Irregularities 4-1 

[H1, H6]

Chapter 4

Buildings with Torsional 

Irregularities [H1, H6]

4.1 Overview

This chapter summarizes the analytical studies for torsionally irregular 

buildings that were designed per ASCE/SEI 7-16, Minimum Design Loads 

and Associated Criteria for Buildings and Other Structures (ASCE, 2017a). 

The effects on building performance of the following torsional irregularities 

were studied: 

• H1, Torsional (stiffness) irregularity. This condition is a Type 1a or 

Type 1b horizontal irregularity, as defined in Table 12.3-1 of ASCE/SEI 

7-16. The torsional studies were mostly focused on this torsional 

irregularity, because it affects the design requirements for new buildings. 

• H6, Torsional (strength) irregularity. This condition is considered an 

irregularity per Section 7.3.1.1.4 in ASCE/SEI 41-17, Seismic Evaluation 

and Retrofit of Existing Buildings (ASCE, 2017b). This condition is not 

considered an irregularity in ASCE/SEI 7. It is included in this study to 

determine if this condition should be considered in ASCE/SEI 7. 

The following are covered in this chapter: (1) objectives of the torsional 

irregularities studies and overview of findings (Section 4.2); (2) methodology 

to assess torsion design provisions (Section 4.3); (3) archetype design space

(Section 4.4); (4) results (Section 4.5); and (5) conclusions and 

recommendations (Section 4.6). 

4.2 Objectives of Studies and Summary of Findings

The analytical torsion studies described in this chapter addressed two 

primary objectives: 

1. Determine the effectiveness of ASCE/SEI 7-16 torsion design 

requirements for preventing seismic-induced collapse of torsionally 

irregular buildings; and 

2. Propose modifications to the ASCE/SEI 7-16 torsion design 

requirements to address deficiencies and/or unnecessary sources of 

conservatism. 
4-2 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

4.2.1 Objective 1: Evaluate ASCE/SEI 7-16 Torsion Design 

Provisions

ASCE/SEI 7-16 seismic design provisions were evaluated systematically to 

address a number of questions relating to the effectiveness of the provisions 

for ensuring adequate collapse resistance of torsionally irregular buildings. 

This included studies to answer the following questions: 

• When are the ASCE/SEI 7-16 seismic provisions unconservative for 

torsionally irregular buildings? When are they conservative?

• How important are the various torsion design requirements (e.g., 

accidental torsion) for ensuring adequate collapse resistance? 

• Are certain prohibitions necessary (e.g., prohibition of buildings in 

Seismic Design Category (SDC) E and F with extreme torsional 

irregularity)? 

4.2.2 Objective 2: Propose Modifications to the ASCE/SEI 7-16

Seismic Torsion Provisions

In addition to evaluating existing provisions for seismic design of torsionally 

irregular buildings, the analytical torsion studies evaluated a number of 

potential revisions to the ASCE/SEI 7-16 requirements. The purpose of the 

proposed revisions is to improve the design process for torsionally irregular 

buildings without adding complexity to the existing ASCE/SEI 7-16 seismic 

provisions. The following were the specific focuses when considering 

potential modifications to ASCE/SEI 7-16: 

• Improve the design of buildings with configurations having inherently 

poor torsion performance, but without over-penalizing other 

configurations that already perform satisfactorily.

• Eliminate sources of unnecessary conservatism for designing torsionally 

irregular buildings. Where possible, this includes eliminating or relaxing 

the code triggers for prohibitions related to torsional irregularities. 

4.2.3 Summary of Findings

The study found that ASCE/SEI 7-16 torsion design provisions are generally 

conservative for most building configurations, with the exception of some 

buildings that rely heavily on the orthogonal lines of lateral resistance to 

resist building torsion (i.e., the lines of resistance orthogonal to the design 

earthquake force). It was also observed that the accidental torsion 

amplification (Section 12.8.4 of ASCE/SEI 7-16) and requiring drift and 

stability limits to be satisfied at the most critical building edge in torsionally 

irregular buildings (Section 12.8.6 of ASCE/SEI 7-16) are important design 
FEMA P-2012 4: Buildings with Torsional Irregularities 4-3 

[H1, H6]

requirements for ensuring adequate collapse resistance of torsionally 

sensitive buildings. 

Based on the findings of this study, the following modifications to 

ASCE/SEI 7-16 would prevent reductions in collapse resistance and make 

collapse capacity more consistent over a large range of building 

configurations and degrees of torsional irregularity: 

• Alter the triggers for requiring a redundancy factor of 1.3 in Section 

12.3.4.2 of ASCE/SEI 7-16 so that fewer buildings are affected.

• Consider the effects of the orthogonal ground motion component for 

designing buildings that are classified as torsionally irregular. 

• Classify buildings as torsionally irregular if more than 75% of their 

lateral strength is located on one side of the center of mass (CM). 

• Allow only the static method of applying accidental torsion (i.e., Section 

12.8.4 of ASCE/SEI 7-16) for buildings with extreme torsional 

irregularity. In other words, do not permit use of 5% mass offsets with

modal response spectrum analysis or linear response history analysis for 

such buildings. 

Based on the findings of this study, the following modifications to 

ASCE/SEI 7-16 would remove some current restrictions that were found to 

be conservative: 

• Do not prohibit extremely torsionally irregular buildings in SDC E and F, 

as long as the lateral system is proportioned according to the 

recommendations in this report. 

• Do not prohibit the equivalent lateral force (ELF) procedure on the basis 

of torsional irregularity. 

4.3 Methodology to Assess Torsion Design Provisions

Torsion design provisions were assessed by comparing the collapse 

resistance of torsionally irregular archetype buildings to the collapse 

resistance of a baseline archetype that is regular in plan. Ideally, the collapse 

resistance should remain relatively constant for varying levels of torsional 

irregularity. Of primary importance is ensuring that the collapse resistance 

does not decrease as the torsional irregularity increases. Of secondary 

importance, but still kept as a priority in this study, is avoiding excessive 

conservatism caused by torsion design requirements (i.e., the code 

requirements should not result in conservatively large increases in collapse 

resistance for torsionally irregular buildings). 
4-4 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

To measure torsional irregularity, this study utilized the Torsional 

Irregularity Ratio (TIR), which is the ratio of the maximum drift at a 

building’s edge to the average drift, given a lateral force with 5% eccentricity

as shown in Figure 4-1. This is identical to the ratio used for determining the 

presence of torsional irregularity in Table 12.3-1 of ASCE/SEI 7-16. Table 

12.3-1 classifies buildings as having a Type 1a torsional irregularity if the 

TIR is greater than 1.2 and Type 1b (extreme) torsional irregularity if the TIR

is greater than 1.4. 

Figure 4-1 Torsional Irregularity Ratio (TIR). 

Archetype buildings used in this study are represented by single-story, 

nonlinear three-dimensional models which were calibrated to represent the 

aggregate behavior of multi-story buildings. These models are described in 

detail in Appendix A. To use single-story representative models effectively, 

the following steps were taken:

1. The models were calibrated so that their design properties (e.g., drift and

stability coefficient) are consistent with that of a multi-story design. 

2. The nonlinear backbones of the single-story models were made to 

approximate the aggregate behavior of a multi-story building backbone. 

3. Nonlinear response history results for a set of single-story archetypes 

were validated through comparison to nonlinear response history results 

of three-dimensional multi-story models. 

Extensive information about modeling multi-story torsion responses with 

single-story models can be found in the literature (e.g., De Stefano and 

Pintucchi, 2008; Anagnostopoulos et al., 2010; Anagnostopoulos et al., 

2015). A key finding of these studies is that emulating the response of more 

realistic multi-story models is an essential step to gleaning meaningful results 

from single-story models, especially for torsional responses. This finding 
FEMA P-2012 4: Buildings with Torsional Irregularities 4-5 

[H1, H6]

informed the above steps taken to ensure that the single-story models

adequately emulated the behavior of the multi-story models. 

4.4 Archetype Design Space

4.4.1 Plan Configurations

More than 2,000 archetype models were analyzed under this study. The 

baseline configuration (Figure 4-2a) has a 1:1 plan aspect ratio with lines of 

lateral resistance (representing either shear walls or moment frames) along 

the perimeter. Archetypes with varying degrees of torsional irregularity were 

created by adjusting the aspect ratio of the building plan and varying the 

locations of the lines of lateral resistance, as illustrated in Figure 4-2b where 

α, β, δ, and γ indicate the location of each line of lateral resistance. 

 

(a) (b)

a 

b = a

 

αa 

βa 

γb δb 

b 

3 4 

1 

2 

Figure 4-2 Plan view of: (a) the baseline archetype configuration; and (b) a 

generic configuration. Thickened lines represent lines of lateral 

resistance. 

Plan configurations for the majority of the archetypes fall into three 

categories that make up the “core” archetype design space, illustrated in 

Figure 4-3: 

• Symmetric, “Sym.” Torsional irregularity was introduced by moving 

all of the seismic-force-resisting system (SFRS) lines toward the center 

of plan by increasing α, β, δ, and γ together, thereby decreasing the 

torsional stiffness of the system. Irregularity in the symmetric 

archetypes is due to torsional flexibility only, not inherent torsion. 

• Double asymmetric, “Double Asym.” These archetypes have inherent 

eccentricity in both orthogonal directions, due to shifting SFRS lines 1 

and 3 away from the building perimeter by increasing α and γ. Lines 2 

and 4 of the SFRS were kept at the perimeter.

• Single asymmetric, “Single Asym.” These archetypes have inherent 

eccentricity in only one direction, due to shifting line 3 of the SFRS 
4-6 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

away from the perimeter by increasing γ. Lines 1, 2, and 4 of the SFRS 

were kept at the perimeter. 

“1:1 Sym” α = β = δ = γ “2:1 Sym” α = β = δ = γ

“4:1 Sym” α = β = δ = γ

“1:1, Double Asym” 

(α = γ ≠ 0, β = δ = 0)

“2:1, Double Asym” (α = γ ≠ 0, 

β = δ = 0) 

“1:1, Single Asym” (γ ≠ 0, 

α = β = δ = 0)

“2:1, Single Asym” (γ ≠ 0, α = β = δ = 0)

“4:1, Single Asym” (γ ≠ 0, α = β = δ = 0)

Figure 4-3 Illustration of archetype configurations. Thickened lines 

represent lines of lateral resistance. 

In addition to the core archetype design space, an additional set of plan 

configurations were utilized to further expand the scope of building layouts 

(and associated irregularities) that were considered in the study. These 

additional configurations have 7:3 aspect ratio and are shown in Figure 4-4 
FEMA P-2012 4: Buildings with Torsional Irregularities 4-7 

[H1, H6]

and Figure 4-5. The “Mixed” archetype variants shown in Figure 4-4 were 

used to evaluate the effects of buildings that have a mixture of SFRSs 

consisting of reinforced concrete shear walls and reinforced concrete moment 

frames. In addition, Figure 4-5 shows building plans without a line of lateral 

resistance on one side, which are referred to as “three-sided” systems in this 

study. 

Figure 4-4 Illustration of “Mixed” archetype configurations.
4-8 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

Figure 4-5 Illustration of “three-sided” archetype configurations.

4.4.2 Baseline Archetypes

The baseline archetypes define three categories of buildings from which all 

of the other archetypes were derived, outlined as follows: 

• Short. The short baseline archetype defines a class of short-period

buildings with an upper bound design period, CuTa = 0.3 s, as defined in

ASCE/SEI 7-16, Section 12.8.2. The properties of this archetype were

calibrated to represent the behavior of a two-story wood shear wall

building. The “short” archetype baseline design was force-controlled
FEMA P-2012 4: Buildings with Torsional Irregularities 4-9 

[H1, H6]

(rather than drift-controlled), which is also the case for the majority of 

the torsionally irregular design variants. 

• Mid-rise. The mid-rise baseline defines a class of buildings with longer 

periods (CuTa = 2.0 s) whose designs were often controlled by drift limits 

and/or stability requirements as they became more torsionally irregular. 

The properties of this archetype were calibrated to represent a 10-12 

story reinforced concrete (RC) special moment frame (SMF) building, 

and it was verified to behave similarly to the 12-story RC SMF baseline 

building developed in Chapter 6. 

• Mixed. The mixed system archetypes were meant to represent a 

combination of special reinforced concrete shear walls (RC SW) and RC 

SMFs, either as a dual system or as a combination in accordance with 

Section 12.2.2 or 12.2.3 of ASCE/SEI 7. The baseline archetype for the 

mixed system represents a building whose SFRS is comprised solely of 

RC SWs. The properties of this baseline archetype were calibrated to 

represent the behavior of a mid-rise RC SW building (CuTa = 0.93 s), and 

it was verified to behave similarly to the 8-story RC SW buildings 

developed in Chapter 5. The RC SW parallel to the moment frame in the 

irregular archetypes started out stronger than the walls in the wall-only 

direction because it is stiffer than the frame and attracts more force. The 

lines of resistance representing RC SMFs are similar to the 8-story 

baseline RC SMF developed for the vertical irregularity studies in 

Chapter 6, except that they are weaker, because the frame is softer than 

the wall and attracts less force. 

Table 4-1 summarizes the key design properties of the baseline archetype 

models. For comparison, the design properties of the two-dimensional 

12-story RC SMF and 8-story RC SW baselines (from Chapters 6 and 5, 

respectively) are also provided in the table. For all archetype designs, 

including the baseline designs and the irregular variants, the period (T) for 

determining seismic base shear is taken as the minimum of T = CuTa and the 

fundamental period computed from the structural model in the direction of 

interest, but not less than the approximate period, Ta. Where the torsional 

mode contained significant modal mass in the translational direction, the 

fundamental period was taken as the longer of the lateral and torsional 

periods; this simplification is not recommended for design because it can 

result in smaller demands, but it is conservative regarding the conclusions 

that are drawn from this study. In the case of the mid-rise archetypes, the 

design base shear was often controlled by Equation 12.5 of ASCE/SEI 7-16 

which requires that the base shear be no less than 0.044SDS. Forces for 

computing drifts were determined using the fundamental period from the 
4-10 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

structural model, and a drift limit of 2% was used for all archetypes. The 

stability design requirements were also enforced in the design process, in 

accordance with Section 12.8.7 of ASCE/SEI 7-16. 

The nonlinear properties of the baseline models are discussed in detail in

Appendix A. It should be noted that, although the nonlinear properties are 

calibrated to match the macro-behavior of wood shear walls, RC frames, and 

RC walls, the purpose is not to study any one of these building systems 

specifically. Rather, the purpose of the various archetypes is to capture a 

range of global system behaviors that could affect the impacts of torsion 

design requirements (e.g., buildings with periods in the constant acceleration 

part of the spectrum and with low P-Delta sensitivity versus buildings with 

periods beyond the constant acceleration part of the spectrum with significant 

P-Delta effects). 

Table 4-1 Design Properties of Baseline Archetypes

Baseline Archetype

Period for Computing 

Design Forces [CuTa, s] 

Analytical 

Period [s] R Cd Cs Drift

Stability 

Coefficient (θ) 

Short 0.30 0.40 6.5 4 0.154 0.7% 0.01

Mid-rise 2.00 2.20(1) 8 5.5 0.044 1.2% 0.07

Comparison: 12-story RC SMF design 2.13 2.58 8 5.5 0.044 1.2%(2) 0.07

Mixed, Baseline has only RC walls 0.93 1.15 6(3) 5 0.108 0.7% 0.02

Comparison: 8-story RC SW 0.93 1.14 6 5 0.108 N/A N/A 

(1) The period of the mid-rise baseline archetype increases to 2.34 s if gravity loading and geometric effects are considered. For 

design, however, geometric effects are accounted for indirectly by dividing displacements by the quantity (1-θ), per Section 

12.8.7 of ASCE/SEI 7-16.

(2) The maximum drift in the 12-story RC SMF is 1.5% and occurs in the upper third of the building. The maximum drift in the 

bottom half of the building, 1.2%, is used for calibrating the simplified model, because that is the portion of the structure that 

experiences damage leading to collapse. 

(3) The RC SW baseline is designed with R = 6, but the mixed system variants are designed with R = 7 in the mixed direction 

and R = 6 in the RC SW direction.

4.4.3 Proportioning the Lateral System for Seismic Design

For each archetype, the properties of the four lines of lateral resistance were 

adjusted to meet strength, drift, and stability requirements, considering the 

effects of inherent torsion, accidental torsion, and any additional code 

requirements that apply (e.g., accidental torsion amplification). 

Two methods were used to proportion the lateral system to meet code 

requirements. Method 1 assumes that the designer can vary strength and 

stiffness of the SFRS independently (i.e., decoupled strength and stiffness)—

for example, an RC moment frame where altering the reinforcing ratio and/or 

section sizes allows strength and stiffness to be adjusted relatively 
FEMA P-2012 4: Buildings with Torsional Irregularities 4-11

[H1, H6]

independently. Method 2 assumes that strength and stiffness remain 

proportional (i.e., coupled)—for example, adding an additional wall to a 

shear wall building or adding an additional bay to a moment frame. In 

reality, most building systems are somewhere between the two extremes, 

(i.e., partially coupled). To bound the possible behaviors, this study used 

both the decoupled and coupled methods of scaling strength and stiffness of 

the SFRS. Therefore, the characteristics of most real structural systems fall 

within the bounds of the studied archetypes.

Method 1: Decoupled strength and stiffness

1. Start with the “baseline” lateral resistance. 

2. Adjust stiffness to meet drift requirements, if necessary.

3. Adjust strength to exactly meet strength requirements. Sometimes this 

results in a decrease in strength for certain lines of lateral resistance.

4. Adjust stiffness and/or strength to meet stability requirements, if 

necessary. 

Method 2: Coupled strength and stiffness

1. Start with the “baseline” lateral resistance. 

2. Scale strength and stiffness by exactly the same amount until strength, 

drift, and stability requirements are satisfied. Some lines of lateral 

resistance may have their strength and stiffness decreased.

4.5 Results

4.5.1 Collapse Performance under Current Code Requirements

Figure 4-6 and Figure 4-7 show the trends in collapse resistance with respect 

to the TIR for short and mid-rise archetypes designed according to ASCE/SEI 

7-16. The relative collapse resistance on the vertical axis is computed by 

dividing the adjusted collapse margin ratio (ACMR) of the variant archetype 

by the ACMR of the baseline archetype. A relative collapse resistance 

greater than 1.0 means that an archetype has better collapse resistance than 

the baseline configuration, and a value less than 1.0 indicates a reduction in 

collapse resistance. The horizontal axis shows the maximum TIR value for 

each variant design (i.e., maximum TIR for the two orthogonal directions), as 

computed in Table 12.3 of ASCE/SEI 7-16. The computed TIR value tends 

to saturate, and even decrease in some cases, with increased inherent 

eccentricity; this causes the trends for some archetype groups to “double 

back” on themselves (e.g., the 2:1 single asymmetric archetypes). This

“doubling back” behavior is explained in more detail in Appendix A. 
4-12 4: Buildings with Torsional Irregularities FEMA P-2012 

 [H1, H6] 

1 1.522.5

Max TIR of the Variant Archetype

0.8

1

1.2

1.4

1.6

1:1 Sym

2:1 Sym

4:1 Sym

1:1 Double Asym

2:1 Double Asym

1:1 Single Asym

2:1 Single Asym

4:1 Single Asym

Fitted Median

+/- 

Figure 4-6 Collapse resistance relative to the baseline for short codeconforming archetypes. Archetypes with decoupled strength 

and stiffness are represented by solid lines with markers; dashed 

lines with markers represent archetypes with coupled strength 

and stiffness. The moving median of all results, +/- one 

logarithmic standard deviation, is overlaid to illustrate the 

general trend. 

1 1.522.5

Max TIR of the Variant Archetype

0.8

1

1.2

1.4

1.6

1.8

1:1 Sym

2:1 Sym

4:1 Sym

1:1 Double Asym

2:1 Double Asym

1:1 Single Asym

2:1 Single Asym

4:1 Single Asym

Fitted Median

+/- 

Figure 4-7 Collapse resistance relative to the baseline for mid-rise codeconforming archetypes. Archetypes with decoupled strength 

and stiffness are represented by solid lines with markers; dashed 

lines with markers represent archetypes with coupled strength 

and stiffness. The moving median of all results, +/- one 

logarithmic standard deviation, is overlaid to illustrate the 

general trend. 

Generally, the collapse resistance of the irregular archetype buildings is 

higher than the collapse resistance of the baseline archetype; this is the result 

of torsion design requirements (e.g., accidental torsion amplification) 

somewhat overcompensating for the negative effects of the torsional 

irregularity. In some cases, however, the collapse resistance declines as 

torsional irregularity increases. An example case of declining collapse 

resistance is the 1:1 single asymmetric archetypes, where torsion moments 

are resisted primarily by lines of lateral resistance that are perpendicular to 

the lateral seismic force. Seismic demands in those lines of resistance result 
FEMA P-2012 4: Buildings with Torsional Irregularities 4-13

[H1, H6]

from lateral forces in both orthogonal directions, even though, the two lateral 

force components are decoupled in the design step, which leads to poor 

performance under bi-directional ground shaking. 

Looking closely at the results in Figure 4-6 and Figure 4-7, the immediate 

increase in collapse resistance for low values of TIR is due to triggering an 

increase in the redundancy factor (ρ) from 1.0 to 1.3, per Section 12.3.4.2 of 

ASCE/SEI 7-16. For simplicity in the design process of the archetypes, it is 

assumed that buildings with TIR > 1.2 do not comply with Table 12.3-3 of 

ASCE/SEI 7-16 and therefore get a redundancy factor of 1.3; systems that do 

comply with Table 12.3-3 would trigger ρ = 1.3 when TIR > 1.4. 

Figure 4-6 and Figure 4-7 provide the results for decoupled strength and 

stiffness (solid lines) and coupled strength and stiffness (dashed lines). In 

most cases, this design difference only minimally affects the collapse 

resistance. Exceptions are buildings that are heavily drift controlled (e.g., the 

2:1 Single asymmetric mid-rise archetypes shown in Figure 4-7). This 

comes from the fact that, for drift-controlled buildings, stiffening the SFRS

enough to satisfy drift limits results in significant overstrength for the 

coupled strength and stiffness design approach, making the building more 

resistant to collapse.

It is critical to note that torsionally irregular archetypes often outperform the 

baseline only because ASCE/SEI 7-16 requires that torsional effects be 

accounted for in the design, and the additional requirements tend to be 

conservative for many of the configurations studied. Assessments of 

torsionally irregular archetypes for which torsion design requirements are not 

followed confirm that torsionally irregular buildings can perform poorly if 

ASCE/SEI 7-16 safeguards for torsional effects are not properly considered 

in the design step. As an example, Figure 4-8 shows the performance of the 

mid-rise archetypes when the seismic torsion safeguards of ASCE/SEI 7-16 

are ignored in the design process; their collapse resistance declines steadily 

and substantially as the TIR increases.
1 1.522.5

Max TIR of the Variant Archetype

1.2

1

0.8

0.6

0.4

0.2

1:1 Sym

2:1 Sym

4:1 Sym

1:1 Double Asym

2:1 Double Asym

1:1 Single Asym

2:1 Single Asym

4:1 Single Asym

Fitted Median

+/- 

Figure 4-8 Trends in collapse resistance for mid-rise archetypes with 

torsional effects neglected in the design process. 

4.5.2 Observations about Torsion Design Requirements 

To quantify the effectiveness and necessity of the various torsion design 

requirements, a number of sensitivity studies were conducted to determine 

how the torsion design requirements affect the collapse resistance of the 

buildings. These studies and results are documented in Appendix A and 

some of the primary findings from these studies are as follows:

 Accidental torsion design requirements are relatively unimportant for 

torsionally regular buildings. This has been observed in past studies as 

well (e.g., DeBock et al., 2014). 

 Simulating accidental torsion effects using modal response spectrum 

analysis with 5% mass offsets is ineffective for torsionally sensitive 

buildings whose fundamental mode is a torsional mode with limited 

modal mass participation in the translational directions (see Section A.5 

in Appendix A for more detail). 

 When checking the drift limits and stability requirements for torsionally 

irregular buildings, measuring the drifts at the building edge rather than 

the center of mass, as required in Section 12.8.6 of ASCE/SEI 7-16, is 

important for ensuring adequate collapse resistance (see Section A.4 in 

Appendix A for more detail). 

 Buildings that rely heavily upon lines of lateral resistance perpendicular 

to the design earthquake force to resist torsion moments tend to be the 

poorest performers, because those lines of resistance also resist seismic 

demands in the perpendicular direction and therefore are “overworked” 

(e.g., see plot for 1:1 Single Asymmetric archetypes in Figure 4-6). For 

this type of building, the study shows that sufficient performance can be 

achieved by implementing the following: 

o Use a redundancy factor (ρ) of 1.3. 

4-14 4: Buildings with Torsional Irregularities FEMA P-2012 

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FEMA P-2012 4: Buildings with Torsional Irregularities 4-15

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o Apply 30% of the design lateral force simultaneously in the 

orthogonal direction, for computing member forces. 

• A torsional strength irregularity, defined by differing demand-to-capacity 

ratios on either side of the center of mass (per ASCE/SEI 41-17), does 

not negatively affect the performance of code-conforming buildings. 

This comes from the fact that a torsional strength irregularity in a codeconforming building only occurs when one side of the building is much 

stronger than required; if one side were too weak, it would no longer be 

code-conforming. A side-study, documented in Appendix A, shows that 

adding strength to one side of a building does not negatively affect 

collapse performance, but also does not provide much benefit in many 

cases. Similar conclusions may be true for some existing buildings, but 

these are outside of the scope of the present study. 

4.5.3 Recommended Minimum Requirements

This section outlines the minimum set of torsion design recommendations 

that were found to be needed to ensure adequate collapse safety of codecompliant buildings. These requirements are based on the analytical studies 

documented in this report, with the objective that the requirements provide 

consistent collapse resistance over a broad range of building configurations 

(i.e., ensure that collapse resistance does not decrease for torsionally irregular 

buildings, but also avoid adding conservatism in the design process, where 

possible). 

Table 4-2 lists suggested modifications to torsion requirements in ASCE/SEI 

7-16. These suggested modifications include both new requirements and 

recommendations for removing existing requirements, with the overall 

recommendations making the design requirements arguably slightly less 

restrictive than the current ASCE/SEI 7-16 requirements. As for added 

requirements, an additional trigger for torsional irregularity is recommended 

for cases where more than 75% of the lateral strength is on one side of the 

center of mass. 

Each of the proposed modifications to the ASCE/SEI 7-16 seismic torsion 

provisions, as outlined in Table 4-2, are summarized below with a brief 

explanation of how the changes to the requirements affect the collapse

performance of torsionally irregular buildings. 

• Require 100%-30% orthogonal load combination for computing 

seismic design forces in torsionally irregular buildings. Adding this 

requirement increases the design force on lines of lateral resistance that 
4-16 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

Table 4-2 Recommended Modifications for ASCE/SEI 7-16 to Achieve Minimum Torsion Design 

Requirements Resulting in Adequate Collapse Resistance for a Broad Range of Building 

Configurations

Torsional Irregularity 

Classification

Triggering Criteria 

for the Irregularity Add Requirements Remove Requirements

Type 1a. Torsional irregularity -TIR > 1.2

-Add additional trigger if

>75% of strength on one

side of the CM.

- Use 100%-30% orthogonal 

load combination rule

-N/A 

Type 1b. Extreme torsional 

irregularity

-TIR > 1.4 - Use 100%-30% orthogonal 

load combination rule

- Automatic ρ = 1.3

- SDC E and F prohibition

- ELF prohibition

Handle with code text (i.e., 

not a defined irregularity 

category)

If one or more of the following 

occurs:

- TIR > 1.4 in both orthogonal 

directions 

- Lines of lateral resistance all 

on same side of CM

- Use 100%-30% orthogonal 

load combination rule

- ρ = 1.3

- SDC E and F prohibition

- ELF prohibition

resist a significant portion of the torsional moment from the lateral 

earthquake force in the orthogonal direction. The benefits of adding this 

requirement are most apparent in the 1:1 Single Asymmetric archetypes. 

To achieve the appropriate design safeguard, the 100%-30% orthogonal 

load combination rule need not be considered for story drift calculations. 

• Trigger Type 1a torsional irregularity if more than 75% of story

strength is on the same side of the center of mass. This 

recommendation results from observing that buildings with significant 

inherent eccentricity can still have TIR < 1.2 (i.e., not be classified as 

torsionally irregular according to Table 12.3-1 in ASCE/SEI 7-16) where

there is significant torsional stiffness from lines of lateral resistance in 

the orthogonal direction. For such buildings, the lines of lateral 

resistance orthogonal to the direction with inherent eccentricity resist the 

majority of the torsional moment and triggering the 100%-30% 

orthogonal load combination rule is necessary for proportioning those 

elements. Without this requirement, some of the three-sided and mixed 

system variants with TIR < 1.2 would perform significantly worse than 

the baseline archetypes (with examples presented in Section A.4 of 

Appendix A).

• Relax the triggers requiring ρ = 1.3. ASCE/SEI 7-16 requires that all 

buildings classified as extremely torsionally irregular have a redundancy 

factor of 1.3, regardless of whether the system is redundant. While some 

torsionally irregular buildings need the benefit of the 30% increase in 

design force, not all do. Only building configurations with TIR > 1.4 in 

both directions or with a large inherent eccentricity (e.g., lines of lateral 
resistance all on the same side of the CM), are found to need the 30% 

increase in design lateral force. 

 Remove prohibition of the ELF design procedure. The archetype 

buildings in the torsion study where designed using the equivalent lateral 

force (ELF) design procedure (for design displacements and distribution 

of design forces), and their performance was shown to be satisfactory 

when the proposed design provisions are implemented (see Figures 4-9, 

4-10, and 4-11). Additionally, the vertical irregular studies in this report 

show that the ELF procedure generally results in more conservative 

vertical distributions of seismic forces, leading to better collapse 

resistance as compared with design using modal response spectrum 

analysis (e.g., Appendix F and Chapter 6). Therefore, the ELF procedure 

should not be prohibited on the basis of a torsional irregularity. 

1 1.522.5

Max TIR of the Variant Archetype

0.8

1

1.2

1.4

1.6

1:1 Sym

2:1 Sym

4:1 Sym

1:1 Double Asym

2:1 Double Asym

1:1 Single Asym

2:1 Single Asym

4:1 Single Asym

Fitted Median

+/- 

1 1.522.5

Max TIR of the Variant Archetype

0.8

1

1.2

1.4

1.6

3-sided, Sym

3-sided, Asym A

3-sided, Asym B

Fitted Median

+/- 

Figure 4-9 Collapse resistance relative to the baseline for short archetypes 

designed with the proposed minimum standards. Archetypes 

with decoupled strength and stiffness are represented by solid 

lines with markers; dashed lines with markers represent 

archetypes with coupled strength and stiffness. The moving 

median of all results, +/- one logarithmic standard deviation, is 

overlaid to illustrate the general trend. 

FEMA P-2012 4: Buildings with Torsional Irregularities 4-17

 [H1, H6] 
1 1.5 2 2.5

Max TIR of the Variant Archetype

0.8

1

1.2

1.4

1.6

1:1 Sym

2:1 Sym

4:1 Sym

1:1 Double Asym

2:1 Double Asym

1:1 Single Asym

2:1 Single Asym

4:1 Single Asym

Fitted Median

+/- 

Figure 4-10 Collapse resistance relative to the baseline for mid-rise archetypes, 

designed with the proposed minimum standards. Archetypes with 

decoupled strength and stiffness are represented by solid lines with 

markers; dashed lines with markers represent archetypes with 

coupled strength and stiffness. The moving median of all results, +/- 

one logarithmic standard deviation, is overlaid to illustrate the 

general trend. 

1 1.5 2 2.5

Max TIR of the Variant Archetype

0.8

1

1.2

1.4

1.6

Mixed, Sym

Mixed, Asym A

Mixed, Asym B

Fitted Median

+/- 

Buildings tuned to avoid 

torsion req’s by making 

TIRmax<1.2 and <75% of 

strength same side of CM 

Building tuned to 

avoid ρ=1.3 by 

making TIRmin<1.4 

Figure 4-11 Collapse resistance relative to the baseline for mixed system 

archetypes, designed with the proposed minimum standards. 

Archetypes with decoupled strength and stiffness are 

represented by solid lines; dashed lines represent archetypes 

with coupled strength and stiffness. The moving median of all 

results, +/- one logarithmic standard deviation, is overlaid to 

illustrate the general trend. 

4-18 4: Buildings with Torsional Irregularities FEMA P-2012 

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FEMA P-2012 4: Buildings with Torsional Irregularities 4-19

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• Require that the accidental torsion loading be computed using a 

static accidental torsional moment when designing buildings with 

extreme torsional irregularity. This recommendation is that, when a 

building with extreme torsional irregularity is designed using linear 

design methods, the accidental torsion loading must be accounted for by 

applying a static accidental torsional moment in accordance with 

Sections 12.8.4.2 and 12.8.4.3 of ASCE/SEI 7-16. It should not be 

permitted to use explicit 5% mass offsets in linear dynamic analysis for 

buildings with extreme torsional irregularity. This recommendation is 

based on the finding that modal response spectrum analysis with 5% 

mass offsets produces unsafe designs for extremely torsionally irregular 

buildings whose torsional modes contain little modal mass in the 

translational direction (e.g., the symmetric archetypes, as shown in 

Section A.5 of Appendix A). This finding is consistent with a previous 

study by De la Llera and Chopra (1994), which illustrated that modal 

response spectrum analysis with 5% mass offsets does not adequately 

amplify accidental torsion effects for buildings with long torsional 

periods. 

• Remove prohibition of extremely torsionally irregular building 

configurations in SDC E and F. If the torsion design provisions 

recommended in this study are utilized, the study shows no reduction in 

collapse resistance for TIR > 1.4 (the cut-off for Type 1b extreme 

torsional irregularity in Table 12.3-1 of ASCE/SEI 7-16) for SDC D 

building designs; therefore, there is no need to prohibit such buildings in 

SDC D. To verify whether this conclusion could be extended to SDC E 

and F, the archetype models were also analyzed with 12 ground motion 

pairs from the FEMA P695 near-field ground motion set having pulse 

characteristics, since the seismic hazard for SDC E and F sites is 

dominated by near-field ground motions. The near-field motions with 

pulses caused all of the archetypes to collapse at lower spectral 

acceleration intensities as compared with the far-field motions; however, 

the trends in relative collapse resistance with TIR were nearly identical to 

those observed with the far-field ground motion set. This demonstrated 

that torsionally irregular buildings still perform equivalently with the 

baseline archetypes (and often somewhat better than), even when 

subjected to pulse-type ground motions. It should be noted that the 

FEMA P695 near-field record set has a broad range of spectral shapes, as 

does the far-field set, therefore the similarity in trends among the two 

ground motion record sets is expected. A significant benefit of removing 

the prohibition of extremely torsionally irregular buildings is that very 

strong and stiff buildings with large plan aspect ratios would no longer 
4-20 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

be prohibited. Such buildings are expected to perform well under 

seismic demands but are often classified as extremely torsionally 

irregular according to Table 12.3-1 of ASCE/SEI 7-16 simply based on 

relative stiffness, regardless of how strong and stiff they are in an 

absolute sense. In a side-study, it was found that such buildings still 

need the proposed force requirements (e.g., the 100%-30% lateral 

seismic load application rule), but they should not be prohibited. With 

the proposed modifications, it is recommended that these buildings no 

longer be prohibited. 

To assess the results of the proposed torsion requirements, Figure 4-9 

through Figure 4-11 provide relative collapse safety results for archetype 

buildings designed with the Table 4-2 modifications. These figures show 

that the performance of the irregular buildings is generally better than that of 

the baseline, even when the TIR is significantly greater than the threshold for 

extreme torsional irregularity (TIR > 1.4). The lowest observed ACMR is 

approximately 90% of the baseline (i.e., a 10% decrease), which is for the 

worst case of a three-sided mid-rise variant with decoupled strength and 

stiffness; this result is annotated in Figure 4-10. However, the proposed 

torsion provisions are still considered satisfactory, even for that archetype, 

for two reasons: 

1. The base shear for computing drifts is based on the fundamental period

of 2.57 s, however, the fundamental mode of vibration is torsionally

dominated. The mode with the most modal mass in the translational ydirection has a significantly shorter period of 0.8 s. In practice, the 

period with the most modal mass should be considered the fundamental 

period for calculating base shear. Allowing the use of the approximate 

period per Section 12.8.2 of ASCE/SEI 7-16, the design period in the ydirection could be taken as T = Ta = 1.45 s. In that case, the base shear 

for computing drifts increases by 80%, raising the design drift to 2.9% in 

the y-direction (well above the 2% limit). Redesigning the archetype 

accordingly results in an ACMR that is within 5% of the baseline ACMR. 

2. The observed 10% reduction in collapse resistance is small, given that it 

only occurs for one archetype. For context, a 10% reduction in ACMR

causes a building with 10% probability of collapse given MCER to 

change to 14% probability of collapse given MCER; this falls within the 

tolerance of the FEMA P695 guidelines, which allow up to a 20% 

probability of collapse given MCER for an individual archetype, even 

though 10% is the upper limit for the average of a group of archetype 

buildings. 
FEMA P-2012 4: Buildings with Torsional Irregularities 4-21

[H1, H6]

4.6 Conclusions and Recommendations

Based on analyses of a broad set of archetype building designs, this chapter 

suggests modifications to the torsional-irregularity design requirements of 

ASCE/SEI 7-16. The modifications include both removing some existing 

requirements to reduce conservatisms and also adding some new 

requirements that were necessary to ensure adequate collapse safety.

The following lists ASCE/SEI 7-16 design requirements that were found to 

add unnecessary conservatism to the design process and are proposed to be 

removed: 

• Prohibition of extremely torsionally irregular buildings in Seismic 

Design Categories E and F. Such buildings need not be prohibited, 

provided that the recommended modifications to the ASCE/SEI 7-16 

seismic design procedures are implemented. 

• Prohibition of the equivalent lateral force procedure. The equivalent 

lateral force procedure is shown to produce safe designs for torsionally

irregular buildings and need not be prohibited on the basis of torsional 

irregularity.

• Triggers for making the redundancy factor, ρ, equal to 1.3. If the 

100%-30% load combination rule is utilized as this study suggests, the 

additional amplification of seismic forces caused by the redundancy 

factor is not always necessary. Therefore, the triggers for making the 

redundancy factor, ρ, equal to 1.3 can be relaxed. 

The following lists new proposed design requirements that are not currently 

in ASCE/SEI 7-16 but are necessary to ensure adequate collapse 

performance of buildings with torsional irregularities: 

• Require a 100%-30% lateral load combination rule for computing design 

forces in torsionally irregular buildings. This elevates the performance 

of buildings that rely heavily on lines of lateral resistance orthogonal to 

the design earthquake force to resist torsion moments. Effects on 

buildings with little to no inherent eccentricity are minimal. Note that 

the 100%-30% lateral load combination is not necessary for evaluating 

story drifts. 

• Classify buildings as Type 1a torsionally irregular if more than 75% of 

the story strength is on the same side of the center of mass. Some 

buildings with large inherent eccentricity can still fall below the 

ASCE/SEI 7-16 threshold for Type 1a torsional irregularity. For such 

buildings, the seismic response in the two orthogonal directions is highly 
4-22 4: Buildings with Torsional Irregularities FEMA P-2012

[H1, H6]

coupled, so triggering the 100%-30% orthogonal combination rule is 

important.

• Require application of a static accidental torsional moment, Mta, (i.e., 

Sections 12.8.4.2 and 12.8.4.3 of ASCE/SEI 7-16) for buildings with 

extreme torsional irregularity. In other words, do not permit use of 

explicit 5% mass offsets in linear dynamic analysis of such buildings. 

It is also found that special treatment of buildings with “torsional strength 

irregularity,” as defined by demand/capacity ratios in ASCE/SEI 41, is not 

necessary for new building design. 
FEMA P-2012 5: Concrete Wall Buildings with 5-1 

Vertical Irregularities [V1, V8]

Chapter 5 

Concrete Wall Buildings with

Vertical Irregularities [V1, V8] 

5.1 Overview and Summary of Findings

This chapter summarizes the analytical studies for reinforced concrete (RC) 

wall buildings that were designed per ASCE/SEI 7-16, Minimum Design 

Loads and Associated Criteria for Buildings and Other Structures (ASCE, 

2017a). The effects on building performance of the following vertical 

irregularities were studied: 

• V1, Soft story irregularity. This condition is Type 1 vertical 

irregularity, as defined in Table 12.3-2 of ASCE/SEI 7-16. The RC wall 

building studies were mostly focused on this irregularity and it is the 

subject of most of this chapter. 

• V8, Wall discontinuity. This condition is not defined as a vertical 

irregularity in current U.S. codes and standards. It is defined in this 

report as a condition where there is an abrupt discontinuity or large 

variance of stiffness along the height of a shear wall. Discussion of this

vertical irregularity is covered in Section 7.6 and a description of a 

limited study conducted on this irregularity is provided in Section B.2. 

The following are covered in this chapter: (1) summary of current design 

procedures for walls and commonly observed vertical irregularities (Section 

5.2); (2) an overview of archetype designs to investigate the impact of 

vertical irregularities (Section 5.3); (3) information related to the modeling 

approach (Section 5.4); (4) an overview of the collapse risk assessment and 

corresponding results (Section 5.5); and (5) conclusions and 

recommendations (Section 5.6). Details supporting the information in this 

chapter, including the RC wall building design process, modeling details, and 

detailed analysis results, are provided in Appendix B. 

The results of the studies described in this chapter show that: (1) the collapse 

risk posed by RC wall buildings, in which walls respond in flexure, is 

relatively low whether or not the system is irregular and whether or not 

failure of the gravity system is considered in the analysis; (2) collapse risk 

does not vary significantly (less than 20%) with the introduction of a vertical 

stiffness irregularity if the collapse risk posed by the baseline wall is not 
5-2 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

excessively small (less than 0.11%); and (3) the use of different modeling 

approaches does not significantly affect collapse risk.

5.2 Design Procedures and Common Irregularities

Reinforced concrete walls are commonly used to resist lateral forces from 

earthquakes and wind. They provide high stiffness and strength under 

service-level loads, can be detailed to provide ductility under design-level 

earthquake loads, and can take on many configurations, including the 

introduction of isolated openings to accommodate architectural requirements. 

Figure 5-1 shows regular and irregular vertical configurations for wall 

systems and Figure 5-2 shows common cross-sectional configurations for 

walls. 

Wall cross section is largely a function of architectural layout. Mid- to highrise buildings typically have walls located around a central service or 

elevator core as illustrated in Figure 5-3. Typically, the core walls are 

arranged to form a closed box, with C, L, or rectangular piers that are 

connected by coupling beams extending over wall openings (Figure 5-2d). 

In low-rise buildings or buildings without a central elevator core, it is 

common to have walls distributed throughout the floor plate as the location 

and shape of the walls is typically constrained by the architectural layout. 

Planar walls (Figure 5-2b) and asymmetric wall configurations are typically 

used, with the L-shape wall layout being the most common asymmetric wall 

configuration. Irregular patterns of openings may be introduced into the wall 

configurations shown in Figure 5-1c to accommodate architectural 

requirements. 

(a) Cantilever wall (b) Coupled wall (c) Walls with vertical irregularities

Figure 5-1 Vertical wall-system configurations (a,b from NIST, 2011). 
FEMA P-2012 5: Concrete Wall Buildings with 5-3 

Vertical Irregularities [V1, V8]

(a) Rectangular shape (b) “Bar bell” shape

(c) Flanged walls in common T, L, C, and I shapes

(d) Possible configuration of a core-wall

Figure 5-2 Common wall cross-sectional configurations 

(NIST, 2011).

 (a) Core wall (b) Distributed planar and flanged walls

Typical

“gravity column”

Typical

Flanged Walls

Figure 5-3 Core wall versus distributed planar and flanged walls. 

Design of continuous flexural concrete walls used as the primary lateralload-resisting system includes: 

• Determination of longitudinal reinforcement required for flexural 

demand. Often much of this reinforcement is concentrated at the ends of 

the walls as it is the optimal location for flexural resistance. These 

regions are referred to as boundary elements in ACI 318-14, Building 

Code Requirements for Structural Concrete (ACI, 2014). 

• Sizing and detailing of confining reinforcement. 

• Design of horizontal reinforcement to meet the shear demand. ACI 

318-14 allows use of a larger strength-reduction factor to calculate shear 

strength if the shear demand corresponds to plastic hinging (ACI, 2014). 
5-4 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

For walls with discontinuities, the design process also requires an adequate 

load path around the discontinuity (ACI, 2014) and placement of reinforcing 

steel to resist loads and ensure capacity through multiple load cycles. This is

further discussed in NIST GCR 11-917-11REV-1, Seismic Design of Cast-inPlace Concrete Special Structural Walls and Coupling Beams (NIST, 2011). 

5.3 Overview of Archetype Designs 

To investigate the impact of vertical irregularities on the earthquake 

performance of mid-rise RC wall buildings, a series of RC wall buildings 

were designed in which lateral loads are resisted by planar reinforced 

concrete walls. An overview of the baseline design (i.e., no vertical 

irregularities) is presented in Chapter 3; details of the design process and all 

wall designs are provided in Appendix B. 

Walls were designed without openings and then with openings located at the 

1st, 1st and 2nd, and an upper story. Opening length was determined to 

achieve a stiffness for the stories with the opening that was either 50% of the 

baseline building or 75% of the baseline building; Section B.3 presents the 

process used to compute story stiffness. Wall demands were determined 

using the ASCE/SEI 7-16 ELF procedure and, for the case of the Dmax design 

spectrum, using the results of a MRSA procedure (ASCE, 2017a). Table 5-1 

presents the design space. 

Table 5-1 Design Space for RC Wall Buildings

Number of 

Designs Stories

Method Used 

to Determine 

Demands

Design 

Spectrum Used 

for Design Stories with Openings

Stiffness of Floor with 

Opening Normalized by 

Stiffness of Floor Above

6 8 ELF Dmax None, 1st, 1st & 2nd, 5th 50% and 75%(1)

5 8 MRSA Dmax None, 1st, 1st & 2nd 50% and 75%

6 8 ELF Bmax None, 1st, 1st & 2nd, 5th 50% and 75%(1)

6 12 ELF Dmax None, 1st, 1st & 2nd, 8th 50% and 75%(1)

6 12 ELF Bmax None, 1st, 1st & 2nd, 5th 50% and 75%(1)

(1) For buildings with openings on the 5th or 8th story, only the case of a wall with an opening producing a section 

stiffness equal to 50% of the section stiffness on adjacent walls was considered.

Figure 5-4 shows elevation views for the 8-story RC wall buildings; 12-story 

elevations are similar. For Dmax designs, an opening of 2.5 ft. was used to 

create a story stiffness equal to 75% of the stiffness of the baseline building 

and an opening of 7.5 ft. was used to create a story with a stiffness equal to 

50% of the story stiffness of the baseline building. For Bmax designs, 
FEMA P-2012 5: Concrete Wall Buildings with 5-5 

Vertical Irregularities [V1, V8]

openings of 1.5 ft. and 5 ft. were used, respectively, to create story stiffnesses 

equal to 75% and 50% of the story stiffnesses of the baseline building. 

(a) (b) (c) (d)

Figure 5-4 Idealized building elevations (a) without openings; (b) with openings in 

1st story; (c) with openings in 1st and 2nd stories; and (d) with openings 

in upper stories (5th for 8-story building, shown here, and 8th for 12-

story building). 

Each RC wall building design has a unique identification tag that includes 

information about all relevant design characteristics. The 8-story RC wall 

building designed using the MRSA method to determine demands for the 

Dmax spectrum with no wall openings is identified as 8-D-0-0-MRSA while 

the 12-story RC wall building designed using the ELF procedure to 

determine demands for the Dmax spectrum with openings in the 1st and 2nd

stories to produce a story stiffness equal to 50% of the 3rd story is identified 

as 12-D-2S-50-ELF. Table 5-2 provides seismic design parameters for the 

RC wall buildings.

Table 5-2 RC Wall Building Periods and Base Shear Demands 

Design ID

Period(s)

from MRSA CuTa [s]

Base Shear Demand: 

Earthquake

Base Shear

Demand: Wind

8-D-0-0-* 1.14 0.93 0.11W

8-D-*-*-* 1.14 – 1.18 0.93 0.11W

8-B-0-0-* 2.03 1.12 0.01W 0.02W

8-B-*-*-* ~2.03 1.12 0.01W 0.02W

12-D-0-0-* 2.41 1.25 0.08W

12-D-*-*-* 2.41 – 2.42 1.25 0.08W

12-B-0-0-* 3.07 1.15 0.01W 0.02W

12-B-*-*-* ~3.07 1.15 0.01W 0.02W

Individual walls were designed to achieve required strength and stiffness and 

were detailed to achieve deformation capacity per ACI 318-14 (ACI, 2014). 
5-6 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

Specified material strengths used for design were cf ′ = 5000 ksi and fy = 60 

ksi. Walls were sized to achieve required strength and stiffness and to keep 

longitudinal reinforcing ratios in heavily reinforced boundary element 

regions below 3%. Appendix B provides detailed design information for the 

8-story baseline shear wall building designed using the ASCE/SEI 7-16 ELF 

procedure (8-D-0-0-ELF) and provides all 8- and 12-story wall designs. 

Design of the baseline 8-story RC wall building (8-D-0-0-ELF) resulted in 

walls 30 ft. long by 2 ft. thick. At the base, the wall included 6 ft. long 

boundary elements with 2.5% longitudinal reinforcement ratios, web region 

longitudinal and horizontal reinforcement was approximately equal to the 

ACI 318-14 minimum of 0.25%, and maximum shear stress demand was

1.9 cf psi. To facilitate comparison of the different wall designs, the 30 ft. 

by 2 ft. gross wall dimensions were maintained for all 8-story wall designs. 

Table 5-3 provides relevant design details for all 8-story wall designs, with: 

• ρBE equal to the boundary element longitudinal reinforcement ratio at the 

base of the wall (two values are provided by walls with openings as 

different reinforcement ratios are provided for boundary elements on the 

interior and exterior of the wall pier); 

• ρweb and ρh equal to the web region longitudinal and horizontal 

reinforcement ratios at the base of the wall;

• ρh_opening equal to the horizontal reinforcement ratio in the wall above the 

openings; and 

• ρCB equal to the coupling beam diagonal reinforcement ratio (total 

diagonal or horizontal bar area divided by coupling beam cross-sectional 

area).

Table 5-3 Design Properties for RC Walls 

Wall ID

Opening 

Length

[ft.]

Boundary 

Element 

Length

[ft.]

ρBE

[%]

ρweb

[%]

ρh 

[%]

ρh_opening

[%]

ρCB

[%]

8-D-*-*-ELF walls are 30 ft. long by 2 ft. thick

8-D-0-0-ELF - 6 2.5 0.25 0.25 - -

8-D-1S-75-ELF 2.5 5 3.5 0.25 0.25 0.65 -

8-D-1S-50-ELF 7.5 5 3.7 0.25 0.25 0.42 -

8-D-2S-75-ELF 2.5 5 3.7 0.25 0.25 0.65 0.71 (diag)

8-D-2S-50-ELF 7.5 5 3.9 0.25 0.25 0.65 0.87 (diag)

8-D-5S-75-ELF 2.5 6 2.5 0.25 0.25 0.25 -

8-D-5S-50-ELF 7.5 6 2.5 0.25 0.25 0.25 -
FEMA P-2012 5: Concrete Wall Buildings with 5-7 

Vertical Irregularities [V1, V8]

Table 5-3 Design Properties for RC Walls (continued)

Wall ID

Opening 

Length

[ft.]

Boundary 

Element 

Length

[ft.]

ρBE

[%]

ρweb

[%]

ρh 

[%]

ρh_opening

[%]

ρCB

[%]

8-B-*-*-ELF walls are 20 ft. long by 2 ft. thick

8-B-0-0-ELF - - 0.25 0.25 0.25 - -

8-B-1S-75-ELF 1.5 - 0.25 0.25 0.25 0.25 -

8-B-1S-50-ELF 5.0 - 0.25 0.25 0.25 0.25 -

8-B-2S-75-ELF 1.5 - 0.25 0.25 0.25 0.25 -

8-B-2S-50-ELF 5.0 - 0.25 0.25 0.25 0.25 -

8-B-5S-75-ELF 1.5 - 0.25 0.25 0.25 0.25 -

8-B-5S-50-ELF 5.0 - 0.25 0.25 0.25 0.25 -

5.4 Modeling RC Wall Response

An overview of the modeling approach for studies covered in this report is 

provided in Section 3.3. The following sections provide more details on 

specific aspects particular to the RC wall building studies. 

5.4.1 Methodology Validation and Comparison Studies 

Both ATENA and OpenSees were used in modeling RC wall buildings for 

this study. Nonlinear models of the RC wall buildings were constructed by 

using finite elements in ATENA (for validation purposes only) and by using 

three different methods in OpenSees, as follows: (1) force-based beamcolumn elements (FBE) with fiber-type section models and the distributed 

plasticity modeling approach developed by Pugh et al. (2015); (2) 

displacement-based beam-column elements (DBE) with fiber-type section 

models and the distributed plasticity modeling approach developed by Pugh 

et al. (2015) and updated by Marafi et al. (2018); and (3) the shear-flexureinteraction multi-vertical line-element model (SFI-MVLEM) developed by 

Kolozvari et al. (2015a,b; 2018). 

Studies validating the modeling approaches for RC wall buildings (against 

experimental data for a large dataset) are described in detail in Section B.4. 

These studies show that the modeling approach provides accurate simulation 

of planar wall response to lateral loading, including onset of lateral strength 

loss for walls that respond in flexure. Similar comparisons for the SFIMVLEM shows accurate simulation of stiffness and strength; this model was 

calibrated to provide simulation of drift capacities that were similar to those 

predicted using the beam-column elements.
5-8 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

Preliminary analyses were conducted using all modeling methods for the 

purposes of validating and comparing the different analysis methods. These 

included: (1) pushover analyses to compare OpenSees to ATENA models; 

(2) dynamic analyses to compare DBE and FBE models in OpenSees; and 

(3) dynamic analyses to compare DBE models and SFI-MVLEM in 

OpenSees. Details of these comparison and validation studies are provided 

in Section B.5. These comparison studies showed significant differences in 

drift capacity, and to a lesser extent stiffness and strength of an RC wall 

building, depending on the method used. These differences could be 

expected to affect the assessment of collapse risk for RC wall buildings and, 

in particular, the impact of vertical irregularities resulting from the 

introduction of openings on this risk. The OpenSees DBE modeling 

approach was selected for the use in the study because:

• The ATENA model, which likely provides the most accurate simulation 

of response, is not practical for dynamic analyses due to the 

computational time required to complete the continuum analyses. 

• The OpenSees FBE modeling approach exhibits failures of the numerical 

solution algorithm that result in an inaccurate and reduced calculation of 

collapse risk. 

• The OpenSees SFI-MVLEM has not be extensively validated for use in 

simulating response beyond onset of strength loss. 

• The OpenSees DBE modeling approach has been extensively validated 

for simulation of onset of strength loss, provides plausible simulation of 

response following onset of strength loss (minimal experimental data 

exist for validation), and provides the greatest numerical robustness and 

efficiency.

5.4.2 Non-Simulated Failure Modes 

The OpenSees and ATENA modeling approaches described in Appendix B 

have been shown to provide accurate simulation of onset of lateral strength 

loss due to compression-controlled flexural failure, which is the most 

common failure mode observed in the laboratory for concrete walls. 

However, building collapse is defined by loss of gravity load carrying 

capacity, not loss of lateral load carrying capacity. Loss of lateral load 

carrying capacity can produce loss of gravity load carrying capacity if large 

story drifts result in instability. However, instability due to P-Delta effects 

may require very large story drifts. Consideration of the gravity system in a 

RC wall building suggests that failure of the gravity system will likely cause 

collapse long before wall instability. Thus, it is necessary to consider the 

non-simulated failure mode of collapse of the gravity load system. 
FEMA P-2012 5: Concrete Wall Buildings with 5-9 

Vertical Irregularities [V1, V8]

Most of the gravity load was assumed to be carried by a two-way reinforced 

concrete “slab-column” gravity system. Slab-column systems must transfer 

shear and moment at the column-slab connection. Typically, these systems 

utilize continuous longitudinal reinforcement of the slab through the column. 

The primary damage mode of flat-slab-to-column connections is punching 

shear. The reinforcement serves to sustain the moment demands resulting 

from vertical and lateral loading. For severely damaged slabs, catenary 

action is needed to prevent full collapse of the floor system (Figure 5-5b). 

Figure 5-5a shows a collapsed building for which catenary action did not 

occur in the exterior connections, demonstrating the need to limit damage to 

slab-column connections to prevent structural collapse. One of the most 

common solutions to increase the strength and deformability of slab-column 

connections is to strengthen the region prone to punching shear. Solutions 

include: (1) addition of shear reinforcement; (2) addition of internal shear 

studs; (3) addition of external shear studs; and (4) addition of column capital. 

Although column capitals have been shown to improve the performance (see, 

for example, Wey and Durrani, 1992), they are typically not desired for

architectural reasons and have fallen out of favor. Instead, engineers have 

sought solutions to improve the response with internal reinforcement. Hueste 

et al. (2009) collected test data to compare the drift capacity of slab-column 

connections with and without shear reinforcement (“improved” specimens 

had either traditional shear reinforcement or internal shear studs, as shown in 

Figure 5-6). In general, the response improved only a modest amount for 

low shear ratios, but a more significant drift capacity is noted for connections 

with higher shear ratios; this can be demonstrated by comparing the markers 

in the two plots. 

(a) (b)

Figure 5-5 Typical response of slab-column connections: (a) collapse of building with 

slab-column connections; (b) catenary action in exterior slab-column 

connection (Pan and Moehle, 1992). 
5-10 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

(a)

(b)

Figure 5-6 Drift of slab-column connections (a) without and (b) 

with shear reinforcement (Hueste et al., 2009). 

As stated above, gravity loads were assumed to be carried primarily by a 

two-way reinforced concrete slab-column system. The assumption is 

extended to include a two-way reinforced concrete slab-column system in 

which shear reinforcement is provided at the column-slab connection. As 

such, the data in Figure 5-6 indicate that the system could be expected to lose 

gravity load carrying capacity at story drift ratio of approximately 5%. 
FEMA P-2012 5: Concrete Wall Buildings with 5-11

Vertical Irregularities [V1, V8]

5.5 Assessment of Collapse Risk 

5.5.1 Overview

The FEMA P695 methodology was used to assess the collapse risk posed by 

the 8- and 12-story RC wall building designs, as described in Section 3.4. 

Nonlinear dynamic analyses were conducted using the OpenSees analysis 

platform and the DBE modeling procedure described above. For each 

building archetype, collapse risk was computed using the suite of nonlinear 

analysis results, for two different definitions of collapse: (1) collapse due to 

failure of the gravity system at a maximum story drift of 5%; and (2) collapse 

due to a sidesway mechanism characterized by a maximum story drift in 

excess of 10%. The following highlight the process (particular to RC wall 

buildings) for determining certain parameters in the FEMA P695 

methodology: 

• System overstrength, Ω, was computed using: (1) the results of nonlinear 

pushover analysis; (2) the OpenSees DBE modeling approach described 

in Chapter 3, Section B.4, Figure 3-14, and Figure 3-15; and (3) the ELF 

load distribution for ELF designs or a modal force distribution for 

MRSA designs.

• System ductility, μ, was defined as μ = δu/δy,eff where δu is the roof drift 

corresponding to 20% lateral strength loss from the pushover analysis 

and δy,eff is the effective drift at yield. The parameter δy,eff was defined 

using pushover analysis data rather than the recommended perioddependent method because the nonlinear response model used this study 

does not overestimate pre-yield stiffness, but instead simulates stiffness 

loss due to concrete cracking. Pushover analyses of RC wall buildings

show that many RC wall buildings have significant residual lateral 

strength such that the definition of ductility based on 20% strength loss 

does not provide an accurate representation of earthquake load resistance

(see Figure 5-7 and Figures B-26 through B-28). Thus, for this study, for 

all wall designs, the adjusted collapse margin ratios (ACMRs) and 

collapse probabilities were also computed for the case of μ = 8, the 

maximum ductility considered in the methodology. 

• Total system collapse uncertainty, βTOT, was defined by the quality of the 

model, design requirements, and test data. The quality of the model, 

design requirements, and test data were taken as “good,” resulting in βTOT

= 0.525. 

Results show that collapse risks for RC wall structures, with and without 

introduction of openings in lower stories, is relatively low (less than 4%). 
5-12 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

5.5.2 Results

Pushover and IDA were conducted for all 8- and 12-story concrete shear wall 

building designs (Table 5-1) using the OpenSees DBE modeling approach. 

Figure 5-7 and Figure 5-8 provide examples of the results from the pushover 

analyses and results from suites of dynamic analyses, respectively. These 

particular figures are for 8-story RC wall buildings designed for the Dmax

spectrum. Appendix B provides the full set of results for all cases described 

in this chapter. The results suggest that the introduction of vertical 

irregularities via openings that reduce story stiffness has relatively little 

impact on collapse risk. 

Dynamic analysis results for the wall configurations listed in Table 5-1 were 

combined with pushover analysis results and assessment of design, modeling, 

and uncertainty to determine collapse probabilities for RC wall buildings 

with vertical irregularities resulting from openings that reduce stiffness. 

Table 5-4 lists collapse probabilities for RC wall buildings designed for the 

Dmax spectrum and Table 5-5 lists these quantities for RC wall buildings

designed for the Bmax spectrum for collapse defined by a maximum story drift 

in excess of 5%. Table B-5 and Table B-6 list these quantities for collapse 

defined by a maximum story drift in excess of 10%. 

Figure 5-9 shows normalized ACMRs versus building height for different 

levels of irregularity for buildings designed using the ELF procedure. Figure 

5-10 shows similar data for buildings designed using the MRSA procedure. 

The data in Figure 5-9 through Figure 5-11, and Tables 5-4, 5-5, B-5, and 

B-6 support the following conclusions for RC wall buildings for which 

collapse is defined by maximum interstory drift in excess of 5% or 10%: 

• Collapse margin ratios are relatively high and collapse probabilities were 

relatively low for the buildings and failure/collapse modes considered in 

this study. The maximum computed collapse risk was 2.3% for collapse 

resulting from interstory drifts in excess of 5% and 10%. 

• For 8- and 12-story RC wall buildings designed for the Dmax spectrum 

and considering collapse associated with failure of the gravity system at 

a maximum interstory drift of 5%, the collapse probability of the solid 

wall system is low (0.5% to 1.2%). The introduction of a vertical 

stiffness irregularity increases collapse risk and reduces the collapse 

margin ratio moderately (maximum reduction is less than 25%). 

• The ASCE/SEI 7-16 classification of irregular versus extremely irregular 

does not consistently correlate with collapse probability. For walls with 

the same height and designed using the same design procedure (i.e., 
FEMA P-2012 5: Concrete Wall Buildings with 5-13

Vertical Irregularities [V1, V8]

8-story wall with an opening in the 1st story designed using the ELF 

procedure), irregular and extremely irregular walls are equally likely to 

have larger or smaller collapse probabilities.

• Severe irregularities located in upper stories of the wall, away from the 

base where flexural yielding occurs, have less impact on collapse 

probability than do irregularities introduced at the base of the wall. 

(a) Continuous wall 

(8-D-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6 

(8-D-5S-50-ELF)

(c) 1st story opening with K1 < 0.5K2

(8-D-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2 

(8-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (8-D-2S-50-ELF)

(f) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (8-D-2S-75-ELF)

Figure 5-7 Base shear versus roof drift for 8-story walls designed for Dmax spectrum using 

the ASCE/SEI 7-16 ELF procedure. Grey marker indicates yield drift (circle) 

and drift at 20% strength loss (square); dashed grey line indicates ductility of 

8. Ki indicates stiffness of story i defined per Section B.3. 
5-14 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

(a) Continuous wall 

(8-D-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6

(8-D-5S-50-ELF)

(c) 1st story opening with K1 < 0.5K2

(8-D-1S-50-ELF)

(d) 1st story opening with K1 < 0.75K2

(8-D-1S-75-ELF)

(e) 1st and 2nd story openings with 

K1 and K2 < 0.5K3 (8-D-2S-50-ELF)

(f) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (8-D-2S-75-ELF)

Figure 5-8 Earthquake intensity at design period, Sa, versus maximum interstory drift for 8-story 

walls designed for Dmax spectrum using the ASCE/SEI-16 ELF procedure. Black line 

indicates median acceleration. Non-simulated collapse defined to occur at 

maximum interstory drift of 5%. Ki indicates stiffness of story i.
FEMA P-2012 5: Concrete Wall Buildings with 5-15

Vertical Irregularities [V1, V8]

Table 5-4 Collapse Probabilities for RC Wall Building Archetypes Designed for the Dmax Spectra for the 

Case of Collapse at Maximum Story Drifts in Excess of 5%

Archetype SCT

>

SMT CMR μT SSF ACMR

ACMR / 

ACMRbaseline

SSF

(μ=8)

ACMR 

(μ =8)

Collapse

Prob. 

(μ =8)

ACMR / 

ACMRbaseline

(μ =8)

8-story RC wall buildings designed for Dmax spectrum using ELF

8-0-0-D-ELF 2.28 0.91 2.50 12.40 1.45 3.60 - 1.40 3.60 0.71 - 

8-1S-50-D-ELF 2.00 0.91 2.20 2.70 1.22 2.70 0.75 1.40 3.20 1.37 0.89

8-1S-75-D-ELF 1.92 0.91 2.10 2.50 1.21 2.60 0.72 1.40 3.10 1.66 0.86

8-2S-50-D-ELF 1.93 0.91 2.10 5.90 1.37 2.90 0.81 1.40 3.10 1.62 0.86

8-2S-75-D-ELF 1.93 0.91 2.10 4.60 1.32 2.80 0.78 1.40 3.10 1.62 0.86

8-5S-50-D-ELF 2.25 0.91 2.50 10.00 1.45 3.60 1.00 1.40 3.60 0.75 1.00

8-story RC wall buildings designed for Dmax spectrum using MRSA

8-0-0-D-MRSA 2.07 0.91 2.30 15.80 1.45 3.30 - 1.40 3.30 1.15 - 

8-1S-50-D-MRSA 1.95 0.91 2.10 5.60 1.36 2.90 0.88 1.40 3.10 1.56 0.94

8-1S-75-D-MRSA 1.91 0.91 2.10 5.40 1.35 2.80 0.85 1.40 3.00 1.72 0.91

8-2S-50-D-MRSA 1.89 0.91 2.10 7.10 1.41 2.90 0.88 1.40 3.00 1.79 0.91

8-2S-75-D-MRSA 1.91 0.91 2.10 6.60 1.39 2.90 0.88 1.40 3.00 1.71 0.91

8-5S-50-D-ELF - - - - - - - - - - - 

12-story RC wall buildings designed for Dmax spectrum using ELF

12-0-0-D-ELF 1.71 0.67 2.50 8.70 1.53 3.90 - 1.50 3.90 0.47 - 

12-1S-50-D-ELF 1.64 0.67 2.40 3.30 1.30 3.20 0.82 1.50 3.70 0.61 0.95

12-1S-75-D-ELF 1.69 0.67 2.50 3.20 1.30 3.30 0.85 1.50 3.90 0.50 1.00

12-2S-50-D-ELF 1.68 0.67 2.50 2.40 1.25 3.10 0.79 1.50 3.80 0.53 0.97

12-2S-75-D-ELF 1.69 0.67 2.50 2.30 1.23 3.10 0.79 1.50 3.80 0.52 0.97

12-5S-50-D-ELF - - - - - - - - - - - 

12-story RC wall buildings designed for Dmax spectrum using MRSA

12-0-0-D-MRSA 1.61 0.67 2.40 20.40 1.53 3.70 - 1.50 3.70 0.66 - 

12-1S-50-D-MRSA 1.45 0.67 2.10 7.30 1.50 3.20 0.86 1.50 3.30 1.15 0.89

12-1S-75-D-MRSA 1.52 0.67 2.20 7.20 1.50 3.40 0.92 1.50 3.50 0.91 0.95

12-2S-50-D-MRSA 1.25 0.67 1.90 3.60 1.33 2.50 0.68 1.50 2.80 2.32 0.76

12-2S-75-D-MRSA 1.42 0.67 2.10 3.60 1.33 2.80 0.76 1.50 3.20 1.27 0.86

12-5S-50-D-MRSA - - - - - - - - - - -
5-16 5: Concrete Wall Buildings with FEMA P-2012

Vertical Irregularities [V1, V8]

Table 5-5 Collapse Probabilities for RC Wall Building Archetypes Designed for the Bmax Spectrum for the 

Case of Collapse at Maximum Story Drifts in Excess of 5%

Archetype SCT

>

SMT CMR μT SSF ACMR

ACMR / 

ACMRbaseline

SSF

(μ=8)

ACMR

(μ =8)

Collapse

Prob. 

(μ =8)

ACMR / 

ACMRbaseline

(μ =8)

8-story RC wall buildings designed for Bmax spectrum using ELF

8-0-0-B-ELF 0.96 0.22 4.50 16.40 1.45 6.40 - 1.40 6.40 0.02 - 

8-1S-50-B-ELF 0.90 0.22 4.20 11.60 1.45 6.00 0.94 1.40 6.00 0.03 0.94

8-1S-75-B-ELF 0.91 0.22 4.20 12.40 1.45 6.10 0.95 1.40 6.10 0.03 0.95

8-2S-50-B-ELF 0.79 0.22 3.70 11.20 1.45 5.30 0.83 1.40 5.30 0.08 0.83

8-2S-75-B-ELF 0.86 0.22 4.00 8.80 1.45 5.80 0.91 1.40 5.80 0.04 0.91

8-5S-50-B-ELF - - - - - - - - - - - 

12-story RC wall buildings designed for Bmax spectrum using ELF

12-0-0-B-ELF 0.76 0.16 4.70 7.70 1.52 7.20 - 1.50 7.30 0.01 - 

12-1S-50-B-ELF 0.77 0.16 4.80 6.70 1.48 7.10 0.99 1.50 7.40 0.01 1.01

12-1S-75-B-ELF 0.77 0.16 4.80 6.50 1.47 7.10 0.99 1.50 7.40 0.01 1.01

12-2S-50-B-ELF 0.52 0.16 3.30 5.60 1.43 4.70 0.65 1.50 5.00 0.11 0.68

12-2S-75-B-ELF 0.74 0.16 4.60 4.90 1.40 6.50 0.90 1.50 7.10 0.01 0.97

12-5S-50-B-ELF - - - - - - - - - - - 

Figure 5-9 Impact of vertical irregularity and building 

height on ACMR for walls designed for Dmax

demands using ASCE/SEI 7-16 ELF procedure. 

Gravity system failure at 5% interstory drift. 
FEMA P-2012 5: Concrete Wall Buildings with 5-17

Vertical Irregularities [V1, V8]

Figure 5-10 Impact of vertical irregularity and building height 

on ACMR for walls designed for Dmax demands 

using ASCE/SEI 7-16 MRSA procedure. Gravity 

system failure at 5% interstory drift. 

Figure 5-11 Impact of vertical irregularity and building height 

on ACMR for walls designed for Bmax demands 

using ASCE/SEI 7-16 ELF procedure. Gravity 

system failure at 5% interstory drift. 

5.6 Conclusions and Recommendations

No code changes are recommended as a result of the study presented in this 

chapter. Analysis results suggest that: (1) collapse probabilities are very low 

for walled buildings without and with openings (typically less than 2%); and 

(2) for most regular systems, vertical irregularities have limited impact on 

collapse risk. 

However, the studies presented in this chapter and Appendix B were limited 

in that: (1) only two building heights were considered; (2) irregularities in the 

form an opening were placed at the center of a wall, which is not the most 

critical location; (3) collapse was solely defined by maximum interstory drift 

without consideration of shear demand-capacity; and (4) numerical modeling 

did not include simulation of interaction of flexural and shear response 

modes. It is recommended that future work address these limitations by 

considering a broader design space and employing more advanced modeling 

techniques. 

FEMA P-2012 6: Moment Frame Buildings with 6-1 

Vertical Irregularities [V1, V2, V5, V6, V7]

Chapter 6 

Moment Frame Buildings with 

Vertical Irregularities 

[V1, V2, V5, V6, V7]

6.1 Overview

This chapter summarizes the analytical studies for vertically irregular steel 

and concrete moment frame buildings that were designed per ASCE/SEI 

7-16, Minimum Design Loads and Associated Criteria for Buildings and 

Other Structures (ASCE, 2017a). The effects on building performance of the

following vertical irregularities were studied: 

• V2, Weight (mass) irregularity. This condition is Type 2 vertical 

irregularity, as defined in Table 12.3-2 of ASCE/SEI 7-16. 

• V1/V5, Soft/weak story irregularities. These conditions are Type 1 

and Type 5 vertical irregularities, respectively, as defined in Table 12.3-2 

of ASCE/SEI 7-16. 

• V6, Strong-column/weak-beam (SCWB) design provisions. This 

design aspect is not classified as a vertical irregularity in ASCE/SEI 

7-16, but rather is handled in material standards. SCWB design

provisions were included in this study of vertical irregularities because of 

their impact on damage localization over building height.

• V7, Gravity-induced lateral demand (GILD) irregularity. This 

design aspect is not currently classified as a vertical irregularity in the 

United States per ASCE/SEI 7-16, although it is categorized as an 

irregularity in the National Building Code of Canada (National Research 

Council of Canada, 2015). It was included in this study to determine if 

this condition should be considered a vertical irregularity in ASCE/SEI 

7. 

The following are covered in this chapter: (1) objectives of the vertical 

irregularities studies with moment frame buildings and overview of findings 

(Section 6.2); (2) methodology to assess vertical irregularity design 

provisions (Section 6.3); (3) archetype design space by system (Section 6.4); 

(4) archetype descriptions, results, and conclusions and recommendations for 
6-2 6: Moment Frame Buildings with FEMA P-2012

Vertical Irregularities [V1, V2, V5, V6, V7]

each of the vertical irregularities studied (Sections 6.5-6.8); and (5) overview 

of conclusions and recommendations (Section 6.9).

6.2 Objectives of Studies and Summary of Findings

The analytical studies of vertical irregularities in steel and moment frame 

buildings were structured to address two primary objectives:

1. Assess the adequacy of the existing ASCE/SEI 7-16 provisions in 

guarding against collapse of buildings with vertical configuration 

irregularities; and

2. Consider whether additional irregularity classifications should be 

recognized in ASCE/SEI 7-16. 

6.2.1 Objective 1: Assess the Adequacy of ASCE/SEI 7-16 Vertical 

Irregularity Provisions

ASCE/SEI 7-16 places additional limits and restrictions on buildings with 

vertical irregularity. These include limits on Seismic Design Category 

(SDC), building height, and analysis methods (i.e., equivalent lateral load 

procedure or modal response spectrum analysis). The studies summarized in 

this chapter are structured to answer the following two questions: 

• Are the existing limitations placed on vertically irregular buildings 

sufficient for providing adequate resistance to collapse?

• Are any of the existing limitations placed on vertically irregular 

buildings unnecessary or too conservative?

6.2.2 Objective 2: Assess the Necessity for Expanding the 

ASCE/SEI 7-16 Vertical Irregularity Provisions

GILD and SCWB design requirements are not addressed in ASCE/SEI 7-16 

as possible irregularity conditions. However, both are considered in this 

study, because they are aspects of building configuration that impact the 

distribution of damage along the height of the building and, therefore, may

affect seismic performance.

Although GILD is not directly addressed in ASCE/SEI 7-16 as a vertical 

irregularity, Dupuis et. al. (2014) led GILD irregularities to be addressed in 

the National Building Code of Canada. The present study addresses the

following two questions regarding buildings with GILD: 

• Does GILD significantly affect collapse performance in buildings which 

are designed considering the induced lateral loading? If so, should any 

limitations or additional requirements be placed on buildings with 

GILD? 
FEMA P-2012 6: Moment Frame Buildings with 6-3 

Vertical Irregularities [V1, V2, V5, V6, V7]

• How does GILD affect the collapse performance in buildings which are

not designed considering the induced lateral forces?

SCWB provisions are currently found in material-specific design provisions 

(e.g., AISC, 2016; ACI, 2014). The following two questions were 

considered in the analytical studies of buildings with varying SCWB design 

requirements: 

• How do modifications of existing SCWB requirements affect collapse 

performance?

• Are there more efficient ways to proportion members for SCWB ratios 

along the height of the building, which could provide similar or enhanced 

collapse performance?

6.2.3 Summary of Findings

The study found that the presence of weight (mass) irregularities, soft/weak 

story irregularities, and gravity-induced lateral demand (GILD) generally do 

not significantly reduce the collapse resistance of moment frame buildings, 

provided that the lateral system is proportioned to satisfy the seismic 

demands (which often increase due to the presence of the irregularity). 

Further, using the equivalent lateral force procedure (ELF) to design 

buildings with mass irregularity resulted in satisfactory, and even superior, 

collapse performance compared with buildings designed using modal 

response spectrum analysis (MRSA). This finding holds even when 

considering the new ASCE/SEI 7-16 provisions that require the MRSA 

design to be scaled to 100% of the base shear from the ELF method (as 

compared with the previous 85% base shear scaling requirement in 

ASCE/SEI 7-10). Based on these findings, this study concludes that the 

limitation on use of the ELF method for buildings with mass irregularity 

(V2) is unnecessary.

6.3 Methodology to Assess Vertical Irregularity Design 

Provisions

Moment frames with varying degrees of irregularity were utilized to examine

the effects of the vertical irregularities on collapse performance. Threedimensional frame designs were developed using linear elastic procedures 

according to ASCE/SEI 7-16 and appropriate material standards (i.e., AISC 

2010a, 2010c, 2016; ACI, 2014). From the three-dimensional design, a twodimensional nonlinear OpenSees model of each building was constructed 

using the methods described in Chapter 3. This study used both steel 
6-4 6: Moment Frame Buildings with FEMA P-2012

Vertical Irregularities [V1, V2, V5, V6, V7]

moment frames and reinforced concrete moment frames to investigate the 

various types of vertical irregularities. 

The adjusted collapse margin ratio (ACMR) of each archetype building was 

determined by incremental dynamic analysis (IDA) using the FEMA P695

approach. The performance of each archetype building is compared to a 

“baseline” version (i.e., one with no structural irregularity) to determine the 

relative impacts of the vertical irregularities on collapse resistance. To avoid 

ambiguity in the comparisons, ACMR of each archetype is computed using 

the same spectral shape factor (SSF) as the baseline model to which it is 

compared. Methods for design and analysis of the moment frame buildings 

are described in more detail in Chapter 3. 

6.4 Archetype Design Space by System

Steel frames were used to examine the effects of mass irregularities, SCWB 

ratios, and GILD irregularities. These were examined in 3-, 9-, and 20-story 

models of both special moment frames (SMFs) and ordinary moment frames 

(OMFs). In total, 151 steel moment frames were designed and analyzed.

Reinforced concrete (RC) moment frames were used to study mass 

irregularities, soft/weak story irregularities, and SCWB ratios. These were

examined in 4-, 8-, 12-, and 20-story RC SMF and OMF models. In total, 

113 RC moment frames were designed and analyzed. 

The following sections provide more detail on the designs for each specific 

type of irregularity. Detailed design documentation (including fundamental 

period and other key parameters) on the steel moment frame and concrete 

moment frame studies is provided in Appendix C and Appendix D, 

respectively.

6.5 Studies of Weight (Mass) Irregularity [V2]

According to ASCE/SEI 7-16 Table 12.3-2, “Weight (mass) irregularity is 

defined to exist where the effective mass of any story is more than 150% of 

the effective mass of an adjacent story. A roof that is lighter than the floor 

below need not be considered.” Figure 6-1 illustrates a weight (mass) 

irregularity. ASCE/SEI 7-16 prohibits the use of the ELF design method for 

buildings with a weight (mass) irregularity. The following questions guided 

this study on the collapse performance of weight (mass) irregular buildings: 

• Does weight (mass) irregularity decrease collapse performance? 

• Does MRSA design result in better collapse resistance than ELF? 
FEMA P-2012 6: Moment Frame Buildings with 6-5 

Vertical Irregularities [V1, V2, V5, V6, V7]

Figure 6-1 Mass irregularity per ASCE/SEI 7-16. 

6.5.1 Archetype Descriptions

Mass irregularity is examined in both steel and RC SMF archetypes by 

increasing the mass of a given story to produce a mass ratio ranging from 1.5

to 3 relative to the adjacent lower story, as depicted in Figure 6-1, and then 

calculating the resulting change in building collapse resistance. Ordinary 

moment frames were not considered, because mass irregularity requirements 

only apply in SDC D, E, and F and the use of OMFs is significantly restricted 

in these SDCs. For each increase in mass ratio, the building was redesigned 

(if needed) considering checks on both strength and story drift requirements. 

Table 6-1 summarizes the archetype design space. 

Table 6-1 Weight (Mass) Irregularity Archetype Space

System Types

Stories SDC

Irregular

Stories

Mass 

Ratios 

Analysis Used 

for Design

RC

Moment 

Frame

Steel 

Moment 

Frame ELF MRSA 

Special 3 Dmax 2, 3 1.5, 2.0, 3.0 × × 

Special 20 Dmax 3, 11, 19 1.5, 2.0, 3.0 × 

Special 20 Dmax 3, 11 2.0, 3.0 × × 

6.5.2 Results

Collapse performance sometimes improves and sometimes diminishes with

increasing mass ratio, as seen in Figure 6-2a (RC frames) and Figure 6-2b 

(steel frames). At first look, it appears that steel buildings are more 

negatively affected by mass irregularity than concrete buildings, but this 

observation is an artifact of the archetype designs, and it is not expected to be 

true in general. The negative trend seen in Figure 6-2b is caused by the 

baseline steel variants having much higher design overstrength than some of 

the irregular variants; the static overstrength of mass irregular steel models 

decreases by as much as 30% relative to the baseline. For comparison, the 

mass-irregular concrete models maintain static overstrength values within 
2% of the baseline. In all of the 3-story MRSA designed steel frame variants 

with mass irregularity at the second story, the member sizes in the steel 

buildings did not change when the mass irregularity was introduced, even 

though the design base shear increased substantially (as much as a 60% 

increase with a mass ratio = 3.0 for the 3-story building). These design 

details are fully documented in the Supporting Documentation of Appendix 

C. Therefore, the decline in collapse resistance in the steel buildings is 

attributed to a reduction in “overdesign”; when the overdesign of each 

member remains nearly the same, as in the RC SMF archetypes shown in 

Figure 6-2, no declines in collapse resistance are observed. Although the 

relative collapse performance decreases with increasing mass ratio in the 

steel buildings, it is important to note that mean interstory drift at the MCE 

remains below the 4% limit set in ASCE/SEI 7-16 Section 16.4.1.2. Figure 

6-3 shows that even for the worst performing mass-irregular building 

(3-story MRSA designed building with a mass ratio of 3.0 at the 3rd floor), 

the interstory drift at MCE is acceptable. 

(a) RC SMF (b) Steel SMF 

Figure 6-2 V2 mass irregularity. Legend indicates design method, number of 

stories, and location of the irregular story. 

Figure 6-3 Interstory drift profile at increments of MCE 

for the 3-story MRSA designed steel building 

with a mass ratio= 3.0 at the 3rd floor. 

6-6 6: Moment Frame Buildings with FEMA P-2012 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
FEMA P-2012 6: Moment Frame Buildings with 6-7 

Vertical Irregularities [V1, V2, V5, V6, V7]

Generally, the mass irregular variants designed with the ELF method perform 

better than those designed with MRSA analysis. This observation is 

important because the only design requirement that is triggered by mass 

irregularity in ASCE/SEI 7-16 is the prohibition of the ELF design procedure 

for SDC D, E, and F. 

The performance of the buildings designed with ELF and MRSA can be 

further investigated by examining the design demands produced by each 

method. Figure 6-4 examines the design forces for an RC frame building 

with a mass irregularity at the third story. The MRSA design picks up the 

increased force demand at the mass-irregular third story; however, overall, 

the ELF designed building will be equally strong at the irregular story and 

stronger than the MRSA buildings at all floors above. 

Figure 6-4 Comparison of ELF and MRSA design forces for a 20-story RC 

frame building with a mass irregularity at the third story. 

The investigation also found that the location of the mass irregularity along 

the height of the building affects collapse performance; archetypes with the 

mass irregularity located where the collapse mechanism is already more 

likely to form (i.e., in lower stories) tend to have lower collapse resistance as 

compared with buildings with mass irregularities located where the collapse 

mechanism is less likely to form (i.e., upper stories). 

0 20 40 60 80

Design Force (kips)

0

5

10

15

20

Stories

ELF

MRSA

0 200 400 600

Story Shear (kips)

0

5

10

15

20

Stories

ELF

MRSA

6.5.3 Conclusion and Recommendations

Based upon the findings in this section, specifically the superior performance 

of ELF designed buildings relative to MRSA designed buildings, it is 

recommended that ELF procedure be allowed for mass-irregular buildings. 

This recommendation is further supported by a broader study of extreme 

mass irregularities documented in Appendix F, where it is shown that the 

ELF procedure generally produces higher story shears and overturning 

moments than MRSA, even for extreme mass ratios up to 10. 
6-8 6: Moment Frame Buildings with FEMA P-2012

Vertical Irregularities [V1, V2, V5, V6, V7]

It is noted that mass irregularities were studied by adjusting the mass of 

single stories at different locations in the building. A future study 

investigating the effects of applying greater mass to multiple floors may be 

of value. 

6.6 Studies of Soft- and Weak-Story Irregularities [V1/V5] 

ASCE/SEI 7-16 limits the analysis procedure, height, and/or SDC for 

buildings with stiffness or strength irregularities. The following questions 

guided this study on the collapse performance of stiffness/strength irregular 

buildings: 

• Are the existing limitations placed on soft/weak story buildings sufficient 

in terms of resistance to collapse?

• Are any of the existing limitations placed on soft/weak story buildings 

conservative?

6.6.1 Archetype Descriptions

Soft/weak story irregularities (illustrated in Figure 6-5 and 6-6) are 

investigated using RC SMFs and OMFs for target strength and stiffness 

ratios between 0.6 and 0.8 relative to the story above. According to 

ASCE/SEI 7-16 Table 12.3-2, a soft story irregularity occurs when the 

stiffness of a story is less than 70% of the stiffness of the story above or less 

than 80% of the average stiffness of the three stories above. If the story 

stiffness is less than 60% of the story above or less than 70% of the average 

of the three stories above, then it has an extreme soft story irregularity. 

Weak story and extreme weak story irregularities occur when the strength of 

a story is less than 80% or 65% of the strength of the story above, 

respectively.

Soft/weak story irregularities were introduced two different ways: (1) by 

increasing story height so that stiffness (and possibly strength) of the story 

are reduced; and (2) by increasing the strength of the story above. Table 6-2 

summarizes the soft/weak story archetype design space. It should be noted 

that all of the soft/weak story archetypes comply with ASCE/SEI 7-16, 

except for height limits and prohibitions of the ELF procedure. Therefore, 

the soft/weak archetypes in this study differ from many of the soft/weak 

story buildings for which poor performance has been observed in past 

earthquakes because many of those buildings had a story that was too 

soft/weak to meet current code requirements. 
FEMA P-2012 6: Moment Frame Buildings with 6-9 

Vertical Irregularities [V1, V2, V5, V6, V7]

Figure 6-5 Soft story irregularity per ASCE/SEI 7-16. 

Figure 6-6 Weak story irregularity per ASCE/SEI 7-16. 

Table 6-2 Soft/Weak Irregularity Archetype Space

System Types

Stories SDC

Irregular 

Stories

Stiffness 

Ratios

Strength 

Ratios

Analysis 

Used for 

Design

RC 

Moment 

Frame

Steel 

Moment 

Frame

Ordinary 4 Bmax 1, 2 0.6, 0.7, 0.8 0.6, 0.8 ELF

Ordinary 12 Bmax 1, 2, 5 0.6, 0.7, 0.8 ELF

Special 4 Dmax 1, 2 0.6, 0.7, 0.8 ELF

Special 8 Dmax 1, 2, 5 0.6, 0.7, 0.8 0.6, 0.8 ELF

Special 12 Dmax 1, 2, 5, 9 0.6, 0.7, 0.8 0.6, 0.8 ELF

Special 20 Dmax 1 0.6, 0.8 ELF
6.6.2 Results 

Figure 6-7 shows that the first method (Method 1) for creating a soft/weak 

story (increased story height) does not result in any consistent positive or 

negative trends in collapse resistance for either SMF or OMF archetypes. 

For all design cases investigated, the collapse performance stays above at 

least 85-90% of the baseline model performance and reaches 130% in some 

cases. Similar observations are made when collapse resistance is plotted 

against relative stiffness, rather than relative strength. 

 

 (a) RC SMF (b) RC OMF 

Figure 6-7 V1/V5 soft/weak story (increase story height to achieve soft/weak story). 

The legends indicate design method, number of stories, and location of the 

irregular story. 

0.6 0.8 1 1.2 1.4

Story Strength Ratio

0.9

1

1.1

1.2

1.3

The lack of a clear trend from Method 1 is mostly because increasing the 

story height may cause the taller story to have lower stiffness, but it often 

does not cause a decrease in the strength of the story for code-conforming 

buildings since the code requires a minimum strength. For example, the 

results for the 12-story RC SMF with increasing story height at the fifth story 

(dark blue dotted line in Figure 6-7a) form a nearly vertical line because 

increasing the story height does not actually reduce story strength. 

The reason that the story strength does not decrease is because the beam 

members at the location of the increased story height are re-proportioned to 

meet the higher demands caused by the taller story—the end result is a story 

with similar strength. Similar results are observed for the OMF variants 

(Figure 6-7b) except that strength is governed by column capacity, rather 

than beam capacity. When examining these results, it is important to keep in 

mind that the “weak” story still meets all of the code force and drift 

demands; this is in stark contrast to non-current-code-conforming weak-story 

buildings that have been severely damaged in past earthquakes. 

6-10 6: Moment Frame Buildings with FEMA P-2012 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
Figure 6-8 shows that second method (Method 2) for achieving a weak 

story—increasing the strength of the story above (no strength adjustment is 

made to any stories beyond the story immediately above the irregular 

story)—tends to result in collapse resistance that is somewhat higher for 

extremely low weak-story strength ratios as compared to moderate weakstory ratios. For example, the 20-story model with a first story irregularity 

(the black line in Figure 6-8a) experiences a 7% increase in collapse capacity 

when the strength ratio decreases from 0.78 (weak story irregularity) to 0.62 

(extreme weak story irregularity). This trend of improved collapse 

performance with decreasing story strength ratio is also reflected in the static 

overstrength for the SMF models (see Figure 6-9). The static overstrength is 

improved by strengthening one of the stories in the building. A consistent 

finding was found in a past study (Haselton et al., 2011), which showed that 

a weak-story irregularity caused by strengthening all the stories above 

similarly does not detrimentally affect the collapse performance of RC 

moment frame buildings. 

 

(a) RC SMF (b) RC OMF 

Figure 6-8 V1 weak story (increase strength in story above). 

Soft/weak story irregularities do not appear to pose a problem in codeconforming moment frame buildings. This is partially because, as long as 

the building is code-conforming, “weak story” really means “strong adjacent 

stories”; the “weak” story still must be strong enough to resist the design 

lateral force demand per code requirements. Similarly, a “soft” story must 

still satisfy story drift requirements, which prevents it from becoming 

excessively soft. It is reasonable to think that the expected collapse 

performance may decline when the weak story causes the damage 

distribution over height to change from several stories to just one or two, as 

has been observed in the poor seismic performance of non-current-codeconforming soft/weak story buildings in past earthquakes. However, in this 

study of code-conforming irregular buildings, such a reduction in collapse 

FEMA P-2012 6: Moment Frame Buildings with 6-11 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
resistant is not observed; rather, the negative effects of having more 

concentrated damage are offset by the positive effects of having strengthened 

members in the adjacent stories. 

 (a) RC SMF (b) RC OMF 

Figure 6-9 V1 weak story overstrenth. Legend indicates design method, number of 

stories, and location of the irregular story. 

6.6.3 Conclusion and Recommendations 

Based upon the findings from this section, specifically the enhanced 

performance of extreme weak story irregular buildings relative to the 

baseline building, the prohibition of extreme weak story irregularities in SDC 

D and the height limitation on in SDC B and C may be overly conservative. 

Further study is recommended to evaluate the prohibition of weak/soft story 

irregularities in SDC E and F. 

It is noted in the previous section that buildings designed using the ELF 

procedure tend to outperform buildings designed using MRSA, in terms of 

collapse resistance. As soft-story irregular buildings are similarly limited to 

MRSA (i.e., ELF is prohibited), a future study may compare the performance 

of ELF and MRSA designed buildings with soft-story irregularity to 

determine if prohibiting the ELF procedure is needed. 

6.7 Studies of Strong-Column/Weak-Beam Design 

Provisions [V6] 

Even though SCWB is not defined as an irregularity, it is a configuration 

characteristic that has been clearly shown to impact system ductility and 

collapse resistance. SCWB requirements are provided by material 

specifications (ACI, 2014; AISC, 2016) and are not specifically addressed in 

ASCE/SEI 7-16. The material standards specify a minimum ratio of the total 

flexural strength of the columns framing into a joint to the total flexural 

strength of beams framing into the joint (i.e., the SCWB ratio), so that 

column failures are limited. Calculation of SCWB ratio is illustrated in 

6-12 6: Moment Frame Buildings with FEMA P-2012 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
FEMA P-2012 6: Moment Frame Buildings with 6-13

Vertical Irregularities [V1, V2, V5, V6, V7]

Figure 6-10; in the figure, Mc is column flexural strength, Mb is the beam 

flexural strength, and i and j are the story and beam numbers, respectively. 

Figure 6-10 Weak-column/strong-beam. 

The following questions are explored in this section: 

• How sensitive is collapse performance to SCWB requirements?

• Could adjusting requirements for SCWB ratio along the height of the 

building (resulting in “stepped” SCWB ratio) provide similar or 

enhanced collapse performance?

6.7.1 Archetype Descriptions

The effects of SCWB are examined by analyzing suites of moment frame 

buildings designed for a range of SCWB ratios. In addition, archetypes with 

stepped SCWB ratios are examined; for these, the minimum SCWB ratio is 

higher at the lower stories and “steps” down in the upper stories of the 

building. For the stepped designs, minimum SCWB ratio at the first, second, 

and third quarters of the buildings are 1.5, 1.0, and 0.8 respectively or 2.0, 

1.5, and 1.0, respectively, with no SCWB ratio requirement in the top 

quarter. Generally speaking, failing to satisfy SCWB requirements would be 

a violation of the material design standards. The archetype design space for 

studying SCWB is summarized in Table 6-3. 

The SCWB variants are designed two ways: (1) “realistic” where the 

minimum SCWB ratio is adjusted in the design, but the design process 

allows the ratio to be greater than the minimum when other design factors 

control the building proportioning (e.g., joint size and minimum reinforcing 

requirements); and (2) “exact” where the design enforces an exact SCWB 

ratio, even if it makes the design unrealistic (e.g., impossible reinforcing 

configurations). 
6-14 6: Moment Frame Buildings with FEMA P-2012

Vertical Irregularities [V1, V2, V5, V6, V7]

Table 6-3 SCWB Archetype Space

System Types

Stories SDC

Distribution of 

SCWB 

Requirements SCWB Ratios

Analysis Used for Design

RC

Moment 

Frame

Steel 

Moment 

Frame ELF MRSA

Ordinary 4 Bmax constant 0.4, 0.7, 1.0 ×

Ordinary 12 Bmax constant 0.4, 0.7, 1.0 ×

Special 4 Dmax constant 0.5, 1.0, 1.5, 2.0 ×

Special 8 Dmax constant 0.5, 1.0, 1.5, 2.0 ×

Special 12 Dmax constant 0.5, 1.0, 1.5, 2.0 ×

Special 12 Dmax stepped 0.8, 1.0, 1.2, 1.5, 2.0 ×

Ordinary 3 Bmax constant 0.4, 0.7, 1.0 × ×

Ordinary 9 Bmax constant 0.4, 0.7, 1.0 × ×

Ordinary 20 Bmax constant 0.4, 0.7, 1.0 × ×

Special 3 Dmax constant 0.5, 1.0, 1.5, 2.0 ×

Special 9 Dmax constant 0.5, 1.0, 1.5, 2.0 ×

Special 20 Dmax constant 0.5, 1.0, 1.5, 2.0 ×

6.7.2 Results

The concrete frames (both SMF and OMF) show a distinct trend of 

increasing collapse performance with increasing SCWB ratio (Figure 6-11)

as a result of stronger plastic hinges at the base of the first story columns and

damage spreading more over the height of the building as the SCWB ratio

increases. Similar observations have been made in a number of prior studies, 

e.g., Haselton et al. (2011) and Elkady (2016). The minimal decline in 

collapse resistance (no more than 10% lowered collapse capacity relative to 

the baseline) for realistic designs with low SCWB ratio is a result of 

increasing the beam strength in order to reduce the SCWB ratio where 

column strength was controlled by lateral force demands rather than capacity 

design requirements (i.e., reducing SCWB ratio actually resulted in a 

stronger building because column strength could not be reduced any further). 

In contrast, the 12-story RC SMF designed to exactly meet a SCWB ratio of 

0.5 (the dark blue dashed line in Figure 6-11a) experiences collapse capacity 

20% lower than the baseline, because other code requirements such as joint 

shear requirements (which often increase column sizes) were not considered 

in the design (note, that joint failure is only modeled in the RC OMF 

archetypes, so RC SMF archetypes with non-conforming joints may have 

even lower collapse resistance if they are susceptible to joint failure). 
 (a) RC SMF (b) RC OMF 

Figure 6-11 V6 strong-column/weak-beam. Baseline in these plots refers to the 

SCWB ratio (SCWBR) of: (a) 1.2 variant for each story height and 

design type; (b) 1.0 variant for each story height and design type. 

Figure 6-12 shows the performance of RC SMF buildings with stepped 

SCWB requirements, showing results for buildings designed by both the 

realistic and exact design methods. Targeting higher SCWB ratio in the 

lower portions of buildings and relaxing SCWB requirements in the upper 

stories may be an efficient way to proportion a building without sacrificing 

collapse resistance because it improves collapse resistance by placing 

additional column strength where it is most effective—the lower portion of 

the building. However, lower collapse resistance of the exact designs with 

low SCWB ratios in the upper stories shows that allowing SCWB ratio to go 

below current code limits, even in the upper portion of the building, can have 

negative implications; the reduced collapse resistance in those buildings is 

caused by column failures in the upper portions of the buildings. Allowing 

lower SCWB ratios in the upper portion of the realistic designs did not cause 

upper story failures or lower the collapse resistance because joint size and 

minimum reinforcing requirements prevented SCWB ratios in the upper 

stories from getting below 0.9 and 1.0 for the interior and exterior joints, 

respectively. It is important to note in both cases (uniform and stepped 

SCWB ratio requirements) that the archetypes with exact SCWB ratios often 

violated one or more ACI design requirements (e.g., reinforcing steel 

detailing, joint strength requirements); therefore, they are valuable for 

determining the effect of a single design constraint (SCWB ratio), but they 

do not necessarily reflect trends in real buildings. 

An additional exact SCWB variant for which the SCWB ratio is set to 1.5 in 

the bottom third of the building and 1.2 elsewhere (rightmost bar of Figure 

6-12) has the best performance of all the exact SCWB designs by a 

significant margin. This result indicates that increasing SCWB ratio in only 

the lower portion of a building boosts collapse resistance, as long as the 

upper stories still meet minimum code requirements for SCWB ratio. 

FEMA P-2012 6: Moment Frame Buildings with 6-15 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
Figure 6-12 V6 stepped SCWB ratio, 12-story RC SMF. 

2.0,1.5,1.0

1.5,1.0,0.8

2.0,1.5,1.0

1.5,1.0,0.8

1.5,1.2

Incremental SCWB Ratio Over Height

0

0.5

1

1.5

Realistic 

Exact 

The steel frames, both SMF and OMF, show less consistent trends with 

increasing SCWB ratio, as seen Figure 6-13. This inconsistent performance 

is partly due to increasing girder sizes to achieve lower SCWB ratio (rather 

than only decreasing column sizes) and partly due to a mechanism shift from 

joint shear yielding at low SCWB ratios to beam failure at higher SCWB 

ratios. A side-study revealed that adding oversized doubler plates to 

completely eliminate panel zone yielding reduced the collapse resistance of 

the archetypes with low SCWB ratio by shifting the failure mechanism from 

the joint panel zones (which are modeled to have no cyclic deterioration and 

continue to harden out to 6% distortion) to the columns and beams (which 

have more rapid strength deterioration). When the panel zones are reinforced 

to prevent yielding, a trend of increasing performance with increasing SCWB 

ratio is produced, similar to what is observed for the RC SMF archetypes. 

The benefit of moderate yielding in the joint panel zone has been noted in 

prior studies as well, e.g., FEMA 355D, State of the Art Report on 

Connection Performance (FEMA, 2000a), and the influence of joint panel 

zone yielding on overall building performance warrants additional study in 

the future. 

 

 (a) Steel SMF (b) Steel OMF 

Figure 6-13 V6 strong-column/weak-beam. Baseline in these plots refers to the 

SCWB ratio (SCWBR) 1.0 variant for each story height and design type. 

0.5 1 1.5 2

Minimum SCWBR

0.6

0.8

1

1.2

1.4

6

ACMR/ACMRbaseline

MRS-3Stories

MRS-9Stories

MRS-20Stories

0.4 0.6 0.8 1

Minimum SCWBR

0.6

0.8

1

1.2

1.4

1.6

ACMR/ACMRbaseline

ELF-3Stories

MRS-9Stories

MRS-20Stories

1.

6-16 6: Moment Frame Buildings with FEMA P-2012 

Vertical Irregularities [V1, V2, V5, V6, V7] 
FEMA P-2012 6: Moment Frame Buildings with 6-17

Vertical Irregularities [V1, V2, V5, V6, V7]

6.7.3 Conclusion and Recommendations

Increasing the required minimum SCWB ratio (even beyond current material 

code requirements) tends to improve collapse performance. The advantage 

of increased SCWB ratio could potentially also be achieved more 

economically by stepping down SCWB ratio requirements along the height 

of a building (with the highest SCWB ratio being in the lower portion of the 

building). To get to a point of specific recommendations for updated SCWB 

requirements, further study is needed to determine the optimal approach for 

stepping down the SCWB requirements over the building height and to

examine the costs of this approach versus other design approaches. 

6.8 Studies of Gravity-Induced Lateral Demands [V7]

Recent studies (Dupuis et al., 2014; Shoraka et al., 2014) on shear wall 

buildings with gravity-induced lateral demand (GILD) have recommended 

that code limits be placed on buildings with GILD irregularities. Those 

studies are based predominately on displacement demands and conclude that 

increasing GILD can cause “ratcheting of displacement demands and 

potentially collapse.” This study seeks to determine whether collapse 

capacity is significantly decreased by GILD irregularities. 

6.8.1 Previous Studies

Dupuis et al. (2014) examined displacement demands on shear wall buildings 

ranging from 5 to 50 stories with GILD irregularity. The GILD demand was 

supplied by sloping gravity columns along the entire height of the building. 

The study found that the GILD irregularity amplified the displacement 

demands significantly relative to an equivalent building without GILD. 

Therefore, limitations on GILD displacement and the method in which the 

building is analyzed were recommended. 

A later study by Shoraka et al. (2014) examined displacement and collapse 

capacity together. For crustal ground motions and GILD ratio up to 0.4 (note 

that the GILD ratio was calculated as the GILD base shear normalized by the 

base yield strength), it was found that collapse capacity is acceptable for 

GILD irregular buildings (similar to the findings of this report). However, it 

is observed that subduction ground motions and GILD achieved through 

eccentric floor spans may have a more significant effect on collapse capacity. 

It is also noted that inclined columns at an intermediate level cause a less 

extreme displacement demand in GILD irregular buildings than when 

columns are inclined along the entire building height. 
6-18 6: Moment Frame Buildings with FEMA P-2012

Vertical Irregularities [V1, V2, V5, V6, V7]

6.8.2 Archetype Descriptions

The effects of GILD irregularities were examined with 20-story steel frame

and 12-story concrete frame buildings; the full set of GILD archetypes is 

summarized in Table 6-4. The “irregularity” is achieved by sloping the 

columns at one of the stories, as shown in Figure 6-14. The severity of the 

irregularity is quantified by a GILD ratio, which is gravity-induced story 

shear (QG) divided by story shear capacity (QV) according to the IBC SEAOC 

Structural/Seismic Design Manual (SEAOC, 2015), illustrated in Figure 

6-14. 

Table 6-4 GILD Archetype Space

System Types

Stories SDC

Irregular

Stories

GILD

Ratios 

Analysis Used for Design

RC

Moment 

Frame 

Steel 

Moment 

Frame ELF MRSA

Ordinary 12 Bmax 1, 2 0.5 × 

Special 12 Dmax 1, 2 0.5 × 

Ordinary 20 Bmax 1, 7, 14 0.1, 0.3, 0.5 × 

Special 20 Dmax 1, 7, 15 0.1, 0.3, 0.6 × 

Figure 6-14 Gravity-induced lateral demand (GILD). 

6.8.3 Results

Figure 6-15 shows variations in collapse resistance for 20-story steel frames 

with GILD ratios up to 0.5. Collapse resistance rarely diminishes more than 

10% and in some cases it improves. Negative effects of GILD are not 

observed for the steel frames because these buildings are designed to account 

for the effects of the GILD (i.e., lateral demands incorporate GILD). 

Shoraka et al. (2014) found that GILD applied along the entire height of the 

building can have a negative effect on collapse performance, but that GILD 

applied over only a portion of the building height results in smaller 

displacement demands relative to the former configuration. Although the 

analyses in this study did not examine a case where GILD is applied along 
the full height of the building, maximum interstory drift and residual drift do 

increase due to GILD, demonstrating agreement with prior studies (Dupuis et 

al., 2014; Shoraka et al., 2014). 

(a) Steel SMF (b) Steel OMF 

Figure 6-15 V7 gravity-induced lateral loading with design for GILD (i.e., 

code-compliant). Legend indicates design method, number of 

stories, and location of the irregular story. 

ACMR/ACMRbaseline

ACMR/ACMRbaseline

The consequences of neglecting GILD in the design process are illustrated in 

Figure 6-16; shown in the figure are the performance of 20-story steel frames 

and 12-story concrete frames with GILD ratios up to 0.5 that are designed 

without considering GILD (e.g., sloping columns are introduced at a 

particular story of the baseline design, but members are not re-proportioned 

for the additional lateral demand). Declines in collapse resistance as great as 

50% are observed; ordinary moment frames are affected most because lower 

SCWB ratios limit their ability to engage the stories adjacent to the story 

with the GILD irregularity. The negative effect of failing to design for GILD 

is also visible in Figure 6-17b, the poorest performing un-designed SMF 

building violates the MCE drift requirements of ASCE 7-16 Section 16.4.1.2; 

Figure 6-17a also shows how the drifts are adequately controlled, even at the 

GILD stories, when GILDs are accounted for in the building design process. 

FEMA P-2012 6: Moment Frame Buildings with 6-19 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
 

 (a) Steel SMF, 20-story (b) RC SMF/OMF, 12-story 

Figure 6-16 V7 gravity-induced lateral loading without design for GILD (i.e., 

not code-compliant, provided to show the effects of GILD when 

not considered in the design). Legend indicates design method, 

number of stories, and location of the irregular story. 

ACMR/ACMRbaseline

ACMR/ACMRbaseline

 

(a) Steel SMF GILD ratio 0.1 at Floor 1 (b) Steel SMF GILD ratio 0.5 at Floor 14 

 (with design for GILD) (without design for GILD) 

Figure 6-17 Mean interstory drift at MCE of the poorest performing GILD 

designed and un-designed irregular buildings. 

6.8.4 Limitations of the GILD Studies 

GILD irregularities were examined in this study for a limited set of archetype 

models, with GILD occurring at only one predetermined story within a given 

building. The models are subjected to only crustal horizontal ground 

accelerations, and, to reduce analysis time and convergence difficulties, 

P-Delta effects are simulated using the “Linear with P-Delta” transformation 

in OpenSees, which is a linear (i.e., not exact) transformation that 

approximates P-Delta effects. 

The effect of GILD on buildings is expected to be more significant when the 

location of the irregular story and the portion of the building prone to damage 

coincide. In the case of the steel 20-story SMF building, it was found that 

6-20 6: Moment Frame Buildings with FEMA P-2012 

 Vertical Irregularities [V1, V2, V5, V6, V7] 
FEMA P-2012 6: Moment Frame Buildings with 6-21

Vertical Irregularities [V1, V2, V5, V6, V7]

the second story was often the most damaged in the baseline model; 

therefore, it would be meaningful to assess the GILD irregularity for the 

second story, where the buildings is most susceptible to damage. 

Additionally, prior studies (Shoraka, 2014; Dupuis, 2014) have shown that 

GILD caused by sloping columns at multiple stories increases displacements 

more than when columns are sloped at only one story. Therefore, the 

archetype design space should be expanded to include buildings with GILD 

at multiple stories rather than just one. 

To test the impact of the vertical ground motion component on collapse 

resistance of buildings with large GILD, the 12-story concrete moment 

frames with GILD of 0.5 were re-analyzed with the vertical ground motion 

component included and their resulting ACMR lowered an additional 6%, 

which does not appear significant. However, lighter buildings may be more 

affected by the vertical component of the ground motion, due to the larger 

columns slopes they can achieve; for context, the column slopes introduced 

in the RC SMF and RC OMF frames to achieve GILD of 0.5 at the second 

story were 3% and 1%, respectively. Nonetheless, it may be reasonable to 

expect that the increasing significance of vertical ground motions one would 

expect to accompany larger column slopes is balanced by including the 

vertical seismic effect in design, as ASCE/SEI 7-16 requires. Further study 

is required to validate this hypothesis.

The effect of using the approximate linear transformation with P-Delta, as 

outlined in Chapter 3, rather than the “exact” corotational transformation in 

OpenSees, was tested by re-evaluating two of the GILD archetypes with the

corotational transformation. For the 12-story RC SMF archetypes with 

GILD ratio of 0.5, ACMR was reduced by 2% and 3% for the variants with 

GILD at the first and second story, respectively, so the more approximate 

linear P-Delta transformation did not affect the collapse analysis results in 

any meaningful manner. 

6.9 Overview of Conclusions and Recommendations 

This study finds that the potentially negative effects of vertical irregularities 

are generally insignificant for moment frame buildings. Therefore, 

prohibitions or penalties placed on buildings with vertical irregularities, 

particularly those within the scope of this study, deserve careful 

re-examination. In making these conclusions, it is important to note that this 

study focused on new code-compliant buildings, where the effects of the 

irregularities (e.g., additional story shear from sloping columns) are 

considered in the design process. Therefore, the general conclusion is that 

the effects of vertical irregularities are insignificant for moment frame 
6-22 6: Moment Frame Buildings with FEMA P-2012

Vertical Irregularities [V1, V2, V5, V6, V7]

buildings when they are designed to fully meet ASCE/SEI 7-16 design 

requirements (but ignoring certain prohibitions, such as on the equivalent 

lateral force (ELF) procedure). The conclusion is not applicable to older, 

non-code-compliant buildings where the effect of irregularities may not have 

been considered in the building design process, for which safety has been 

clearly shown to be deficient in past earthquakes. 

Generally, moment frame buildings designed with the ELF procedure have 

collapse resistance that meets or exceeds their counterparts designed with

modal response spectrum analysis (MRSA), even when MRSA demands are 

scaled to achieve 100% of the ELF base shear. This observation holds for 

regular and irregular archetypes alike. Therefore, prohibiting the ELF 

procedure on the basis of a vertical irregularity seems unnecessary. A future 

study may further investigate the scope of applicability of this finding by 

examining the relative performance of ELF and MRSA designed buildings 

with additional configurations and site locations. 

Specific conclusions for each irregularity studied in this chapter are 

described in the following sections. 

6.9.1 Weight (Mass) Irregularity [V2]

Weight (mass) irregularity tends to reduce collapse resistance, but not 

dramatically. The location of the mass irregularity along the height of the 

building moderately affects collapse performance; archetypes with the mass 

irregularity in lower stories (where the building is already more likely to

have damage) tend to have lower collapse capacity than those with mass 

irregularities in their upper stories. The ELF procedure, which is currently 

prohibited for designing buildings with mass irregularities, tends to produce 

safer buildings than MRSA. 

6.9.2 Soft/Weak Story Irregularity [V1/V5]

Soft/weak story irregularities do not appear to pose a problem in moment 

frame buildings, as long as they meet code demands (e.g., strength 

requirements and drift limits). This is due to the fact that “weak story” really 

means “strong adjacent stories” if the “weak” story is still strong enough to 

resist the required lateral force demand per current code. It is logical to 

expect the collapse performance to still reduce in situations where the 

distribution of damage over height changes from several stories to just one as 

the result of a weak story irregularity, but for the design cases evaluated in 

this study, the negative effects of having more concentrated damage are 

offset by the positive effects of having strengthened members in the adjacent 

stories. This finding is consistent with other past studies on this topic. Based 
FEMA P-2012 6: Moment Frame Buildings with 6-23

Vertical Irregularities [V1, V2, V5, V6, V7]

upon this study, the prohibition of extreme weak story irregularities in SDC 

D and the height limitation on in SDC B and C may be overly conservative. 

Further study is recommended to evaluate the prohibition of weak/soft story 

irregularities in SDC E and F. 

6.9.3 Strong-Column/Weak-Beam [V6]

Strong-column/weak-beam (SCWB) is not categorized as an irregularity in 

ASCE/SEI 7-16, but it is an aspect of configuration that affects the 

distribution of damage over the height of the building, and which can have a 

corresponding impact on seismic performance. As shown in prior studies, 

increasing SCWB ratios generally improves collapse resistance. It is also 

found that implementing higher SCWB ratios in the lower stories of a 

building (where damage most commonly occurs) may improve collapse 

resistance, but this was based on a limited initial study. The studies show 

that this stepped approach may be an effective way to improve collapse 

safety at minimal material cost, although a broader study is needed to set 

limits for stepped designs. The future study could examine different building 

configurations, as well as a broader range of stepped SCWB ratio 

configurations; for steel frames specifically, the economy of increasing 

column sizes to remove the need for doubler plates is also something that 

could be further investigated. 

6.9.4 Gravity-Induced Lateral Demand [V7]

Gravity-induced lateral demand (GILD) is not currently identified as an 

irregularity in ASCE/SEI 7-16. GILD does not significantly affect the 

collapse performance of a building, as long as the additional lateral force is 

taken into account in proportioning the lateral system. However, failing to 

account for GILD in the building design process can result in significant 

reductions in collapse resistance, particularly if the irregularity occurs at a 

location in the building where earthquake damage already tends to 

accumulate (i.e., the first few stories). Although the findings suggest that 

buildings with GILD do not need special treatment in ASCE/SEI 7, the GILD 

studies were limited to a relatively small number of archetypes, and further 

study is recommended.

FEMA P-2012 7: Discussion of Other Irregularities 7-1 

[H2, H3, H4, H5, V3, V4, V8]

Chapter 7 

Discussion of Other Irregularities

[H2, H3, H4, H5, V3, V4, V8]

This chapter discusses several irregularities found in ASCE/SEI 7-16 that 

were not the subject of the extensive analysis described in earlier chapters. 

This chapter describes the irregularity, discusses its trigger and consequences 

relative to ASCE/SEI 7-16, and where warranted, suggests revisions to 

current ASCE/SEI 7-16 requirements. The following irregularities are 

discussed: 

• H2, Reentrant corner 

• H3, Diaphragm discontinuity 

• H4, Out-of-plane offset 

• H5, Nonparallel system

• V3, Vertical geometric 

• V4, In-plane discontinuity 

• V8, Wall discontinuity

7.1 Reentrant Corner [H2] Irregularity

ASCE/SEI 7-16 Table 12.3-1 defines a reentrant corner irregularity where 

both plan projections of the structure beyond a reentrant corner are greater 

than 15% of the plan dimension of the structure in the given direction. A 

reentrant corner might be thought of as a “notch” taken out of the plan of a 

structure, such as that shown in Figure 7-1. The concern is that this 

condition can generate additional demands on the horizontal and vertical 

elements in the seismic-force-resisting system (SFRS), particularly near the 

reentrant corner, not otherwise captured using conventional analytical 

methods. 

Discussion of reentrant corners in seismic design pre-standards and standards 

stretches back to at least ATC-3-06 Section 3.4.1 (ATC, 1978), which called 

for classifying a structure as “irregular” if a building had “reentrant corners 

with significant dimensions.” The qualifier “significant” was not defined in 

the provisions, but the ATC-3-06 Commentary has figures suggesting that 
7-2 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

notches amounting to at least 15% to 20% of the plan dimension for L, U, T, 

and X plan geometries would be considered irregular. 

Figure 7-1 Example of reentrant corner. 

Figure 7-2 compares ATC-3-06 Commentary Figure C3-4 showing three of 

these plan geometries, with how the geometries would appear if the 15% to 

20% notches were drawn to scale. Only the X plan geometry is drawn 

reasonably to scale. Examination of the other plan geometries shows that the 

15% to 20% notches are actually significantly smaller than suggested by 

appearance of the ATC-3-06 Commentary figure, making the eventually 

adopted 15% trigger appear quite conservative; nevertheless, the trigger 

stuck.

Figure 7-2 Comparison of reentrant corner examples as proportioned in ATC-3-06 Commentary and drawn 

to scale. 

Starting with 1985 Uniform Building Code (UBC) Section 2312(h)3 and 

1985 NEHRP Provisions Section 3.4.1, using the qualitative term “highly 

irregular shapes,” building codes and pre-standards began to address 

buildings with reentrant corners (International Conference of Building 
FEMA P-2012 7: Discussion of Other Irregularities 7-3 

[H2, H3, H4, H5, V3, V4, V8]

Officials, 1985; FEMA, 1986). The 1988 UBC Table 23-N defined as 

irregular a building where “both projections of the structure beyond a 

reentrant corner are greater than 15 percent of the plan dimensions of the 

structure in the given direction” (International Conference of Building 

Officials, 1988). Similar language can be found in the 1988 NEHRP 

Provisions in Section 3.41 and Table 3-3 and SEAOC Blue Books from 

1988, 1990, and 1996 (FEMA, 1988; SEAOC, 1988, 1990, 1996). 

Subsequent editions of ASCE/SEI 7-16 also used the 15% plan dimension as 

a trigger for classifying a building as irregular.

According to ASCE/SEI 7-16 Section 12.3.3.4, when a structure is classified 

as having a reentrant corner irregularity, diaphragm forces increase by 25% 

for the design of: 

1. Connections of diaphragms to vertical elements and to collectors;

2. Collectors and their connections, including connections to vertical 

elements, of the seismic-force-resisting system.

The increased diaphragm forces apply not just to stories of the building that 

have the reentrant corner but for all other stories, as well, because ASCE/SEI 

7-16 uses the introductory phrase, “For structures assigned to Seismic Design 

Categories D, E, or F...” Forces calculated using the seismic load effects 

including the overstrength factor, Ω0, need not be increased by 25%. 

Although reentrant corners were not studied analytically in this project, a 

review of the data generated for irregularities that were studied, particularly 

torsional response, suggests that reconsidering the existing irregularity 

trigger is warranted. 

The irregularity trigger should continue to consider the size of a reentrant 

corner as it relates to both dimensions of a building. For example, Figure 7-3 

shows how the ratios of Xp/X and Yp/Y together are likely better predictors of 

reentrant corner irregularities of significance than either Xp/X or Yp/Y alone. 

The irregularity trigger could consider the relative mass of the one diaphragm 

section relative to the other. If a reentrant corner impacts only a small 

portion of the structure, then it will have limited impact on the response of 

the entire structure, even if the building geometry meets the current 

definition of a reentrant corner. While maintaining a focus on demands

resisted by collectors and their connections related to the reentrant corner 

appears reasonable, the significance of this irregularity on the behavior of the 

diaphragm as a whole should also be considered. 
7-4 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

(a) Not a reentrant corner irregularity because (b) Reentrant corner irregularity because 

significant plan offset does not occur about both axes. significant plan offsets occur about both axes.

Figure 7-3 Impact considering dimensions of plan offsets about both axes in identifying reentrant 

corner irregularity. 

For example, if the dimensions of the cantilever portion of the diaphragm in 

a square building footprint are 0.15L about both X- and Y-axes, the plan 

offset would be 0.85L, which would trigger the reentrant corner irregularity. 

On the other hand, the mass of the smaller, cantilevered section of the 

diaphragm is only 3% of the total floor area. When Xp/X and Yp/Y both equal 

either 0.25 or 0.3, the mass of the smaller section of the diaphragm is still 

only 10% and 15.5% of the total floor mass, respectively. If Xp/X and Yp/Y

are significantly different, the relative mass would change even more slowly.

This suggests that some of the current penalties imposed when a reentrant 

corner irregularity is triggered, such as increases on the connection demands 

of diaphragms to vertical elements of the SRFS, may be difficult to justify.

While the number of different building geometries are infinite, the relatively 

small area of the mass of the cantilevered section of the geometries for plan 

offsets of less than 25% suggests that the 15% trigger may be unrealistically 

conservative.

Based on these observations, it appears that the 15% trigger could be relaxed 

along the following lines:

1. A reentrant corner irregularity should be triggered when both Xp/X and 

Yp/Y are greater than 25% as shown in Figure 7-3. 

2. Although the efficacy of the currently required force increase itself was 

not studied analytically, the increase in diaphragm forces should be 

limited to the stories with the reentrant corner irregularity, the elements 

at the corner should be classified as collectors and the required strength 
FEMA P-2012 7: Discussion of Other Irregularities 7-5 

[H2, H3, H4, H5, V3, V4, V8]

of these elements should be increased by 25%. Recognizing the potential 

for load redistribution within the SFRS due to the reentrant corner, these 

recommendations could also be applied to the stories above and below 

the reentrant corner.

3. In lieu of the prescriptive 25% increase in required strength, a diaphragm 

response analysis considering diaphragm flexibility could be undertaken 

to better assess the response of the building due to the reentrant corner.

7.2 Diaphragm Discontinuity [H3] Irregularity

ASCE/SEI 7-16 Table 12.3-1 classifies a structure as irregular when it has a 

diaphragm discontinuity, which is defined as “a diaphragm with an abrupt 

discontinuity or variation in stiffness, including one that has a cutout or open 

area greater than 50% of the gross enclosed diaphragm area, or a change in 

effective diaphragm stiffness of more than 50% from one story to the next,” 

as shown in Figure 7-4 (ASCE, 2017a). 

Figure 7-4 Diaphragm discontinuity comprising 50% of the gross floor area

drawn to scale. 

According to ASCE/SEI 7-16 Section 12.3.3.4, when a structure is classified 

as having a diaphragm discontinuity irregularity, diaphragm forces increase 

by 25% for the design of: 

1. Connections of diaphragms to vertical elements and to collectors;

2. Collectors and their connections, including connections to vertical 

elements, of the seismic-force-resisting system.

As with the reentrant corner irregularity, the increased diaphragm forces in 

Seismic Design Categories C through F apply not just to stories of the 

building that have the diaphragm discontinuity, but for all other stories as 

well. Forces calculated using the seismic load effects including the 

overstrength factor, Ω0, need not be increased. 

There are two diaphragm discontinuity triggers: (1) one that relates to the 

size of openings (i.e., the 50% trigger) or other changes in diaphragm 
7-6 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

strength or stiffness within a single floor; and (2) one that relates to a change 

in diaphragm stiffness from one floor to the next. 

The 50% opening trigger appears to be overly permissive, as shown in Figure 

7-4, as an opening of this size leaves little of the diaphragm around the 

opening to distribute loads to the seismic-force-resisting system. With 

openings of this size, diaphragm flexibility also begins to be a potential issue. 

Diaphragm force increases and a requirement to treat the elements around the 

opening as collector elements may be a reasonable requirement.

The trigger related to a change in stiffness from one level to another, which 

reflects a vertical issue triggered by a horizontal element, does not appear 

relevant to diaphragm irregularity classification. ATC-3-06 Section 3.4.1 

classifies a structure as irregular if the diaphragm at any single level has 

significant changes in strength or stiffness. Although not quantified, this 

description is consistent with diaphragms that have openings or changes in 

thickness on a single floor that might impact the distribution of seismic 

forces and result in force concentrations in the diaphragm or create torsion 

not otherwise accounted for in a typical analysis, as noted in the ATC-3-06 

Commentary. ATC-3-06 focuses on diaphragm changes on a single level 

rather than from one level to another. 

The first appearance of the changes in diaphragm stiffness between adjacent 

floors triggering a horizontal irregularity is the 1988 Uniform Building Code

(UBC) Table 23-N and the 1988 NEHRP Provisions, where the 50% stiffness 

change is listed (International Conference of Building Officials, 1988; 

FEMA, 1988). Prior editions of the UBC and NEHRP Provisions did not 

contain this trigger, nor did editions of the Blue Book prior to 1996. In the 

1996 Blue Book, the 50% stiffness change appears for the first time in that 

publication (SEAOC, 1996). 

Common examples where diaphragm strength or stiffness changes from one 

level to another are:

• Steel deck or plywood roof diaphragms (i.e., generally flexible 

diaphragms) above floors with concrete filled diaphragms; 

• Floors with thickened slabs needed to resist high gravity loads or to assist 

in distribution of seismic loads at podium levels. 

While these changes in stiffness from one floor to another may result in force 

redistributions that would not be captured in typical seismic analyses 

idealizing the diaphragm as fully rigid or fully flexible, the 25% force 

increase for all levels in the building does not appear warranted as the impact 

of the change in diaphragm strength or stiffness is expected to be focused on 
FEMA P-2012 7: Discussion of Other Irregularities 7-7 

[H2, H3, H4, H5, V3, V4, V8]

the floor with the significantly different diaphragm strength or stiffness and 

perhaps, a level or two above and below that floor. The studies of mass 

irregularities studied in this project suggest that adequate protection against 

collapse can be expected if the irregularity is accounted for in the design. 

Therefore, it is recommended that these changes in diaphragm strength and 

stiffness be addressed through appropriate modifications to the analytical 

model. 

Possible approaches to address the impact of a significant change in 

diaphragm strength or stiffness include: 

1. Explicit modeling of the diaphragm stiffness for the level with the 

changed strength or stiffness.

2. In lieu of explicitly modeling the diaphragm, the force increase 

prescribed by ASCE/SEI 7-16 Section 12.3.3.4 could be required for the 

level with the strength of stiffness change as well as the level above and 

below. 

7.3 Out-of-Plane Offset [H4] and In-Plane Discontinuity 

[V4] Irregularities

These two irregularities represent discontinuities in the load path between the 

vertical elements of the seismic-force-resisting system above and below an 

offset. In both discontinuities the vertical element above the discontinuity 

does not continue below insofar as its resistance to the horizontal (shear) 

forces, which must be transferred to other vertical elements below that level 

either through an in-plane or out-of-plane load path. The irregularity 

provisions address both this load path for horizontal forces and the load path 

for the overturning of the discontinuous element.

ASCE/SEI 7-16 Table 12.3-1 defines a structure to have an out-of-plane 

offset irregularity if the horizontal forces from the discontinued vertical 

element above the discontinuity must be transferred through a diaphragm or 

similar element in order to reach the vertical element or elements below. 

Similarly, ASCE/SEI 7-16 Table 12.3-2 defines a structure to have an 

“in-plane discontinuity in vertical lateral force-resisting element irregularity” 

if there is an in-plane offset of a vertical seismic-force-resisting element 

resulting in overturning demand on a supporting structural element (ASCE, 

2017a). Figure 7-5 shows idealizations of buildings with out-of-plane and 

in-plane discontinuities in wall systems. 
7-8 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

 

Figure 7-5 Walled buildings classified as irregular due to out-of-plane and in-plane offset of the wall 

system. 

According to ASCE/SEI 7-16 Section 12.3.3.3, when a structure has an 

out-of-plane offset or in-plane discontinuity: 

1. Members that support discontinuous walls or frames as well as the 

connections between those members and the discontinuous wall or frame 

must be designed to resist seismic load effects, including overstrength. 

For capacity-limited design, seismic load effects including overstrength 

are defined by the capacity-limited horizontal seismic load effect 

(Section 12.4.3.2). (Such capacity-limited design is permitted for all 

systems and is required for certain systems. For example, AISC 341 

requires capacity design for special concentrically braced frame (SCBF), 

buckling restrained braced frame (BRBF), eccentrically braced frame 

(EBF), and special plate shear wall (SPSW) systems.) For all other 

cases, seismic load effects including overstrength are calculated using the 

overstrength factor, Ω0, to amplify horizontal seismic forces.

2. Design forces for structures assigned to Seismic Design Category D, E, 

or F must be increased by 25% for the design of: 

a. connections of diaphragms to vertical elements and to collectors; 

b. collectors and their connections, including connections to vertical 

elements, of the seismic-force-resisting system

with the exception that forces calculated using the seismic load effects 

including the overstrength factor, Ω0, need not be increased. 

7.3.1 Impact of Out-Of-Plane and In-Plane Discontinuities in RC 

Wall Buildings

No new research was conducted as part of the current study to investigate the 

impact of in-plane and out-of-plane discontinuities on building performance 

to earthquake loading. Instead, the results of previous work addressing this 

issue in RC wall buildings were reviewed. Specifically, NIST GCR 

14-917-25, Recommendations for Seismic Design of Reinforced Concrete 
FEMA P-2012 7: Discussion of Other Irregularities 7-9 

[H2, H3, H4, H5, V3, V4, V8]

Wall Buildings Based on Studies of the 2010 Maule, Chile Earthquake 

(NIST, 2014), which documents the results of an investigation of the impact 

on earthquake performance of in-plane and out-of-plane discontinuities in 

reinforced concrete walls was reviewed. 

A general review of building drawings and earthquake damage patterns for 

multiple buildings damaged during the 2010 Maule, Chile earthquake 

resulted in the observation that damage was concentrated where: 

• Severe horizontal or vertical discontinuities were introduced into a wall 

and supplemental reinforcement was not provided to assist in transfer of 

forces through the discontinuity; and 

• Wall area was reduced substantially in a lower story, including cases 

where walls were supported on very small piers (i.e., columns). 

As part of the NIST study, building drawings and damage patterns were 

reviewed for four mid-rise reinforced concrete wall buildings that were 

moderately to severely damaged during the earthquake. Each of the 

buildings employed multiple walls to resist both gravity and earthquake 

loads; each of the buildings included multiple walls with local in-plane and 

out-of-plane discontinuities. A total of 120 wall discontinuities were 

identified and classified as: (1) wall termination in which an upper wall is 

terminated such that no lower wall exists in the story below; (2) wall opening 

in which there is a new opening in a lower wall; (3) wall shift in which there 

is a change in the centroid of a wall cross-section, including a change in the 

dimension or location of a wall flange; and (4) flag wall in which a change in 

the dimension of the web of a wall in which the upper wall is larger than the 

lower wall. Each discontinuity was quantified using multiple measures: 

change in wall area, the change in wall dimension, the movement of the wall 

centerline, and the movement of the wall centroid. Measures of the severity 

of the wall discontinuity were compared with observed damage. 

The NIST study concluded that damage is correlated with: (1) a change from 

one story to the story below in the location of the centroid of the wall that 

exceeds 30% of the in-plane length of the wall in the direction of the change; 

and (2) a reduction in the centerline length of the wall greater than 30% 

going from an upper to a lower story. 

The findings of the NIST study suggest two possible revisions to the current 

ASCE/SEI 7-16 requirements with respect to consideration of in-plane and 

out-of-plane discontinuities: 

1. The required increase in forces used for design of connections of 

diaphragms to vertical elements and collectors, and of collectors and 
7-10 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

their connections, per Section 12.3.3.4 of ASCE/SEI 7-16, need only be 

applied in the vicinity of the discontinuity and not throughout the entire 

structure.

2. The NIST study of local wall geometric discontinuities, using ASCE/SEI 

31-03 and ASCE/SEI 41-06 (which have since been combined in 

ASCE/SEI 41), found that Tier 2 “lack[s] correlation at the individual 

component level, [but] is consistent with the observed performance of 

the overall building in the earthquake,” and Tier 3 “generally resulted in 

a conservative assessment of performance at the component level” and 

“provided an acceptably accurate measure of overall building 

performance.” Since there is no corresponding Tier 1 checklist item, the 

NIST study recommends adding a Tier 1 Basic Structural Checklist item 

to flag walls with changes in cross-sectional geometry from one story to 

the story below that results in either a change in the location of the 

centroid of the wall that exceeds 30% of the length of the wall in the 

direction of the move or a reduction in the centerline length of wall that 

exceeds 30%. Since geometric changes of this magnitude would be 

identified by ASCE/SEI 7-16 as irregularity type V3 or V4, no 

corresponding change to ASCE/SEI 7-16 is needed.

7.4 Nonparallel System [H5] Irregularity

ASCE/SEI 7-16 Table 12.3-1 defines a building with a nonparallel system 

irregularity when any of the lateral force-resisting elements are not parallel to 

a major orthogonal axis of the seismic-force-resisting system. This is not an 

irregularity per se, but represents a condition where otherwise acceptable 

simplifications of analysis (e.g., using only independent orthogonal 

directions of load) are not appropriate. 

ASCE/SEI 7-16 does not prohibit this condition, but instead adds modeling 

requirements in the design of the building. These additional requirements 

include: 

• Required three-dimensional structural modeling (per Section 12.7.3 and 

Section 16.2.2 in ASCE/SEI 7-16);

• Consideration of direction of loading through the orthogonal 

combination procedure per Sections 12.5.3 and 12.5.4 (e.g., the “100%-

30%” orthogonal combination rule) or orthogonal ground motions 

applied simultaneously (where response history analysis is used); and

• Prohibition on using the equivalent lateral force (ELF) procedure for a 

building taller than 160 feet in a high-seismic zone (SDC D, E, or F) (per 

Table 12.6-1 in ASCE/SEI 7-16).
FEMA P-2012 7: Discussion of Other Irregularities 7-11

[H2, H3, H4, H5, V3, V4, V8]

While this condition was not analytically studied, it is assumed that the 

remedy of additional structural modeling requirements appropriately handles 

this configuration condition. Future studies may be able to validate the 

removal of the prohibition on the ELF procedure for the H5 condition since 

past studies have shown that designs based on the ELF procedure generally 

result in a lower probability of collapse than those based on the modal 

response spectrum analysis (MRSA) procedure (FEMA, 2009; NIST, 2010; 

NIST, 2012). 

7.5 Vertical Geometric [V3] Irregularity

ASCE/SEI 7-16 Table 12.3-1 defines a building to have a vertical geometric 

irregularity where the horizontal width of the seismic-force-resisting system 

changes by more than 30% between two adjacent stories. Similar to the H5 

irregularity, the code remedy is to add an additional modeling requirement. 

In this case, only one requirement is included: 

• A prohibition on the equivalent lateral force (ELF) procedure for a 

building taller than 160 feet in a high-seismic zone (SDC D, E, or F) (per 

Table 12.6-1 in ASCE/SEI 7-16) 

The vertical geometric irregularity definition was developed as a qualitative 

indicator of systems that could have a non-uniform distribution of stiffness, 

for which the load pattern assumed in the equivalent lateral force procedure 

could be inaccurate. However, as noted earlier, past studies have shown that 

the ELF procedure generally produces buildings that have a lower calculated 

probability of collapse than buildings designed by the MRSA procedure. 

Since the soft story irregularity (V1) captures the most concerning nonuniform stiffness distribution based on explicit stiffness calculations, it may 

be possible to eliminate the less direct V3 irregularity. However, this would 

require further study.

7.6 Wall Discontinuity [V8] Irregularity

A review of earthquake damage to RC wall buildings, as well as 

consideration of current design practice, suggests the potential need for code 

language addressing wall discontinuities such as shown in Figure 7-6. 

These types of discontinuities were investigated as part of the development 

of NIST GCR 14-917-25, Recommendations for Seismic Design of 

Reinforced Concrete Wall Buildings Based on Studies of the 2010 Maule, 

Chile Earthquake (NIST, 2014). This study used data collected following 

the 2010 Maule, Chile earthquake. Design to accommodate load transfer 

above and below stacked openings in walls is addressed in detail in Moehle 
7-12 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

(2015) and NIST (2011). Section B.1 provides more details on previous 

research and studies related to discontinuities in walls. Given the previous 

work addressing these types of discontinuities and the availability of 

guidance on design to accommodate these discontinuities, it was concluded 

that code changes would not be recommended. The following sections 

summarize previous research as well as design recommendations addressing 

wall discontinuities. Section B.2 provides more details on a limited study 

conducted on this type of irregularity. 

Figure 7-6 Vertical wall discontinuities potentially constituting an 

irregularity.

7.6.1 Discontinuities Associated with Initiation or Termination of 

Stacked Openings in Walls

A vertical discontinuity arises when coupled walls terminate in a solid wall 

panel below or above the coupled region (Figure B-3a). The solid panel zone

above or below the stacked openings can be subjected to large shear stresses 

when the wall system is loaded laterally, and significant damage has been 

observed in RC wall buildings in the vicinity of this type of discontinuity 

(Figure B-3b and Figure B-4). The vulnerability of this panel zone to high 

shear demand has also been investigated by Naeim et al. (1990) using linear 

finite element analysis.

NIST (2011) provides a discussion of the issues to be considered in design, 

and Moehle (2015) provides a detailed discussion of design of these panel 

zone discontinuity regions that exist above and below stacked openings. The 

discussion in Moehle (2015) includes calculations and figures demonstrating 

that shear in the panel zone results from anchorage of wall pier boundary 

element reinforcement. Moehle (2015) also includes the following design 

recommendations: (1) provide two layers of heavy horizontal “chord” 

reinforcement above and below the primary anchorage zone for wall pier 

longitudinal reinforcement; (2) provide reinforcement within the panel zone 
FEMA P-2012 7: Discussion of Other Irregularities 7-13

[H2, H3, H4, H5, V3, V4, V8]

to carry shear associated with anchorage of the wall pier longitudinal 

reinforcement; (3) continue 50% of wall pier reinforcement through to the 

base or top of the wall; and (4) use a capacity designed approach that 

accounts for overstrength of reinforcing steel. 

The above suggests that the discontinuities associated with initiation or 

termination of stacked openings in a wall is best addressed not at the system 

level via classification as a vertical structural irregularity, but as a local 

design and detailing issue. As such, changes to ASCE/SEI 7-16 to address 

this irregularity are not recommended; instead, it is recommended that efforts

be made to encourage appropriate design and detailing of the region in the 

vicinity of the irregularity. 

7.6.2 Discontinuities Associated with Increased Wall Area to 

Capture Forces Introduced by New Structural Elements

Wall geometry may change significantly over the height of the building to 

reflect increased or reduced lateral demand; most often changes in demand 

are associated with changes in floor plan. Figure 7-6 includes two vertical 

discontinuities associated with the addition of wall flanges to resist forces 

introduced by an expanded floor plan. Damage to RC wall buildings suggest 

that changes in wall geometry can result in damage and inadequate 

performance under earthquake loading.

The impact on earthquake performance of changes in wall cross section was 

investigated as part of the NIST GCR 14-917-25 report, which documents 

RC wall building damage resulting from the 2010 Maule, Chile earthquake 

(NIST, 2014). This NIST study resulted in the conclusion that significant 

earthquake damage was correlated with a change in the centerline length or 

the location of the centroid of the wall of greater than 30%. However, this 

study specifically concluded that only changes resulting in a reduction in 

wall centerline length going from one story to the story below were 

detrimental to RC wall building performance. Damage data indicated that 

increasing wall centerline length from one story to the story below rarely 

resulted in damage. Thus, on the basis of this NIST study, changes to 

ASCE/SEI 7-16 are not recommended to address this type of discontinuity. 

However, as discussed in Section 4.3 of NIST (2011), shear lag effects for 

flanged sections should be included in the design, most commonly by means 

of effective flange widths as defined in ACI 318-14.

Based on recommendations in NIST (2014), a Tier 1 Basic Structural 

Checklist item should be added to ASCE/SEI 41-17 to flag walls with local 

discontinuities caused by changes in cross-sectional geometry from one story 

to the story below that exceed either: (1) a reduction in centerline length 
7-14 7: Discussion of Other Irregularities FEMA P-2012

[H2, H3, H4, H5, V3, V4, V8]

greater than 30% (in either orthogonal direction); or (2) a change in centroid

location greater than 30% of the wall length measured in the direction of the 

change. For more information on related damage data that supports this 

recommendation, see Section B.1.2.
FEMA P-2012 8: Recommended Improvements 8-1 

Chapter 8 

Recommended Improvements

The regularity-related requirements found in current codes and standards 

generally reflect the best judgment of practitioners and academics based 

primarily on anecdotal observations and fairly simple linear static and linear 

dynamic analyses, without explicit consideration of collapse probability. The 

studies described in this report are some of the few to apply modern 

analytical and probabilistically based techniques to systematically evaluate 

the performance of buildings with and without irregularities.

Chapters 4 through 7 provide a detailed assessment of the significance of 

structural irregularities (in most cases, in terms of collapse probability), 

current code triggers, and the effectiveness of related code provisions. In 

many cases irregular structures that satisfy current code requirements have 

safety against collapse in an earthquake comparable to that for regular 

structures. In a few cases detailed studies suggest that code triggers or 

design requirements should be strengthened or can be relaxed to achieve 

comparable collapse resistance. This chapter summarizes recommended 

improvements for the seismic design of buildings with configuration 

irregularities and identifies areas for future study.

8.1 Codes and Standards

This section summarizes recommended improvements to ASCE/SEI 7-16 for 

seismic design of new buildings and ASCE/SEI 41-17 for seismic evaluation 

and retrofit of existing buildings. 

8.1.1 NEHRP Recommended Provisions and ASCE/SEI 7-16

Recommended improvements to ASCE/SEI 7-16 are summarized by four 

categories: (1) revised triggers and prohibitions; (2) revised modeling 

requirements; (3) revised design requirements; and (4) improved 

commentary and other clarifications.

Revised Triggers and Prohibitions

Torsionally Irregular Buildings [H1]: Based on explicit collapse 

assessments, as detailed in Chapter 4, the following revisions are 

recommended for torsionally irregular buildings: 
8-2 8: Recommended Improvements FEMA P-2012

• Classify buildings as torsionally irregular if more than 75% of their 

lateral strength is located at or on one side of the center of mass.

• Do not prohibit extremely torsionally irregular buildings in Seismic 

Design Categories E and F.

• Do not prohibit use of the equivalent lateral force procedure for 

torsionally irregular buildings.

Reentrant Corner and Diaphragm Discontinuity Irregularities [H2, H3]: 

Considering the historical development of reentrant corner and diaphragm 

discontinuity irregularities and reasonably anticipated consequences, as 

detailed in Chapter 7, the following revisions are recommended:

• A reentrant corner irregularity should be triggered where both Xp/X and 

Yp/Y are greater than 25% (rather than the current 15%).

• A diaphragm discontinuity irregularity should be triggered where a 

cutout or open area is greater than 25% of the gross enclosed diaphragm 

area (rather than the current 50%).

Mass (Weight) Irregularity [V2]: Based on explicit collapse assessments, 

as detailed in Chapter 6, and global behavior comparisons of buildings with 

mass irregularity, as detailed in Appendix F, it is recommended that 

irregularity Type V2 be eliminated. The only consequence of that 

irregularity is a requirement to base the design on the results of modal 

response spectrum analysis (MRSA), but MRSA is found to provide no 

advantage over the equivalent lateral force (ELF) procedure.

Revised Modeling Requirements

P-Delta Effects: P-Delta effects in three-dimensional models can be 

categorized as global translational (P-Delta), local deformational (P-delta), 

and rotational (P-θ); all should be considered where torsion response is 

important. The global translational P-Delta effect can be captured by 

ensuring that all vertical loads on the building are included in the model. 

Local deformational P-delta effects can be captured in the element 

formulation (for instance, using consistent geometric stiffness rather than 

linearized geometric stiffness) or by discretizing individual elements to 

capture second order effects in the analysis solution. If portions of the 

gravity system are not modeled explicitly, then the remaining vertical loads 

on unrepresented elements should be applied to “leaning columns,” which 

are vertical elements that are pinned to the diaphragms.

To capture twisting response more accurately, including P-θ effects, vertical 

loads should be applied to the structure at the locations where they are 
FEMA P-2012 8: Recommended Improvements 8-3

expected to occur. Location is important for simulating P-θ, because P-θ is a 

cross-product of P-Delta with the distance vector from the center of rigidity; 

in other words, the torque caused by P-Delta from a given column is equal to 

the lateral P-Delta component of that column times its perpendicular distance 

(lever arm) to the center of rigidity.

As an alternative to modeling vertical loads on every vertical component in a 

building, P-θ effects in rigid diaphragm models can be simulated by placing 

leaning columns strategically throughout the plan, such that the center of 

gravity and radius of gyration of the leaning column loads are the same as the 

center of gravity and radius of gyration of the actual vertical load carrying 

elements in the building. For the rectangular buildings in Chapter 4 of this 

study, this was accomplished by placing one leaning column in each 

quadrant of the building plan, each located one polar radius of gyration from 

the center of mass (i.e., assuming an equally distributed gravity system in the 

actual building).

Gravity-Induced Lateral Demands: Section 12.7.3 of ASCE/SEI 7-16

should be revised to address gravity-induced lateral demands. For instance, 

the requirement could read, “Where the configuration of structural elements 

is such that application of gravity loads induces lateral demands on the 

seismic-force-resisting system, those effects shall be considered explicitly in 

the mathematical model used to determine seismic design forces and drifts.”

Story Stiffness and Strength [V1, V5]: To assess soft story and weak story 

vertical configuration irregularities and to determine the redundancy factor, 

ρ, in accordance with Table 12.3-3 of ASCE/SEI 7-16, story stiffness and 

strength should be computed as follows.

For each story in each orthogonal direction, the apparent story stiffness 

should be computed as:

Kx = Vx / (δx – δx-1)

where:

Vx = the story shear at level x determined by an elastic analysis using the 

forces defined in Section 12.8.3 of ASCE/SEI 7-16; and

δx = the deflection at the center of mass of level x determined by an elastic 

analysis using the forces defined in Section 12.8.3 of ASCE/SEI 7-16.

For each story in each orthogonal direction, the story lateral strength should 

be computed as the sum the shear contributions of seismic-force-resisting 

elements as follows:
8-4 8: Recommended Improvements FEMA P-2012

• Brace members. The shear contribution for each brace is the horizontal 

component of the lesser of the connection capacity or brace capacity. 

The brace capacity (in tension or compression) should be consistent with

the direction of load application being considered. Where uplift of a 

shallow foundation, column capacity, or the capacity of an element 

supporting a discontinuous frame controls the response, the computed 

strength should reflect that limit state.

• Moment frame columns. The shear contribution is that corresponding 

to the least lateral capacity. For frame columns with weak columnstrong beam conditions, the shear contribution is the lesser of that 

developed when the top and bottom of the column are at flexural 

capacity, or the column shear capacity. For frame columns with a strong 

column-weak beam condition, the shear contribution is the lesser of the 

shear corresponding to development of flexural yielding at each end of 

the column (from adjoining beam yield hinges or column base 

connection capacity), or the column shear capacity.

• Shear wall piers. The shear contribution is the lesser of either the shear 

at development of the flexural strength, or the shear strength. Where 

wall flexure controls the response, both the 1.2D and 0.9D axial load 

cases should be considered. Where the capacity of an element 

supporting a discontinuous wall controls the response, the computed 

strength should reflect that limit state.

Revised Design Requirements

Torsionally Irregular Buildings [H1]. Based on explicit collapse 

assessments, as detailed in Chapter 4, the following revisions are 

recommended for torsionally irregular buildings:

• Require consideration of orthogonal loading effects, such as by the 

100%-30% orthogonal combination procedure of ASCE/SEI 7-16

Section 12.5.3.1, for all torsionally irregular buildings assigned to 

Seismic Design Category C, D, E, or F.

• Require use of redundancy factor, ρ = 1.3 (for Seismic Design Category 

D, E, or F), only where the structure has extreme torsional irregularity in 

both orthogonal directions or lines of lateral resistance in a given

direction are all on one side of the center of mass.

• Require that effects of accidental torsion be accounted for by application 

of a static accidental torsional moment (rather than explicit 5% mass 

offsets in linear dynamic analysis) for buildings with extreme torsional 

irregularity assigned to Seismic Design Category B, C, D, E, or F.
FEMA P-2012 8: Recommended Improvements 8-5

Design Forces for Collectors and Connections [H1, H2, H3, H4, V4]. 

Section 12.3.3.4 of ASCE/SEI 7-16 requires that design forces determined in 

accordance with Section 12.10.1.1 be increased for connections of 

diaphragms to vertical elements and to collectors and for collectors and their 

connections, for systems with one of several horizontal or vertical 

irregularities. Considering the historical development of these irregularities 

and reasonably anticipated consequences, as detailed in Chapters 4 and 7, it 

is recommended to limit the extent of such increased forces as follows:

• For structures with torsional stiffness irregularity [H1] or reentrant 

corner irregularity [H2], increased forces need be considered only at 

levels with the irregularity.

• For structures with diaphragm discontinuity irregularity [H3], out-ofplane offset irregularity [H4], or in-plane discontinuity irregularity [V4] 

increased forces need be considered only at levels with the irregularity 

and at adjacent levels above and below, due to possible load 

redistribution within the seismic-force-resisting system.

Recognizing the approximate nature of diaphragm inertial forces computed 

in accordance with Section 12.10.1.1 of ASCE/SEI 7-16, exceptions to the 

related force increases for irregular structures could be made where transfer 

conditions and diaphragm flexibility are modeled explicitly.

Improved Commentary and Other Clarifications

In addition to the technically substantive recommendations made above, the 

following revisions would improve the clarity and application of regularityrelated code requirements.

• For ease of reference, the item numbers that appear in Tables 12.3-1 and 

12.3-2 of ASCE/SEI 7-16 could be prepended with H or V to indicate 

class of irregularity—horizontal or vertical. For instance, “irregularity 

type 4 of Table 12.3-1” becomes “irregularity H4.”

• The commentary figures in ASCE/SEI 7-16 should be updated using 

those from this document. In particular, the figure for V4 in ASCE/SEI

7-16 is incorrect as it reflects the definition of that irregularity in 

ASCE/SEI 7-05.

• For the simple redundancy exception in ASCE/SEI 7-16 Section 12.3.4.2 

item b, “regular in plan at all levels” means “without irregularity type 1b, 

4, or 5 as defined in Table 12.3-1”.

• Section 12.3.2.2 of ASCE/SEI 7-16 should be revised in indicate that 

“Structures with more than one story that have one or more of the 
8-6 8: Recommended Improvements FEMA P-2012

irregularity types...” are subject to the requirements, and “one-story 

buildings in any Seismic Design Category or for” should be struck from 

exception 2.

• The designation for irregularity type H5 could be changed from 

“nonparallel system” to “non-orthogonal systems” to better reflect the 

concern that two-dimensional analysis in each of two orthogonal 

directions cannot capture system behavior adequately.

• The triggering condition for vertical geometric irregularity [V3] could be 

inverted as “the horizontal dimension of the seismic-force-resisting 

system in any story is less than 75% of that in an adjacent story” so that 

the trigger focuses attention on the story with the reduced stance.

8.1.2 ASCE/SEI 41-17

Based on recommendations in NIST (2014), as detailed in Chapter 7, a Tier 1 

Basic Structural Checklist item should be added to ASCE/SEI 41-17 to flag 

walls with local discontinuities caused by changes in cross-sectional 

geometry from one story to the story below that exceed either: (1) a reduction 

in centerline length greater than 30% (in either orthogonal direction); or (2) a 

change in centroid location greater than 30% of the wall length measured in 

the direction of the change.

8.2 Future Studies and Development

The studies described in this report sought to improve the design of new 

buildings with configuration irregularities, where possible as informed by 

explicit collapse assessments using the FEMA P695 method. Although this 

study has been the most comprehensive consideration to date of collapse 

resistance for several categories of structural irregularity, future studies could 

be used to further validate the findings and enlarge the scope of issues 

treated. In particular, improvements can be made in explicit collapse 

assessment, design sensitivities could be better identified, and several 

irregularities or systems types could be given more detailed consideration.

8.2.1 Explicit Collapse Assessment Improvements

“To the extent possible, nonlinear models” used in the FEMA P695 method 

“include explicit simulation of all significant deterioration mechanisms that 

could lead to structural collapse” (FEMA, 2009). The effects of other 

behaviors that could trigger collapse can be considered though not simulated 

explicitly. Non-simulated collapse conditions are often computed using story 

drift or other indirect metrics. Test results used to establish backbone curves, 

both for elements that are modeled explicitly and for behaviors that are 
FEMA P-2012 8: Recommended Improvements 8-7

assessed indirectly, often characterize behavior to displacements or rotations 

associated with loss of resistance to lateral loading, rather than loss of 

gravity-load resistance. The accuracy of collapse assessments could be 

improved by developing a more robust set of backbone curves that represent 

behavior to the point of loss of gravity-load resistance. Gravity framing 

systems are a good example where this improved representation could have a 

profound effect on collapse predictions, but the same is true of any element 

that supports gravity loads. ASCE/SEI 41-17 approximates this 

consideration, in one instance, by doubling life safety and collapse 

prevention acceptance criteria for coupling beams of reinforced concrete 

shear wall systems with short spans and bottom reinforcement that is 

continuous into supporting walls, but a testing-based criterion would be more 

consistent with the FEMA P695 process.

The shear-flexure-interaction models discussed in Chapter 5 and Appendix B

could be further developed to improve collapse assessment predictions.

8.2.2 Design Sensitivity Studies

Recent research has shown that the ELF procedure produces designs that 

generally have a lower probability of collapse than those designed using 

modal response spectrum analysis. Future study may be able to validate 

removal of the prohibition on the ELF procedure for additional irregularities, 

such as type V3.

ASCE/SEI 7-16 Section C12.9.1.4.1 describes changes made to address 

unacceptable collapse performance of designs based on modal response 

spectrum analysis and notes that even those changes do “not necessarily 

achieve the intended collapse performance.” This project’s findings for 

regular baseline structures and irregular variants confirm that ELF designs 

generally produce better collapse performance than MRSA designs. Further 

study addressing this disparity is recommended.

The detailed analyses undertaken in this project show that the collapse 

resistance of “barely code-conforming” designs is more sensitive than 

expected for more realistic designs of buildings with or without irregularities. 

A study of standard practice versus minimal design could be informative, 

especially if accompanied by FEMA P-58 risk assessments to show how 

much “savings” the minimal designs produce (FEMA, 2012b).

This project has focused on comparing the collapse resistance of properly 

designed buildings with and without irregularities. It could be useful to study 

the robustness of designs where possible misinterpretations or errors of 

application are made.
8-8 8: Recommended Improvements FEMA P-2012

8.2.3 Strong-Column/Weak-Beam Requirements

The objectives of strong-column/weak-beam (SCWB) requirements in the 

concrete and steel design standards are consistent. Section R18.7.3 of ACI 

318-14 describes the intent “to reduce the likelihood of yielding in columns,”

which could result “in a column failure mechanism that can lead to collapse.” 

Commentary Section E3.4a of ANSI/AISC 341-16 explains that “the SC/WB 

concept is more of a global frame concern” because “weak column frames... 

are likely to exhibit an undesirable response at those stories with the highest 

column demand-to-capacity ratios.” Since the objective is directly related to 

global system performance associated with the target reliabilities for 

structural stability set forth in Section 1.3.1.3 of ASCE/SEI 7-16, 

consideration could be given to adding a general requirement related to 

strong-column/weak-beam behavior in ASCE/SEI 7.

Reinforced Concrete Moment Frames. The strong-column/weak-beam 

studies of reinforced concrete moment frames, detailed in Section 6.7.2, 

suggest that using larger SCWB ratios at lower stories where critical collapse 

mechanisms usually concentrate and lower ratios in upper stories may have 

design merit. This approach could be studied further to assess whether it 

could be refined to improve economy without reducing collapse resistance.

Steel Moment Frames. Like earlier studies, the SCWB studies of steel 

moment frames, detailed in Section 6.7.2, suggest that yielding in the joint 

panel zone improves collapse resistance relative to frames with inelastic 

response concentrated in beams outside the panel zone. However, since the 

backbone curves commonly used for panel zones reflect no degradation, 

while those for beams do degrade, it seems that this beneficial effect could be 

unrealistically overestimated. Further study of the relative importance and 

consequences of panel zone and beam yielding could inform steel moment 

frame models that more correctly reflect collapse resistance.

8.2.4 More Detailed Considerations

Additional Structural Systems. Although a range of structural systems was

considered in the explicit collapse assessments of this project, further studies 

could be performed using masonry shear walls, wood frame shear walls, steel 

concentrically braced frames, and steel eccentrically braced frames. It is 

expected that the general trends related to configuration irregularity would 

hold for these systems, but material-specific configuration subtleties could be 

investigated. For instance, ANSI/AISC 341 limitations on K-bracing and the 

relative proportion of braces in tension and compression, and requirements

for V- and inverted V-braced frames could be better informed by explicit 

collapse assessments. With respect to reentrant corners or diaphragm 
FEMA P-2012 8: Recommended Improvements 8-9

discontinuities, understanding implications of different diaphragm materials

and location of vertical elements in the SFRS relative to discontinuities may 

benefit from more detailed study.

Combinations of Systems. With the exception of the mixed system studies 

reported in Chapter 4, the archetypes investigated by this project use the 

same structural system along two orthogonal axes. Section 12.2.2 of 

ASCE/SEI 7-16 allows combinations of framing systems in different 

directions, and Section 12.2.3 allows horizontal or vertical combinations of 

framing systems in the same direction, with direction on the selection of 

seismic response parameters. The collapse resistance of systems with these 

configurations has not been assessed explicitly, but could be in future studies.

Buildings with Multiple Irregularities. Although some real buildings 

include multiple irregularities that could interact, the analyses of this project 

treat irregularities separately, just as they are defined independently in codes. 

Future studies could include archetypes with combinations of vertical and/or 

horizontal irregularities to assess whether performance problems compound. 

As discussed in Chapter 2, many of the buildings that collapsed in past 

earthquakes have both soft/weak story irregularity and torsional irregularity. 

The code rules for buildings with those irregularities were prompted by 

observations of that damage, but explicit collapse assessments for a broad 

design space of buildings with multiple irregularities have not yet been 

performed.

Wall Discontinuity [V8] and In-Plane Discontinuity [V4]. Appendix B 

reports differences in performance of walls with openings depending on the 

location of the opening and direction of loading. Additional studies could 

help to clarify where the introduction of an opening near the end of wall 

should be classified as an in-plane discontinuity [V4]. Perhaps that 

classification could be based on the location of neutral axis for the overall 

wall section with respect to the opening or the anticipated magnitude of 

localized compressive demands.

Gravity-Induced Lateral Demand. The studies of systems with gravityinduced lateral demand (GILD), detailed in Chapter 6, consider demands 

induced by all columns at a single story leaning in the same direction by a 

uniform amount. The same GILD ratio, which is gravity induced story shear 

(QG) divided by story shear capacity (QV), could be produced by columns 

sloping over multiple stories or by one or a few columns leaning more 

severely. Similarly, a broader set of analyses could help to identify which 

stories are most sensitive to the GILD effect for various baseline archetypes. 
8-10 8: Recommended Improvements FEMA P-2012

Such further studies could be undertaken with an expanded archetype design 

space to validate this project’s findings.

Consideration of Accidental Torsion Effects in Dynamic Analysis. 

Chapter 4 and Appendix A report reductions in collapse resistance for 

torsionally sensitive buildings proportioned for accidental torsion effects by 

explicit mass offsets in (linear) modal response spectrum analysis. Similar 

studies should be undertaken to assess whether the explicit mass offset 

method could be permitted for linear response history analysis and whether it 

should continue to be required for nonlinear response history analysis (per 

Section 16.3.4 of ASCE/SEI 7-16).
FEMA P-2012 A: Torsion Studies A-1

Appendix A

Torsion Studies

This Appendix documents more detail of the torsion studies, which were 

completed in support of the findings and recommendations summarized in 

Chapter 4 of this report. The sections of this Appendix are independent of 

one another (i.e., they can be read in any order), but they depend on Chapter 

4 for context. For detailed results of the torsion studies, see the electronic 

Supporting Documentation for Appendix A: Torsion Studies Tabulated 

Designs and Results. 

A.1 Development and Validation of Simplified 3D Models

A.1.1 Nonlinear Backbones for Modeling the Seismic-ForceResisting System

The seismic-force-resisting systems (SFRSs) of the archetype models were 

modeled with shear springs defined by nonlinear backbones, illustrated in 

Figure A-1. The short baseline model emulates the global properties of a 

two-story wood shear wall building for which damage accumulates primarily 

in the lower story and P-Delta effects are small. Data for calibrating the 

short baseline archetype were taken from a prior study of wood light frame 

buildings (DeBock et al., 2016). 

The mid-rise baseline backbone has characteristics similar to the baseline 12-

story reinforced concrete (RC) special moment frame (SMF) that was 

developed to study vertical irregularities in Chapter 6, which has significant 

P-Delta effects. Key properties of the 12-story baseline building are listed in 

Table A-1 for the purpose of comparison. 

In the mixed system archetypes, lines of lateral resistance representing RC 

walls used a backbone similar to the backbones computed for RC walls in 

Chapter 5; the RC wall parallel to the moment frame (Figure A-2) started out 

stronger than the walls in the wall-only direction, because it is stiffer than the 

frame and attracts more force. The lines of resistance representing RC SMFs 

are similar to the 8-story baseline RC SMF developed for the vertical 

irregularity studies in Chapter 6, except that they are weaker because the 

frame is softer than the wall and attracts less force.
A-2 A: Torsion Studies FEMA P-2012

0

0.1

0.2

0.3

0.4

0 0.02 0.04 0.06 0.08 0.1

Force (Fraction of Gravity)

Drift Ratio

Short

0

0.1

0.2

0.3

0.4

0 5 10 15

Displacement (in)

Short 

Backbone

With

Leaning

Column

Backbone

Without

Leaning

Column

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.02 0.04 0.06 0.08

Force (Fraction of Gravity)

Drift Ratio

Mid-Rise

0

0.02

0.04

0.06

0.08

0.1

0.12

0 10 20 30 40 50

Displacement (in)

Mid-Rise

Backbone

With

Leaning

Column

Backbone

Without

Leaning

Column

0

0.05

0.1

0.15

0.2

0 0.02 0.04 0.06

Force (Fraction of Gravity)

Drift Ratio

RC Wall

0

0.05

0.1

0.15

0.2

0 10 20 30 40 50

Displacement (in)

RC Wall

Backbone

With

Leaning

Column

Backbone

Without

Leaning

Column

Figure A-1 Backbone properties of the baseline archetypes representing short, mid-rise, 

and RC wall type buildings. 
FEMA P-2012 A: Torsion Studies A-3

Table A-1 Model Information for Baseline Archetypes

Baseline Archetype

Height of Model(1)

[ft.] Overstrength (Ω)

Period-Based 

Ductility (μ) ACMR

“Short” 12 2.11 9.9 1.8

“Mid-rise” 56 1.66 5.3 1.9

Comparison: 12-story 

RC SMF model 158 1.53 5.2 1.9

“RC Wall” 69 1.33 17 3.0

Comparison: 8-story 

RC wall models 106 1.11, 1.35 8.6, 12.4 2.9, 3.3

(1) Important for simulating P-Delta

Figure A-2 Backbone properties for lines of lateral resistance representing 

the “wall” and “frame” that make up the mixed system (in the 

long direction of the mixed system archetypes). 

The heights of the three-dimensional nonlinear models were determined so 

that P-Delta effects approximate those of their multi-story counterparts at 

story drifts ranging from 3% to 6%, where P-Delta effects are critical for 

determining the onset and progression of collapse. Figure A-1 and Figure 

A-2 show the nonlinear backbones of the baseline archetypes, with and 

without leaning columns included in the models. Key properties of the 

baseline archetypes are summarized in Table A-1. The heights of the 

P-Delta columns in the nonlinear mid-rise model are shorter than the height 

that is used for drift calculations in the design step because drifts tend to 

concentrate in fewer stories as the building becomes nonlinear. The drifts 

shown in Figure A-1 are consistent with maximum story drift ratios observed 

in the high-end multi-story models, not roof drifts. 

The cyclic properties of the nonlinear springs were modeled with peakoriented material properties having relatively low cyclic deterioration. 

Cyclic deterioration effects were minimized in the simplified models for the 

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50

Force (Fraction of Gravity)

Displacement (in)

Mixed RC Wall and Frame

RC Wall Backbone

With Leaning

Column

RC Wall Backbone

Without Leaning

Column

RC Frame

Backbone With

Leaning Column

RC Frame

Backbone Without

Leaning Column
following reasons: (1) cyclic deterioration is a system/material dependent 

property and this study is intended to capture torsion effects in a more 

generic sense; and (2) collapse capacity has been shown to be relatively 

insensitive to cyclic deterioration properties in comparison with other 

parameters such as peak strength and negative stiffness (Ibarra, 2003, 2005). 

Figure A-3 illustrates the cyclic behavior of the short baseline model. Force (Fraction of gravity)

Figure A-3 Cyclic properties of the short baseline 

backbone (leaning columns excluded). 

A.1.2 Scaling of Nonlinear Backbones 

The strength and stiffness of the nonlinear backbones that represent lines of 

lateral resistance were scaled to match the changes in strength and stiffness 

that were determined in the design step. Scaling of the strength and stiffness 

were applied to each branch of the nonlinear backbone, therefore ductility 

did not change. Figure A-4 shows how the backbones change when strength 

and stiffness are altered: (a) illustrates perfectly coupled strength and 

stiffness while (b) and (c) illustrate decoupled strength and stiffness. 

(a) (b) (c) 

Displacement

Force

Coupled Stiffness

and Strength

Displacement

Force

Increase Strength more

than Stiffness

Force

Figure A-4 Effects of scaling strength and stiffness of the nonlinear backbones, illustrated with the short 

archetype, as follows: (a) identical increases in strength and stiffness (coupled); (b) strength 

increase greater than stiffness increase (decoupled); and (c) stiffness increase greater than 

strength increase (decoupled). P-Delta effects are excluded for this illustration. The solid 

black line represents the baseline; blue-dotted and red-dashed lines represent incremental 

increases in strength and stiffness. 

A-4 A: Torsion Studies FEMA P-2012
FEMA P-2012 A: Torsion Studies A-5 

A.1.3 3D Modeling Approach

Three-dimensional single-story models of the archetypes were made in

OpenSees (McKenna et al., 2000). The SFRS was modeled with nonlinear 

shear springs located at each line of lateral resistance. The diaphragm was 

modeled as rigid with a lumped mass located at its center. For archetypes 

without inherent eccentricity, the mass was offset by 5% of the building 

dimension in each orthogonal direction (simultaneously) to produce torsion. 

The rotational inertia of the building mass was determined assuming an even 

distribution of the mass across the building plan. Four leaning columns, or 

P-Delta columns, were included in the models, each one radius of gyration 

away from the center of plan. Figure A-5 shows a plan view of a 3D model. 

Figure A-5 Plan view of a single story model including placement of 

leaning (P-Delta) columns, mass offset, and SFRS. 

Incremental dynamic analysis (IDA) was performed for the 22 FEMA farfield ground motions. Both components of the ground motion were applied 

simultaneously to the model. Two IDAs were performed for each pair of 

ground motions—one with the ground motion in its original orientation and 

another with the ground motion rotated 90 degrees, so a total of 44 IDAs 

were performed for each archetype. Buildings were considered collapsed if 

the drift ratio exceeded 10% at any location in plan due to failure of the 

gravity system.

A.1.4 Validation of Single-Story 3D Models

The single-story 3D models were intended to represent the macro-behavior 

of multi-story buildings. Therefore, a subset of multi-story models were used 

to validate their performance. The “high-end” multi-story models are similar 

in plan to the single-story models, but they are 12 stories tall and use the 

12-story RC SMF baseline for their lines of lateral resistance. The lines of 

lateral resistance were moved systematically to introduce torsional 

irregularity, but they were not redesigned. 
A-6 A: Torsion Studies FEMA P-2012

Figure A-6 shows the reduction in collapse resistance that occurs for a 2:1 

aspect ratio variant when one line of lateral resistance is moved away from 

the perimeter, but the SFRS is not re-designed to resist torsion forces. Figure 

A-7 shows a trend similar to the one observed in Figure A-6, but for the case 

when all four lines of lateral resistance are moved toward the center of the 

building plan. 

0

0.2

0.4

0.6

0.8

1

1.2

ACMR / ACMR

0 0.25 0.5 0.75 1

Perimeter Frame

γ

ATC 123 Short

ATC 123 Mid-rise

12-story "High-end"

ATC 123 Mid-rise, Less Conservative

a

b

γ

*

b

+ CM

Figure A-6 Trends in collapse resistance of 2:1 aspect ratio single 

asymmetric archetypes with increasing eccentricity, but no reproportioning of the SFRS for torsion demands. 

Figure A-7 Trends in collapse resistance of 2:1 aspect ratio symmetric 

archetypes with increasing torsional irregularity (TIR), but no 

re-proportioning of the SFRS for torsion demands. 

Performance of the short archetypes declines less quickly, because they are 

less sensitive to rotational P-Delta effects (or P-θ). The mid-rise archetype, 

which is intended to represent buildings similar to the “high-end” 12-story 

model, is conservative for predicting the effects of torsional response on 

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1 1.5 2 2.5 3

ACMR / ACMRPerimeter Frame

Max TIR of the Variant Archetype

ATC 123 Short

ATC 123 Mid-Rise

12-story "High-End"

ATC 123 Mid-Rise,

Less Conservative
FEMA P-2012 A: Torsion Studies A-7

collapse. It is conservative, because the height of the leaning columns is 

calibrated to match the P-Delta effects in the multi-story building during the 

onset and progression of collapse, when maximum story drifts are high (3% 

to 5%) and have localized to a few stories. Therefore, P-Delta effects at 

lower drifts are over-estimated in the simplified mid-rise models. As a 

result, P-θ effects are overestimated when torsional responses cause 

significant displacement of the leaning columns prior to the lines of lateral 

resistance degrading. 

Based on these comparisons, it is concluded that the simplified 3D models 

for short archetypes are adequate for assessing torsion design provisions. 

However, the mid-rise variants with leaning columns one radius of gyration 

from the center of mass (CM) would lead to conservative conclusions when 

torsional P-θ effects play a significant role in the collapse mechanism. 

Therefore, a modified, less conservative, version of mid-rise archetype 

models were created by modeling the leaning columns at 70% of the radius 

of gyration from the CM to compensate for their over-estimation of P-θ; the 

results in Chapter 4 and in this Appendix are obtained from the archetypes 

with the conservatism reduced.

A.2 Torsional Strength Irregularity

ASCE/SEI 41 classifies buildings as torsionally irregular if the demand to 

capacity ratio (DCR) is significantly higher on one side of the CM than the 

other. The potential negative outcome of uneven strength distribution is that 

yielding on one side of the CM may cause the center of rigidity (CR) to move 

farther away from the CM, thus increasing the torsional response.

To assess the effects of torsional strength irregularity on collapse 

performance, a suite of symmetric code-conforming archetypes was

developed. Torsional strength irregularities were introduced by increasing 

the strength of the lines of lateral resistance on one side of the CM in:

(a) both orthogonal directions; and (b) one orthogonal direction. This was 

done for three different aspect ratios and for torsionally-flexible variants 

(lines of lateral resistance near center of plan, high TIR) and for torsionally

stiff variants (lines of lateral resistance at the perimeter, low TIR). 

Collapse resistance, relative to the baseline model, for the short and mid-rise

archetypes with torsional strength irregularity is shown in Figure A-8 and

Figure A-9, respectively. For these archetypes, torsional strength irregularity 

does not decrease collapse resistance, as long as the building is codeconforming, but it sometimes will increase the collapse resistance. 
A-8 A: Torsion Studies FEMA P-2012

Figure A-8 Relative collapse resistance of symmetric short archetypes

having strength irregularities due to lower DCR on one side 

of the center of mass.

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.2 0.4 0.6 0.8 1.0

ACMR / ACMRBaseline

DCR of the Variant Achetype

1:1 Sym, TIR=1.05

1:1 Sym, TIR=1.56

2:1 Sym, TIR=1.08

2:1 Sym, TIR=1.94

4:1 Sym, TIR=1.09

4:1 Sym, TIR=2.07

Figure A-9 Relative collapse resistance of symmetric mid-rise

archetypes having strength irregularities due to lower DCR

on one side of the center of mass.

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.2 0.4 0.6 0.8 1.0

ACMR / ACMRBaseline

DCR of the Variant Archetype

1:1 Sym, TIR=1.05

1:1 Sym, TIR=1.56

2:1 Sym, TIR=1.08

2:1 Sym, TIR=1.94

4:1 Sym, TIR=1.09

4:1 Sym, TIR=2.07

A.3 Importance of Checking Drift and Stability 

Requirements at the Building’s Edge for Torsionally 

Irregular Buildings

An important finding of the torsional irregularity studies is that enforcing 

drift and stability limits at the building edge (rather than CM) is critical for 

providing adequate collapse resistance for torsionally sensitive buildings. 

Figure A-10 shows steady declines in collapse resistance for the mid-rise 

archetypes when drift and stability checks are performed at the CM rather 

than the building edge. Comparing the trends to Figure 4-8, it is seen that 
 

collapse resistance is sometimes nearly as poor as when torsion is neglected 

entirely in the design process (e.g., the 1:1 Single Asymmetric archetypes). 

1 1.5 2 2.5

Max TIR of the Variant Archetype

0.4

0.6

0.8

1

1.2

1:1 Sym

2:1 Sym

4:1 Sym

1:1 Double Asym

2:1 Double Asym

1:1 Single Asym

2:1 Single Asym

4:1 Single Asym

Figure A-10 Trends in collapse resistance for mid-rise archetypes 

proportioned according to ASCE/SEI 7-16 to resist seismic 

forces, but with a redundancy (ρ) of 1.0 and drift/stability 

checks performed at the CM, rather than the edge of the 

building. Archetypes with decoupled strength and stiffness are 

represented by solid lines; dashed lines represent archetypes 

with coupled strength and stiffness. 

A.4 Rationale for Triggering Type 1a Torsional 

Irregularity When >75% of Strength is on One Side of 

the CM 

In Chapter 4, it is recommended that buildings with more than 75% of their 

strength on one side of the CM be classified as torsionally irregular. The 

reason for this recommendation is to invoke the 100%-30% orthogonal 

earthquake load combination rule for buildings with significant inherent 

eccentricity. The 100%-30% orthogonal load combination rule is necessary

to account for the coupling of dynamic responses in the two orthogonal 

directions. Specifically, lines of resistance orthogonal to the direction with 

inherent eccentricity have to resist seismic forces in their own direction in 

addition to torsional moments caused by shaking in the eccentric direction; 

failure to account for this coupling effect when designing the SFRS results in 

under-designing lines of resistance perpendicular to the direction with 

eccentricity. 

In many cases, buildings with significant inherent eccentricity are already

classified as torsionally irregular due to having TIR > 1.2. However, 

buildings that are rectangular in plan can have significant eccentricity in the 

long direction and still have TIR < 1.2. For example, the three-sided and 

mixed system archetype buildings all have TIR less than 1.2 for the cases 

where lines of resistance in the short-direction are at or near the perimeter. 

The circled data points in Figure A-11 through Figure A-13 show the 

FEMA P-2012 A: Torsion Studies A-9 
1.6

1.4

1.2

1

0.8

Not classified as irregular 

in ASCE/SEI 7-16 

1 1.5 2 2.5

Max TIR of the Variant Archetype

3-sided, Sym

3-sided, Asym A

3-sided, Asym B

1.6

1.4

1.2

1

0.8

Not classified as irregular 

in ASCE/SEI 7-16 

1 1.5 2 2.5

Max TIR of the Variant Archetype

3-sided, Sym

3-sided, Asym A

3-sided, Asym B

 

performance of these buildings if all of the proposed modifications from

Chapter 4 are used, except that torsional irregularity is based solely on TIR 

(as in ASCE/SEI 7-16). The 3-sided archetypes were designed with a 

redundancy factor, ρ, of 1.3 in the long direction, which is triggered by

having all of the lines of resistance on the same side of the CM. A 

redundancy factor of 1.3 would not be triggered under current ASCE/SEI 

7-16 design procedures, so the three-sided archetypes with TIR < 1.2 would 

perform even worse than observed in Figure A-11 and Figure A-12 if they

were proportioned according to ASCE/SEI 7-16. 

Figure A-11 

Figure A-12 

Trends in collapse resistance for short 3-sided variants designed 

with all of the recommended torsion provisions from Chapter 4, 

except that torsional irregularity is determined only by TIR (as in 

ASCE/SEI 7-16). 

Trends in collapse resistance for mid-rise 3-sided variants 

designed with all of the recommended torsion provisions 

from Chapter 4, except that torsional irregularity is 

determined only by TIR (as in ASCE/SEI 7-16). 

A-10 A: Torsion Studies FEMA P-2012 
1.6

1.4

Mixed, Sym

1.2 Mixed, Asym A

Mixed, Asym B

1

0.8

1 1.5 2 2.5

Max TIR of the Variant Archetype

Not classified as irregular 

in ASCE/SEI 7-16 

Figure A-13 Trends in collapse resistance for mixed system variants 

designed with all of the recommended torsion provisions 

from Chapter 4, except that torsional irregularity is 

determined only by TIR (as in ASCE/SEI 7-16). 

A.5 Application of 5% Mass Offsets to Simulate 

Accidental Torsion with Modal Response Spectrum 

Analysis 

Applying 5% mass offsets in lieu of the static accidental torsion moments set 

forth in Section 12.8.4 of ASCE/SEI 7-16 is insufficient for some building 

configurations. The most negatively affected configurations are those whose 

fundamental mode of vibration is a torsional mode with relatively little 

modal mass in the lateral direction. This is caused by the torsion mode 

having too little effect on the analysis due to its small participation factor. 

The symmetric archetypes are examples of buildings with torsional modes 

that have little modal participation in their lateral directions. 

Table A-2 shows the effects on the required strength and stiffness for plansymmetric torsionally irregular archetypes when the two design methods for 

accidental torsion are used. At moderate levels of torsional irregularity, the 

5% mass offset method significantly increases force and drift demands. 

However, at high levels of torsional irregularity, offsetting the mass 5% 

makes very little difference in the design values. This finding is consistent 

with a previous study by De la Llera and Chopra (1994); they showed that 

simulating accidental torsion with 5% mass offsets in modal response 

spectrum analysis amplifies accidental torsion when the lateral and torsional 

modes have similar periods, but the amplifying effect of the dynamic 

analysis diminishes as the torsional period becomes significantly longer than 

the translational period. For reference, the torsional periods for the buildings 

in Table A-2 are >140% of the lateral periods. 

FEMA P-2012 A: Torsion Studies A-11 
A-12 A: Torsion Studies FEMA P-2012

Table A-2 Differences in Strength and Stiffness Required When 5% Mass Offsets are Used 

in Lieu of Static Accidental Torsion Moments for Torsionally Irregular Symmetric 

Archetype Buildings (in the More Critical Direction) 

Required Strength Relative to Baseline Required Stiffness Relative to Baseline(2)

Plan 

Aspect 

Ratio TIR(1)

Static 5% 

Accidental Mass 

Torsion Offsets Difference 

Static 

Accidental 5% Mass 

Torsion Offsets Difference 

1 

1.31 1.15 1.12 -3% 1.05 1.05 0% 

1.56 1.66 1.40 -16% 1.47 1.00 -32%

2.25 2.71 1.41 -48% 4.42 1.00 -77%

2 

1.22 1.14 1.45 27% 1.00 1.40 40% 

1.53 1.35 1.20 -11% 1.42 1.20 -15%

2.04 2.27 1.14 -50% 3.74 1.12 -70%

4 

1.26 1.17 1.55 32% 1.00 1.50 50% 

1.60 1.43 1.24 -13% 1.65 1.30 -21%

2.09 2.37 1.17 -51% 3.99 1.20 -70%

(1) Due to differences in stiffness, TIR (torsional irregularity ratio) is slightly different between the versions with

static accidental torsion moments versus those designed with modal response spectrum analysis and 5% mass

offsets. The reported TIR values are for the latter.

(2) The stability coefficient and story drift of the baseline are 0.07 and 1.2%, respectively, so the required

stiffness does not increase immediately as torsional irregularity is introduced.

Figure A-14 shows the performance of symmetric archetypes when they are

designed using modal response spectrum analysis with mass offsets equal to 

(+/–)5% of the perpendicular direction. The results show that directly 

accounting for accidental torsion in the modal response spectrum analysis

procedure using 5% mass offsets in the structural model can lead to poor 

performance in extremely torsionally irregular buildings. 

Figure A-14 Collapse performance of symmetric archetypes designed with

modal analysis and accidental torsion applied directly by 

offsetting the mass (+/–) 5% of the perpendicular building 

dimension in the structural model. 

1 1.5 2 2.5 3

Max TIR of the Variant Archetype

0.6

0.8

1

1.2

1:1 Sym

2:1 Sym

4:1 Sym

Fitted Median

+/- 
FEMA P-2012 A: Torsion Studies A-13 

A.6 Explanation of Why Some Trends in the Results Plots 

Double Back on Themselves 

Some of the trends in the results plots “double back” because the TIR that is 

used to gauge torsional irregularity in ASCE/SEI 7-16 Table 12.3-1 saturates 

and eventually declines at large levels of torsional irregularity. Figure A-15 

illustrates this phenomenon for the single asymmetric archetype 

configuration. Saturation (and eventual reduction) of TIR only occurs when 

inherent eccentricity becomes very large, and it is observed to a greater 

degree if the building dimension perpendicular to the applied lateral load is 

larger than the building dimension parallel to the applied lateral load. 

Type 1b

Type 1a a

b

γ

*

b

+ CM

Figure A-15 Illustration of how the torsional irregularity ratio (TIR) computed in 

ASCE/SEI 7-16 Table 12.3-1 varies with plan aspect ratio and 

eccentricity (after Korolyk and Wagner, 2016). The horizontal lines 

show the ASCE/SEI 7-16 thresholds for Type 1a Torsional Irregularity 

and Type 1b Extreme Torsional Irregularity. The thickened lines in the 

building plan (right) represent lines of lateral resistance. All lines of 

lateral resistance are equally stiff for computing TIR in this example. 

FEMA P-2012 B: Concrete Wall Studies B-1

Appendix B

Concrete Wall Studies

This Appendix supports and supplements the information and results 

presented in Chapter 5. Section B.1 provides a summary of past 

investigations of reinforced concrete (RC) walls with irregularities. Section 

B.2 provides information on a limited study that was conducted to investigate 

wall discontinuity (V8) irregularities in RC wall buildings. Section B.3 

provides details of the process to design the RC wall buildings used to assess 

the impact of openings on building performance. Section B.4 and Section 

B.5 describe validation and comparison studies of analytical methods used in 

the RC wall building studies. Section B.6 presents all the analysis results 

generated as part of the study on RC wall buildings, including tables 

summarizing collapse probabilities, results from pushover analyses, and 

results from the dynamic response history analysis. 

Design calculations and detailed RC wall designs are provided in the 

electronic Supporting Documentation for Appendix B: Part 1, Concrete 

Shear Wall Detailed Design Information and Part 2, Concrete Shear Wall 

Building Drawings. 

B.1 Past Investigations of Concrete Walls with 

Irregularities 

The following sections provide an overview of past investigations of RC 

shear walls with irregularities from observed damage in past earthquakes, 

quantification studies, and laboratory test results. 

B.1.1 Damage of Concrete Walls with Irregularities in Past 

Earthquakes

Damage to RC wall buildings during recent earthquakes demonstrates the 

potential for vertical irregularities to impact earthquake performance. 

Observed damage also suggests which vertical irregularities are highly 

correlated with damage and are particularly detrimental to building 

performance.

2010 Maule Earthquake. Evaluation of buildings damaged during the 2010 

M8.8 Maule earthquake identified a number of building system design and 

configuration issues that could be expected to result in poor earthquake 

performance. These issues include discontinuities in walls; coupling of walls 
B-2 B: Concrete Wall Studies FEMA P-2012

via slabs, beams, and spandrels; wall demands induced by nonstructural 

elements; and wall axial demands. These issues are described in detail in 

Appendix D of NIST GCR 14-917-25, Recommendations for Seismic Design 

of Reinforced Concrete Wall Buildings Based on Studies of the 2010 Maule, 

Chile Earthquake (NIST, 2014), and addressed in Birely (2012). The 

following provides a brief description of the building configuration issues 

considered to be most highly correlated with earthquake damage.

Many of the RC wall buildings damaged during the 2010 Maule earthquake 

were observed to have significant vertical discontinuities in walls that were 

primary elements of the lateral load resisting system. Figure B-1 and Figure 

B-2 show vertical discontinuities in which a significant length of wall is lost 

from an upper to a lower story. Appendix D of NIST GCR 14-917-25

discusses vertical discontinuities in detail and provides vertical discontinuity 

data for the Chilean buildings that were studied. 

Figure B-1 Coupled walls in upper stories do not continue to lower story 

(Plaza del Rio Building, Concepción, Chile). Photo courtesy of 

Ken Elwood.

A vertical discontinuity also arises when coupled walls terminate in a solid 

wall panel either below or above the coupled region, or both, as shown in 

Figure B-3a. The solid panel constitutes a discontinuity region that can be 

subjected to large shear stresses when the coupled walls are loaded laterally. 

Figure B-3b shows a typical reinforcement layout in the vicinity of this 

discontinuity and damage observed following the 2010 Maule earthquake. 

Figure B-4 shows similar damage patterns in a wall system with a similar 

discontinuity observed following the Loma Prieta earthquake (Moehle, 
FEMA P-2012 B: Concrete Wall Studies B-3 

2015). Detailed descriptions of this particular discontinuity are provided in 

NIST (2014) and Moehle (2015). 

Figure B-2 A change in the wall section from the upper to lower story results in a loss 

of wall area and localization of flexural yielding (Plaza del Rio Building, 

Concepción, Chile). Photo courtesy of Ken Elwood.

(a) (b)

Figure B-3 Vertical discontinuity(ies) in coupled wallsL (a) Coupled walls with stack 

of openings terminating in a solid wall; and (b) damage map from axis 8 

of the Alto Rio Building in Concepción, Chile following the 2010 Maule 

earthquake (image from NIST, 2014).
B-4 B: Concrete Wall Studies FEMA P-2012

Figure B-4 Damage to building sustained during the 

1989 Loma Prieta earthquake (image 

from Moehle, 2015).

2016 Meinong Earthquake. The 2016 M6.7 Meinong earthquake in 

southern Taiwan resulted in severe damage to reinforced concrete buildings. 

For the majority of the damaged buildings, lateral loads were primarily 

resisted by moment resisting frames. However, a couple of high-rise 

buildings with reinforced concrete walls and frames were damaged. Figure 

B-5 shows an example of a reinforced concrete wall with openings. As 

shown in the figure, the primary damage was to a “column” at the exterior of 

the wall. It is likely that the large axial force on the column resulted in the 

compression damage. 

Overview of Findings. Based on review of earthquake damage following

the 2010 Maule earthquake, and supported by other damage data presented 

above, primary findings with respect to the impact of building configuration, 

design, and detailing on earthquake performance are as follows (Birely,

2012): 

• Damaged walls often did not have a clearly defined location where a 

plastic hinge could form. 

• Detailing was poor in damaged buildings. Wall confining reinforcement 

was light, widely spaced, did not have 135-degree hooks and, in some 

cases, was nonexistent. 
FEMA P-2012 B: Concrete Wall Studies B-5

Figure B-5 Damage to “column” at wall discontinuity in a 20-story high-rise 

building (2016 Meinong earthquake; image from Pujol et al., 2017).

• Wall longitudinal bars that terminated into a lower region without 

sufficient vertical and horizontal reinforcement resulted in damage 

between the two terminated bar regions.

• The location of wall reinforcement splices affected the location and 

concentration of damage.

• Lateral load can be transferred through severe vertical discontinuities in a 

wall. However, this requires adequate detailing around the discontinuity 

in the individual wall and adequate detailing and strength in the 

components (beams or slab) that contribute to the load transfer. 

• Several damaged buildings had relatively thin walls (6-in. thickness). It 

is expected that performance of a building with well-detailed, thick, but 

fewer walls would be superior to that of a building with many poorlydetailed thin walls. However, minor damage was observed in a wall 

constructed of relatively poorly-detailed 6-in. thick walls. 

• Damage consistent with wall coupling, such as crushing of wall concrete 

due to high compressive loads and cracking and crushing of concrete in 

coupling beams and slabs, was observed; however, the extent of the 

impact from coupling requires further evaluation.

• Buildings that were essentially undamaged typically had a thick, wellreinforced mat foundation and a continuous core.
B-6 B: Concrete Wall Studies FEMA P-2012

B.1.2 Quantification of Vertical Discontinuities in Concrete 

Walls Using Field Data

Vertical discontinuity is used to describe a significant change in the crosssectional area or reinforcement layout of a wall from one story to the next. 

Typically, a reduction in cross-sectional or reinforcement area from an upper 

story to a lower story is more critical than a reduction from a lower to an 

upper story. A study conducted by Birely (2012) sought to quantify 

discontinuities for inclusion in evaluation methods, such as the Tier 1 

Procedure of ASCE/SEI 31, Seismic Evaluation of Existing Buildings

(ASCE, 2003).

The ASCE 31 Tier 1 checklists consider vertical discontinuities in buildings 

by considering the load path, verifying that all lateral load resisting elements 

are continuous to the foundation, and by considering the relative stiffness and 

strength of a floor relative to the floor above and below it. However, damage 

to mid-rise RC wall buildings in the 2010 Maule earthquake suggests that 

local changes in the stiffness and strength of individual building components 

may be highly correlated with damage. In Birely (2012), a discontinuity was 

considered to be any location where the cross-section of a wall at any given 

floor (referred to as the upper wall) differed from the cross-section of the 

wall at the floor below (referred to as the lower wall). In the four buildings 

studied, discontinuities typically fell into one of the following categories:

• Termination of a wall from the upper floor to the lower floor;

• Openings present in the lower section of the wall (Figure B-6a);

• Shift in the centroid of the cross-section, including a relocation of a wall

flange(s) (Figure B-6b); or

• Flag-shaped wall, where the upper wall is larger than the lower wall 

(Figure B-6c).

When assessing the damage levels for the discontinuities, the difference 

between the damage in the lower and upper floors was considered. Thus, for 

the wall in Figure B-6c, the damage level is equal to 4 (i.e., 4 (lower floor) – 

0 (upper floor) = 0) and for the wall in Figure B-6a, the damage level is equal 

to 3 (i.e., 4 (lower floor) – 1 (upper floor) = 3). For walls where there is no 

change in the level of damage at the discontinuity or where the damage level 

is higher in the upper wall, such as the wall in Figure B-6b, the damage level 

is defined as zero (0). 
FEMA P-2012 B: Concrete Wall Studies B-7 

(a) Opening (b) Shift (c) Flag 

 shaped

Damage Legend

Figure B-6 Discontinuities observed in walls in Chilean buildings and 

corresponding damage.

The following measures were used to quantify the discontinuities observed in 

the walls:

• The change in wall area, normalized by the area of upper wall and 

reported as a percentage.

• The change in the maximum east-west and north-south dimensions of the 

wall, normalized by the dimension of the upper wall in that direction and 

reported as a percentage. This is calculated by the dimensions of the 

rectangle in which the wall is inscribed.

• Τhe change in the centerline length of the wall normalized by that of the 

upper wall and reported as a percentage. The centerline length, Lcl, of the 

wall is the total length of wall as measured along the centerline of the 

cross-section. Distinction is also made in the total length of wall in the 

x- and y-directions.

• The change in the in-plane coordinates of the geometric centroid of the 

wall, normalized by the length of the wall in the same direction and 

reported as a percentage. This number is always reported as a negative 

number to facilitate comparison with the measures defined above.

The complexity of the discontinuities ranged from simple, isolated flagshaped walls (for which damage was easily attributed to the reduced wall 

length and area) to walls with multiple adjacent discontinuities (for which 

damage was not easily attributed to any individual discontinuity). On the 

basis of these data, it was recommended that in concrete shear walls that are 

continuous to the foundation, local discontinuities caused by changes in 

cross-sectional geometry from one story to the story below shall not exceed: 

(1) a reduction in centerline length greater than 30% (in either orthogonal 

direction); or (2) a change in the centroid location greater than 30% of the 

wall length measured in the direction of the change. 
B-8 B: Concrete Wall Studies FEMA P-2012

B.1.3 Laboratory Test Results for Concrete Walls with Vertical 

Irregularities

A number of laboratory test programs have studied the earthquake 

performance of slender, flexure-controlled walls with vertical discontinuities 

resulting from the introduction of openings. Test programs reviewed for this 

study are listed and briefly described below. The studies have mixed results, 

with some studies suggesting that openings have minimal impact on wall 

performance (e.g., Yanez et al., 1992; Taylor, 1995; Shiu et al., 1981; Noda 

et al., 1997; Kato et al., 1999; Wu, 2005) and others indicating that openings 

can reduce drift capacity (Ali and Wight, 1991; Wu, 2005) or improve drift 

capacity (Wu, 2005). These mixed results are likely due to the wide 

variation in the design procedures and detailing employed in the different 

studies. In most cases, the results of these experimental studies support those 

of the simulation-based studies presented in Section B.2, in that well-detailed 

walls with openings placed near the middle of the wall exhibit deformation 

capacities similar to, or slightly larger than, those exhibited by solid walls, 

while walls with openings placed close to the perimeter of the wall exhibit 

reduced deformation capacity as the openings increase compressive demands 

at the perimeter of the wall.

Experimental investigations of the impact of openings on wall performance 

that were reviewed are briefly summarized below:

• RC Structural Walls with Staggered Openings (Ali and Wight, 1991). 

Ali and Wight tested four barbell concrete walls. The first specimen was 

solid and served as the reference. The other three specimens had

staggered openings placed within the web region of the wall, with each 

of the three specimens having openings placed progressively further 

from the boundary element and closer to the center of the wall. The 

staggered openings had minimal impact on wall response up to a drift of 

approximately 1%, beyond which the openings resulted in premature 

compression-shear failure of the web region of the wall, as the solid wall 

exhibited a drift capacity of 3%. 

• Seismic Behavior of Walls with Irregular Openings (Yanez et al., 1992). 

Yanez et al. tested six walls with different opening sizes and 

arrangements, including staggered openings and stacked openings 

centered on the centerline of the wall. On the basis of the experimental 

data, Yanez et al. concluded that performance was not affected by the 

size and arrangement of openings, with all wall specimens exhibiting a 

drift capacity of 2.5% to 3.0%.
FEMA P-2012 B: Concrete Wall Studies B-9

• Design of Slender Reinforced Concrete Walls with Openings (Taylor,

1995). Taylor tested two walls, each with a single opening placed at the 

base of the wall within the unconfined and lightly reinforced web region 

of wall. The specimens represent a planar wall (Thomsen and Wallace, 

1995) and a barbell wall (Ali and Wight, 1991) tested as part of other 

studies, with a single opening placed at the base of the solid reference 

walls used in the other studies. Experimental data show the opening 

having minimal impact on performance for the planar wall and, similar to 

the results obtained by Ali and Wight, resulting in significant reduction 

in deformation capacity for the barbell wall.

• Earthquake Resistant Structural Walls: Test of Walls with and without 

Openings (Shiu et al., 1981). Shiu et al. tested a solid wall and a wall 

with stacked openings centered on the centerline of the wall. Walls 

exhibited similar deformation capacity, but different failure modes.

• Tests of Reinforced Concrete Cantilever Walls with Openings (Noda et 

al., 1997) and Strength and Deformation Capacity of Cantilever 

Structural Walls with Openings (Kato et al., 1999). Six two-story walls 

with different opening sizes, reinforcement ratios, and configurations 

(stacked at the centerline of the wall or stacked at the perimeter of the 

wall) were tested to investigate the impact of openings on wall 

performance. The research team concluded that: (1) walls with openings 

can behave in a ductile manner and fail in flexure similar to solid walls 

provided sufficient reinforcement is added to both sides of the opening; 

and (2) diagonal reinforcement around the openings had a major 

influence in increasing the shear strength of these walls.

• Design of Reinforced Concrete Walls with Openings for Strength and 

Ductility (Wu, 2005). Wu tested six I-shaped walls including a solid 

wall, three walls with openings located in one half of the wall, and two 

walls with openings centered on the centerline of the wall. Wall 

openings varied in length. In the best cases, walls with openings 

centered on the centerline of the wall exhibited substantially greater drift 

capacity than the solid wall. A wall with an opening located very close 

to the wall flange exhibited reduced deformation capacity in comparison 

with the solid wall. 

• Seismic Behavior of Reinforced Concrete Shear Walls with Regular and 

Staggered Openings after the Strong Earthquakes between 2009 and 

2011 (Marius, 2013). Marius tested five walls—one solid wall, three 

walls with staggered openings, and one coupled wall—to investigate the 

potential for staggered wall openings to improve wall performance. The 

research team concluded that: (1) walls with staggered openings are 
B-10 B: Concrete Wall Studies FEMA P-2012

stiffer than coupled walls; (2) walls with staggered openings that result in 

a small and a large pier at the wall base exhibit compression-shear failure 

of the small pier; (3) coupled walls with inadequately detailed coupling 

beams exhibit wall failure due to coupling beam failure; and (4) walls 

with staggered openings exhibit diagonal shear cracking between 

openings. 

B.2 Investigation of Vertical Irregularity Using Nonlinear 

Continuum Analysis 

Nonlinear continuum-type analysis using ATENA software was conducted to 

investigate the impact on wall performance of the horizontal location of an 

opening introduced in the bottom story of a mid-rise wall. The study used 

modeling recommendation per Whitman (2015) for simulating the response 

of reinforced concrete walls using ATENA. Whitman (2015) demonstrates, 

using an experimental data set comprising approximately twenty planar wall 

test specimens, that these recommendations result in accurate and precise 

simulation of strength, deformation capacity, and failure mode for concrete 

walls with varying design parameters subjected to cyclic lateral loading. In 

the Whitman study, as in the study conducted for this project, simulations 

applied constant gravity load and lateral load under monotonically increasing 

displacement demand. 

An 8-story wall (30 ft. long, 2 ft. thick, 106 ft. tall) with uniformly 

distributed vertical and horizontal reinforcement was used as the reference 

wall configuration for this study. Four opening locations were considered: 

(1) no opening (reference configuration); (2) openings at the center of the 

wall; (3) openings on the right side of the wall; and (4) openings on the left 

side of the wall. In the simulation, lateral loading was applied at the top of 

the wall to produce monotonically increasing lateral displacement; thus, 

walls with openings on the left and right sides of the wall exhibited different 

behavior depending on whether the opening was in the tension or 

compression region of the wall. Figure B-7 shows the reference wall 

configuration with openings (7.5 ft. long by 10 ft. tall), as well as the 

supplemental horizontal reinforcement added above the opening to prevent 

damage directly above the opening. 

All analyses employed a lateral load at the top of the wall to produce 

monotonically increasing displacement of the wall to the right such that an 

opening on the right side of the wall affected the compression region of the 

wall while an opening on the left affected the tension region. Figure B-8

shows base shear, normalized by c g f A′ with cf ′ = 6500 psi and Ag equal to 

the area of the reference wall (Ag = 60 ft.

2

), versus drift at the point of the 
FEMA P-2012 B: Concrete Wall Studies B-11

applied load. Figure B-8 shows that introducing an opening in the middle of 

the wall has minimal impact on the stiffness, strength, and deformation 

capacity of the wall while introducing an opening near the edge of a wall has 

significant impact on wall strength and deformation capacity. Reduction in 

wall strength results when an opening reduces the area of reinforcing steel 

near the edge of the wall that is available to carry tension. Reduction in wall 

deformation capacity results when an opening reduces the area of concrete 

and reinforcing steel near the edge of the wall that is available to carry 

compressive load, triggering early onset of a compression failure at the edge 

of the wall. 

Figure B-7 Wall configurations and designs used for ATENA analyses to 

investigate the impact of opening location. Wall is 30 ft. long 

by 2 ft. thick by 106 ft. tall.
B-12 B: Concrete Wall Studies FEMA P-2012

Figure B-8 Normalized base shear stress( ( ) ) / with in psi ′ ′ V Af f base g c c

versus drift at the effective height. 

B.3 RC Wall Building Design Process 

A series of RC wall buildings were designed in which lateral loads are 

resisted by planar reinforced concrete walls. Walls were designed without 

openings and with openings located at the 1st, 1st and 2nd, and an upper story. 

Opening length was determined to achieve a stiffness for the stories with the 

opening that was either 75% or 50% of the stiffness of the baseline building. 

Story stiffness was computed as K = V/∆ with V and ∆ defined as shown in 

Figure B-9. This approach was established early in the project and differs 

from the approach recommended in Appendix G. Wall demands were 

determined using the ELF procedure per ASCE/SEI 7-16, Minimum Design 

Loads and Associated Criteria for Buildings and Other Structures (ASCE, 

2017a) and for the case of the Dmax design spectrum, using the results of a 

modal response spectrum analysis (MRSA). When using MRSA, 10 modes 

considered for each analysis and a mass participation of more than 97% was 

achieved in all cases.

Figure B-9 Story stiffness calculation (K = V/∆).
FEMA P-2012 B: Concrete Wall Studies B-13

B.3.1 Building Prototype

The walls designed represent a structural RC wall as part of an 8-story and a 

12-story building. The prototypes of the buildings are shown in Figure B-10. 

For the 8-story building, two walls are used in each direction and for the 

12-story building four walls are used in each direction to resist lateral loads. 

ASCE/SEI 7-16 and ACI 318-14, Building Code Requirements for Structural 

Concrete (ACI, 2014), were used to design the shear walls with the following 

assumptions:

• Wind loading:

o Exposure category B

o Wind speed for strength = 130 mph

o Wind speed for stiffness = 100 mph

• Earthquake loading:

o Seismic Design Categories B and D; for each category the maximum 

spectral acceleration was used.

o Site Class: C - Very dense soil and soft rock

o Risk Category: II

• Gravity loading:

o Dead load (materials + mechanical) = 175 psf (floors)

= 140 psf (roof)

o Live load (area load + partitions) = 50 psf + 15 psf (partitions) 

= 65 psf (floors) 

= 20 psf + 0 psf (partitions) 

= 20 psf (roof)

• ASCE/SEI 7-16 load cases were considered:

Load Case 4: 1.2D + 1.0W + 0.5L

Load Case 5: 0.9D + 1.0W

Load Case 6: (1.2 + 0.2SDS)D + ρQE + 0.5L

Load Case 7: (0.9 – 0.2SDS)D + ρ QE

with ρ = 1.0 used for all designs.

• Figure B-10 shows plan view for 8- and 12-story buildings and:

o Footprint is 120 ft. × 120 ft.

o Center of stiffness and mass coincide (no eccentricity)
B-14 B: Concrete Wall Studies FEMA P-2012

(a) 8-story building (b) 12-story building

Figure B-10 Building prototypes. Shown wall length (30 ft.) is for Dmax designs; wall length is 20 ft. for Bmax

designs.

• For both 8-story and 12-story building designs: 

o Walls were designed for gravity load on the basis of assumed dead 

and live loads and the framing patterns shown in Figure B-10. The 

dead loads above are assumed to be distributed over the entire area.

o Earthquake demands were increased by 5% to account for accidental 

torsion. 

• For the 8-story building (Figure B-10a): 

o Two planar walls were located in each direction. 

o For Dmax designs, Load Case 7 controlled strength design. Wall 

longitudinal and horizontal reinforcement was designed to meet 

moment and shear demands associated with earthquake loads. Two 

30 ft. walls were required to meet flexural strength requirements for 

earthquake load without excessive longitudinal reinforcement ratios. 

Two 30 ft. walls provide adequate stiffness to meet seismic drift 

requirements.

o For Bmax designs, two 20 ft. walls were required to meet seismic drift 

limits. Load Case 5 (wind) controlled strength design. Minimum 

reinforcement ratios were adequate to meet flexure and shear 

demands associated with wind loading. 

• 12-story building (Figure B-10b): 

o Four planar walls were located in each direction. 
FEMA P-2012 B: Concrete Wall Studies B-15

o For Dmax designs, Load Case 7 controlled strength design. Wall 

longitudinal and horizontal reinforcement were designed to meet 

moment and shear demands associated with earthquake loads. Four 

20 ft. walls were required to meet flexural strength requirements for 

earthquake load, without excessive longitudinal reinforcement ratios. 

Four 30 ft. walls provide adequate stiffness to meet seismic drift 

requirements.

o For Bmax designs, four 20 ft. walls were required to meet wind drift 

limits. Load Case 5 (wind) controlled strength design. Minimum 

reinforcement ratios were adequate to meet flexure and shear 

demands associated with wind loading. 

B.3.2 Wall Design

All walls were designed per ACI 318-14. The longitudinal reinforcements

were designed such that the wall was tension-controlled for flexure. The 

design was based on the following:

• Specified concrete compressive strength, cf ′ = 5000 psi

• Yield strength of steel bars, fy = 60 ksi

• Length of the wall, lw = 30 ft. (Dmax) = 20 ft. (Bmax)

• Thickness of the wall, tw = 2 ft.

For wall regions with boundary elements, the cross-section configuration 

shown in Figure B-11 was assumed. Per ACI 318-14, the nominal flexural 

strength, Mn, was defined by the compression strain in the extreme concrete 

fiber reaching a magnitude of -0.003 in/in. The maximum longitudinal 

reinforcement ratio considered for wall boundary elements, ρv.BE, was 3%. 

This limit was chosen based on the practical constraint that in splice regions 

the longitudinal reinforcement ratio would double to 6%, and reinforcement 

ratios in excess of 6% can impair concrete placement and significantly 

reduce constructability. For calculation of the wall nominal flexural strength, 

a fiber-type section model and the OpenSees software platform were used. 

The OpenSees Concrete01 and Steel01 material models were employed to 

simulate the stress strain response of concrete and steel. Concrete and steel 

models employed the material strengths listed above; the the impact on steel 

confinement on concrete response and steel hardening were not included in 

the analysis. 

Wall sections were designed such that φMn exceeded the flexural demand. 

Per ACI 318-14 Section 21.2.2, φ = 0.9 in was used, as allowed for the case 

of steel strain in excess of 0.005 in./in. at Mn. Spacing of longitudinal 
B-16 B: Concrete Wall Studies FEMA P-2012

reinforcement and reinforcement detailing were according to Section 11.7 

and Chapter 25 of ACI 318-14 (ACI, 2014).

Figure B-11 Typical wall section and assumed strain 

distribution.

Shear design was in accordance with ACI 318-14 Sections 18.10.2 and 

18.10.4. Shear demand was as defined by ASCE/SEI 7-16, with no 

amplification to account for dynamic response of yielding structure. In 

almost all web regions of the walls, shear demands were such that minimum 

shear reinforcement requirements of Section 18.10.2.1 controlled the design, 

and horizontal and vertical reinforcement ratios within the web region were 

0.0025 (ρl = ρt = 0.0025). In the vicinity of wall openings, where shear 

demands increased due to the discontinuity, horizontal and vertical 

reinforcement ratios increased significantly. Design of these regions was in 

accordance with ACI 318-14 Sections 11.7 and Chapter 25.

The transverse reinforcement in the boundary elements was designed in 

accordance with ACI 318-14 Sections 18.10.6.4, 11.7 and Chapter 25.

B.3.3 Design of Wall Panel Zone

According to Moehle (2015), “panel zone” is the region or element of a 

structural wall subjected to relatively uniform shear which can be with or 

without normal stresses. The forces from adjacent wall segments are

resolved and as a result the nominal shear stress in the panel zone may be 

bigger than the ones in the adjacent wall segments. Moehle uses a useful 

solution by assuming no weights for the walls and equal dimensions (lw) as 

shown in Figure B-12. After assuming T2 = C2, and from horizontal 

equilibrium of the chord along ab, T2 = C2 = v1lhbw/2. And from horizontal 

equilibrium of chords along ef and ij, T2 = C2 = v2lwbw. Both quantities 

should be equal and after rearranging it is found that:

2

h

2 1

w

l

v v

l =
FEMA P-2012 B: Concrete Wall Studies B-17

This relation indicates how different and bigger v1 is relative to v2. To find 

that, the vertical equilibrium of forces were taken in the vertical chords and 

that required:

T1 = (v1 + v2)hsbw = 1

2

h

1sw

w

l vhb

l

    +

 

Hence the shear stress in the panel zone can be found:

1

1

2

1

1

h s w

w

T

v l h b

l

  =  

+  

The shear reinforcement above and below the punches, which resembles a 

panel zone, is designed both in accordance with ACI 318-14 and using the 

method suggested by Moehle (2015). In almost all the cases, Moehle’s

method controls the design of shear reinforcement for the region above the 

punch. However, the depth of the panel zone, hs, is extended whenever it 

would not meet the requirements of Section 18.10.4 of ACI 318-14 for shear 

strength. Consequently, the amount of reinforcement in the chord is 

calculated by considering the moment induced by the couple from the two 

boundary elements on each side of the opening (tension and compression). 

In other words, the two horizontal chords above the opening, have the same 

or larger moment capacity as the ones from the boundary reinforcements on 

each side of the punch.

Figure B-12 Forces in the panel zone (Moehle, 2015).

B.3.4 Design of Coupling Beams 

The coupling beams were designed according to Section 18.7 of ACI 318-14. 

Shear forces in the coupling beams were found using “Section Cut” in 

SAP2000. For each coupling beam, two groups of diagonally placed bars 
B-18 B: Concrete Wall Studies FEMA P-2012

were used symmetric about the midspan. ACI 318-14 requires transverse 

reinforcement to be provided for either diagonal bars or for the entire beam 

cross section according to Section 18.7.5.2 of ACI 318-14. Transverse 

reinforcement was provided in the entire beam cross section. 

B.3.5 RC Wall Building Design Summaries

Table B-1 Summary of Parameters Used in the Design and Analysis (8-Story Building – Dmax)

8-story, Special Concrete Wall (8-D-0-0-ELF)

Design Parameters

Dead Load:

Live Load:

Seismic Weight:

Total building seismic weight: 

Wind Speed: 

Risk Category: 

Importance Factor:

Typical = 175 psf; Roof = 140 psf

Typical = 65 psf; Roof = 20 psf

Typical = 190 psf; Roof = 147.5 psf

W = 21276 kips

110 mph (strength); 85 mph (service)

II

Ie = 1.0

Special Concrete Walls: R = 6; Cd = 5

Site Class C

Seismic Design Category D: SDS = 1.5; SD1 = 0.6

Material properties: c beam , f ′ = 5 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms Iwall = 0.5Ig

Design based on Equivalent Lateral Force Procedure

Calculated period:

Upper limit period:

Seismic response coefficient:

Controlling equation:

Seismic base shear (two walls):

Tx = 1.14 s

CuTx = 0.925 s

Cs,x = 0.108

Equation 12.8-3, ASCE/SEI 7-16

Vx = 2300 kips = 0.108W

(Load Case 7)

Drift limits considered: 0.020hx (seismic); h/400(wind)

Design base shear (including accidental

torsion) (two walls): V = 2358 kips = 0.18W

Controlling lateral design criteria: Two 30 ft. walls required to provide adequate flexural strength to 

meet earthquake demands.

Two 30 ft. walls in each direction provide adequate strength without 

excessive longitudinal reinforcement ratios (boundary element 

longitudinal reinforcement ratio = 2.5%).

Two 30 ft. walls in each direction provide adequate stiffness to meet 

drift limits for seismic demands (max. interstory drift = 0.55%).
FEMA P-2012 B: Concrete Wall Studies B-19

Table B-2 Summary of Parameters Used in the Design and Analysis (12-story Building – Dmax)

12-story, Special Concrete Wall (12-D-0-0-ELF)

Design Parameters

Dead Load:

Live Load:

Seismic Weight:

Total building seismic weight:

Wind Speed:

Risk Category: 

Importance Factor:

Typical = 175 psf; Roof = 140 psf

Typical = 65 psf; Roof = 20 psf

Typical = 190 psf; Roof = 147.5 psf

W = 32220 kips

110 mph (strength); 85 mph (service)

II

Ie = 1.0

Special Concrete Walls: R = 6; Cd = 5

Site Class C

Seismic Design Category D: SDS = 1.5; SD1 = 0.6

Material properties: c beam , f ′ = 5 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms Iwall = 0.5Ig

Design based on Equivalent Lateral Force Procedure

Calculated period:

Upper limit period:

Seismic response coefficient:

Controlling equation:

Seismic base shear (four walls):

Tx = 1.69 s

CuTx = 1.25 s

Cs,x = 0.08

(Equation 12.8-3, ASCE/SEI 7-16)

Vx = 2582 kips = 0.080W

(Load Case 7)

Drift limits considered: 0.020hx (seismic); h/400 (wind)

Design base shear (including accidental

torsion) (two walls): V = 2647 kips = 0.082W

Controlling lateral design criteria: Four 30 ft. walls required to provide adequate flexural strength to 

meet earthquake demands.

Four 30 ft. walls in each direction provide adequate strength without 

excessive longitudinal reinforcement ratios (boundary longitudinal 

reinforcement ratio = 2.1%).

Four 30 ft. walls in each direction provide adequate stiffness to meet 

drift limits for seismic demands (max. interstory drift = 0.9%).
B-20 B: Concrete Wall Studies FEMA P-2012

Table B-3 Summary of Parameters Used in the Design and Analysis (8-Story Building – Bmax)

8-story, Ordinary Concrete Wall (8-D-0-0)

Design Parameters

Dead Load:

Live Load:

Seismic Weight:

Total building seismic weight: 

Wind Speed:

Risk Category: 

Importance Factor:

Typical = 175 psf; Roof = 140 psf

Typical = 65 psf; Roof = 20 psf

Typical = 190 psf; Roof = 147.5 psf

W = 21276 kips

110 mph (strength); 85 mph (service)

II

Ie = 1.0

Special Concrete Walls: R = 5; Cd = 4

Site Class C

Seismic Design Category B: SDS = 0.22; SD1 = 0.055

Material properties: c beam , f ′ = 5 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms Iwall = 0.5Ig

Design based on Equivalent Lateral Force Procedure

Calculated period:

Upper limit period:

Seismic response coefficient:

Controlling equation:

Seismic base shear (two walls):

Wind base shear (two walls):

Tx = 2.03 s

CuTx = 1.12 s

Cs,x = 0.01

Equation 12.8-5, ASCE/SEI 7-16

Vx = 210 kips = 0.010W

(Load Case 7)

Vx = 350 kips = 0.016W

(Load Case 5)

Drift limits considered: 0.020hx (seismic); h/400 (wind)

Design base shear (including accidental

torsion) (two walls): V = 350 kips = 0.016W

Controlling lateral design criteria: Two 20 ft. walls required to provide adequate stiffness under 

earthquake loading. Max. story drift under earthquake loading is 

1.63%.

Two 20 ft. walls in each direction provide adequate flexural 

strength with minimum longitudinal reinforcement (ρ = 0.25%) to 

meet wind load demands.
FEMA P-2012 B: Concrete Wall Studies B-21

Table B-4 Summary of Parameters Used in the Design and Analysis (12-Story Building – Bmax)

12-story, Ordinary Concrete Wall (12-D-0-0)

Design Parameters

Dead Load:

Live Load:

Seismic Weight:

Total building seismic weight:

Wind Speed:

Risk Category: 

Importance Factor:

Typical = 175 psf; Roof = 140 psf

Typical = 65 psf; Roof = 20 psf

Typical = 190 psf; Roof = 147.5 psf

W = 21276 kips

110 mph (strength); 85 mph (service)

II

Ie = 1.0

Special Concrete Walls: R = 5; Cd = 4

Site Class C

Seismic Design Category B: SDS = 0.22; SD1 = 0.055

Material properties: c beam , f ′ = 5 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms Iwall = 0.5Ig

Design based on Equivalent Lateral Force Procedure

Calculated period:

Upper limit period:

Seismic response coefficient:

Controlling equation:

Seismic base shear (four walls):

Wind base shear (four walls):

Tx = 3.07 s

CuTx = 1.52 s

Cs,x = 0.01

(Equation 12.8-5, ASCE/SEI 7-16)

Vx = 322 kips = 0.010W

(Load Case 7)

Vx = 590 kips = 0.018W

(Load Case 5)

Drift limits considered: 0.020hx (seismic); h/400 (wind)

Controlling lateral design: Seismic Strength

Design base shear (including accidental

torsion) (two walls): V = 590 kips = 0.018W

Controlling lateral design criteria: Four 20 ft. walls required to provide adequate stiffness under 

earthquake loading. Max. story drift under earthquake loading is 

1.35%.

Four 20 ft. walls in each direction provide adequate flexural 

strength with minimum longitudinal reinforcement (ρ = 0.25%) to

meet wind demands.
B-22 B: Concrete Wall Studies FEMA P-2012

B.4 Modeling Wall Response

To investigate the impact of vertical irregularities on RC wall building

collapse risk, the FEMA P695 methodology was used with nonlinear 

dynamic analyses using OpenSees. For all building designs, nonlinear 

dynamic analyses were conducted using both the displacement- and the 

force-based distributed-plasticity, beam-column elements with fiber-type 

cross-section models. For an 8-story planar and an 8-story coupled wall, 

collapse assessments were conducted also using the using the shear-flexureinteraction multi-vertical-line-elements model (SFI-MVLEM) (Kolozvari et 

al., 2015a,b; 2018). For all of these analyses the concrete and steel 

constitutive models available in OpenSees were employed. To validate the 

use of OpenSees for simulation of the nonlinear response of walls with 

openings, OpenSees analysis results were compared with those from 

nonlinear quasi-static analysis conducted using continuum-type solid element 

models and the ATENA software platform. ATENA and OpenSees analysis 

methods have been shown, using large experimental data sets, to provide 

accurate stimulation of stiffness, strength, and deformation capacity for 

planar walls exhibiting flexure-controlled response in the laboratory (Marafi 

et al., 2018; Pugh et al., 2015; Whitman, 2015). Figure B-13 shows 

simulated and measured normalized base shear versus drift at the point of 

applied lateral load for a typical flexure-controlled wall specimen. OpenSees 

element formulations are computationally efficient, and thus ideal for use in 

assessing collapse risk via the FEMA P695 procedure, which requires 

numerous nonlinear time-history analyses. The following sections 

summarize the different modeling approaches. 

B.4.1 ATENA

Overview. The ATENA software was selected for continuum-type analysis 

of the model RC walls because: (1) the ATENA concrete constitutive model 

provides automatic regularization of material softening in both tension and 

compression using an element characteristic length, which minimizes mesh 

sensitivity resulting from localization of damage and enables accurate 

simulation of onset of strength loss; and (2) the ATENA concrete constitutive 

model simulates concrete dilation under compressive loading such that the 

impact of confining reinforcement is explicitly simulated.

Constitutive Modeling. The concrete constitutive model used:

(1) continuum damage theory with fixed cracks to define concrete tensile 

response; and (2) plasticity theory with non-associated flow to define 

concrete compressive response. For tension, concrete fracture energy and a 

mesh-dependent length were used to define the tensile post-peak stress 
FEMA P-2012 B: Concrete Wall Studies B-23

versus cracking strain response. For compression, the concrete stress versus 

plastic strain curve is parabolic to maximum strength with linear softening to 

produce zero compressive strength at a user-defined plastic deformation; 

plastic strain at zero compressive strength is defined as the plastic 

deformation divided by a mesh-dependent length. Calibration of the NC2 

model to simulate the response of concrete was conducted by Whitman 

(2015). 

A relatively simple reinforcing steel model was used for the analyses. 

Boundary element longitudinal steel and confining steel were modeled using 

truss elements embedded in the concrete matrix with perfect bond. Web 

region vertical and horizontal steel was modeled as “smeared” across 

individual concrete elements with perfect bond. The stress-strain response of 

reinforcement was modeled using a phenomenological model in which the 

envelope to the stress-strain history is defined as either bilinear or multilinear 

based on coupon test data, and unload-reload response was modeled using 

Menegotto-Pinto curves to simulate the Bauschinger effect. Neither bar 

buckling nor bar fracture are modeled as ATENA does not support tracking 

of strain as required to determine onset of buckling and post-buckling 

fracture. Non-simulated failure criteria were established by Whitman (2015) 

to enable accurate prediction of onset of lateral strength loss in the event that 

this is controlled by bar buckling or fracture. To enhance numerical stability 

and robustness, a small volume (0.1%) of elastic, smeared horizontal and 

vertical reinforcement was added in the regions of the wall that were 

expected to sustain nonlinear deformation demands 

Comparison of Simulated and Measured Response. The ATENA 

modeling approach was validated using 21 planar wall specimens (Whitman, 

2015). Figure B-13 shows normalized base shear versus drift as simulated 

using the ATENA modeling approach and as measured in the laboratory for 

two specimens.
B-24 B: Concrete Wall Studies FEMA P-2012

(a) Response as measured and (b) Response as measured and as simulated using

as simulated using ATENA (Whitman, 2015) OpenSees displacement-based element

 

(c) Response as measured and as simulated (d) Response as measured and 

using OpenSees force-based elements (Pugh, 2012) as simulated using OpenSees SFI-MVLEM

Figure B-13 Wall response histories as measured and as simulated using OpenSees and ATENA specimen 

RW1 – bar fracture failure (Cross-Section Aspect Ratio [CSAR] = 12; Axial Load Ratio = 10.5, 

Vmax = 2.6 c g f A ).

B.4.2 OpenSees 

Dynamic analyses of RC wall buildings to investigate collapse risk were 

conducted using OpenSees with walls modeled using: (1) the force-based 

beam-column element (FBE) with fiber-type section models and the 

modeling approach developed by Pugh et al. (2015); (2) the displacementbased beam-column element (DBE) with fiber-type section models and the 

modeling approach developed by Pugh et al. (2015) and updated by Marafi et 

al. (2018); and (3) the SFI-MVLEM developed by Kolozvari et al. (2015a,b; 

2018). The modeling approaches developed by Pugh et al. (2015) and 

Marafi et al. (2018) employ regularization of material softening to achieve 

mesh-objective simulation of strength loss and have been verified, using a 

large database of planar and non-planar wall tests, to provide accurate, meshobjective, simulation of onset of strength loss, which is required for accurate 
FEMA P-2012 B: Concrete Wall Studies B-25

assessment of collapse risk. For this study, concrete and steel material 

response models used in the SFI-MVLEM were calibrated such that the SFIMVLEM predicted drift capacities for the wall designs that were equal to 

those predicted using models comprising distributed-plasticity beam-column 

elements. 

Elements and Mesh Size. Displacement- and force-based fiber-type beamcolumn elements as well as the SFI-MVLEM were used to assess collapse 

risk. Figure B-14 and Figure B-15 show the models used to represent the 

walls, the RC wall buildings, and wall cross-sections.

The FBE employs the assumption of a linear moment distribution and 

constant axial load distribution along the length of the element, as well as the 

assumption that flexure and shear response are decoupled. As such, one FBE 

per story provides a highly accurate representation of the moment and axial 

load distributions that develop in a wall, in which lateral earthquake loads 

and axial loads may be approximated as being applied to the wall at the floor 

level. Using the FBE, multiple fiber-type section models are employed along 

the length of the element to provide accurate simulation of deformations in 

regions in which flexural yielding occurs. Fiber-section models employ 

multiple confined and unconfined concrete fibers and steel fibers to provide 

accurate simulation of the flexural response of sections. One FBE with five 

fiber sections per element is used vertically per story. Fiber sections employ 

150 concrete and steel fibers to provide accurate simulation of section 

response. Figure B-14 and Figure B-15 show models with one FBE used per 

story.

The DBE employs the assumptions of a linear curvature field and a constant 

axial strain field. Thus, multiple elements are required, per story, to provide 

an accurate representation of the curvature and strain fields that develop in 

regions of the wall in which nonlinear flexural behavior occurs. As with the 

FBE, multiple fiber-type sections models are employed within each element. 

Six DBEs were used per story, each with five fiber section models. Figure 

B-14 and Figure B-15 show models of the walls and buildings with six DBEs 

used per story. 
B-26 B: Concrete Wall Studies FEMA P-2012

One force-based 

element OR six 

displacement-based 

elements OR six SFIMVLEM elements

Figure B-14 OpenSees model configurations for walls with and without openings. 

One force-based element with five fiber sections OR six 

displacement-based elements, each with five fiber sections 

OR six SFI-MVLEMs each with one fiber section

Figure B-15 OpenSees model configuration for RC wall building. 

The SFI-MVLEM employs the fixed-strut angle approach (Orakcal et al., 

2012) to characterize the biaxial constitutive response of the two-dimensional 

RC panel fibers that compose the SFI-MVLEM (Orakcal et al., 2004). 

Axial-shear coupling is achieved within each two-dimensional fiber through

the two-dimensional RC panel constitutive model. Integration of fiber 

stresses to determine element response results in simulation of coupled axialflexural-shear responses at the element level. All material models are cyclic 

in nature, such that the SFI-MVLEM also represents cyclic response. A 

constant distribution of curvature is assumed over the element height such 

that biaxial stresses and strains are constant within each fiber. Since element 

shear strength and stiffness are determined from integration of the twodimensional fiber stresses and stiffnesses, explicit definition of shear 
FEMA P-2012 B: Concrete Wall Studies B-27

response is not required. For simulation of RC wall buildings, SFI-MVLEM 

building models employed the same number of elements as were used for the 

DBE models and the same number of cross-section fibers as were used for 

the DBE and FBE models. Figure B-14 and Figure B-15 show models of the 

walls and buildings with six SFI-MVLEM elements used per story.

Constitutive Models for Displacement- and Force-Based Beam-Column 

Element Models. Concrete response was simulated using the OpenSees 

Concrete02 material mode. In compression, this model represents a 

quadratic response to peak strength with linear deterioration to a residual 

compressive strength. In tension, the model represents a linear response 

history to tensile strength with linear strength loss to zero tensile capacity. 

Tensile strength for unconfined and confined concrete was defined as 4 cf ′

psi. Regularization of post-peak response in tension is not required as 

concrete cracking does not result in section or element softening. 

Unconfined concrete was assumed to reach peak strength at a strain of -

0.002. Confined concrete strength and strain at maximum strength were 

defined using the model by Saatcioglu and Razvi (1992). Per the 

recommendations of Pugh et al. (2015) and Marafi et al. (2018), concrete 

post-peak response was defined by the unconfined or confined concrete 

crushing energy and a mesh-dependent length; this was required to ensure 

that simulation of onset of strength loss was accurate and did not depend on 

mesh size. Concrete residual strength is defined as 20% of peak strength for 

confined concrete and 10% of peak strength for unconfined concrete. 

For reinforcing steel, the OpenSees Steel02 model was used. Reinforcing 

steel is assumed to lose compressive and tensile strength, due to buckling, at 

the regularized strain at which concrete strength deteriorates to the residual 

compressive strength. 

Figure B-16 shows concrete and steel material model response under cyclic 

loading. Figure B-17 shows regularization of concrete and steel response 

using unconfined, Gfc, and confined concrete, Gfcc, crushing energies and L, 

which is the element length associated with the fiber section in which the 

material model is used. For the FBE, when strength loss occurs, deformation 

localizes in a section and L is taken equal to the length assigned to each fiber 

section. For the DBE, when strength loss occurs, deformation localizes in an 

element and L is taken equal to the element length. The red ‘X’ in Figure 

B-17 shows the strain at which reinforcing steel loses strength due to 

buckling. Pugh et al. (2015) and Marafi et al. (2018) provide additional 

information on the material regularization method used for modeling.
B-28 B: Concrete Wall Studies FEMA P-2012

(a) (b) 

Figure B-16 Nonlinear 1D cyclic material models. (a) Yassin cyclic concrete model, which employs the 

monotonic Modified Kent-Park model (Yassin, 1994; Scott et al., 1982) as presented by 

Orakcal et al. (2006). Note that compressive stress-strain is positive. (b) Menegotto-PintoFilippou reinforcing steel model (Filippou et al., 1983) as presented by Orakcal et al. (2006). 

(a) unconfined concrete (b) confined concrete 

compression envelope compression envelope

X 

Reinforcing steel 

buckling

Figure B-17 Regularization of concrete material response using mesh dependent 

length. Note that steel buckling occurs at ε20u and ε20c. (Figure 

adapted from Pugh et al., 2015)

Constitutive Models for SFI-MVLEM. Material models for concrete and 

steel and all parameters necessary to define the constitutive models used in 

the SFI-MVLEM were identical to the one used in the DBE, to ensure 

consistent comparison between the modeling approaches. 

B.5 Preliminary Analyses to Investigate Modeling 

Assumptions and Identify a Preferred Modeling 

Approach

OpenSees and ATENA analyses were conducted to investigate modeling 

assumptions and assess the performance of the 8-story RC wall buildings 

designed for the Dmax spectrum using the ASCE/SEI 7-16 ELF procedure. 

These analyses comprised pushover analyses using both software platforms 

as well as dynamic analyses using the OpenSees models. 
FEMA P-2012 B: Concrete Wall Studies B-29

Significant observations and conclusions of the analyses are described in the 

following sections.

B.5.1 Modeling Assumptions Employed for OpenSees and ATENA 

Analyses

Analyses conducted to investigate wall performance and the impact of 

various modeling assumptions employed the modeling procedures described 

in this Appendix and in Chapter 3. 

All nonlinear analyses employed expected material properties. Expected 

material strengths were defined following the recommendations of the 

Guidelines for Performance-Based Seismic Design of Tall Buildings (PEER, 

2010). Following these recommendations, unconfined concrete compressive 

strength was increased by 30% from 5000 psi to 6500 psi and reinforcing 

steel yield strength was increased by 17% from 60 ksi to 72 ksi. 

Longitudinal reinforcing steel was assumed to reach an ultimate strength of 

105 ksi at a fracture strain of 0.20. 

Gravity load was applied for all pushover and dynamic analyses. Following 

the recommendations of FEMA P695, gravity load was defined by:

1.05D + 0.25L

where D is the nominal dead load of the structure and L is the nominal live 

load, defined as follows: 

• Dead load (materials and mechanical) on all floors = 175 psf 

• Dead load (materials and mechanical) on roof = 140 psf

• Live load (area load plus partitions) on all floors = 50 + 15 psf = 65 psf

• Live load (area load plus partitions) on roof = 20 + 0 psf = 20 psf 

The wall tributary area was used to determine the gravity load applied to the 

wall. 

For dynamic OpenSees analyses the total gravity load that could be expected 

to destabilize the wall was included in the analysis via use of a P-Delta 

column (Figure B-15). The total building gravity load attributed to the wall 

(half the total gravity load applied to the building), less the gravity load 

applied directly to the wall, was applied to a “P-Delta” column adjacent to 

the wall. The P-Delta column was assigned a flexural stiffness 

approximately equal to the sum of the flexural stiffnesses of all of the gravity 

columns attributed to the wall (half the total number of gravity columns) and 

an axial stiffness that was similarly defined. The P-Delta column was linked 

to the wall via essentially rigid, axial-only elements. Initially the P-Delta 
B-30 B: Concrete Wall Studies FEMA P-2012

column was included in pushover analyses; however, essentially no 

difference was observed between results with and without the P-Delta 

column. Thus, the P-Delta column was subsequently included only in 

dynamic analyses. 

Where monotonic pushover analyses were conducted in OpenSees, the 

ASCE/SEI 7-16 ELF lateral load distribution was applied under generalized 

displacement control. For ATENA analyses, lateral load was applied as a 

single point load at the effective height associated with the ELF load 

distribution.

B.5.2 Pushover Analyses to Compare OpenSees and ATENA 

Models

ATENA and all three OpenSees modeling approaches described in Section 

5.4 were used to perform pushover analyses of the 8-story RC wall buildings 

designed by the Dmax spectrum using the ELF procedure (walls with no 

openings, openings at the 1st story, openings at the 1st and 2nd stories, and 

openings at the 5th story). Pushover analyses were performed using the 

modeling procedure described in Section 5.4 and the model configurations 

shown in Figure B-14 and Figure B-15. Lateral load was applied as a point 

load (series of point loads for the ATENA model) under displacement control 

at the effective height of the ELF lateral load distribution. Simulated base 

shear versus drift at the effective height is presented in Figure B-18. 

The data in Figure B-18 support the following observations:

• OpenSees models predict approximately the same strength and stiffness 

for all of the wall configurations.

• The OpenSees SFI-MVLEM model predicts different drift capacity 

and/or post-peak response than is predicted using the OpenSees DBE and 

FBE models.

• The ATENA model predicts approximately the same pre-peak response 

as is predicted using the OpenSees models; though it predicts greater 

strength for three of five wall configurations and greater stiffness for two 

of five wall configurations.

• OpenSees DBE and FBE models predict approximately the same 

response.

• OpenSees DBE/FBE models, OpenSees SFI-MVLEM and ATENA 

models all predict different drift capacities and post-peak stiffnesses. 
FEMA P-2012 B: Concrete Wall Studies B-31

No analyses conducted 

for this case.

(a) Continuous wall (no openings)

(8-D-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6

(8-D-5S-50-ELF)

(c) 1st story opening with 

K1 < 0.5K2 (8-D-1S-50-ELF)

(d) 1st story opening with 

K1 < 0.75K2 (8-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1, and K2, < 0.5K3 (8-D-2S-50-ELF)

(f) 1st and 2nd story openings with 

K1 and K2, < 0.75K3 (8-D-2S-75-ELF)

Figure B-18 Base shear versus drift at effective height for 8-story walls as 

simulated using ATENA (grey), OpenSees DBE (black), and 

SFI-MVLEM (red) models. Note that lateral load is applied as a 

point load at the effective height of the ELF load distribution. Ki

indicates stiffness of story i defined per Section B.3. 

Differences in simulated strength and stiffness are attributed to difference in 

the way that shear-flexure interaction is simulated, with the DBE/FBE 

elements simulating no flexure-shear interaction, the SFI-MVLEM 

simulating constrained flexure-shear interaction (shear strain constrained to 

be constant over the cross-section), and the ATENA model providing 

simulation of unconstrained flexure-shear interaction. 

Ultimately the differences between the individual OpenSees models and 

between the OpenSees and ATENA models suggest the potential for: (1) the 

OpenSees line-element models to provide inaccurate simulation of response 

for walls with irregular configurations for which response is not entirely 

flexure-controlled; and (2) the potential the deformation capacities predicted 
B-32 B: Concrete Wall Studies FEMA P-2012

using DBE, FBE, and SFI-MVLEM models to result in significant 

differences in assessment of collapse risk. 

B.5.3 Dynamic Analyses to Compare OpenSees DisplacementBased and Force-Based Beam-Column Element Models

Incremental dynamic analyses of the 8-story RC wall buildings were 

conducted to investigate the difference in collapse risk resulting from use of 

OpenSees DBE versus FBE to simulate wall response. Figure B-19 shows 

incremental dynamic analysis results for the 8-story archetype without 

openings (8-0-0-ELF) modeled using the DBEs (Figure B-19a) and using the 

FBEs (Figure B-19b). Figure B-19 shows spectra acceleration at the 

fundamental period of the structure, Sa, versus maximum interstory drift for 

the suite of far-field motions provided for use with the FEMA P695 

procedure. Red dots in the figures indicate the “last converged analysis” 

achieved prior to an increase in the ground motion amplitude resulting in a 

“non-converged” solution; black dots indicate a non-simulated collapse at a 

maximum interstory drift of 5%. The black line indicates median spectral 

acceleration, SCT is the spectral acceleration for which 50% of the records 

result in building collapse, and SMT is the spectral acceration at the design 

period of the structure for the MCE. Figure B-20 shows similar data for the 

8-story archetype with an opening at the 1st-story resulting in a 50% 

reduction in stiffness for that story. 

(a) DBE model (b) FBE model

SCT = 2.32g

SMT = 0.91g

SCT = 1.72g 

SMT = 0.91g 

Figure B-19 Earthquake spectral acceleration at the design period of the 

structure, Sa, versus maximum interstory drift for the 8-story 

continuous wall building designed for Dmax spectrum using the 

ASCE/SEI 7-16 ELF procedure. 

The data in Figure B-19 and Figure B-20 show that when the FBE is used, 

there are many more analyses that “fail to converge” at intensity levels less 

than that resulting in collapse, defined by a maximum interstory drift of 5%. 

These failures to converge result from either instability of the global 

structural system, suggesting a true building collapse due to development of 

a side-sway mechanism, or, for the models comprising FBEs, a failure of the 

FBE intra-element solution algorithm, which may or may not be indicative of 
FEMA P-2012 B: Concrete Wall Studies B-33

a true building collapse. These failures to converge at lower intensity levels 

result in a lower SCT value and calculation of a higher collapse risk for the 

models comprising FBE. Thus, the model comprising FBEs is considered to 

over-predict the true collapse risk, and models comprising DBEs are 

preferred to those comprising FBEs. 

(a) DBE model (b) FBE model

SCT = 1.99g 

SMT = 0.91g 

SCT = 1.14g

SMT = 0.91g

Figure B-20 Earthquake intensity at design period, Sa, versus maximum 

interstory drift for 8-story RC wall building with opening at 1st

story resulting in 50% stiffness loss and designed for Dmax

spectrum using the ASCE/SEI 7-16 ELF procedure. 

B.5.4 Dynamic Analyses to Compare Models Comprising 

OpenSees Displacement-Based Beam-Column Elements 

and SFI-MVLEM

Incremental dynamic analyses of the 8-story RC wall buildings were also 

conducted to investigate the difference in collapse risk resulting from use of 

a model comprising DBEs, which assume a linear shear model and 

decoupling of flexure and shear action, versus the SFI-MVLEs, which 

assume flexure and shear response are coupled and thus result in simulation 

of a nonlinear shear response. Figure B-21 shows dynamic analysis results 

for a single ground motion for the 8-story RC wall building archetype 

without openings (8-0-0-ELF) for models comprising DBEs and SFIMVLEMs. The same ground motion was used for both models which 

resulted in collapse (maximum interstory drift in excess of 5%) for the 

building model comprising SFI-MVLEMs. The data in Figure B-21 enable 

comparison of the DBE and SFI-MVLEM models on the basis of simulated: 

(1) roof displacement history (Figure B-21a); (2) base shear history (Figure 

B-21b); (3) the vertical interstory drift profile of the RC wall building at the 

timestep corresponding to the maximum interstory drift for each model 

(Figure B-21c); and (4) shear forces and moments (Figure B-21d,e). In 

addition, local (first story) wall hysteretic responses are compared to assess 

the behavior of the models within the plastic hinge region including (Figure 

B-21f): (1) shear force versus total displacement; (2) shear force versus shear 

displacement; and (3) moment versus rotation. 
B-34 B: Concrete Wall Studies FEMA P-2012

(b) Base shear force history (c) Drift profile (d) V profile (e) M profile

(i) Base shear vs. total displacement (ii) Base shear vs. shear displacement (iii) Moment vs. rotation

(f) Wall responses over the first story

(a) Roof displacement history

Figure B-21 Simulated response quantities for models comprising SFI-MVLEM and displacement-based 

beam-column element responses for collapse-level of shaking.

Results presented in Figure B-21 show that the model comprising SFIMVLEM predicts substantially larger roof drifts and interstory drifts than 

does the model comprising DBEs (Figure B-21a,c), while the DBE model 

predicts substantially larger shear forces than does the SFI-MVLEM model 

the history of base shear (Figure B-21b,d). Differences in the maximum base 

moments predicted using the two models are substantially less, with the DBE 

model predicting a maximum base moment that is approximately 25% larger 

than that predicted using the SFI-MVLEM (Figure B-21e). Vertical profiles 

of predicted interstory drifts (Figure B-21c) and story shear (Figure B-21d) 

show that maximum base shear and interstory drift predicted using the two 

models differ by as much as 50%. The data in Figure B-21c show that a 

significant portion (20-60%) of the interstory drift over the wall height is 

associated with nonlinear shear deformations (dashed blue line in Figure 

B-21c) that are not captured using the DBE. 
FEMA P-2012 B: Concrete Wall Studies B-35

The data in Figure B-21f show force-displacement response, as predicted 

using the two models, in the bottom story of the wall where inelastic 

deformation is greatest. These data clearly highlight the differences between 

the two models. In particular, the data show the highly nonlinear shear 

response that is predicted using the SFI-MVLEM. This nonlinear shear 

response results from nonlinear flexural yielding and coupling of the shear 

and flexural response through the multi-dimensional concrete model. The 

nonlinear shear response predicted using the SFI-MVLEM differs 

substantially from the linear shear response predicted using the DBE model. 

These data also show that the DBE model predicts a larger moment capacity 

and smaller flexural deformations than are predicted using the SFI-MVLEM. 

The difference in predicted moment capacity likely results from differences 

in axial load distributions that result from the different model formulations; 

larger flexural deformations in the SFI-MVLEM model are likely due to the 

flexure-shear interaction with shear demand resulting in increased inelastic 

deformation that produces larger flexural, as well as large, shear 

deformations.

Figure B-22 compares data from incremental dynamic analysis (IDA) of the 

8-story RC wall building without openings (8-0-0-ELF) for a selected ground 

motion as obtained using the SFI-MVLEM and DBE models. These data 

show that for all ground motion intensity levels beyond those that are 

associated with essentially elastic wall response, the SFI-MVLEM model 

predicts maximum interstory drifts that are larger than those predicted using 

the DBE model. The difference in predicted maximum interstory drift 

increases with increasing ground motion intensity. The larger drifts 

predicted by the SFI-MVLEM are attributed to the nonlinear shear response 

and are consistent with the data shown in Figure B-22. 

Figure B-23 provides the IDA data for the 8-story RC wall building

archetype without openings (8-0-0-ELF) for the FEMA P695 far-field ground 

motion suite as obtained using the SFI-MVLEM and DBE wall models. 

With collapse defined by a maximum interstory drift greater than 5%, the 

Collapse Margin Ratio (CMR) predicted using the SFI-MVLEM (CMRSFI = 

2.36) is less than that predicted using the DBE model (CMRDBE = 2.75), due 

to the larger deformations and interstory drifts predicted using the SFIMVLEM. 
B-36 B: Concrete Wall Studies FEMA P-2012

Figure B-22 Comparison of SFI-MVLEM and displacement-based 

beam column element IDA results for selected ground 

motion.

(a) DBE (8-0-0-DBE-ELF) (b) SFI-MVLEM (8-0-0-SFI-ELF)

Max Interstory Drift

0 0.01 0.02 0.03 0.04 0.05 0.06

Sa [g]

0

1

2

3

4

5

6

7

8

S C T = 2.50 g

S M T = 0.91 g

CMR = 2.75

COV 0 . 0 5 = 0.40

mean

mean +/- 

collapse

Max Interstory Drift

0 0.01 0.02 0.03 0.04 0.05 0.06

Sa [g]

0

1

2

3

4

5

6

7

8

S C T = 2.15 g

S M T = 0.91 g

CMR = 2.36

COV 0 . 0 5 = 0.42

mean

mean +/- 

collapse

Figure B-23 Comparison of SFI-MVLEM and displacement-based IDA analysis results for 8-story RC wall 

building without openings (8-0-0-ELF).

Figure B-24 provides IDA data for the 8-story RC wall building with an 

opening in the first story that reduces story stiffness to 50% of the adjacent 

story stiffness. These IDA data were created using the FEMA P695 far-field 

ground motion suite as obtained using the SFI-MVLEM and DBE wall 

models. Due to presence of the opening, the CMR is slightly reduced (3-4% 

reduction) for both models. 
FEMA P-2012 B: Concrete Wall Studies B-37

(a) DBE (8-1S-50-DBE-ELF) (b) SFI-MVLEM (8-1S-50-SFI-ELF)

Max Interstory Drift

0 0.01 0.02 0.03 0.04 0.05 0.06

Sa [g]

0

1

2

3

4

5

6

7

8

S C T = 2.40 g

S M T = 0.91 g

CMR = 2.63

COV 0 . 0 5 = 0.50

mean

mean +/- 

collapse

Max Interstory Drift

0 0.01 0.02 0.03 0.04 0.05 0.06

Sa [g]

0

1

2

3

4

5

6

7

8

S C T = 2.09 g

S M T = 0.91 g

CMR = 2.29

COV 0 . 0 5 = 0.45

mean

mean +/- 

collapse

Figure B-24 Comparison of SFI-MVLEM and displacement-based IDA analysis results for 8-story archetype 

with opening at the first floor (8-1S-50-ELF).

Comparison of the SFI-MVLEM and DBE model results for simulation of 

the nonlinear response of concrete RC wall buildings subjected to 

monotonically increasing as well as dynamic lateral loading shows: 

• SFI-MVLEM predicts larger interstory drifts and smaller base shear 

demands than does the DBE model; 

• Use of the SFI-MVLEM results in prediction of larger collapse risk and 

smaller CMRs than are predicted using the DBE; and 

• Both models predict approximately the same, small change in collapse 

risk associated with introduction of an opening in the 1st story of a RC 

wall building. 

B.5.5 Identification of a Preferred Modeling Approach for 

Assessing the Impact of Vertical Irregularities on the 

Collapse Risk Posed by RC Wall Buildings 

The data in Section B.5.2 through Section B.5.4 show significant differences 

in drift capacity, and to a lesser extent stiffness and strength of a RC wall 

buildings, predicted using the OpenSees and ATENA models discussed 

above. These differences could be expected to affect the assessment of 

collapse risk for RC wall buildings and, in particular, the impact of vertical 

irregularities resulting from the introduction of openings on this risk. The 

OpenSees DBE modeling approach was selected for the use in the study 

because:

• The ATENA model, which likely provides the most accurate simulation 

of response, cannot be used for dynamic analyses.
B-38 B: Concrete Wall Studies FEMA P-2012

• The OpenSees FBE modeling approach exhibits failures of the numerical 

solution algorithm that result inaccurate, reduced calculation of collapse 

risk. 

• The OpenSees SFI-MVLEM has not be extensively validated for use in 

simulating response beyond onset of strength loss. 

• The OpenSees DBE modeling approach has been extensively validated 

for simulation of onset of strength loss, provides plausible simulation of 

response following onset of strength loss (minimal experimental data 

exist for validation), and provides the greatest numerical robustness and 

the greatest numerical efficiency.

B.6 Analysis Results

Results of analyses conducted to assess collapse risk of the archetype RC 

wall building designs are presented in Tables B-5 and B-6 and Figures B-25

through B-34; for these analyses, collapse is defined by a maximum 

interstory drift greater than 10%, except for Figures B-29 and B-31 where it 

is defined by a maximum interstory drift greater that 5%. Figures B-35

through B-37 present the ratios of the ACMRs for buildings comprising walls 

with openings to those comprising walls without openings 

(ACMR/ACMRbaseline) and thereby provide understanding of the impact on 

collapse risk of introducing the openings. The data in these figures show the 

following:

• Collapse probabilities for all of the RC wall building designs, including 

those comprising walls with and without openings that significantly 

reduced story stiffness, are low (less than 2%).

• Collapse probabilities are very low (less than 0.11%) and ACMRs very 

large (greater than 5.0) for the baseline RC wall building designs that 

comprise walls without openings. 

For RC wall buildings designed for Seismic Design Category B, for which 

wall strength was determined by wind loads, collapse probabilities for the 

baseline RC wall building comprising walls without openings were 

extremely small (less than 0.02%) and ACMRs extremely large (greater than 

6.5). For these designs, the introduction of openings that reduced story 

stiffness by more than 25% had minimal impact on the ACMR (less than 10% 

change). For these designs, the introduction of openings in the bottom two 

stories that reduced story stiffness by more than 50%, resulted in significant 

changes in the ACMR (greater than 30% for the 12-story building). 

However, resulting collapse probabilities remained extremely low (0.11% or 

less); thus, the data were not considered to warrant additional study or code 

revisions.
FEMA P-2012 B: Concrete Wall Studies B-39

Table B-5 Collapse Probabilities for RC Wall Building Archetypes Designed for the Dmax Spectrum for 

the Case of Collapse at Maximum Story Drifts in Excess of 10%

Archetype ŜCT SMT CMR μT SSF ACMR

ACMR / 

ACMRbaseline

SSF

(μ=8)

ACMR

(μ=8)

Collapse

Prob. 

(μ=8)

ACMR / 

ACMRbaseline

(μ=8)

8-story walled buildings designed for Dmax spectrum using ELF

8-0-0-D-ELF 3.29 0.91 3.60 12.40 1.45 5.20 - 1.40 5.20 0.08 -

8-1S-50-D-ELF 2.18 0.91 2.40 2.70 1.22 2.90 0.56 1.40 3.50 0.88 0.67

8-1S-75-D-ELF 2.09 0.91 2.30 2.50 1.21 2.80 0.54 1.40 3.30 1.10 0.63

8-2S-50-D-ELF 2.08 0.91 2.30 5.90 1.37 3.10 0.60 1.40 3.30 1.13 0.63

8-2S-75-D-ELF 2.08 0.91 2.30 4.60 1.32 3.00 0.58 1.40 3.30 1.14 0.63

8-5S-50-D-ELF 3.06 0.91 3.40 10.00 1.45 4.90 0.94 1.40 4.90 0.13 0.94

8-story walled buildings designed for Dmax spectrum using MRSA

8-0-0-D-MRSA 3.15 0.91 3.50 15.80 1.45 5.00 - 1.40 5.00 0.11 -

8-1S-50-D-MRSA 2.19 0.91 2.40 5.60 1.36 3.30 0.66 1.40 3.50 0.87 0.70

8-1S-75-D-MRSA 2.11 0.91 2.30 5.40 1.35 3.10 0.62 1.40 3.40 1.04 0.68

8-2S-50-D-MRSA 2.05 0.91 2.30 7.10 1.41 3.20 0.64 1.40 3.30 1.22 0.66

8-2S-75-D-MRSA 2.07 0.91 2.30 6.60 1.39 3.20 0.64 1.40 3.30 1.16 0.66

8-5S-50-D-ELF - - - - - - - - - - -

12-story walled buildings designed for Dmax spectrum using ELF

12-0-0-D-ELF 2.69 0.67 4.00 8.70 1.53 6.10 - 1.50 6.10 0.03 -

12-1S-50-D-ELF 1.88 0.67 2.80 3.30 1.30 3.60 0.85 1.50 4.30 0.28 0.70

12-1S-75-D-ELF 1.92 0.67 2.90 3.20 1.30 3.70 0.85 1.50 4.40 0.24 0.72

12-2S-50-D-ELF 1.85 0.67 2.80 2.40 1.25 3.40 0.82 1.50 4.20 0.30 0.69

12-2S-75-D-ELF 1.89 0.67 2.80 2.30 1.23 3.50 0.80 1.50 4.30 0.27 0.70

12-5S-50-D-ELF - - - - - - - - - - -

12-story walled buildings designed for Dmax spectrum using MRSA

12-0-0-D-MRSA 2.44 0.67 3.60 20.40 1.53 5.60 - 1.50 5.60 0.05 -

12-1S-50-D-MRSA 1.56 0.67 2.30 7.30 1.50 3.50 0.98 1.50 3.60 0.78 0.64

12-1S-75-D-MRSA 1.68 0.67 2.50 7.20 1.50 3.70 0.98 1.50 3.80 0.53 0.68

12-2S-50-D-MRSA 1.31 0.67 1.90 3.60 1.33 2.60 0.87 1.50 3.00 1.83 0.54

12-2S-75-D-MRSA 1.48 0.67 2.20 3.60 1.33 2.90 0.87 1.50 3.40 1.01 0.61

12-5S-50-D-MRSA - - - - - - - - - - -
B-40 B: Concrete Wall Studies FEMA P-2012

Table B-6 Collapse Probabilities for RC Wall Building Archetypes Designed for the Bmax Spectrum for the 

Case of Collapse at Maximum Story Drifts in Excess of 10%

Archetype ŜCT SMT CMR μT SSF ACMR

ACMR / 

ACMRbaseline

SSF

(μ=8)

ACMR

(μ =8)

Collapse

Prob. 

(%) 

(μ =8))

ACMR / 

ACMRbaseline

(μ =8)

8-story RC wall buildings designed for Bmax spectrum using ELF

8-0-0-B-ELF 0.97 0.22 4.5 16.4 1.45 6.5 - 1.4 6.5 0.02 -

8-1S-50-B-ELF 0.91 0.22 4.2 11.6 1.45 6.1 0.94 1.4 6.1 0.03 0.94

8-1S-75-B-ELF 0.92 0.22 4.3 12.4 1.45 6.2 0.95 1.4 6.2 0.03 0.95

8-2S-50-B-ELF 0.81 0.22 3.8 11.2 1.45 5.4 0.83 1.4 5.4 0.06 0.83

8-2S-75-B-ELF 0.89 0.22 4.1 8.8 1.45 5.9 0.91 1.4 5.9 0.04 0.91

8-5S-50-B-ELF - - - - - - - - - - -

12-story RC wall buildings designed for Bmax spectrum using ELF

12-0-0-B-ELF 0.79 0.16 4.9 7.7 1.52 7.5 - 1.5 7.5 0.01 -

12-1S-50-B-ELF 0.78 0.16 4.8 6.7 1.48 7.2 0.96 1.5 7.4 0.01 0.99

12-1S-75-B-ELF 0.79 0.16 4.9 6.5 1.47 7.3 0.97 1.5 7.6 0.01 1.01

12-2S-50-B-ELF 0.52 0.16 3.3 5.6 1.43 4.7 0.63 1.5 5.0 0.11 0.67

12-2S-75-B-ELF 0.75 0.16 4.7 4.9 1.40 6.5 0.87 1.5 7.1 0.01 0.95

12-5S-50-B-ELF - - - - - - - - - - -
FEMA P-2012 B: Concrete Wall Studies B-41

(a) Continuous wall 

(8-D-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6

(8-D-5S-50-ELF)

(c) 1st story opening with K1 < 0.5K2

(8-D-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2

(8-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (8-D-2S-50-ELF)

(f) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (8-D-2S-75-ELF)

Figure B-25 Base shear versus roof drift for 8-story walls designed for Dmax spectrum using 

the ASCE/SEI7-16 ELF procedure. Grey marker indicates yield drift (circle) 

and drift at 20% strength loss (square); dashed grey line indicates ductility of 

8. Ki indicates stiffness of story i defined per Section B.3. 
B-42 B: Concrete Wall Studies FEMA P-2012

No analysis conducted

for this case.

(a) Continuous wall 

(8-D-0-0- MRSA)

(b) 5th story opening with K5 < 0.5K6

(c) 1st story opening with K1 < 0.5K2

(8-D-1S-50-MRSA)

(d) 1st story opening, with K1 < 0.75K2

(8-D-1S-75-MRSA)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (8-D-2S-50-MRSA)

(f) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (8-D-2S-75-MRSA)

Figure B-26 Base shear versus roof drift for 8-story walls designed for Dmax spectrum 

using the ASCE/SEI 7-16 MRSA procedure. Grey marker indicates yield 

drift (circle) and drift at 20% strength loss (square); dashed grey line 

indicates ductility of 8. Ki indicates stiffness of story i defined per 

Section B.3. 
FEMA P-2012 B: Concrete Wall Studies B-43

No analysis conducted

for this case.

(a) Continuous wall 

(12-D-0-0-ELF)

(b) 8th story opening with K8 < 0.5K9

(c) 1st story opening with K1 < 0.5K2

(12-D-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2

(12-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (12-D-2S-50-ELF)

(f) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (12-D-2S-75-ELF)

Figure B-27 Base shear versus roof drift for 12-story walls designed for Dmax spectrum using 

the ASCE/SEI 7-16 ELF procedure. Grey marker indicates yield drift (circle) and 

drift at 20% strength loss (square); dashed grey line indicates ductility of 8. Ki

indicates stiffness of story i defined per Section B.3. 
B-44 B: Concrete Wall Studies FEMA P-2012

No analysis conducted

for this case.

(a) Continuous wall 

(12-D-0-0-MRSA)

(b) 5th story opening with K5 < 0.5K6

(c) 1st story opening with 50% stiffness 

(12-D-1S-50-MRSA)

(d) 1st story opening with 75% stiffness 

(12-D-1S-75-MRSA)

(e) 1st and 2nd story openings with 50% 

stiffness (12-D-2S-50-MRSA)

(f) 1st and 2nd story openings with 75% stiffness 

(12-D-2S-75-MRSA)

Figure B-28 Base shear versus roof drift for 12-story walls designed for Dmax spectrum 

using the ASCE/SEI 7-16 MRSA procedure. Grey marker indicates yield 

drift (circle) and drift at 20% strength loss (square); dashed grey line 

indicates ductility of 8. Ki indicates stiffness of story i defined per Section

B.3.
FEMA P-2012 B: Concrete Wall Studies B-45

(a) Continuous wall 

(8-D-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6

(8-D-5S-50-ELF)

(c) 1st story opening, with K1 < 0.5K2

(8-D-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2

(8-D-1S-75-ELF)

(e) 1st and 2nd story openings with 

K1 and K2 < 0.5K3 (8-D-2S-50-ELF)

(f) ) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (8-D-2S-75-ELF)

Figure B-29 Earthquake intensity at design period, Sa, versus maximum inter-story drift for 

8-story walls designed for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure. Black line indicates spectral acceleration at which 50% of motions

result in collapse defined by maximum inter-story drift in excess of 5%. Ki

indicates stiffness of story i defined per Section B.3.
B-46 B: Concrete Wall Studies FEMA P-2012

(a) Continuous wall 

(8-D-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6

(8-D-5S-50-ELF)

(c) 1st story opening with K1 < 0.5K2

(8-D-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2

(8-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (8-D-2S-50-ELF)

(f) 1st and 2nd story openings with 

K1 and K2 < 0.75K3 (8-D-2S-75-ELF)

Figure B-30 Earthquake intensity at design period, Sa, versus maximum interstory drift 

for 8-story walls designed for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure. Black line indicates spectral acceleration at which 50% of 

motions result in collapse defined by maximum interstory drift in excess 

of 10%. Ki indicates stiffness of story i defined per Section B.3.
FEMA P-2012 B: Concrete Wall Studies B-47

No analysis conducted

for this case.

(a) Continuous wall 

(12-D-0-0-ELF)

(b) 8th story opening with K8 < 0.5K9

(c) 1st story opening with K1 < 0.5K2

(12-D-1S-50-ELF)

(d) 1st story opening with K1 < 0.75K2

(12-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (12-D-2S-50-ELF)

(f) 1st and 2nd story openings with

K1 and K2 < 0.75K3 (12-D-2S-75-ELF)

Figure B-31 Earthquake intensity at design period, Sa, versus maximum inter-story drift for 

12-story walls designed for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure. Black line indicates spectral acceleration at which 50% of motions 

result in collapse defined by maximum inter-story drift in excess of 5%. Ki

indicates stiffness of story i defined per Section B.3.
B-48 B: Concrete Wall Studies FEMA P-2012

No analysis conducted

for this case.

(a) Continuous wall 

(12-D-0-0-ELF)

(b) 8th story opening with K8 < 0.5K9

(c) 1st story opening with K1 < 0.5K2

(12-D-1S-50-ELF)

(d) 1st story opening with K1 < 0.75K2

(12-D-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (12-D-2S-50-ELF)

(f) 1st and 2nd story openings with

K1 and K2 < 0.75K3 (12-D-2S-75-ELF)

Figure B-32 Earthquake intensity at design period, Sa, versus maximum inter-story drift 

for 12-story walls designed for Dmax spectrum using the ASCE/SEI 7-16 ELF 

procedure. Black line indicates spectral acceleration at which 50% of 

motions result in collapse defined by maximum inter-story drift in excess of 

10%. Ki indicates stiffness of story i defined per Section B.3.
FEMA P-2012 B: Concrete Wall Studies B-49

No analysis conducted

for this case.

(a) Continuous wall 

(8-B-0-0-ELF)

(b) 5th story opening with K5 < 0.5K6

(8-B-5S-50-ELF)

(c) 1st story opening with K1 < 0.5K2

(8-B-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2

(8-B-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (8-B-2S-50-ELF)

(f) 1st and 2nd story openings with

K1 and K2 < 0.75K3 (8-B-2S-75-ELF)

Figure B-33 Earthquake intensity at design period, Sa, versus maximum interstory drift for 

8-story walls designed for Bmax spectrum using the ASCE/SEI 7-16 ELF 

procedure. Black line indicates spectral acceleration at which 50% of 

motions result in collapse defined by maximum interstory drift in excess of 

10%. Ki indicates stiffness of story i defined per Section B.3.
B-50 B: Concrete Wall Studies FEMA P-2012

No analysis conducted

for this case.

(a) Continuous wall 

(12-B-0-0-ELF)

(b) 5th story opening with K8 < 0.5K9

(12-B-5S-50-ELF)

(c) 1st story opening with K1 < 0.5K2

(12-B-1S-50-ELF)

(d) 1st story opening, with K1 < 0.75K2

(12-B-1S-75-ELF)

(e) 1st and 2nd story openings with

K1 and K2 < 0.5K3 (12-B-2S-50-ELF)

(f) 1st and 2nd story openings with

K1 and K2 < 0.75K3 (12-B-2S-75-ELF)

Figure B-34 Earthquake intensity at design period, Sa, versus maximum interstory drift for 12-story 

walls designed for Bmax spectrum using the ASCE/SEI 7-16 ELF procedure. Black line 

indicates spectral acceleration at which 50% of motions result in collapse defined by 

maximum interstory drift in excess of 10%. Ki indicates stiffness of story i defined per 

Section B.3.
FEMA P-2012 B: Concrete Wall Studies B-51

Figure B-35 Impact of vertical irregularity and building height 

on ACMR for walls designed for Dmax demands 

using ASCE/SEI 7-16 ELF procedure. Nonsimulated collapse at 10% interstory drift.

Figure B-36 Impact of vertical irregularity and building height 

on ACMR for walls designed for Dmax demands 

using ASCE/SEI 7-16 MRSA procedure. Nonsimulated collapse at 10% interstory drift.

Figure B-37 Impact of vertical irregularity and building height 

on ACMR for walls designed for Bmax demands 

using ASCE/SEI 7-16 ELF procedure. 

Non-simulated collapse at 10% interstory drift.

FEMA P-2012 C: Steel Moment Frame Studies C-1

Appendix C

Steel Moment Frame Studies

This Appendix provides the following information on the steel moment 

frame studies: (1) Bmax and Dmax steel moment frame baseline designs; and 

(2) summary of the steel moment frame archetype results. For details on the 

steel moment frame designs with irregularities (i.e., mass irregularity, strongcolumn/weak-beam, and gravity-induced lateral demand) and for detailed 

results of the steel moment frame studies, see the electronic Supporting 

Documentation for Appendix C: Steel Moment Frame Irregularity Designs 

and Detailed Results. 

C.1 Steel Moment Frame Baseline Designs 

The archetype space as outlined in Chapter 6 includes 3-, 9-, and 20-story 

buildings each in a high and low seismicity zone. The high seismicity zone 

was represented by the Los Angeles region in California (Seismic Design 

Category Dmax) and the low seismicity zone was represented by the Boston 

region in Massachusetts (Seismic Design Category Bmax).

The steel moment frame buildings were designed per ASCE/SEI 7-16

Minimum Design Loads and Associated Criteria for Buildings and Other 

Structures (ASCE, 2017a) and AISC 341-10, Seismic Provisions for 

Structural Steel Buildings (AISC, 2010b). Dynamic analysis per Section

12.9 in ASCE/SEI 7-16 was used for calculating the member forces and story 

drifts.

Based upon the analyses undertaken, all the three buildings in the higher 

seismicity zone are governed by seismic forces and were designed to satisfy 

a story drift limit of 0.02. Generally, the buildings in the low seismicity zone 

are governed by wind forces and were designed to satisfy a story drift limit 

of H/400, where H is the building height. This is toward the lower end of the 

range discussed in ASCE/SEI 7-16 Commentary Appendix C.1.2 (ASCE, 

2017a). A wind event of 50-year mean recurrence interval calculated, as 

discussed in Appendix C of ASCE/SEI 7-16, was used to design for 

satisfying serviceability requirements.

The post-Northridge SAC Model Buildings of Los Angeles and Boston area, 

in Appendix B of FEMA 355C (FEMA, 2000b), were used as the base 

models for the designs. These were selected because they have been used in 
C-2 C: Steel Moment Frame Studies FEMA P-2012

a variety of different studies since FEMA 355C was concluded. The building 

configuration and loading criteria match those of the SAC models, except 

that the 20-story buildings have a bay width of 30 feet, rather than 20 feet, 

because the 30-foot bay was judged to be more realistic. Figures C-1 

through C-3 show the building configurations and Table C-1 summarizes the 

loading criteria.

Figure C-1 Baseline steel moment frame building elevations.

Figure C-2 Baseline SDC Dmax steel moment frame building plans.

Figure C-3 Baseline SDC Bmax steel moment frame building plans.
FEMA P-2012 C: Steel Moment Frame Studies C-3

Table C-1 Typical Design Loading

Typical Floor Loads Load (psf)

Dead Load 96.0

Seismic Weight 86.0

Seismic Partitions 10.0

Office LL (Reducible) 50.0

Typical Roof Loads Load (psf)

Dead Load 83.0

Seismic Weight 83.0

Roof LL (Reducible) 20.0

Typical Roof Loads at Penthouse Load (psf)

Dead Load 116.0

Seismic Weight 116.0

Roof LL (Reducible) 20.0

As required by the analysis matrix, baseline designs were developed using 

the modal response spectrum analysis (MRSA) and equivalent lateral force 

(ELF) methods.

C.1.1 Low Seismicity Zone (SDC Bmax) – Steel Ordinary Moment 

Frame Design

Each of the three buildings in the low seismicity zone was designed to satisfy 

two criteria: most efficient design with deeper girders, and the strongcolumn/weak-beam design with stronger columns and relatively shallower 

girders. The code does not mandate satisfaction of the strong-column/weakbeam criterion in an ordinary moment frame building, but it has been 

investigated in the analyses.

Relevant wind and seismic loading criteria are summarized in Table C-2.

All the buildings in the SDC Bmax (lower seismicity) region are story drift 

governed. The wind story drift has been limited to 0.25% (H/400), similar to 

the original SAC models. Per ASCE/SEI 7-16 (Commentary on Wind 

Serviceability requirements), story drift of the structure should be limited 

within H/300 to H/600. This study used the H/400 limit used in the SAC 

models.

The member sizes in the SDC Bmax models remained more or less the same as 

in the SAC models. The base shear charts show that the wind serviceability 

base shear is almost the same based on either 1993 edition of The BOCA 

National Building Code (BOCA, 1993) or ASCE/SEI 7-16 provisions. Some 
C-4 C: Steel Moment Frame Studies FEMA P-2012

of the member sizes were made more efficient in the design by increasing the 

member depth and reducing the member weight.

Table C-2 Low Seismicity Zone Seismic and Wind 

Design Values

Wind Design Criteria

Site Address: SDC Bmax

V_Basic Wind Speed (Strength) 130 mph

V_Basic Wind Speed (Serviceability) 100 mph

Wind Importance Factor 1

Wind Exposure B

Seismic Design Criteria ASCE/SEI 7-16

Site Address: SDC Bmax

TL 6 s

Site Class D

SS 0.480g

S1 0.198g

Fa 1.000

Fv 1.000

SMS 0.480g

SM1 0.198g

SDS 0.320g

SD1 0.132g

Risk Category II

SDC B

The designs of the SDC Bmax models have two versions:

Model 1: a non-strong-column/weak-beam design, which is the most 

efficient design satisfying the H/400 story drift limit.

Model 2: a strong-column/weak-beam design, which encourages beam 

yielding before column yielding, thereby limiting column hinging and 

potentially poor building performance.

The difference in frame tonnage between the two models varies from about 

12% in the 3- and 9-story buildings and about 2% in the 20-story building. 

Considering that the gravity members form a large part of the total building 

steel quantity, the increase in frame steel quantities would have a relatively 

small impact on the overall steel weight.
FEMA P-2012 C: Steel Moment Frame Studies C-5

C.1.1.1 3-Story OMF Building

Figures C-4 and C-5 illustrate the geometry of the 3-story building. The base 

shear calculated for this building is as follows (seismic governs):

• Seismic: 292 kips (design period, T = CuTa = 0.859 s)

• Wind: 244 kips

Figure C-4 Baseline SDC Bmax steel 

moment frame building 

typical 3-story elevation.

Figure C-5 Baseline SDC Bmax steel 

moment frame building 

typical 3-story plan.

The wind and seismic shears are comparable but the wind story drift limit of 

h/400 is 8 times more stringent than the seismic story drift limit of 0.02. The 

structure was designed to satisfy both seismic and wind forces and story drift 

limits. 

The baseline frame designs for the non-strong-column/weak-beam model are 

summarized in Tables C-3 and C-4 for MRSA and ELF designs, respectively. 

Using frame sizes from Table C-3 for ELF analysis resulted in a maximum 

story drift of 2.5% between the third and second floor. The beam sizes were 

increased as shown in Table C-4 to meet the allowable 2% story drift 

requirement using ELF analysis.

The baseline frame designs for the strong-column/weak-beam model are 

summarized in Tables C-5 and C-6 for MRSA and ELF designs, respectively. 

Using frame sizes from Table C-5 for ELF analysis resulted in a maximum 

story drift of 2.3% between the third and second floor. The beam sizes were 

increased as shown in Table C-6 to meet the allowable 2% story drift 
C-6 C: Steel Moment Frame Studies FEMA P-2012

requirement using ELF analysis. A variant on the frame designs was 

developed eliminating doubler plates, as summarized in Table C-7 and Table 

C-8.

Table C-3 V0030101 Baseline 

MRSA Design: Non-Strong-Column/Weak-Beam

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W14×53 W14×99 Yes W21×44

3rd W14×53 W14×99 Yes W21×62

2nd W14×53 W14×99 Yes W21×62

Notes: Model 1: MRSA Design, Non-Strong-Column/Weak-Beam

Steel Tonnage 1.85 psf (Columns: 0.81 psf, Beams: 1.04 psf)

Table C-4 V0030102 Baseline

ELF Design: Non-Strong-Column/Weak-Beam

Story/Floor

Columns

Doubler

Plates Girder

ELF Story Drift Moment Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×53 W14×99 No W21×57 1.07% 1.48% 0.49 0.49

3rd W14×53 W14×99 Yes W24×76 1.48% 2.00% 0.6 0.62

2nd W14×53 W14×99 Yes W24×76 1.20% 1.53% 0.53 0.59

Notes: Model 1: ELF Design, Non-Strong-Column/Weak-Beam

Steel Tonnage 2.09 psf (Columns: 0.81 psf, Beams: 1.28 psf)

Table C-5 V0030103 Baseline

MRSA Design: Strong-Column/Weak-Beam

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W14×82 W14×145 Yes W21×44

3rd W14×82 W14×146 Yes W21×50

2nd W14×82 W14×147 Yes W21×50

Notes: Model 2: MRSA Design, Strong-Column/Weak-Beam

Steel Tonnage 2.09 psf (Columns: 1.20 psf, Beams: 0.89 psf)
FEMA P-2012 C: Steel Moment Frame Studies C-7

Table C-6 V0030104 Baseline

ELF Design: Strong-Column/Weak-Beam

Story/Floor

Columns

Doubler

Plates Girder

ELF Story Drift Moment Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×53 W14×99 No W21×44 1.10% 1.51% 1.07 1.03

3rd W14×53 W14×99 No W24×62 1.37% 1.81% 1.29 1.25

2nd W14×53 W14×99 No W24×62 0.95% 1.20% 1.2 1.2

Notes: Model 2: ELF Design, Strong-Column/Weak-Beam

Steel Tonnage 1.84 psf (Columns: 0.81 psf, Beams: 1.03 psf)

Table C-7 V0030105 Baseline

MRSA Design: Strong-Column/Weak-Beam Design

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W14×120 W14×211 No W21×44

3rd W14×132 W14×233 No W21×50

2nd W14×132 W14×233 No W21×50

Notes: Model 3: MRSA Design, Strong-Column/Weak-Beam, No 

Doubler Plates

Steel Tonnage 2.76 psf (Columns: 1.87 psf, Beams: 0.89 psf)

Table C-8 V0030106 Baseline

ELF Design: Strong-Column/Weak-Beam Design

Story/Floor

Columns

Doubler

Plates Girder

ELF Story Drift

Ext Int ΔX ΔY

Roof W14×120 W14×211 No W21×44 1.21% 1.62%

3rd W14×132 W14×233 No W21×50 1.37% 1.77%

2nd W14×132 W14×233 No W21×50 0.80% 1.00%

Notes: Model 2: ELF Design, Strong-Column/Weak-Beam

Steel Tonnage 2.76 psf (Columns: 1.87 psf, Beams: 0.89 psf)

C.1.1.2 9-Story OMF Building

Figures C-6 and C-7 illustrate the geometry of the 9-story building. The base 

shear calculated for this building is as follows (wind governs):

• Seismic: 358 kips (design period, T = CuTa = 2.138 s)

• Wind: 950 kips

Corner columns were oriented such that the pinned connection frames into 

the column web. Other column sections were oriented with their strong axis

parallel to the longitudinal direction of the frame. 
C-8 C: Steel Moment Frame Studies FEMA P-2012

The baseline frame designs are summarized in Tables C-9 and C-10 for the 

ELF design for non-strong-column/weak-beam frames and strongcolumn/weak-beam frames, respectively. The frame sizes designed for the 9-

story building in Boston satisfying wind and seismic demands also satisfy 

story drift levels for ELF analysis.

Figure C-6 Baseline SDC Bmax steel 

moment frame building 

typical 9-story elevation.

Figure C-7 Baseline SDC Bmax steel 

moment frame building 

typical 9-story plan.
FEMA P-2012 C: Steel Moment Frame Studies C-9

Table C-9 V0090101 Baseline

MRSA Design: Non-Strong-Column/Weak-Beam Design

Story/Floor

Columns

Doubler

Plates Girder

ELF Story Drift

Ext Int ΔX ΔY

Roof W14×48 W14×90 No W21×44 0.70% 0.71%

9th W14×48 W14×90 No W24×84 0.93% 0.93%

8th W14×74 W14×145 No W27×84 0.86% 0.86%

7th W14×74 W14×145 No W30×108 0.87% 0.87%

6th W14×120 W14×211 No W33×118 0.74% 0.74%

5th W14×120 W14×211 No W33×118 0.74% 0.74%

4th W14×145 W14×311 No W33×130 0.60% 0.60%

3rd W14×145 W14×311 No W33×141 0.57% 0.57%

2nd W14×193 W14×398 No W36×194 0.56% 0.56%

1st W14×193 W14×398 No W21×44 - -

Notes: Model 1: Non-Strong-Column/Weak-Beam Design

(Design is governed by drift due to wind ≤ 0.25% limit)

Steel Tonnage 5.10 psf (Columns: 2.40 psf, Beams: 2.70 psf)

Table C-10 V0090102 Baseline

MRSA Design: Strong-Column/Weak-Beam Design

Story/Floor

Columns

Doubler

Plates Girder

ELF Story Drift Moment Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×99 W14×176 No W21×44 0.82% 0.83% 1.39 1.29

9th W14×99 W14×176 No W21×44 0.97% 0.97% 2.72 2.55

8th W14×145 W14×283 No W24×68 0.85% 0.85% 1.79 1.82

7th W14×145 W14×283 No W27×84 0.80% 0.80% 1.52 1.65

6th W14×211 W14×398 No W30×90 0.72% 0.72% 1.61 1.74

5th W14×211 W14×398 No W30×90 0.66% 0.66% 1.91 2.07

4th W14×257 W14×455 No W33×118 0.58% 0.58% 1.44 1.51

3rd W14×257 W14×455 No W33×118 0.58% 0.58% 1.57 1.62

2nd W14×283 W14×500 No W33×118 0.54% 0.54% 1.63 1.7

1st W14×283 W14×00 No W21×44 - -

Notes: Model 3: Strong-Column/Weak-Beam Design

(Design is governed by drift due to wind ≤ 0.25% limit while satisfying moment ratio < 1.0)

Steel Tonnage 5.84 psf (Columns: 3.77 psf, Beams: 2.07 psf)
C-10 C: Steel Moment Frame Studies FEMA P-2012

C.1.1.3 20-Story OMF Building

Figures C-8 and C-9 illustrate the geometry of the 20-story building. The 

base shear calculated for this building is as follows (wind governs):

• Seismic: 750 kips (design period, T = CuTa = 3.977 s)

• Wind: 3116 kips (east-west); 2580 kips (north-south)

Corner columns were oriented such that the pinned connection frames into 

the column web. Other column sections were oriented with their strong axis 

parallel to the longitudinal direction of the frame. The basement floor (-1 

Level) has simple connections.

Figure C-8 Baseline SDC Bmax steel 

moment frame building 

typical 20-story elevation.

Figure C-9 Baseline SDC Bmax steel 

moment frame building 

typical 20-story plan.
FEMA P-2012 C: Steel Moment Frame Studies C-11

Table C-11 V0200101 Baseline

MRSA Design: Non-Strong-Column/Weak-Beam Design

Story/Floor

Columns

Doubler

Ext Next to Ext Int Plates Girder

Roof W14×109 W24×117 W24×131 No W21×48

20th W14×109 W24×117 W24×131 No W24×76

19th W14×159 W36×150 W36×150 No W27×84

18th W14×159 W36×150 W36×150 No W30×99

17th W14×193 W36×182 W36×210 No W30×108

16th W14×193 W36×182 W36×210 No W33×118

15th W14×283 W36×262 W36×282 No W33×118

14th W14×283 W36×262 W36×282 No W36×135

13th W14×283 W36×262 W36×302 No W36×135

12th W14×283 W36×262 W36×302 No W36×182

11th W14×311 W36×262 W36×302 No W36×182

10th W14×311 W36×262 W36×302 No W36×182

9th W14×342 W36×302 W36×361 No W36×210

8th W14×342 W36×302 W36×361 No W36×210

7th W14×342 W36×302 W36×361 No W36×256

6th W14×342 W36×302 W36×361 No W36×256

5th W14×370 W36×330 W36×395 No W36×256

4th W14×370 W36×330 W36×395 No W36×282

3rd W14×455 W36×395 W36×487 No W36×282

2nd W14×455 W36×395 W36×487 No W36×302

Level 1 W14×455 W36×395 W36×487 No W24×62

Basement W14×455 W36×395 W36×487 No W24×84

Notes: Model 1: Non Strong-Column/Weak-Beam Design

Steel Tonnage 6.92 psf (Columns: 3.03 psf, Beams: 3.89 psf)
C-12 C: Steel Moment Frame Studies FEMA P-2012

Table C-12 V0200102 Baseline

MRSA Design: Strong-Column/Weak-Beam Design

Story/Floor

Columns

Doubler

Ext Next to Ext Int Plates Girder

Roof W14×109 W24×117 W24×117 No W18×35

20th W14×109 W24×117 W24×117 No W24×76

19th W14×159 W36×150 W36×150 No W27×84

18th W14×159 W36×150 W36×150 No W30×99

17th W14×193 W36×210 W36×182 No W30×108

16th W14×311 W36×210 W36×182 No W33×118

15th W14×311 W36×302 W36×282 No W33×118

14th W14×370 W36×302 W36×282 No W36×135

13th W14×370 W36×330 W36×302 No W36×135

12th W14×370 W36×330 W36×302 No W36×160

11th W14×426 W36×361 W36×302 No W36×170

10th W14×426 W36×361 W36×302 No W36×170

9th W14×455 W36×395 W36×361 No W36×194

8th W14×455 W36×395 W36×361 No W36×194

7th W14×500 W36×441 W36×395 No W36×232

6th W14×500 W36×441 W36×395 No W36×232

5th W14×605 W36×487 W36×441 No W36×232

4th W14×605 W36×487 W36×441 No W36×247

3rd W14×665 W36×487 W36×487 No W36×247

2nd W14×665 W36×487 W36×487 No W36×262

Level 1 W14×665 W36×487 W36×487 No W24×55

Basement W14×665 W36×487 W36×487 No W24×84

Notes: Model 2: Strong-Column/Weak-Beam Design

Steel Tonnage 7.12 psf (Columns: 3.53 psf, Beams: 3.59 psf)

C.1.2 High Seismicity Zone (SDC Dmax) – Steel Special Moment 

Frame Design

The 3-, 9-, and 20-story buildings were designed for SDC Dmax, as well. The 

3- and 9-story buildings were designed to satisfy two criteria: (1) code design 

meeting the minimum code requirements for special moment frames per 

AISC 341-10; and (2) performance-based plastic design, also called the 

Energy Method, which calculates the demand on the seismic members based 

on the ultimate story drift to which the structure is subjected. The energy 

method provides a parallel design to the code design.
FEMA P-2012 C: Steel Moment Frame Studies C-13

The buildings were designed to a story drift limit of 2% for a design based

earthquake and to a story drift limit of 3% for a maximum-considered 

earthquake (MCE). The columns in the code design were designed to satisfy 

the strong-column/weak-beam principle with Mpc*/ Mpb*>1.00; in the energy 

method the beams and the columns are designed to sustain seismic demands 

generated due to the story drift of the structure (Goel and Chao, 2008).

The frame elements designed using the energy method are heavier than those 

designed by code design because the buildings in the code design do not 

reach the 2% story drift limit under a design based earthquake. 

Reduced beam section (RBS) connections per AISC 358-10 were used as the 

prequalified connections for the steel special moment frames. The RBS 

dimensions, shown in Figure C-10, were considered explicitly when 

evaluating the frame story drift.

Figure C-10 Reduced beam section profiles.

As required by the analysis matrix, baseline designs were developed using 

MRSA and ELF methods. Relevant wind and seismic loading criteria are 

summarized in Table C-13. Table C-14 indicates RBS profiles used in the 

high seismicity zone studies.

During the course of baseline frame design, it was observed that the member 

sizes of the SDC Dmax 3- and 9-story buildings could be reduced compared to 

the SAC models. The original SAC model for the Los Angeles 9-story 

building was used to study this.

Even accounting for the shift in design methodology between the 1994

Uniform Building Code (UBC-94; International Conference of Building 

Officials, 1994) (working) and ASCE/SEI 7-16 (strength), it was observed 

that the base shear for the Los Angeles 9-story building increased from the 

original SAC design parameters. On the other hand, the story drift limit also
C-14 C: Steel Moment Frame Studies FEMA P-2012

relaxed from h/400 or 0.25% in UBC-94 (working/elastic) to 2% in 

ASCE/SEI 7-16 (strength/inelastic). For some frame members, it was 

possible to reduce the sizes in the SDC Dmax 3- and 9-story buildings.

Table C-13 High Seismicity Zone Seismic and Wind Design Values

Wind Design Criteria

Site Address: SDC Dmax

V_Basic Wind Speed (Strength) 110 mph

V_Basic Wind Speed (Serviceability) 85 mph

Wind Importance Factor 1

Wind Exposure B

Seismic Design Criteria ASCE/SEI 7-16

Site Address: SDC Dmax

TL 8 s

Site Class D

SS 2.250g

S1 0.600g

Fa 1.000

Fv 1.500

SMS 2.250g

SM1 0.900g 

SDS 1.500g

SD1 0.600g

Risk Category II

SDC D

Table C-14 Reduced Beam Section Profiles Used in SDC Dmax Buildings

Beam Size a (in.) b (in.) c (in.) R (in.)

W24×76 to W34×103 6 18 2.00 21.25

W24×131 to W24×229 8 18 2.75 16.10

W27×94 to W27×129 6 20 2.25 23.35

W27×146 to W27×217 8 20 2.75 19.56

W30×108 to W30×148 7 22 2.25 28.01

W30×173 to W30×261 9 22 3.00 21.67

W33×130 to W33×169 7 24 2.50 30.05

W33×201 to W33×291 9 24 3.25 23.78

W36×150 to W36×256 8 27 2.75 34.51

W36×230 to W36×282 10 27 3.50 27.79
FEMA P-2012 C: Steel Moment Frame Studies C-15

This phenomenon was not observed in the 20-story building. The seismic 

base shear of the 20-story building increased by about 110%, which is 

significant, and even the relaxation in the story drift limit from UBC-94 to

ASCE/SEI 7-10 did not help and the sizes had to be increased to meet all 

code provisions.

C.1.2.1 3-Story SMF Building

Figure C-11 and Figure C-12 illustrate the geometry of the 3-story building 

from which the baseline moment frame designs were developed. The base 

shear calculated for this building is as follows (seismic governs):

• Seismic: 679 kips (design period, T = CuTa = 0.735 s)

• Wind: 346 kips

Figure C-11 Baseline SDC Dmax steel moment frame 

building typical 3-story elevation.

Figure C-12 Baseline SDC Dmax steel moment 

frame building typical 3-story plan.

Table C-15 V0300201 Baseline

MRSA Design

Story/ 

Floor

Columns

Doubler

Plates Girder

MRSA Story 

Drift

Moment 

Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×159 W14×176 No W24×55 1.75% 1.77% 2.00 1.15

3rd W14×159 W14×176 Yes W27×94 1.86% 1.88% 1.89 1.09

2nd W14×159 W14×176 Yes W27×94 1.36% 1.37% 1.75 1.05

Notes: Model 1: Code Design

Steel Tonnage 2.81 psf (Columns: 1.53 psf, Beams: 1.28 psf)
C-16 C: Steel Moment Frame Studies FEMA P-2012

The MRSA frame sizes in Table C-16, when subjected to ELF analysis, 

resulted in drifts exceeding the allowable 2% limit. The frame sizes were 

increased as shown in Table C-17 to meet the allowable 2% story drift 

requirement.

Table C-16 V0300202 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Plates Girder

MRSA Story 

Drift

Moment 

Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×132 W14×159 No W24×55 1.90% 1.91% 1.62 1.03

3rd W14×176 W14×283 No W27×94 1.65% 1.66% 1.82 1.43

2nd W14×176 W14×283 No W27×94 1.11% 1.12% 1.99 1.84

Notes: Model 2: Code Design, No Doubler Plates

Steel Tonnage 3.12 psf (Columns: 1.84 psf, Beams: 1.28 psf)

Table C-17 V0300203 Baseline

ELF Design

Story/Floor

Columns

Doubler

Plates Girder

ELF Story Drift

Moment 

Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×211 W14×311 No W27×94 1.79% 1.80% 1.33 1.06

3rd W14×311 W14×370 No W33×130 1.98% 1.98% 1.88 1.32

2nd W14×311 W14×370 No W33×130 1.33% 1.33% 2.2 1.43

Notes: Model 2: ELF Design, No Doubler Plates

Steel Tonnage 4.74 psf (Columns: 2.87psf, Beams: 1.87 psf)

Table C-18 V0300204 Baseline

Energy Method

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W14×257 W14×455 No W24×94

3rd W14×257 W14×455 No W30×108

2nd W14×311 W14×500 No W33×130

Notes: Model 3: Energy Method

Steel Tonnage 5.43 psf (Columns: 3.59 psf, Beams: 1.84 psf)

C.1.2.2 9-Story SMF Building

Figures C-13 and C-14 illustrate the geometry of the 9-story building. The 

base shear calculated for this building is as follows (seismic governs):

• Seismic: 1341 kips (design period, T = CuTa = 1.830 s)

• Wind: 816 kips
FEMA P-2012 C: Steel Moment Frame Studies C-17

Corner columns were oriented such that the pinned connection frames into 

the column web. Other column sections were oriented with their strong axis 

parallel to the longitudinal direction of the frame. 

Figure C-13 Baseline SDC Dmax steel 

moment frame building 

typical 9-story elevation.

Figure C-14 Baseline SDC Dmax steel 

moment frame building 

typical 9-story plan.

The baseline frame designs are summarized in Tables C-19 and C-20 for the 

code-complying baseline MRSA design and for design without doubler 

plates (i.e., column sizes were increased), respectively. 

The frame sizes in Tables C-19 and C-20, when analyzed with the ELF 

method, resulted in story drifts substantially exceeding the 2% allowable 

story drift limit at all story levels. The frame sizes were increased as shown 

in Table C-21 in order to meet the allowable 2% story drift requirement using 

ELF analysis. Optimal sizes were chosen that simultaneously satisfy story 

drift and strong-column/weak-beam requirements. Conforming to ELFbased frame sizes results in a steel tonnage that is 1.7 times the weight per 

square foot tonnage using MRSA-based design.

Table C-22 summarizes the results from the energy-based design 

methodology. Deep column section were selected inasmuch as the method 
C-18 C: Steel Moment Frame Studies FEMA P-2012

generally results in larger column sizes than do designs based on MRSA or 

ELF methods.

Table C-19 V0900201 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W14×132 W14×145 Yes W21×50

9th W14×132 W14×145 Yes W24×76

8th W14×193 W14×211 Yes W24×84

7th W14×193 W14×211 Yes W27×94

6th W14×233 W14×257 Yes W27×94

5th W14×233 W14×257 Yes W30×108

4th W14×257 W14×283 Yes W30×108

3rd W14×257 W14×283 Yes W30×108

2nd W14×283 W14×370 No W33×130

1st W14×283 W14×370 No W33×130

Notes: Model 1: Code Design

Steel Tonnage 5.32 psf (Columns: 2.83 psf, Beams: 2.49 psf)

Table C-20 V0900202 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W14×145 W14×159 No W21×50

9th W14×145 W14×159 No W24×76

8th W14×193 W14×283 No W24×84

7th W14×193 W14×283 No W27×94

6th W14×233 W14×311 No W27×94

5th W14×233 W14×311 No W30×108

4th W14×257 W14×311 No W30×108

3rd W14×257 W14×311 No W30×108

2nd W14×283 W14×370 No W33×130

1st W14×283 W14×370 No W33×130

Notes: Model 2: Code Design, No Doubler Plates

Steel Tonnage 5.6 psf (Columns: 3.1 psf, Beams: 2.49 psf)
FEMA P-2012 C: Steel Moment Frame Studies C-19

Table C-21 V0900203 Baseline

ELF Design

Story/ 

Floor

Columns

Doubler

Plates Girder

ELF Story Drift Moment Ratio

Ext Int ΔX ΔY Ext Int

Roof W14×233 W14×311 No W27×94 1.28% 1.30% 1.47 1.06

9th W14×233 W14×311 No W30×116 1.67% 1.67% 2.06 1.48

8th W14×370 W14×398 No W36×150 1.74% 1.74% 1.79 1.1

7th W14×370 W14×398 No W36×150 1.92% 1.92% 2.23 1.24

6th W14×398 W14×426 No W36×182 1.95% 1.95% 1.87 1.04

5th W14×398 W14×426 No W36×194 1.96% 1.95% 1.8 1

4th W14×455 W14×500 No W36×232 1.80% 1.80% 1.6 0.99

3rd W14×455 W14×500 No W36×232 1.90% 1.90% 1.7 0.99

2nd W14×455 W14×550 No W36×232 1.92% 1.92% 1.67 1.04

1st W14×455 W14×550 No W36×232 - - 1.64 1.09

Notes: Model 2 Revised: ELF Design, No Doubler Plates

Steel Tonnage 9.44 psf (Columns: 4.85 psf, Beams: 4.59 psf)

Table C-22 V0900204 Baseline

Energy Method

Story/Floor

Columns

Doubler

Ext Int Plates Girder

Roof W27×336 W27×539 No W30×108

9th W27×336 W27×539 No W33×130

8th W27×336 W27×539 No W40×149

7th W27×368 W36×652(1) No W40×167

6th W27×368 W36×652(1) No W40×183

5th W27×539 W36×652(1) No W40×199

4th W27×539 W36×652(1) No W40×199

3rd W27×539 W36×652(1) No W40×199

2nd W27×539 W36×652(1) No W40×199

1st W27×539 W36×652(1) No W33×130

(1) Section deeper than 30 in.

Notes: Model 3: Energy Method

Steel Tonnage 12.46 psf (Columns: 8.03 psf, Beams: 4.43 psf)

C.1.2.3 20-Story SMF Building

Figures C-15 and C-16 illustrate the geometry of the 20-story building. The 

base shear calculated for this building is as follows (seismic governs):

• Seismic: 3500 kips (design period, T = CuTa = 3.403 s)

• Wind: 2155 kips (east-west); 1810 kips (north-south)
C-20 C: Steel Moment Frame Studies FEMA P-2012

Corner columns are box sections because they participate in orthogonal 

frames. The orthogonal load combinations in ASCE/SEI 7-16 were used to 

determine demands on the corner columns. Other column sections oriented 

with their strong axis parallel to the longitudinal direction of the frame. The 

basement floor (-1 Level) has simple connections.

Figure C-15 Baseline SDC Dmax steel 

moment frame building 

typical 20-story elevation.

Figure C-16 Baseline SDC Dmax steel 

moment frame building 

typical 20-story plan.

Designs based on MRSA and the ELF method were developed, with and 

without doubler plates (i.e., the columns were upsized). Tables C-23 through 

C-26 summarize the resulting baseline designs.
FEMA P-2012 C: Steel Moment Frame Studies C-21

Table C-23 V02002011 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Plates Girder

Ext

[HSS Section]

North-South Frame

Next to Ext Int

Roof 15×15×1.00 W27×129 W27×129 Yes W24×76

20th 15×15×1.00 W27×129 W27×129 Yes W33×130

19th 15×15×1.00 W27×235 W27×235 Yes W33×130

18th 15×15×1.00 W27×235 W27×235 Yes W33×130

17th 15×15×1.00 W27×235 W27×235 Yes W33×130

16th 15×15×1.00 W27×235 W27×235 Yes W36×150

15th 15×15×1.00 W27×235 W27×235 Yes W36×150

14th 15×15×1.00 W27×281 W27×258 Yes W36×150

13th 15×15×1.00 W27×281 W27×258 Yes W36×150

12th 15×15×1.25 W27×368 W27×336 Yes W36×170

11th 15×15×1.25 W27×368 W27×336 Yes W36×170

10th 15×15×1.25 W27×368 W27×336 Yes W36×182

9th 15×15×1.50 W27×539 W27×539 No W36×182

8th 15×15×1.50 W27×539 W27×539 No W36×194

7th 15×15×1.50 W27×539 W27×539 No W36×194

6th 15×15×1.50 W27×539 W27×539 No W36×210

5th 15×15×2.00 W27×539 W27×539 No W36×210

4th 15×15×2.00 W27×539 W27×539 No W36×210

3rd 15×15×2.00 W27×539 W27×539 No W36×210

2nd 15×15×2.00 W27×539 W27×539 Yes W36×262

Level 1 15×15×2.00 W27×539 W27×539 No W30×116

Basement 15×15×2.00 W27×539 W27×539 No W27×94

Notes: Model 1: MRSA Design

Steel Tonnage 6.68 psf (Columns: 3.28 psf, Beams: 3.40 psf)
C-22 C: Steel Moment Frame Studies FEMA P-2012

Table C-24 V02002012 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Plates Girder

Ext

[HSS Section]

East-West Frame

Next to Ext Int

Roof 15×15×1.00 W27×129 W27×129 Yes W24×76

20th 15×15×1.00 W27×129 W27×129 Yes W24×76

19th 15×15×1.00 W27×129 W27×129 Yes W30×108

18th 15×15×1.00 W27×161 W27×161 Yes W30×108

17th 15×15×1.00 W27×161 W27×161 Yes W30×108

16th 15×15×1.00 W27×194 W27×194 Yes W30×116

15th 15×15×1.00 W27×194 W27×194 Yes W30×116

14th 15×15×1.00 W27×217 W27×217 Yes W33×130

13th 15×15×1.00 W27×217 W27×217 Yes W33×130

12th 15×15×1.25 W27×258 W27×258 Yes W33×130

11th 15×15×1.25 W27×258 W27×258 Yes W36×150

10th 15×15×1.25 W27×258 W27×258 Yes W36×150

9th 15×15×1.50 W27×336 W27×307 Yes W36×150

8th 15×15×1.50 W27×336 W27×307 Yes W36×150

7th 15×15×1.50 W27×336 W27×307 Yes W36×150

6th 15×15×1.50 W27×336 W27×307 Yes W36×150

5th 15×15×2.00 W27×368 W27×336 No W36×150

4th 15×15×2.00 W27×368 W27×336 No W36×160

3rd 15×15×2.00 W27×539 W27×539 No W36×170

2nd 15×15×2.00 W27×539 W27×539 No W36×182

Level 1 15×15×2.00 W27×539 W27×539 No W30×116

Basement 15×15×2.00 W27×539 W27×539 No W27×94

Notes: Model 1: MRSA Design

Steel Tonnage 6.68 psf (Columns: 3.28 psf, Beams: 3.40 psf)
FEMA P-2012 C: Steel Moment Frame Studies C-23

Table C-25 V02002021 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Plates Girder

Ext

[HSS Section]

North-South Frame

Next to Ext Int

Roof 15×15×1.00 W27×307 W27×307 No W24×76

20th 15×15×1.00 W27×307 W27×307 No W33×130

19th 15×15×1.00 W27×307 W27×307 No W33×130

18th 15×15×1.00 W27×307 W27×307 No W33×130

17th 15×15×1.00 W27×307 W27×307 No W33×130

16th 15×15×1.00 W27×336 W27×336 No W36×150

15th 15×15×1.00 W27×336 W27×336 No W36×150

14th 15×15×1.00 W27×336 W27×336 No W36×150

13th 15×15×1.00 W27×336 W27×336 No W36×150

12th 15×15×1.00 W27×368 W27×368 No W36×170

11th 15×15×1.25 W27×368 W27×368 No W36×170

10th 15×15×1.25 W27×539 W27×539 No W36×182

9th 15×15×1.25 W27×539 W27×539 No W36×182

8th 15×15×1.50 W27×539 W27×539 No W36×194

7th 15×15×1.50 W27×539 W27×539 No W36×194

6th 15×15×1.50 W27×539 W27×539 No W36×210

5th 15×15×2.00 W27×539 W27×539 No W36×210

4th 15×15×2.00 W27×539 W27×539 No W36×210

3rd 15×15×2.00 W27×539 W27×539 No W36×210

2nd 15×15×2.00 W27×539 W27×539 No W36×262

Level 1 15×15×2.00 W27×539 W27×539 No W30×116

Basement 15×15×2.00 W27×539 W27×539 No W27×94

Notes: Model 2: MRSA Design, No Doubler Plates

Steel Tonnage 7.04 psf (Columns: 3.67 psf, Beams: 3.37 psf)
C-24 C: Steel Moment Frame Studies FEMA P-2012

Table C-26 V02002022 Baseline

MRSA Design

Story/Floor

Columns

Doubler

Plates Girder

Ext

[HSS Section]

East-West Frame

Next to Ext Int

Roof 15×15×1.00 W27×194 W27×194 No W24×76

20th 15×15×1.00 W27×194 W27×194 No W24×76

19th 15×15×1.00 W27×281 W27×281 No W30×108

18th 15×15×1.00 W27×281 W27×281 No W30×108

17th 15×15×1.00 W27×281 W27×281 No W30×108

16th 15×15×1.00 W27×307 W27×307 No W30×116

15th 15×15×1.00 W27×307 W27×307 No W30×116

14th 15×15×1.00 W27×307 W27×307 No W33×130

13th 15×15×1.00 W27×307 W27×307 No W33×130

12th 15×15×1.00 W27×307 W27×307 No W33×130

11th 15×15×1.25 W27×336 W27×336 No W36×150

10th 15×15×1.25 W27×336 W27×336 No W36×150

9th 15×15×1.25 W27×336 W27×336 No W36×150

8th 15×15×1.50 W27×336 W27×336 No W36×150

7th 15×15×1.50 W27×336 W27×336 No W36×150

6th 15×15×1.50 W27×336 W27×336 No W36×150

5th 15×15×2.00 W27×336 W27×336 No W36×150

4th 15×15×2.00 W27×368 W27×368 No W36×160

3rd 15×15×2.00 W27×368 W27×368 No W36×170

2nd 15×15×2.00 W27×539 W27×539 No W36×182

Level 1 15×15×2.00 W27×539 W27×539 No W30×116

Basement 15×15×2.00 W27×539 W27×539 No W27×94

Notes: Model 2: MRSA Design, No Doubler Plates

Steel Tonnage 7.04 psf (Columns: 3.67 psf, Beams: 3.37 psf)
FEMA P-2012 C: Steel Moment Frame Studies C-25

C.2 Summary of Steel Moment Frame Results

Table C-27 Steel Moment Frame Results 

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V00301011 3 Baseline_MRS

_Non-SCWB Bmax MRSA 0.859 1.55 3.20 4.42 1.00

V00301012 3 Baseline_MRS

_Non-SCWB Bmax MRSA 0.859 1.80 2.51 3.76 1.00

V00301021 3 Baseline_ELF

_Non-SCWB Bmax ELF 0.859 1.39 3.58 4.07 1.00

V00301022 3 Baseline_ELF

_Non-SCWB Bmax ELF 0.859 1.61 2.86 3.43 1.00

V00301031 3 Baseline_MRS

_SCWB Bmax MRSA 0.859 1.48 3.25 7.01 1.00

V00301032 3 Baseline_MRS

_SCWB Bmax MRSA 0.859 1.72 2.53 6.01 1.00

V00301041 3 Baseline_ELF

_SCWB Bmax ELF 0.859 1.66 2.05 3.98 1.00

V00301042 3 Baseline_ELF

_SCWB Bmax ELF 0.859 1.93 1.60 3.84 1.00

V00301051 3

Baseline_MRS 

SCWB (No 

Doubl. Plates)

Bmax MRSA 0.859 1.34 4.32 8.04 1.00

V00301052 3

Baseline_MRS 

SCWB (No 

Doubl. Plates)

Bmax MRSA 0.859 1.55 3.36 6.84 1.00

V60301011 3 SCWB 0.4 Bmax ELF 0.859 1.56 2.21 4.87 1.04

V60301012 3 SCWB 0.4 Bmax ELF 0.859 1.81 1.71 4.34 0.99

V60301021 3 SCWB 0.7 Bmax ELF 0.859 1.55 2.44 4.45 0.95

V60301022 3 SCWB 0.7 Bmax ELF 0.859 1.79 1.87 4.11 0.94

V60301031 3 SCWB 1.0 Bmax ELF 0.859 1.47 3.25 4.68 1.00

V60301032 3 SCWB 1.0 Bmax ELF 0.859 1.71 2.24 4.37 1.00

V00901011 9 Baseline_Non

-SCWB Bmax MRSA 2.138 2.94 4.54 3.93 1.00

V00901012 9 Baseline_Non

-SCWB Bmax MRSA 2.138 2.89 4.60 4.41 1.00

V00901021 9 Baseline_SCWB

(No Dbl. Plates) Bmax MRSA 2.138 2.84 7.43 5.42 1.00
C-26 C: Steel Moment Frame Studies FEMA P-2012

Table C-27 Steel Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V00901022 9 Baseline_SCWB

(No Dbl. Plates) Bmax MRSA 2.138 2.71 7.96 5.40 1.00

V60901011 9 SCWB 0.4 Bmax MRSA 2.138 2.50 4.82 8.32 1.53

V60901012 9 SCWB 0.4 Bmax MRSA 2.138 2.46 4.85 8.93 1.60

V60901021 9 SCWB 0.7 Bmax MRSA 2.138 2.76 4.34 5.24 0.97

V60901022 9 SCWB 0.7 Bmax MRSA 2.138 2.71 4.40 5.48 0.98

V60901031 9 SCWB 1.0 Bmax MRSA 2.138 2.82 4.45 5.43 1.00

V60901032 9 SCWB 1.0 Bmax MRSA 2.138 2.77 4.53 5.58 1.00

V02001011 20 Non-SCWB Bmax MRSA 3.977 3.51 8.16 9.16 1.00

V02001012 20 Non-SCWB Bmax MRSA 3.977 3.48 7.90 9.72 1.00

V02001021 20 Baseline Bmax MRSA 3.977 3.41 9.09 5.19 1.00

V02001022 20 Baseline Bmax MRSA 3.977 3.45 8.90 6.27 1.00

V62001011 20 SCWB 0.4 Bmax MRSA 3.977 3.33 7.01 5.01 1.02

V62001012 20 SCWB 0.4 Bmax MRSA 3.977 3.29 6.62 7.20 1.12

V62001021 20 SCWB 0.7 Bmax MRSA 3.977 3.31 7.77 5.55 1.13

V62001022 20 SCWB 0.7 Bmax MRSA 3.977 3.29 7.93 6.88 1.08

V62001031 20 SCWB 1.0 Bmax MRSA 3.977 3.30 9.59 4.90 1.00

V62001032 20 SCWB 1.0 Bmax MRSA 3.977 3.30 9.21 6.40 1.00

V72001011 20 1st Story 

α = 0.1 Bmax MRSA 3.98 3.51 8.15 8.47 0.96

V72001021 20 1st Story 

α = 0.3 Bmax MRSA 3.98 3.51 8.11 8.10 0.92

V72001031 20 1st Story 

α = 0.5 Bmax MRSA 3.98 3.50 8.08 7.71 0.87

V72001041 20 7th Story 

α = 0.1 Bmax MRSA 3.98 3.51 8.05 8.33 0.94

V72001051 20 7th Story 

α = 0.3 Bmax MRSA 3.98 3.50 7.91 8.12 0.92

V72001061 20 7th Story 

α = 0.5 Bmax MRSA 3.98 3.49 8.00 8.70 0.99

V72001071 20 14th Story 

α = 0.1 Bmax MRSA 3.98 3.51 8.10 8.70 0.99

V72001081 20 14th Story 

α = 0.3 Bmax MRSA 3.98 3.51 7.96 8.14 0.92
FEMA P-2012 C: Steel Moment Frame Studies C-27

Table C-27 Steel Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V72001091 20 14th Story 

α = 0.5 Bmax MRSA 3.98 3.51 7.80 8.34 0.95

V00302011 3 Baseline_MRS Dmax MRSA 0.735 1.18 2.33 2.37 1.00

V00302012 3 Baseline_MRS Dmax MRSA 0.735 1.19 2.26 2.23 1.00

V00302021 3 Baseline_MRS

(No Dbl Plates) Dmax MRSA 0.735 1.12 2.68 2.27 1.00

V00302022 3 Baseline_MRS 

(No Dbl Plates) Dmax MRSA 0.735 1.13 2.60 2.21 1.00

V00302031 3 Baseline_ELF Dmax ELF 0.735 0.80 4.73 2.92 1.00

V00302032 3 ELF Dmax ELF 0.735 0.80 4.61 2.89 1.00

V00302041 3 Energy Method Dmax Energy 0.735 0.79 4.71 3.04 1.00

V00302042 3 Energy Method Dmax Energy 0.735 0.80 4.59 3.05 1.00

V20302011 3 Baseline_MRS Dmax MRSA 0.735 1.09 2.74 2.39 1.00

V20302012 3 Baseline_MRS Dmax MRSA 0.735 1.11 2.66 2.28 1.00

V20302021 3 MR 1.5_FLR2

_MRS Dmax MRSA 0.735 1.11 2.47 2.18 0.91

V20302022 3 MR 1.5_FLR2

_MRS Dmax MRSA 0.735 1.12 2.38 2.07 0.91

V20302031 3 MR2.0_FLR2 Dmax MRSA 0.735 1.12 2.25 2.10 0.88

V20302032 3 MR2.0_FLR2

_MRS Dmax MRSA 0.735 1.13 2.17 1.87 0.82

V20302041 3 MR3.0_FLR2 Dmax MRSA 0.735 1.15 1.90 1.83 0.77

V20302042 3 MR3.0_FLR2

_MRS Dmax MRSA 0.735 1.16 1.82 1.74 0.77

V20302051 3 MR3.0_FLR3

_MRS Dmax MRSA 0.735 1.16 2.27 1.77 0.74

V20302052 3 MR3.0_FLR3_

MRS Dmax MRSA 0.735 1.17 2.19 1.72 0.76

V20302061 3 Baseline_ELF Dmax ELF 0.735 0.80 4.72 2.87 1.00

V20302062 3 Baseline_ELF Dmax ELF 0.735 0.80 4.60 2.82 1.00

V20302071 3 MR 1.5_FLR2

_ELF Dmax ELF 0.735 0.80 4.24 2.64 0.92

V20302072 3 MR 1.5_FLR2

_ELF Dmax ELF 0.735 0.81 4.13 2.58 0.91

V20302081 3 MR 1.5_FLR2

_ELF (revised) Dmax ELF 0.735 0.77 4.18 2.83 0.99
C-28 C: Steel Moment Frame Studies FEMA P-2012

Table C-27 Steel Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V20302082 3 MR 1.5_FLR2

_ELF (revised) Dmax ELF 0.735 0.77 4.08 2.73 0.97

V20302091 3 MR2.0_FLR2

_ELF Dmax ELF 0.735 0.72 3.89 2.59 0.90

V20302092 3 MR2.0_FLR2

_ELF Dmax ELF 0.735 0.72 3.80 2.49 0.88

V20302101 3 MR3.0_FLR2

_ELF Dmax ELF 0.735 0.73 4.08 2.36 0.82

V20302102 3 MR3.0_FLR2

_ELF Dmax ELF 0.735 0.74 3.98 2.31 0.82

V20302111 3 MR3.0_FLR3

_ELF Dmax ELF 0.735 0.76 4.84 2.62 0.91

V20302112 3 MR3.0_FLR3

_ELF Dmax ELF 0.735 0.76 4.74 2.55 0.90

V60302011 3 SCWB 0.5 Dmax MRSA 0.735 1.65 2.05 2.01 0.88

V60302012 3 SCWB 0.5 Dmax MRSA 0.735 1.66 1.95 1.92 0.85

V60302021 3 SCWB 1.0 Dmax MRSA 0.735 1.32 2.47 2.30 1.00

V60302022 3 SCWB 1.0 Dmax MRSA 0.735 1.33 2.40 2.26 1.00

V60302031 3 SCWB 1.2 Dmax MRSA 0.735 1.45 2.29 2.44 1.06

V60302032 3 SCWB 1.2 Dmax MRSA 0.735 1.46 2.21 2.41 1.07

V60302041 3 SCWB 1.5 Dmax MRSA 0.735 1.47 1.98 2.16 0.94

V60302042 3 SCWB 1.5 Dmax MRSA 0.735 1.49 1.91 2.10 0.93

V60302051 3 SCWB 2.0 Dmax MRSA 0.735 1.38 2.31 2.25 0.98

V60302052 3 SCWB 2.0 Dmax MRSA 0.735 1.40 2.24 2.12 0.94

V00902011 9

Baseline

_Conforming -

AISC 341-10

Dmax MRSA 1.83 2.82 1.84 2.08 1.00

V00902012 9

Baseline

_Conforming -

AISC 341-10

Dmax MRSA 1.83 2.86 1.80 1.99 1.00

V00902021 9

Baseline

_Conforming -

AISC 341-10 

No Dbl

Dmax MRSA 1.83 2.81 1.84 2.22 1.00

V00902022 9

Baseline

_Conforming -

AISC 341-10 

No Dbl

Dmax MRSA 1.83 2.84 1.80 2.08 1.00
FEMA P-2012 C: Steel Moment Frame Studies C-29

Table C-27 Steel Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V00902031 9

Baseline_Conf

orming - ELF 

No Dbl

Dmax ELF 1.83 1.81 4.26 3.07 1.00

V00902032 9

Baseline

_Conforming -

ELF No Dbl

Dmax ELF 1.83 1.83 4.17 2.87 1.00

V00902041 9

Baseline

_Conforming -

Energy

Dmax Energy 1.83 1.28 5.65 4.39 1.00

V00902042 9

Baseline

_Conforming -

Energy

Dmax Energy 1.83 1.30 5.54 4.39 1.00

V60902011 9 SCWB 0.5 Dmax MRSA 1.83 2.21 2.55 1.02 0.69

V60902012 9 SCWB 0.5 Dmax MRSA 1.83 2.23 2.36 0.93 0.74

V60902021 9 SCWB 1.0 Dmax MRSA 1.83 2.87 1.64 1.47 1.00

V60902022 9 SCWB 1.0 Dmax MRSA 1.83 2.90 1.56 1.27 1.00

V60902031 9 SCWB 1.2 Dmax MRSA 1.83 3.08 1.46 1.42 0.97

V60902032 9 SCWB 1.2 Dmax MRSA 1.83 3.11 1.39 1.30 1.03

V60902041 9 SCWB 1.5 Dmax MRSA 1.83 3.00 1.57 1.75 1.20

V60902042 9 SCWB 1.5 Dmax MRSA 1.83 3.03 1.53 1.65 1.30

V60902051 9 SCWB 2.0 Dmax MRSA 1.83 2.95 1.55 1.97 1.34

V60902052 9 SCWB 2.0 Dmax MRSA 1.83 2.99 1.51 1.86 1.47

V02002011 20

Baseline

_Conforming -

AISC 341-10

Dmax MRSA 3.403 3.53 1.67 2.01 1.00

V02002012 20

Baseline

_Conforming -

AISC 341-10

Dmax MRSA 3.403 3.11 2.11 1.78 1.00

V02002021 20

Conforming -

AISC 341-10 

No Dbl

Dmax MRSA 3.403 3.58 1.66 1.93 1.00

V02002022 20

Baseline

_Conforming -

AISC 341-10 

No Dbl

Dmax MRSA 3.403 3.17 2.09 1.38 1.00

V22002011 20 Baseline - Mass Dmax MRSA 3.403 3.53 1.67 2.12 1.00

V22002012 20 Baseline - Mass Dmax MRSA 3.403 3.11 2.11 2.02 1.00

V22002021 20 1.5_STORY3 Dmax MRSA 3.403 3.52 1.65 1.96 0.92
C-30 C: Steel Moment Frame Studies FEMA P-2012

Table C-27 Steel Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V22002022 20 1.5_STORY3 Dmax MRSA 3.403 3.10 2.09 1.96 0.97

V22002031 20 2.0_STORY3 Dmax MRSA 3.403 3.52 1.62 1.91 0.90

V22002032 20 2.0_STORY3 Dmax MRSA 3.403 3.10 2.05 2.00 0.99

V22002041 20 3.0_STORY3 Dmax MRSA 3.403 3.52 1.58 1.75 0.82

V22002042 20 3.0_STORY3 Dmax MRSA 3.403 3.10 2.00 1.81 0.90

V22002051 20 1.5_STORY11 Dmax MRSA 3.403 3.56 1.66 2.03 0.96

V22002052 20 1.5_STORY11 Dmax MRSA 3.403 3.65 1.58 1.72 0.85

V22002061 20 2.0_STORY11 Dmax MRSA 3.403 3.58 1.65 1.96 0.93

V22002062 20 2.0_STORY11 Dmax MRSA 3.403 3.68 1.55 1.86 0.92

V22002071 20 3.0_STORY11 Dmax MRSA 3.403 3.69 1.69 1.92 0.91

V22002072 20 3.0_STORY11 Dmax MRSA 3.403 3.80 1.49 1.61 0.80

V22002081 20 1.5_STORY19 Dmax MRSA 3.403 3.62 1.63 2.16 1.02

V22002082 20 1.5_STORY19 Dmax MRSA 3.403 3.72 1.58 1.90 0.94

V22002091 20 2.0_STORY19 Dmax MRSA 3.403 3.68 1.64 2.02 0.95

V22002092 20 2.0_STORY19 Dmax MRSA 3.403 3.77 1.55 1.87 0.92

V22002101 20 3.0_STORY19 Dmax MRSA 3.403 3.78 1.61 1.89 0.89

V22002102 20 3.0_STORY19 Dmax MRSA 3.403 3.80 1.72 1.78 0.88

V62002011 20 SCWB 0.5 Dmax MRSA 3.4 3.93 1.09 1.80 0.89

V62002012 20 SCWB 0.5 Dmax MRSA 3.4 3.49 1.36 2.10 0.77

V62002021 20 SCWB 1.0 Dmax MRSA 3.4 3.75 1.56 2.03 1.00

V62002022 20 SCWB 1.0 Dmax MRSA 3.4 3.31 1.96 2.71 1.00

V62002031 20 SCWB 1.2 Dmax MRSA 3.4 3.51 1.84 2.08 1.02

V62002032 20 SCWB 1.2 Dmax MRSA 3.4 3.10 2.33 1.34 0.50

V62002041 20 SCWB 1.5 Dmax MRSA 3.4 3.54 1.79 1.63 0.80

V62002042 20 SCWB 1.5 Dmax MRSA 3.4 3.13 2.27 1.24 0.46

V62002051 20 SCWB 2.0 Dmax MRSA 3.4 3.50 1.68 1.91 0.94

V62002052 20 SCWB 2.0 Dmax MRSA 3.4 3.08 2.13 1.30 0.48

V72002011 20 1st Story 

α = 0.1 Dmax MRSA 3.403 3.53 1.67 1.75 0.87

V72002021 20 1st Story 

α = 0.3 Dmax MRSA 3.403 3.48 1.69 2.09 1.04
FEMA P-2012 C: Steel Moment Frame Studies C-31

Table C-27 Steel Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period [s]

Static 

Overstrength,

Ω

ACMR

(const. 

SSF)

ACMR/

ACMRbaseline

V72002031 20 1st Story 

α = 0.5 Dmax MRSA 3.403 3.45 1.71 1.94 0.97

V72002041 20 7th Story 

α = 0.1 Dmax MRSA 3.403 3.52 1.69 2.04 1.02

V72002051 20 7th Story 

α = 0.3 Dmax MRSA 3.403 3.59 1.77 1.86 0.92

V72002061 20 7th Story 

α = 0.5 Dmax MRSA 3.403 3.54 1.81 1.81 0.90

V72002071 20 14th Story 

α = 0.1 Dmax MRSA 3.403 3.64 1.67 1.99 0.99

V72002081 20 14th Story 

α = 0.3 Dmax MRSA 3.403 3.61 1.67 1.95 0.97

V72002091 20 14th Story 

α = 0.5 Dmax MRSA 3.403 3.53 1.69 1.99 0.99

V720020012 20

Baseline -

GILD 

Undesigned

Dmax MRSA 3.403 0.00 1.67 2.01 1.00

V720020212 20 1st Story 

α = 0.3 Dmax MRSA 3.403 3.53 1.66 1.84 0.92

V720020312 20 1st Story 

α = 0.5 Dmax MRSA 3.403 3.53 1.64 1.77 0.88

V720020812 20 14th Story 

α = 0.3 Dmax MRSA 3.403 3.53 1.67 1.88 0.94

V720020912 20 14th Story 

α = 0.5 Dmax MRSA 3.403 3.53 1.66 1.05 0.52

FEMA P-2012 D: Concrete Moment Frame Studies D-1

Appendix D

Concrete Moment Frame Studies

This Appendix provides the following information on the concrete moment 

frame studies: (1) Bmax and Dmax concrete moment frame baseline designs; 

and (2) summary of the concrete moment frame archetype results. For 

details on the concrete moment frame designs with irregularities (i.e., soft 

story, mass ratio irregularity, weak story, strong-column/weak-beam, and 

gravity-induced lateral demand) and for detailed results of the concrete 

moment frame studies, see the electronic Supporting Documentation for 

Appendix D: Concrete Moment Frame Irregularity Designs and Detailed 

Results. 

D.1 Concrete Moment Frame Baseline Designs

The intent of the archetype designs is to create structural models that 

represent realistic modern structures. In order to achieve that goal, design 

assumptions and structural properties were selected to represent common 

building stock and design practice. The archetype space includes 4-, 8-, 12-, 

and 20-story buildings each in high and low seismicity zones (see Table 

D-1). Hypothetical Bmax and Dmax sites were selected for the low and high 

seismicity zones respectively. Table D-2 provides a summary of the design 

values used for all concrete moment frame designs.

Table D-1 Summary of Baseline Reinforced Concrete Frame Archetypes

Baseline Reinforced Concrete Moment Frame Designs

Model ID

Number of 

Stories Frame Detail SDC Modification

V104101 4 SMF Dmax Baseline

V104201 4 OMF Bmax Baseline

V108101 8 SMF Dmax Baseline

V112101 12 SMF Dmax Baseline

V112201 12 OMF Bmax Baseline

V120101 20 SMF Dmax Baseline
D-2 D: Concrete Moment Frame Studies FEMA P-2012

Table D-2 Common Design Values Used for All RC MF Designs

Common Design Properties

Dead Load 175 psf

Partition Load 15 psf

Roof Load 140 psf

Live Load 65 psf

f′c Beams 5000 psi

f′c Col 7000 psi

Beam Design Stiffness 0.35EIg

Column Design Stiffness 0.7EIg

D.1.1 Low Seismicity Zone (SDC Bmax) – RC Ordinary Moment 

Frame Design

D.1.1.1 4-Story OMF Building

Figures D-1 and D-2 illustrate the geometry of the 4-story RC ordinary 

moment frame (OMF) building. Tables D-3 and D-4 provide design values 

and a summary of the design, respectively, for the 4-story OMF building.

Figure D-1 Baseline RC moment frame 

building typical 4-story elevation. 

Figure D-2 Baseline RC moment frame 

building typical 4-story plan. 
FEMA P-2012 D: Concrete Moment Frame Studies D-3

Table D-3 Design Values – 4-Story RC OMF Baseline

4-story, RC OMF (V104201)

Design Parameters

Dead Load: Typical = 175 psf; Roof = 140 psf

Live Load: Typical = 65 psf; Roof = 20 psf

Seismic Weight: Typical = 190 psf; Roof = 147.5 psf

Total Tributary Seismic Weight: W = 2583 kips

Wind Speed: 110 mph (strength); 85 mph (service)

Risk Category: II

Importance Factor: Ie = 1.0

Reinforced Concrete SMFs: R = 3; Cd = 2.5; Ω0 = 3

Site Class C 

Seismic Design Category D: SDS = 0.32; SD1 = 0.132

Material properties: f′c, beam = 4 ksi; f′c, col = 4 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms: Ibeam = 0.35Ig; Icol = 0.70Ig

Design based on Equivalent Lateral Force Procedure

Calculated period(s): Tx = 1.933 s; Ty = 1.933 s

Upper limit period: CuTax = 0.93 s; CuTay = 0.93 s

Seismic response coefficient: Cs,x = 0.048; Cs,x = 0.048

Controlling equation: (12.8-3)

Seismic base shear: Vx = 123 kips; Vy = 123 kips

Story drift limits applied: 0.020hsx (seismic); h/400 (wind)

Design base shear: Vx = 123 kips; Vy = 123 kips

Controlling lateral design: Seismic strength
D-4 D: Concrete Moment Frame Studies FEMA P-2012

Table D-4 4-Story RC OMF Baseline Design Summary: V104201

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

4

21×18 [9] 21×18 [18] 18×18 [7.5] 18×18 [7.5] 0.05% N/A

(0.0125, 0.0014) (0.0125, 0.0007) (0.0106, 0.0047, 

0.0016)

(0.0106, 0.0047, 

0.0016) (N/A)

3

21×18 [9] 21×18 [9] 18×18 [7.5] 18×18 [7.5] 0.6% 0.89

(0.0125, 0.0014) (0.0125, 0.0014) (0.0121, 0.0047, 

0.0016)

(0.0121, 0.0047, 

0.0016) (1.49)

2

21×18 [9] 21×18 [9] 24×18 [10.5] 24×18 [10.5] 0.6% 1.35

(0.0125, 0.0014) (0.0125, 0.0014) (0.0110, 0.0057, 

0.0012)

(0.0110, 0.0057, 

0.0012) (1.25)

1

21×18 [9] 21×18 [9] 24×18 [10.5] 24×18 [10.5] 0.5% 1.09

(0.0208, 0.0014) (0.0208, 0.0014) (0.0110, 0.0057, 

0.0012)

(0.0110, 0.0057, 

0.0012) (1.15)

D.1.1.2 8-Story OMF Building

No 8-story RC ordinary moment frames were developed for this study.

D.1.1.3 12-Story OMF Building

Figures D-3 and D-4 illustrate the geometry of the 12-story RC OMF 

building. Tables D-5 and D-6 provide design values and a summary of the 

design, respectively, for the 12-story OMF building.

Figure D-3 Baseline RC moment frame 

building typical 12-story

elevation. 

15' 11 @ 13'
FEMA P-2012 D: Concrete Moment Frame Studies D-5

Figure D-4 Baseline RC moment frame 

building typical 12-story plan. 

Table D-5 Design Values – 12-Story RC OMF Baseline

12-story, RC OMF (V112201)

Design Parameters

Dead Load: Typical = 175 psf; Roof = 140 psf

Live Load: Typical = 65 psf; Roof = 20 psf

Seismic Weight: Typical = 190 psf; Roof = 147.5 psf

Total Tributary Seismic Weight: W = 8055 kips

Wind Speed: 110 mph (strength); 85 mph (service)

Risk Category: II

Importance Factor: Ie = 1.0

Reinforced Concrete SMFs: R = 3; Cd = 2.5; Ω0 = 3

Site Class C 

Seismic Design Category D: SDS = 0.32; SD1 = 0.132

Material properties: f'c, beam = 4 ksi; f'c, col = 4 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms: Ibeam = 0.35Ig; Icol = 0.70Ig

Design based on Equivalent Lateral Force Procedure

Calculated period(s): Tx = 4.506 s; Ty = 4.506 s

Upper limit period: CuTax = 2.44 s; CuTay = 2.44 s

Seismic response coefficient: Cs,x = 0.018; Cs,x = 0.018

Controlling equation: (12.8-3)

Seismic base shear: Vx = 146 kips; Vy = 146 kips

Story drift limits applied: 0.020hsx (seismic); h/400 (wind)

Design base shear: Vx = 147.5 kips (wind); Vy = 147.5 kips (wind)

Controlling lateral design: Seismic strength & wind strength
D-6 D: Concrete Moment Frame Studies FEMA P-2012

Table D-6 12-Story RC OMF Baseline Design Summary: V112201

Level

Columns

depth x width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth x width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story 

Drift

Δ

Strength and 

Stiffness Ratio to 

Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

12

21×21 [9] 21×21 [18] 21×21 [9] 21×21 [9] 0.2% NA

(0.0107, 0.0012) (0.0107, 0.0006) (0.0065, 0.0034, 

0.0012)

(0.0065, 0.0034, 

0.0012) (NA)

11

21×21 [9] 21×21 [9] 21×21 [9] 21×21 [9] 0.3% 0.97

(0.0107, 0.0012) (0.0107, 0.0012) (0.0087, 0.0034, 

0.0012)

(0.0087, 0.0034, 

0.0012) (1.27)

10

21×21 [9] 21×21 [9] 21×21 [9] 21×21 [9] 0.5% 1.02

(0.0107, 0.0012) (0.0107, 0.0012) (0.0099, 0.0034, 

0.0012)

(0.0099, 0.0034, 

0.0012) (1.05)

9

21×21 [9] 21×21 [9] 21×21 [9] 21×21 [9] 0.6% 1.08

(0.0107, 0.0012) (0.0107, 0.0012) (0.0110, 0.0045, 

0.0012)

(0.0110, 0.0045, 

0.0012) (1.02)

8

21×21 [9] 21×21 [9] 24×21 [10.5] 24×21 [10.5] 0.6% 1.06

(0.0107, 0.0012) (0.0107, 0.0012) (0.0095, 0.0049, 

0.0010)

(0.0095, 0.0049, 

0.0010) (1.02)

7

21×21 [9] 21×21 [9] 24×21 [10.5] 24×21 [10.5] 0.7% 1.21

(0.0142, 0.0012) (0.0142, 0.0012) (0.0095, 0.0049, 

0.0010)

(0.0095, 0.0049, 

0.0010) (1.1)

6

21×21 [9] 21×21 [9] 27×21 [12] 27×21 [12] 0.6% 1.12

(0.0142, 0.0012) (0.0142, 0.0012) (0.0083, 0.0043, 

0.0009)

(0.0083, 0.0043, 

0.0009) (1.11)

5

21×21 [9] 21×21 [9] 27×21 [12] 27×21 [12] 0.6% 1.02

(0.0142, 0.0012) (0.0142, 0.0012) (0.0083, 0.0043, 

0.0009)

(0.0083, 0.0043, 

0.0009) (1.15)

4

21×21 [9] 21×21 [9] 33×21 [10] 33×21 [10] 0.5% 1.15

(0.0142, 0.0012) (0.0142, 0.0012) (0.0067, 0.0034, 

0.0011)

(0.0067, 0.0034, 

0.0011) (1.16)

3

21×21 [9] 21×21 [9] 33×21 [10.5] 33×21 [10.5] 0.5% 1.03

(0.0142, 0.0012) (0.0142, 0.0012) (0.0067, 0.0034, 

0.0010)

(0.0067, 0.0034, 

0.0010) (1.03)

2

21×21 [9] 21×21 [9] 33×21 [10.5] 33×21 [10.5] 0.5% 1.02

(0.0142, 0.0012) (0.0142, 0.0012) (0.0067, 0.0034, 

0.0010)

(0.0067, 0.0034, 

0.0010) (1.01)

1

21×21 [9] 21×21 [9] 33×21 [10.5] 33×21 [10.5] 0.5% 0.99

(0.0178, 0.0012) (0.0178, 0.0012) (0.0067, 0.0041, 

0.0010)

(0.0067, 0.0041, 

0.0010) (0.94)
FEMA P-2012 D: Concrete Moment Frame Studies D-7

D.1.2 High Seismicity Zone (SDC Dmax) – RC Special Moment 

Frame Design 

D.1.2.1 4-Story SMF 

Figures D-5 and D-6 illustrate the geometry of the 4-story RC special 

moment frame (SMF) building. Tables D-7 and D-8 provide design values 

and a summary of the design, respectively, for the 4-story SMF building.

Figure D-5 Baseline RC moment frame 

building typical 4-story

elevation. 

Figure D-6 Baseline RC moment frame 

building typical 4-story plan. 

Table D-7 Design Values – Baseline 4-Story RC SMF

4-story, RC SMF (V104101)

Design Parameters

Dead Load: Typical = 175 psf; Roof = 140 psf

Live Load: Typical = 65 psf; Roof = 20 psf

Seismic Weight: Typical = 190 psf; Roof = 147.5 psf

Total Tributary Seismic Weight: W = 2583 kips

Wind Speed: 110 mph (strength); 85 mph (service)

Risk Category: II

Importance Factor: Ie = 1.0
D-8 D: Concrete Moment Frame Studies FEMA P-2012

Table D-7 Design Values – Baseline 4-Story RC SMF (continued)

4-story, RC SMF (V104101)

Design Parameters (continued)

Reinforced Concrete SMFs: R = 8; Cd = 5.5; Ω0 = 3.0

Site Class C 

Seismic Design Category D: SDS = 1.5; SD1 = 0.6

Material properties: f'c, beam = 5 ksi; f'c, col = 7 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms: Ibeam = 0.35Ig; Icol = 0.70Ig

Design based on Equivalent Lateral Force Procedure

Calculated period(s): Tx = 1.12 s; Ty = 1.12 s

Upper limit period: CuTax = 0.81 s; CuTay = 0.81 s

Seismic response coefficient: Cs,x = 0.092; Cs,x = 0.092

Controlling equation: (12.8-3)

Seismic base shear: Vx = 239 kips; Vy = 239 kips

Story drift limits applied: 0.020hsx (seismic); h/400 (wind)

Design base shear: Vx = 239 kips; Vy = 239 kips

Controlling lateral design: Seismic strength

Table D-8 4-Story RC SMF Baseline Design Summary: V104101

Level

Columns

depth × width [tie spacing]

(ρtotal , ρsh)

Beams

depth × width [hoop spacing]

(ρtop , ρbot , ρsh) Story 

Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio to 

Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

4

26×22 [2.5] 26×22 [2.5] 24×18 [5] 24×18 [5] 1.2% 1.16 NA

(0.0110, 

0.0107)

(0.0110, 

0.0107)

(0.0081, 0.0046, 

0.0044)

(0.0081, 0.0046, 

0.0044) (0.74) (NA)

3

26×22 [2.5] 26×22 [2.5] 24×18 [5] 24×18 [5] 1.5% 1.96 0.89

(0.0110, 

0.0107)

(0.0165, 

0.0107)

(0.0097, 0.0046, 

0.0044)

(0.0097, 0.0046, 

0.0044) (1.65) (1.58)

2

30×22 [3.5] 30×22 [3.5] 34×20 [5] 34×20 [5] 1.2% 1.37 1.75

(0.0119, 

0.0102)

(0.0167, 

0.0102)

(0.0069, 0.0048, 

0.0039)

(0.0069, 0.0048, 

0.0039) (1.22) (1.54)

1

30×22 [3.5] 30×22 [3.5] 34×20 [5] 34×20 [5] 1.0% 1.89 0.87

(0.0167, 

0.0102)

(0.0167, 

0.0102)

(0.0069, 0.0048, 

0.0039)

(0.0069, 0.0048, 

0.0039) (1.44) (1.22)
FEMA P-2012 D: Concrete Moment Frame Studies D-9

D.1.2.2 8-Story SMF

Figures D-7 and D-8 illustrate the geometry of the 8-story RC SMF building. 

Tables D-9 and D-10 provide design values and a summary of the design, 

respectively, for the 8-story SMF building.

Figure D-7 Baseline RC moment frame building 

typical 8-story elevation. 

Figure D-8 Baseline RC moment frame building 

typical 8-story plan. 

Table D-9 Design Values – 8-Story RC SMF Baseline

8-story, RC SMF (V108101)

Design Parameters

Dead Load: Typical = 175 psf; Roof = 140 psf

Live Load: Typical = 65 psf; Roof = 20 psf

Seismic Weight: Typical = 190 psf; Roof = 147.5 psf

Total Tributary Seismic Weight: W = 5319 kips

Wind Speed: 110 mph (strength); 85 mph (service)

Risk Category: II

Importance Factor: Ie = 1.0

Reinforced Concrete SMFs: R = 8; Cd = 5.5; Ω0 = 3.0

Site Class C 

Seismic Design Category D: SDS = 1.5; SD1 = 0.6

Material properties: f′c, beam = 5 ksi; f′c, col = 7 ksi; fy = 60 ksi 15' 7 @ 13'
D-10 D: Concrete Moment Frame Studies FEMA P-2012

Table D-9 Design Values – 8-Story RC SMF Baseline (continued)

8-story, RC SMF (V108101)

Analysis

Centerline modeling of beams and columns

Rigid diaphragms: Ibeam = 0.35Ig; Icol = 0.70Ig

Design based on Equivalent Lateral Force Procedure

Calculated period(s): Tx = 2.105 s; Ty = 2.105 s

Upper limit period: CuTax = 1.49 s; CuTay = 1.49 s

Seismic response coefficient: Cs,x = 0.050; Cs,x = 0.050

Controlling equation: (12.8-3)

Seismic base shear: Vx = 268 kips; Vy = 268 kips

Story drift limits applied: 0.020hsx (seismic); h/400 (wind)

Design base shear: Vx = 268 kips; Vy = 268 kips

Controlling lateral design: Seismic strength

Table D-10 8-Story RC SMF Baseline Design Summary: V108101

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story 

Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness 

Ratio to 

Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

8 26×26 [3] 26×26 [3] 28×20 [6] 28×20 [6] 0.7% 1.01 NA

(0.0116, 

0.0101)

(0.0116, 

0.0101)

(0.0073, 0.0047, 

0.0033)

(0.0073, 0.0047, 

0.0033) (0.62) (NA)

7 26×26 [3] 26×26 [3] 28×20 [5.5] 28×20 [5.5] 1.2% 2.04 0.88

(0.0116, 

0.0101)

(0.0116, 

0.0101)

(0.0073, 0.0047, 

0.0036)

(0.0073, 0.0047, 

0.0036) (1.26) (1.21)

6 26×26 [3] 26×26 [3] 28×20 [5] 28×20 [5] 1.6% 1.77 0.98

(0.0116, 

0.0101)

(0.0139, 

0.0101)

(0.0085, 0.0047, 

0.0039)

(0.0085, 0.0047, 

0.0039) (1.31) (1.06)

5 30×26 [3] 30×26 [3] 28×20 [4.5] 28×20 [4.5] 1.5% 1.68 1.18

(0.0101, 

0.0101)

(0.0121, 

0.0101)

(0.0097, 0.0071, 

0.0044)

(0.0097, 0.0071, 

0.0044) (1.27) (1.3)

4 30×26 [3] 30×26 [3] 34×20 [4.5] 34×20 [4.5] 1.4% 1.43 1.24

(0.0101, 

0.0101)

(0.0141, 

0.0101)

(0.0078, 0.0057, 

0.0044)

(0.0078, 0.0057, 

0.0044) (1.21) (1.18)

3 30×26 [3] 30×26 [3] 34×20 [4.5] 34×20 [4.5] 1.4% 1.39 1.00

(0.0101, 

0.0101)

(0.0141, 

0.0101)

(0.0078, 0.0057, 

0.0044)

(0.0078, 0.0057, 

0.0044) (1.36) (1.04)
FEMA P-2012 D: Concrete Moment Frame Studies D-11

Table D-10 8-Story RC SMF Baseline Design Summary: V108101 (continued)

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story 

Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness 

Ratio to 

Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

2 30×26 [3] 30×26 [3] 34×20 [4] 34×20 [4] 1.4% 1.20 1.11

(0.0101, 

0.0101)

(0.0141, 

0.0101)

(0.0088, 0.0067, 

0.0049)

(0.0088, 0.0067, 

0.0049) (1.24) (1.05)

1 30×26 [3] 30×26 [3] 34×20 [4] 34×20 [4] 1.0% 1.53 0.90

(0.0161, 

0.0101)

(0.0141, 

0.0101)

(0.0088, 0.0067, 

0.0049)

(0.0088, 0.0067, 

0.0049) (1.24) (1.23)

D.1.2.3 12-Story SMF

Figures D-9 and D-10 illustrate the geometry of the 12-story RC SMF 

building. Tables D-11 and D-12 provide design values and a summary of the 

design, respectively, for the 12-story SMF building.

Figure D-9 Baseline RC moment frame building 

typical 12-story elevation. 

Figure D-10 Baseline RC moment frame 

building typical 12-story plan. 

15' 11 @ 13'
D-12 D: Concrete Moment Frame Studies FEMA P-2012

Table D-11 Design Values – 12-Story RC SMF Baseline

12-story, RC SMF (V112101)

Design Parameters

Dead Load: Typical = 175 psf; Roof = 140 psf

Live Load: Typical = 65 psf; Roof = 20 psf

Seismic Weight: Typical = 190 psf; Roof = 147.5 psf

Total Tributary Seismic Weight: W = 8055 kips

Wind Speed: 110 mph (strength); 85 mph (service)

Risk Category: II

Importance Factor: Ie = 1.0

Reinforced Concrete SMFs: R = 8; Cd = 5.5; Ω0 = 3.0

Site Class C 

Seismic Design Category D: SDS = 1.5; SD1 = 0.6

Material properties: f'c, beam = 5 ksi; f'c, col = 7 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms: Ibeam = 0.35Ig; Icol = 0.70Ig

Design based on Equivalent Lateral Force Procedure

Calculated period(s): Tx = 2.575 s; Ty = 2.575 s

Upper limit period: CuTax = 2.13 s; CuTay = 2.13 s

Seismic response coefficient: Cs,x = 0.044; Cs,x = 0.044

Controlling equation: (12.8-5)

Seismic base shear: Vx = 354 kips; Vy = 354 kips

Story drift limits applied: 0.020 hsx (seismic); h/400 (wind)

Design base shear: Vx = 354 kips; Vy = 354 kips

Controlling lateral design: Seismic strength
FEMA P-2012 D: Concrete Moment Frame Studies D-13

Table D-12 12-Story RC SMF Baseline Design Summary: V112101

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story 

Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio to 

Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

12 30×26 [3] 30×26 [3] 26×24 [5.5] 26×24 [5.5] 0.8% 1.27 NA

(0.0101, 

0.0076)

(0.0102, 

0.0101)

(0.0066, 0.0043, 

0.0030)

(0.0066, 0.0043, 

0.0030) (0.79) (NA)

11 30×26 [3] 30×26 [3] 26×24 [5.5] 26×24 [5.5] 1.2% 2.56 0.79

(0.0101, 

0.0076)

(0.0102, 

0.0101)

(0.0066, 0.0043, 

0.0030)

(0.0066, 0.0043, 

0.0030) (1.61) (1.37)

10 30×26 [3] 30×26 [3] 26×24 [4] 26×24 [4] 1.5% 2.22 1.03

(0.0101, 

0.0076)

(0.0102, 

0.0101)

(0.0077, 0.0053, 

0.0033)

(0.0077, 0.0053, 

0.0033) (1.42) (1.13)

9 30×26 [3] 30×26 [3] 26×24 [4.5] 26×24 [4.5] 1.4% 1.95 1.02

(0.0101, 

0.0076)

(0.0161, 

0.0101)

(0.0087, 0.0053, 

0.0036)

(0.0087, 0.0053, 

0.0036) (1.69) (1.35)

8 34×26 [3] 34×26 [3] 38×24 [4.5] 38×24 [4.5] 1.1% 1.31 1.78

(0.0107, 

0.0076)

(0.0142, 

0.0101)

(0.0065, 0.0042, 

0.0036)

(0.0065, 0.0042, 

0.0036) (1.26) (1.48)

7 34×26 [3] 34×26 [3] 38×24 [4.5] 38×24 [4.5] 1.1% 1.48 1.03

(0.0107, 

0.0076)

(0.0142, 

0.0101)

(0.0065, 0.0042, 

0.0036)

(0.0065, 0.0042, 

0.0036) (1.38) (1.06)

6 34×26 [3] 34×26 [3] 38×24 [4] 38×24 [4] 1.2% 1.44 1.05

(0.0107, 

0.0076)

(0.0142, 

0.0101)

(0.0065, 0.0049, 

0.0041)

(0.0065, 0.0049, 

0.0041) (1.32) (1.02)

5 34×26 [3] 34×26 [3] 38×24 [4] 38×24 [4] 1.2% 1.39 0.99

(0.0107, 

0.0076)

(0.0142, 

0.0101)

(0.0065, 0.0049, 

0.0041)

(0.0065, 0.0049, 

0.0041) (1.34) (1.01)

4 34×26 [3] 34×26 [3] 38×24 [4] 38×24 [4] 1.2% 1.34 0.99

(0.0107, 

0.0076)

(0.0142, 

0.0101)

(0.0065, 0.0049, 

0.0041)

(0.0065, 0.0049, 

0.0041) (1.37) (1.01)

3 34×26 [3] 34×26 [3] 38×24 [4] 38×24 [4] 1.2% 1.27 1.05

(0.0124, 

0.0076)

(0.0142, 

0.0101)

(0.0072, 0.0049, 

0.0041)

(0.0072, 0.0049, 

0.0041) (1.33) (1.02)

2 34×26 [3] 34×26 [3] 38×24 [4] 38×24 [4] 1.2% 1.32 1.00

(0.0124, 

0.0076)

(0.0142, 

0.0101)

(0.0072, 0.0049, 

0.0041)

(0.0072, 0.0049, 

0.0041) (1.36) (1.05)

1 34×26 [3] 34×26 [3] 38×24 [3.5] 38×24 [3.5] 0.8% 1.60 0.95

(0.0178, 

0.0101)

(0.0178, 

0.0101)

(0.0072, 0.0056, 

0.0047)

(0.0072, 0.0056, 

0.0047) (1.44) (1.22)
D-14 D: Concrete Moment Frame Studies FEMA P-2012

D.1.2.4 20-Story SMF

Table D-13 provides design values and Tables D-14 and D-15 provide summaries

of the designs for the 20-story ELF and MRSA design buildings, respectively.

Table D-13 Design Values – 20-Story RC SMF Baseline

20-story, SMF, Dmax (V120101)

Design Parameters

Dead Load: Typical = 175 psf; Roof = 140 psf

Live Load: Typical = 65 psf; Roof = 20 psf

Seismic Weight: Typical = 190 psf; Roof = 147.5 psf

Total effective seismic weight: W = 13527 kips

Wind Speed: 110 mph (strength); 85 mph (service)

Risk Category: II

Importance Factor: Ie = 1.0

Reinforced Concrete SMFs: R = 8; Cd = 5.5; Ω0 = 3.0

Site Class C

Seismic Design Category D: SDS = 1.5; SD1 = 0.6

Material properties f'c, beam = 5 ksi; f'c, col = 7 ksi; fy = 60 ksi

Analysis

Centerline modeling of beams and columns

Rigid diaphragms: Ibeam = 0.35Ig; Icol = 0.70Ig

Design based on Equivalent Lateral Force Procedure

Calculated period(s): Tx = 3.657 s; Ty = 3.657 s

Upper limit period: CuTa,x = 3.363 s; CuTa,y = 3.363 s

Seismic response coefficient: Cs,x = 0.044; Cs,y = 0.044

Controlling equation: (12.8-5)

Seismic base shear: Vx = 595 kips; Vy = 595 kips

Story drift limits applied: 0.020 hsx(seismic); h/400 (wind)

Design base shear: Vx = 595 kips; Vy = 595 kips

Controlling lateral design: Seismic strength

Table D-14 20-Story RC SMF Baseline ELF Design Summary: V120101

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

20 28×28 [2.5] 28×28 [2.5] 28×26 [5.5] 28×26 [5.5] 0.7% 0.90 NA

(0.0100, 

0.0112)

(0.0100, 

0.0112)

(0.0070, 0.0036, 

0.0027)

(0.0070, 0.0036, 

0.0027) (0.58) (NA)
FEMA P-2012 D: Concrete Moment Frame Studies D-15

Table D-14 20-Story RC SMF Baseline ELF Design Summary: V120101 (continued)

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

19 28×28 [2.5] 28×28 [2.5] 28×26 [5] 28×26 [5] 0.9% 1.80 0.90

(0.0100, 

0.0112)

(0.0140, 

0.0112)

(0.0070, 0.0036, 

0.0030)

(0.0070, 0.0036, 

0.0030) (1.4) (1.72)

18 32×28 [2.5] 32×28 [2.5] 34×26 [4.5] 34×26 [4.5] 1.0% 1.48 1.31

(0.0105, 

0.0112)

(0.0140, 

0.0112)

(0.0066, 0.0038, 

0.0034)

(0.0066, 0.0038, 

0.0034) (1.26) (1.38)

17 32×28 [2.5] 32×28 [2.5] 34×26 [4] 34×26 [4] 1.0% 1.69 1.04

(0.0105, 

0.0112)

(0.0158, 

0.0112)

(0.0066, 0.0048, 

0.0038)

(0.0066, 0.0048, 

0.0038) (1.42) (1.22)

16 36×28 [2.5] 36×28 [2.5] 40×26 [3.5] 40×26 [3.5] 1.0% 1.41 1.38

(0.0109, 

0.0112)

(0.0156, 

0.0112)

(0.0064, 0.0048, 

0.0043)

(0.0064, 0.0048, 

0.0043) (1.23) (1.24)

15 36×28 [2.5] 36×28 [2.5] 40×26 [3.5] 40×26 [3.5] 1.1% 1.57 1.07

(0.0109, 

0.0112)

(0.0156, 

0.0112)

(0.0064, 0.0056, 

0.0043)

(0.0064, 0.0056, 

0.0043) (1.29) (1.07)

14 36×28 [2.5] 36×28 [2.5] 40×26 [3.5] 40×26 [3.5] 1.1% 1.52 0.99

(0.0109, 

0.0112)

(0.0156, 

0.0112)

(0.0064, 0.0056, 

0.0043)

(0.0064, 0.0056, 

0.0043) (1.3) (1.05)

13 36×28 [2.5] 36×28 [2.5] 40×26 [3.5] 40×26 [3.5] 1.1% 1.30 1.05

(0.0109, 

0.0112)

(0.0171, 

0.0112)

(0.0072, 0.0056, 

0.0043)

(0.0072, 0.0056, 

0.0043) (1.29) (1.07)

12 40×32 [2.5] 40×32 [2.5] 42×26 [3] 42×26 [3] 1.1% 1.32 1.19

(0.0110, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0061, 

0.0050)

(0.0076, 0.0061, 

0.0050) (1.22) (1.15)

11 40×32 [2.5] 40×32 [2.5] 42×26 [3] 42×26 [3] 1.1% 1.51 1.00

(0.0110, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0061, 

0.0050)

(0.0076, 0.0061, 

0.0050) (1.3) (1.04)

10 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.1% 1.44 0.99

(0.0110, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0061, 

0.0050)

(0.0076, 0.0061, 

0.0050) (1.31) (1.03)

9 40×32 [2.5] 40×32 [2.5] 42×26 [3] 42×26 [3] 1.1% 1.37 1.00

(0.0110, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0061, 

0.0050)

(0.0076, 0.0061, 

0.0050) (1.32) (1.03)

(0.0245, 

0.0123)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.38) (1.34)

8 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.1% 1.29 1.05

(0.0110, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.26) (1.03)
D-16 D: Concrete Moment Frame Studies FEMA P-2012

Table D-14 20-Story RC SMF Baseline ELF Design Summary: V120101 (continued)

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

7 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.1% 1.29 1.00

(0.0123, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.28) (1.03)

6 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.1% 1.29 1.00

(0.0123, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.29) (1.03)

5 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.1% 1.30 1.00

(0.0135, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.3) (1.03)

4 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.0% 1.30 1.00

(0.0135, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.32) (1.03)

3 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 1.0% 1.29 1.00

(0.0147, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.34) (1.05)

2 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 0.9% 1.39 1.00

(0.0160, 

0.0098)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.36) (1.09)

1 40×32 [2.5] 40×32 [2.5] 42×26 [2.5] 42×26 [2.5] 0.9% 2.04 0.91

(0.0245, 

0.0123)

(0.0135, 

0.0098)

(0.0076, 0.0069, 

0.0060)

(0.0076, 0.0069, 

0.0060) (1.38) (1.34)

Table D-15 20-Story RC SMF Baseline MRSA Design Summary: V120301

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

20 28×28 [2.5] 28×28 [2.5] 26×26 [5.5] 26×26 [5.5] 0.8% 0.98 NA

(0.0100, 

0.0112)

(0.0100, 

0.0112)

(0.0076, 0.0039, 

0.0027)

(0.0076, 0.0039, 

0.0027) (0.64) (NA)

19 28×28 [2.5] 28×28 [2.5] 26×26 [5] 26×26 [5] 1.0% 1.98 0.84

(0.0100, 

0.0112)

(0.0120, 

0.0112)

(0.0076, 0.0039,

0.0030)

(0.0076, 0.0039, 

0.0030) (1.41) (1.71)

18 28×28 [2.5] 28×28 [2.5] 30×26 [4.5] 30×26 [4.5] 1.1% 1.69 1.12

(0.0100, 

0.0112)

(0.0120, 

0.0112)

(0.0065, 0.0044, 

0.0034)

(0.0065, 0.0044, 

0.0034) (1.21) (1.3)
FEMA P-2012 D: Concrete Moment Frame Studies D-17

Table D-15 20-Story RC SMF Baseline MRSA Design Summary: V120301 (continued)

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

17 28×28 [2.5] 28×28 [2.5] 30×26 [4.5] 30×26 [4.5] 1.2% 1.70 0.96

(0.0100, 

0.0112)

(0.0140, 

0.0112)

(0.0065, 0.0044, 

0.0034)

(0.0065, 0.0044, 

0.0034) (1.33) (1.24)

16 32×28 [2.5] 32×28 [2.5] 36×26 [4.5] 36×26 [4.5] 1.1% 1.41 1.33

(0.0105, 

0.0112)

(0.0140, 

0.0112)

(0.0062, 0.0036, 

0.0034)

(0.0062, 0.0036, 

0.0034) (1.25) (1.27)

15 32×28 [2.5] 32×28 [2.5] 36×26 [4.5] 36×26 [4.5] 1.2% 1.61 1.01

(0.0105, 

0.0112)

(0.0140, 

0.0112)

(0.0062, 0.0036, 

0.0034)

(0.0062, 0.0036, 

0.0034) (1.43) (1.05)

14 32×28 [2.5] 32×28 [2.5] 36×26 [4.5] 36×26 [4.5] 1.3% 1.60 0.99

(0.0105, 

0.0112)

(0.0140, 

0.0112)

(0.0062, 0.0036, 

0.0034)

(0.0062, 0.0036, 

0.0034) (1.46) (1.02)

13 32×28 [2.5] 32×28 [2.5] 36×26 [4] 36×26 [4] 1.3% 1.58 1.07

(0.0105, 

0.0112)

(0.0140, 

0.0112)

(0.0062, 0.0045, 

0.0038)

(0.0062, 0.0045, 

0.0038) (1.37) (1.07)

12 40×32 [2.5] 40×32 [2.5] 40×26 [3.5] 40×26 [3.5] 1.1% 1.41 1.40

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0080, 0.0040, 

0.0043)

(0.0080, 0.0040, 

0.0043) (1.21) (1.24)

11 40×32 [2.5] 40×32 [2.5] 40×26 [3.5] 40×26 [3.5] 1.2% 2.26 0.95

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0064, 0.0048, 

0.0043)

(0.0064, 0.0048, 

0.0043) (1.53) (1.02)

10 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.2% 2.22 0.99

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0064, 0.0048, 

0.0043)

(0.0064, 0.0048, 

0.0043) (1.55) (1)

9 40×32 [2.5] 40×32 [2.5] 40×26 [3.5] 40×26 [3.5] 1.3% 2.16 1.00

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0064, 0.0048, 

0.0043)

(0.0064, 0.0048,

0.0043) (1.57) (0.99)

8 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.3% 1.87 1.14

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0072, 0.0056, 

0.0050)

(0.0072, 0.0056, 

0.0050) (1.39) (0.98)

7 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.4% 1.80 1.00

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0072, 0.0056, 

0.0050)

(0.0072, 0.0056, 

0.0050) (1.41) (0.98)

6 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.4% 1.72 1.00

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0072, 0.0056, 

0.0050)

(0.0072, 0.0056, 

0.0050) (1.43) (0.98)

5 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.5% 1.63 1.06

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0072, 0.0064, 

0.0050)

(0.0072, 0.0064, 

0.0050) (1.37) (0.98)
D-18 D: Concrete Moment Frame Studies FEMA P-2012

Table D-15 20-Story RC SMF Baseline MRSA Design Summary: V120301 (continued)

Level

Columns

depth × width 

[tie spacing]

(ρtotal , ρsh)

Beams

depth × width 

[hoop spacing]

(ρtop , ρbot , ρsh) Story Drift

Δ

Moment 

ratio, 

ΣMc/ΣMb

Exterior 

(Interior)

Strength and 

Stiffness Ratio 

to Story Above

Strength 

Exterior Interior Exterior Interior (Stiffness)

4 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.5% 1.39 1.06

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0080, 0.0064, 

0.0050)

(0.0080, 0.0064, 

0.0050) (1.31) (0.99)

3 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.5% 1.30 1.00

(0.0110, 

0.0098)

(0.0110, 

0.0098)

(0.0080, 0.0064, 

0.0050)

(0.0080, 0.0064, 

0.0050) (1.34) (1.01)

2 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 1.4% 1.40 1.00

(0.0135, 

0.0098)

(0.0110, 

0.0098)

(0.0080, 0.0064, 

0.0050)

(0.0080, 0.0064, 

0.0050) (1.36) (1.06)

1 40×32 [2.5] 40×32 [2.5] 40×26 [3] 40×26 [3] 0.9% 2.10 0.91

(0.0209, 

0.0098)

(0.0123, 

0.0098)

(0.0080, 0.0064, 

0.0050)

(0.0080, 0.0064, 

0.0050) (1.44) (1.35)

D.2 Summary of Reinforced Concrete Moment Frame 

Results

Table D-16 Reinforced Concrete Moment Frame Results

Model 

ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period 

[s]

Static 

Overstrength, 

Ω

ACMR 

(const. 

SSF)

ACMR/

ACMRbaseline

V104101 4 Baseline Dmax ELF 0.81 1.12 1.63 2.80 1.00

V104102 4 0.8 SS 1 Dmax ELF 0.85 1.22 1.65 2.91 1.04

V104103 4 0.7 SS 1 Dmax ELF 0.89 1.40 1.61 2.75 0.98

V104104 4 0.6 SS 1 Dmax ELF 0.95 1.57 1.57 2.48 0.88

V104105 4 0.8 SS 1&2 Dmax ELF 0.92 1.41 1.67 2.86 1.02

V104106 4 0.7 SS 1&2 Dmax ELF 1.00 1.56 1.70 2.98 1.06

V104107 4 0.6 SS 1&2 Dmax ELF 1.10 1.91 1.59 2.81 1.00

V604102 4 0.5 SCWB Dmax ELF 0.81 1.12 1.60 2.69 0.96

V604103 4 1.0 SCWB Dmax ELF 0.81 1.12 1.60 2.73 0.97

V604104 4 1.5 SCWB Dmax ELF 0.81 1.12 1.66 2.94 1.05

V604105 4 2.0 SCWB Dmax ELF 0.81 0.97 1.81 3.17 1.13

V604107 4 0.5 SCWB Exact Dmax ELF 0.81 1.12 2.19 2.20 1.06

V604108 4 1.0 SCWB Exact Dmax ELF 0.81 1.12 1.99 2.17 1.04

V604106 4 1.2 SCWB Exact Dmax ELF 0.81 1.12 1.98 2.08 1.00
FEMA P-2012 D: Concrete Moment Frame Studies D-19

Table D-16 Reinforced Concrete Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees

Model 

Period 

[s]

Static 

Overstrength, 

Ω

ACMR 

(const. 

SSF)

ACMR/

ACMRbaseline

V604109 4 1.5 SCWB Exact Dmax ELF 0.81 1.12 1.95 3.02 1.45

V604110 4 2.0 SCWB Exact Dmax ELF 0.81 0.97 1.97 3.30 1.59

V108101 8 Baseline Dmax ELF 1.49 2.04 1.63 2.28 1.00

V108102 8 0.8 SS 1 Dmax ELF 1.53 2.13 1.53 2.12 0.93

V108103 8 0.7 SS 1 Dmax ELF 1.57 2.30 1.51 2.02 0.89

V108104 8 0.6 SS 1 Dmax ELF 1.62 2.40 1.55 2.09 0.92

V108105 8 0.8 SS 1&2 Dmax ELF 1.59 2.37 1.50 1.97 0.87

V108106 8 0.7 SS 1&2 Dmax ELF 1.67 2.45 1.51 1.94 0.85

V108107 8 0.6 SS 1&2 Dmax ELF 1.76 2.69 1.54 2.17 0.95

V108108 8 0.8 SS 5 Dmax ELF 1.55 2.13 1.65 2.33 1.02

V108109 8 0.7 SS 5 Dmax ELF 1.59 2.14 1.72 2.25 0.99

V108110 8 0.6 SS 5 Dmax ELF 1.64 1.96 1.98 2.56 1.13

V608102 8 0.5 SCWB Dmax ELF 1.49 2.04 1.63 2.17 0.96

V608103 8 1.0 SCWB Dmax ELF 1.49 2.04 1.63 2.17 0.96

V608104 8 1.5 SCWB Dmax ELF 1.49 2.04 1.65 2.55 1.12

V608105 8 2.0 SCWB Dmax ELF 1.49 1.81 1.82 3.03 1.33

V112101 12 Baseline Dmax ELF 2.13 2.44 1.53 1.93 1.00

V112102 12 0.8 SS 1 Dmax ELF 2.17 2.57 1.47 1.73 0.90

V112103 12 0.7 SS 1 Dmax ELF 2.17 2.58 1.50 1.84 0.95

V112104 12 0.6 SS 1 Dmax ELF 2.25 2.70 1.48 1.83 0.95

V112105 12 0.8 SS 1&2 Dmax ELF 2.23 2.64 1.46 1.89 0.98

V112106 12 0.7 SS 1&2 Dmax ELF 2.30 2.69 1.45 1.96 1.02

V112107 12 0.6 SS 1&2 Dmax ELF 2.40 2.90 1.47 2.19 1.14

V112108 12 0.8 SS 5 Dmax ELF 2.19 2.54 1.60 2.11 1.09

V112109 12 0.7 SS 5 Dmax ELF 2.23 2.55 1.62 2.24 1.16

V112110 12 0.6 SS 5 Dmax ELF 2.28 2.49 1.72 2.49 1.29

V512102 12 0.8 WS 1 Dmax ELF 2.13 2.39 1.60 1.91 0.99

V512103 12 0.6 WS 1 Dmax ELF 2.13 2.36 1.68 2.09 1.09

V512104 12 0.8 WS 1&2 Dmax ELF 2.13 2.32 1.77 2.13 1.10

V512105 12 0.6 WS 1&2 Dmax ELF 2.13 2.04 1.87 2.51 1.30

V512106 12 0.8 WS 5 Dmax ELF 2.13 2.41 1.56 1.87 0.97

V512107 12 0.6 WS 5 Dmax ELF 2.13 2.39 1.58 1.93 1.00
D-20 D: Concrete Moment Frame Studies FEMA P-2012

Table D-16 Reinforced Concrete Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period 

[s]

Static 

Overstrength, 

Ω

ACMR 

(const. 

SSF)

ACMR/

ACMRbaseline

V612102 12 0.5 SCWB Dmax ELF 2.13 2.54 1.51 1.73 0.90

V612103 12 1.0 SCWB Dmax ELF 2.13 2.44 1.52 1.79 0.93

V612104 12 1.5 SCWB Dmax ELF 2.13 2.44 1.53 1.98 1.03

V612105 12 2.0 SCWB Dmax ELF 2.13 2.14 1.65 2.25 1.16

V612107 12 0.5 SCWB Exact Dmax ELF 2.13 2.54 2.27 1.51 0.81

V612108 12 1.0 SCWB Exact Dmax ELF 2.13 2.44 1.67 1.65 0.88

V612106 12 1.2 SCWB Exact Dmax ELF 2.13 2.44 1.56 1.87 1.00

V612109 12 1.5 SCWB Exact Dmax ELF 2.13 2.44 1.55 1.99 1.07

V612110 12 2.0 SCWB Exact Dmax ELF 2.13 2.14 1.70 2.30 1.23

V612111 12

2.0, 1.5, 1.0 

Stepped SCWB Dmax Design Min 2.13 2.41 1.51 2.06 1.07

V612112 12

1.5, 1.0, 0.8 

Stepped SCWB Dmax Design Min 2.13 2.53 1.54 1.97 1.02

V612113 12

2.0, 1.5, 1.0 

Stepped SCWB 

Exact Dmax Exact 2.13 2.41 1.51 1.63 0.87

V612114 12

1.5, 1.0, 0.8 

Stepped SCWB 

Exact Dmax Exact 2.13 2.53 1.54 1.50 0.81

V612116 12

1.5, 1.2 Stepped 

SCWB Exact Dmax Exact 2.13 2.44 1.56 1.95 1.04

V7121011 12

SMF - GILD 0.5 

at 1 Dmax ELF 2.13 2.44 1.43 1.64 0.85

V7121021 12

SMF - GILD 0.5 

at 2 Dmax ELF 2.13 2.44 1.39 1.63 0.85

V120101 20 Baseline Dmax ELF 3.36 3.22 1.41 2.00 1.00

V120103 20 0.6 SS 1 Dmax ELF 3.43 3.39 1.40 1.88 0.94

V120104 20 0.7 SS 1 Dmax ELF 3.48 3.44 1.43 1.94 0.97

V120301 20 Baseline Dmax MRSA 3.36 3.46 1.23 1.93 1.00

V520102 20 0.8 WS 1 Dmax ELF 3.36 3.19 1.45 2.07 1.07

V520103 20 0.6 WS 1 Dmax ELF 3.36 3.19 1.51 2.24 1.16

V220102 20 2.0 MR 3rd Flr Dmax ELF 3.36 3.20 1.43 1.99 1.03

V220103 20 3.0 MR 3rd Flr Dmax ELF 3.36 3.19 1.39 1.95 1.01

V220104 20 2.0 MR 11th Flr Dmax ELF 3.36 3.27 1.42 2.12 1.10

V220105 20 3.0 MR 11th Flr Dmax ELF 3.36 3.20 1.39 2.22 1.15

V220302 20 2.0 MR 3rd Flr Dmax MRSA 3.36 3.46 1.19 1.90 0.99

V220303 20 3.0 MR 3rd Flr Dmax MRSA 3.36 3.41 1.39 1.91 0.99
FEMA P-2012 D: Concrete Moment Frame Studies D-21

Table D-16 Reinforced Concrete Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period 

[s]

Static 

Overstrength, 

Ω

ACMR 

(const. 

SSF)

ACMR/

ACMRbaseline

V220304 20 2.0 MR 11th Flr Dmax MRSA 3.36 3.47 1.21 2.11 1.10

V220305 20 3.0 MR 11th Flr Dmax MRSA 3.36 3.54 1.20 2.21 1.14

V104201 4 Baseline Bmax ELF 0.93 2.28 1.41 3.97 1.00

V104202 4 0.8 SS 1 Bmax ELF 0.97 2.55 1.30 3.72 0.94

V104203 4 0.7 SS 1 Bmax ELF 1.02 2.77 1.28 3.81 0.96

V104204 4 0.6 SS 1 Bmax ELF 1.08 2.92 1.36 4.40 1.11

V104205 4 0.8 SS 1&2 Bmax ELF 1.05 2.88 1.29 4.05 1.02

V104206 4 0.7 SS 1&2 Bmax ELF 1.14 3.25 1.23 4.25 1.07

V104207 4 0.6 SS 1&2 Bmax ELF 1.26 3.40 1.30 4.88 1.23

V604202 4 0.4 SCWB Bmax ELF 0.93 2.28 1.41 3.76 0.97

V604203 4 0.7 SCWB Bmax ELF 0.93 2.28 1.41 3.76 0.97

V604204 4 1.0 SCWB Bmax ELF 0.93 2.28 1.46 3.88 1.00

V604205 4 0.4 SCWB Exact Bmax ELF 0.93 2.28 1.62 3.46 0.92

V604206 4 0.7 SCWB Exact Bmax ELF 0.93 2.28 1.55 3.39 0.90

V604207 4 1.0 SCWB Exact Bmax ELF 0.93 2.28 1.54 3.78 1.00

V112201 12 Baseline Bmax ELF 2.44 5.22 1.45 2.36 1.00

V112202 12 0.8 SS 1 Bmax ELF 2.48 5.27 1.49 2.53 1.07

V112203 12 0.7 SS 1 Bmax ELF 2.52 5.33 1.49 2.35 0.99

V112204 12 0.6 SS 1 Bmax ELF 2.58 5.46 1.47 2.38 1.01

V112205 12 0.8 SS 1&2 Bmax ELF 2.55 5.30 1.39 2.66 1.13

V112206 12 0.7 SS 1&2 Bmax ELF 2.63 5.63 1.58 2.55 1.08

V112207 12 0.6 SS 1&2 Bmax ELF 2.74 5.84 1.52 2.60 1.10

V112208 12 0.8 SS 5 Bmax ELF 2.51 5.16 1.50 2.51 1.06

V112209 12 0.7 SS 5 Bmax ELF 2.55 5.11 1.47 2.86 1.21

V112210 12 0.6 SS 5 Bmax ELF 2.60 5.15 1.45 2.64 1.12

V512202 12 0.8 WS 1 Bmax ELF 2.44 5.03 1.46 2.16 0.92

V512203 12 0.65 WS 1 Bmax ELF 2.44 4.92 1.46 2.17 0.92

V512204 12 0.8 WS 1 & 2 Bmax ELF 2.44 4.95 1.47 2.03 0.86

V512205 12 0.65 WS 1 & 2 Bmax ELF 2.44 4.65 1.55 2.50 1.06

V512206 12 0.8 WS 5 Bmax ELF 2.44 5.04 1.46 2.32 0.98

V512207 12 0.65 WS 5 Bmax ELF 2.44 4.90 1.46 2.28 0.96

V7122011 12

OMF - GILD 

0.5 at 1

Bmax

ELF 2.44 0.00 1.06 1.16 0.49
D-22 D: Concrete Moment Frame Studies FEMA P-2012

Table D-16 Reinforced Concrete Moment Frame Results (continued)

Model ID

Design Configuration Building Performance Summary

No. of 

Stories Irregularity SDC

Design 

Method

Design 

Period 

(CuTa) 

[s]

OpenSees 

Model 

Period 

[s]

Static 

Overstrength, 

Ω

ACMR 

(const. 

SSF)

ACMR/

ACMRbaseline

V7122021 12

OMF - GILD 0.5 

at 2

Bmax

ELF 2.44 5.22 1.09 1.34 0.57

V612202 12 0.4 SCWB Bmax ELF 2.44 5.22 1.47 2.36 0.93

V612203 12 0.7 SCWB Bmax ELF 2.44 5.22 1.37 2.36 0.93

V612204 12 1.0 SCWB Bmax ELF 2.44 5.22 1.45 2.54 1.00

V612205 12 0.4 SCWB Exact Bmax ELF 2.44 5.22 1.79 1.71 0.84

V612206 12 0.7 SCWB Exact Bmax ELF 2.44 5.22 1.55 1.95 0.96

V612207 12 1.0 SCWB Exact Bmax ELF 2.44 5.22 1.47 2.04 1.00
FEMA P-2012 E: Results of Quality Control Review E-1

Appendix E

Results of Quality Control 

Review

E.1 Overview of Quality Control Review

Quality control review work was conducted for each of the analytical studies 

reflected this report, which include: (1) torsional studies; (2) concrete shear 

wall studies; (3) steel moment frame studies; and (4) concrete moment frame 

studies. The following were the focus areas of each of the reviews:

• Archetype Design. This work included checking the: (1) layout of 

elements; (2) design base shear; (3) appropriateness of limit states and 

controlling criteria; and (4) element proportioning and reinforcement.

• FEMA P695 Analysis Input. This work included checking: (1) the 

models for consistency with the design (e.g., layout, proportioning, 

backbone curves, cyclic performance criteria); (2) that irregularities were 

modeled as intended (e.g., strength ratios, stiffness ratios, 

strong-column/weak-beam ratios); (3) P-Delta for the gravity system; 

and (4) the appropriateness of the boundary conditions.

• FEMA P695 Analysis Results. This work included checking: (1) trends

in metadata (e.g., normalized ACMR, P(Collapse|MCE)); (2) structural 

period(s) (e.g., design period, T1 from the models); (3) peak pushover 

strength factor; (4) static overstrength factor; (5) trends in the distribution 

of mean story drifts (e.g., 33% MCE, 66% MCE, MCE, and near 

collapse); (6) controlling response parameters and mechanisms; 

(7) trends for special versus ordinary systems; and (8) hysteresis results

(spot-checking only). In addition to this, a complementary analysis was 

conducted for a reinforced concrete shear wall archetype for the purposes

of comparing analysis results. 

E.2 Results from Quality Control Review

E.2.1 Torsional Studies

Review work of the torsional studies included: (1) review of backbone 

behavior of the archetype models; (2) review of cyclic deterioration behavior 

of the archetype models; (3) a check of the FEMA P695 analysis process, 

including a comparison of the differences between the typical FEMA P695 
E-2 E: Results of Quality Control Review FEMA P-2012

analysis and the modified method used for the studies in this report; and (4) a 

check of the archetype structural design process spreadsheets. The following 

were noted from this work:

• Observation: Mid-rise archetype models had a higher P-Delta when 

compared to similar models from previous studies. Resolution: This is 

reflected in Appendix A. Also, this finding indicates that the torsion 

studies cast a wider net between short and mid-rise models.

• Observation: The capping point was slightly higher in the archetype 

model when compared to models from prior studies (i.e., failure at 6% 

roof drift versus ~2-3% from prior studies). Resolution: Effective 

building heights are different so failure deflections are actually similar. 

• Observation: Cyclic deterioration behavior of the archetype models is

low. Resolution: The cyclic properties of the nonlinear springs were 

modeled with peak-oriented material properties having relatively low 

cyclic deterioration. Cyclic deterioration effects were minimized in the 

simplified models for the following reasons: (1) cyclic deterioration is a 

system/material dependent property and the study was intended to 

capture torsion effects in a more generic sense; and (2) collapse capacity 

has been shown to be relatively insensitive to cyclic deterioration 

properties in comparison with other parameters such as peak strength and 

negative stiffness (Haselton et al., 2011). As such, it was determined that 

this finding does not significantly impact the conclusions and 

recommendations resulting from the torsion studies. This finding is 

reflected in Chapter 4.

All findings from the review work for the torsion studies were addressed and 

are reflected in this report.

E.2.2 Concrete Shear Wall Studies

Review work of the concrete shear wall studies included review of the: 

(1) analysis techniques and possible implications; (2) archetype design; 

(3) structural calculations; and (4) analysis results. In particular, the 

following were noted:

• Limitations of Analysis Techniques.

o Failure modes modeling was limited in that: (1) compression flexural 

failure were assessed and modeled, but out-of-plane instability of the 

compression boundary and tension failure were not considered; 

(2) shear failure was not considered and could have been assessed by 

post-processing; and (3) loss of axial load carrying capacity in the 
FEMA P-2012 E: Results of Quality Control Review E-3

concrete shear walls was not considered (i.e., the approach used was 

associated with slab rotation and could have some considerable bias).

o System-level modeling included planar walls that were only 

subjected to 2D loading, where the effect of biaxial loading was not 

considered. Wall-slab interaction was also not considered.

• Limitations of Design Space. The design space was limited in that the 

archetypes: (1) only covered planar walls, leaving out flanged walls (e.g., 

T-shaped walls); (2) only considered two building heights (8- and 

12-story buildings) and did not cover building heights (e.g., 3- and 

5-story buildings) that might have a more significant stiffness reduction; 

(3) only considered one type of wall detailing; and (4) only covered walls 

with low shear stress. 

E.2.3 Steel Moment Frame Studies

Review work of the steel moment frame studies included review of the: 

(1) archetype designs; (2) analytical models used in the collapse analyses;

and (3) collapse analysis results used to evaluate vertical irregularities V2 

(weight or mass), V6 (strong-column/weak-beam), and V7 (gravity-induced 

lateral demand). In particular, the following were conducted:

• Archetype Designs. Inputs were checked for appropriate seismic 

parameters for the given seismic design category, material strength, 

frame geometry, and wind load and gravity load distribution for the 

given design case. The resulting frame designs were checked for 

strength, drift, and strong-column/weak-beam compliance for the given 

design case. Details of the steel moment frame design process and final 

frame designs are found in Appendix C.

• Analytical Models for Collapse Analysis. Quality control review of the 

OpenSees models used for collapse analyses included a review of a 

typical frame design and the routines used to produce the various 

OpenSees models required for the different analytical cases. The review 

included checking material nonlinear modeling parameters, damping 

model, frame geometry, and gravity load distribution for the given design 

case. Tool Command Language (TCL) subroutines used to generate the 

TCL files for the OpenSees models were also reviewed.

• Collapse Analysis Results. Quality control review of the analytical 

results included scrutiny of the methodology used to estimate collapse 

fragilities (i.e., the Baker method), the solution method for direct 

integration (i.e., Newton Raphson), and the impact of the time-step used 

for direct integration and methodology used to scale the geometric mean 
E-4 E: Results of Quality Control Review FEMA P-2012

spectra to produce collapse. A sensitivity study was performed that 

confirmed that the 0.02-second time-step used in the nonlinear analyses 

was sufficiently short to capture all significant peaks in the response (i.e., 

the 4% response increase using a shorter time step was judged to be not 

significant). Lastly, the results were reviewed to confirm that they 

appeared reasonable with respect to drift (e.g., comparing expected 

increases between the 33% and 66% MCE runs or lateral displacement 

distribution up the height of the building), the shape and trend of the 

incremental dynamic analyses (e.g., a search for illogical results from 

non-convergence or collapse), and the general shape of the pushover 

curves.

Overall, the quality control review work demonstrated that the steel moment 

frame studies and corresponding conclusions were reasonable and did not 

require any modifications. 

E.2.4 Concrete Moment Frame Studies

Review work of the concrete moment frame studies included the following:

• Archetype Designs. Inputs were checked for appropriate seismic 

parameters for the given seismic design category, material strength, 

frame geometry, wind load and gravity load distribution for the given 

design case. The resulting frame designs were checked for strength, drift 

and strong-column/weak-beam compliance, using standard ASCE/SEI 

7-16 load combinations and standard envelope design procedures. No 

accidental torsion was included and the 3D ETABS models described 

below were completely symmetrical. Details of the concrete moment 

frame design process and final frame designs are found in Appendix D.

• Comparison Studies. Independent 3D ETABS analysis and design runs 

for the 8- and 12-story baseline buildings were conducted for comparison 

to the 2D plane frame runs used in the studies. Reasonably good 

agreement was observed for the reinforcement ratios. It was concluded 

that these 2D tables used a “broad brush” for the selection of the 

respective flexural reinforcement ratios. ETABS output indicated 

different required reinforcement ratios for each story level, whereas the 

2D design grouped as many as five levels with the same beam flexural 

rebar. The beam hoops follow the specified beam flexural reinforcement 

grouping and many levels list the same hoop reinforcement ratios. 

Tabulated 2D design column longitudinal rebar and confinement 

reinforcement were also in general agreement with the 3D ETABS 

design runs. Typically, reinforcement ratios agreement was on the order 
FEMA P-2012 E: Results of Quality Control Review E-5

of +/-10% between the results from the 3D ETABS study and the 2D 

study described in this report.

Overall, the quality control review work demonstrated that the concrete 

moment frame studies and corresponding conclusions were reasonable and 

did not require any modifications. 

FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-1

Appendix F

Global Behavior of Buildings 

with Mass Irregularity [V2]

This Appendix documents a series of analyses performed to test the 

generality of the observation made in Section 6.5.3 that, in terms of collapse 

resistance for buildings with mass irregularity, modal response spectrum 

analysis (MRSA) provides no advantage over the equivalent lateral force 

(ELF) procedure. For Figures F-29 through F-124 referenced in this 

Appendix, see the electronic Supporting Documentation for Appendix F: 

Additional Figures.

F.1 Background

ASCE/SEI 7-16 defines a mass irregularity to exist where the effective mass 

of a story is more than 150% of that of an adjacent story; the only design 

consequence is that use of the ELF procedure is prohibited for structures with 

mass irregularity. Chapter 6 reports the results of explicit collapse 

assessment of 20-story and 3-story concrete special moment frame (SMF) 

buildings and steel SMF buildings with mass ratios that might be realistically 

expected in practice (1.5, 2.0, and 3.0) at selected stories. Those archetypes 

were proportioned using MRSA with designs being adjusted as needed to 

satisfy all design requirements, including the effects of actual mass ratios. 

For a few archetypes separately proportioned using the ELF procedure, it 

was found that their collapse resistance exceeded that of the systems 

proportioned using MRSA. Based on this finding, it is proposed that the ELF 

procedure could be permitted for structures with mass irregularity, such that 

that irregularity need not be assessed when selecting a suitable analysis 

procedure for system proportioning.

Since explicit collapse assessments were performed only for moment frame 

buildings and for mass ratios that do not exceed 3.0, there is some question 

of the generality of the findings. The concern is that “stiffness and mass 

irregularities may significantly affect the vertical distribution of forces” 

making the “modal analysis procedure, which can account for these 

discontinuities, ... necessary” (SEAOC, 2013).
F-2 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

F.2 Expanded Design Space and Assessment Method

F.2.1 Expanded Design Space

An expanded design space was developed to test the sensitivity of the 

vertical distribution of forces used in proportioning the overall system. The 

expanded design space includes systems with shear-type response (typical of 

moment frames) and cantilever-type response (typical of shear walls). 

Systems of 3-, 10-, and 20-stories are considered in a regular configuration 

(identical mass at all stories) and with a severe mass irregularity (mass ratio 

of 3.0, 5.0, or 10.0) at a single story; a variety of locations are considered for 

the irregular story.

Figure F-1 and Table F-1 show the design space. The archetype perimeter 

frame building has a plan area of 120 feet by 120 feet, with story heights of 

12’-6” and 30’-0” bays. The design is for Seismic Design Category Dmax 

with SDS = 1.5, SD1 = 0.6, and Cu = 1.4. All archetypes are proportioned using 

the results of the ELF procedure. Figure F-2 through Figure F-4 show 

member sizes for the moment frame archetypes. Reinforced concrete (RC) 

shear wall (SW) archetypes have 30-ft-long walls on each side with wall 

thicknesses of 24 inches, 18 inches, and 12 inches, respectively, for the 20-

story, 10-story, and 3-story buildings.

Figure F-1 Expanded design space for assessment of global behavior of 

buildings with mass irregularity.
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-3

Table F-1 System Properties for Expanded Design Space

Stories T = CuTa (s) R Cs

(per framing line)

w (kip) W (kip) V (kip)

Baseline

Steel SMF

(shear)

3 0.712 8 0.105 700 2100 221

10 1.866 8 0.066 700 7000 462

20 3.248 8 0.066 700 14000 924

RC SW

(cantilever)

3 0.424 5 0.283 900 2700 764

10 1.047 5 0.115 900 9000 1032

20 1.760 5 0.068 900 18000 1227

Irregular (x3)

Steel SMF

(shear)

3 0.712 8 0.105 700 3500 369

10 1.866 8 0.066 700 8400 554

20 3.248 8 0.066 700 15400 1016

RC SW

(cantilever)

3 0.424 5 0.283 900 4500 1273

10 1.047 5 0.115 900 10800 1238

20 1.760 5 0.068 900 19800 1350

Irregular (x5)

Steel SMF

(shear)

3 0.712 8 0.105 700 4900 516

10 1.866 8 0.066 700 9800 647

20 3.248 8 0.066 700 16800 1109

RC SW

(cantilever)

3 0.424 5 0.283 900 6300 1782

10 1.047 5 0.115 900 12600 1444

20 1.760 5 0.068 900 21600 1472

Irregular (x10)

Steel SMF

(shear)

3 0.712 8 0.105 700 8400 885

10 1.866 8 0.066 700 13300 878

20 3.248 8 0.066 700 20300 1340

RC SW

(cantilever)

3 0.424 5 0.283 900 10800 3054

10 1.047 5 0.115 900 17100 1960

20 1.760 5 0.068 900 26100 1779
F-4 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Figure F-2 Member sizes for the 20-story steel SMF baseline archetype.
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-5

Figure F-3 Member sizes for the 10-story steel SMF baseline archetype.

Figure F-4 Member sizes for the 3-story steel SMF baseline archetype.
F-6 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Figure F-5 shows that the RC SW archetypes have cantilever-type response. 

Figure F-6 shows that the SMF archetypes have shear-type response.

Figure F-5 Cantilever-type response of RC SW archetypes.

Figure F-6 Shear-type response of steel SMF archetypes.
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-7

F.2.2 Assessment Method for Global Behavior

Rather than completing the detailed design of each archetype and explicitly 

assessing its collapse resistance using the FEMA P695 method, the MRSA 

and ELF procedures are used to determine differing vertical distributions of 

story forces so that the related global behavior metrics of story shear, story 

overturning moment, and story drift (which would drive the detailed design) 

can be compared. For the ELF procedure story forces are determined in 

accordance with Section 12.8.3 of ASCE/SEI 7-16, including the exponent, 

k, related to structure period, which varies from 1.0 to 2.0 for structures with 

periods from 0.5 to 2.5 seconds. For the MRSA response parameters are 

computed in accordance with Section 12.9.1 of ASCE/SEI 7-16, including 

scaling of forces to 100% of the ELF base shear. For all analyses section 

cuts are used to compute story shear and story overturning moment, and 

generalized displacements are used to compute maximum story drift in 

accordance with Section 12.8.6 of ASCE/SEI 7-16.

For each archetype, the distribution of story shear, story overturning moment, 

and maximum story drift from MRSA and the ELF procedure can be 

compared. The simplest assessment of the conservatism of the ELF 

procedure can be made by comparing the shear ratio and moment ratio 

(ELF/MRSA) for each story to 1.0. Where the ELF/MRSA ratio exceeds 

1.0, the ELF procedure global demands, which would drive detailed design 

and thus collapse resistance, are conservative. Where the ELF/MRSA ratio 

is less than 1.0, ratios for the baseline (regular) condition should be 

considered to determine whether mass irregularity is the cause of the smaller

values. Even where mass irregularity appears to reduce conservatism 

compared to the baseline condition, detailed results should be compared to 

assess whether the reduction has practical significance to the design; for 

instance, where story shear or moment at the top of a building is very small 

compared to the base shear or moment, the computed story shear or story 

moment ratios may exaggerate the significance of the difference.

F.3 Findings

In all cases, except for the 3-story reinforced concrete shear wall (RC SW)

archetypes (where the difference is inconsequential), the story drifts 

computed using the ELF procedure exceed those computed using MRSA. 

The ELF story shear and story moment for the baseline (regular) buildings 

exceed those from MRSA, except at the top of 10- or 20-story archetypes and 

for the 3-story RC SW archetypes. Differences for the 3-story RC SW

baseline archetype are inconsequential, and the shear and moment ratios 

actually improve as the mass ratio increases (Figure F-7 and Figure F-8).
F-8 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

As discussed in Section C12.8.3 of ASCE 7-16, the exponent k used in the 

ELF procedure “is intended to approximate the effect of higher modes” and 

the horizontal forces computed “are intended to provide lateral seismic forces 

at individual levels that are consistent with enveloped results from more 

accurate analyses.” Although the ELF/MRSA shear and moment ratios at the 

top of the 10- and 20-story baseline archetypes can be well below 1.0, the 

story shears and moments at those levels are so much smaller than the base 

shear and base moment that the differences are unlikely to be significant for 

practical designs.

In some cases, the conservatism of the ELF procedure increases as irregular 

mass ratio increases. For instance, the 20-story RC SW and SMF archetypes 

exhibit this behavior where the mass irregularity occurs at Level 2 (Figure

F-9 and Figure F-10).

In other cases, the increasing mass ratio reduces the conservatism of the ELF 

procedure, but the ELF/MRSA shear and moment ratios still exceed 1.0 or 

are no worse than the ratios for the baseline (regular) building. For instance, 

the 20-story RC SW and SMF archetypes exhibit this behavior where the 

mass irregularity occurs at Level 8 (Figure F-11, Figure F-12, and Figure 

F-13).

For three archetypes (20-story SMF with irregular mass at Level 14, 20-story 

RC SW with irregular mass at Level 14, and 10-story RC SW with irregular 

mass at Level 5), reductions in ELF/MRSA ratio for increasing mass ratio 

identify areas where detailed results should be compared.

For the 20-story SMF with irregular mass at Level 14 (Figure F-14 and 

Figure F-15) ELF/MRSA ratios are less than 1.0 in stories above the mass 

irregularity. However, the detailed results (Figure F-16 through Figure F-18) 

show that this is an artifact of very small story shears and moments at the top 

of the building. When compared with the base shear and base moment, those

differences are inconsequential.

For the 20-story RC SW with irregular mass at Level 14 and the 10-story RC 

SW with irregular mass at Level 5 (Figure F-19, Figure F-20, Figure F-21, 

and Figure F-22) ELF/MRSA ratios are less than 1.0 in stories above the 

mass irregularity. However, the detailed results (Figure F-23 through Figure 

F-25, and Figure F-26 through Figure F-28) show that the story shears and 

moments above the mass irregularity have similar trends and are small 

compared to the base shear and base moment. Those differences would not 

significantly affect the detailed design unless the horizontal dimension of the 

seismic-force-resisting system were also reduced at those levels; if that were 
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-9

the case irregularity V3 would exist and MRSA would be required by Table 

12.3-2 of ASCE/SEI 7-16.

F.4 Recommendations

Comparison of the global behavior metrics of story shear, story overturning 

moment, and story drift (which would drive detailed design) for systems with 

shear-type response or cantilever-type response show that the ELF procedure 

produces results that would be appropriate for design. In most cases the ELF 

demands for systems with large mass ratios (up to 10) are greater than or 

close to the MRSA demands. In the few cases where ELF demands are 

noticeably less than MRSA demands, practical designs would still be 

conservative unless the horizontal dimension of the seismic-force-resisting

system were greatly reduced above the mass irregularity; such a reduction

would produce a V3 (vertical geometric) irregularity, thus requiring use of 

the MRSA method for design of the system. These analyses, together with 

the results of the explicit collapse assessments reported in Chapter 6, suggest 

that there is no need to define mass irregularity in ASCE/SEI 7-16 for 

buildings and nonbuilding structures similar to buildings. If there are 

nonbuilding structures whose mass distribution requires special consideration 

(such as MRSA), appropriate requirements for those structures should be 

provided in Chapter 15 of ASCE/SEI 7.

Figure F-7 3-story RC SW, irregular mass at Level 2, story shear ratios (ELF/MRSA). This figure is reproduced 

as Figure F-75 in the electronic Supporting Documentation for Appendix F: Additional Figures.

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5

Elevation (ft)

Shear ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
F-10 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Figure F-8 3-story RC SW, irregular mass at Level 2, story moment ratios (ELF/MRSA). 

This figure is reproduced as Figure F-76 in the electronic Supporting 

Documentation for Appendix F: Additional Figures.

Figure F-9 20-story RC SW, irregular mass at Level 2, story moment ratios (ELF/MRSA). 

This figure is reproduced as Figure F-34 in the electronic Supporting 

Documentation for Appendix F: Additional Figures.

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-11

Figure F-10 20-story SMF, irregular mass at Level 2, story moment ratios (ELF/MRSA). This 

figure is reproduced as Figure F-82 in the electronic Supporting Documentation 

for Appendix F: Additional Figures.

Figure F-11 20-story RC SW, irregular mass at Level 8, story shear ratios (ELF/MRSA). This 

figure is reproduced as Figure F-39 in the electronic Supporting Documentation 

for Appendix F: Additional Figures.

0

50

100

150

200

250

0 0.5 1 1.5 2

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10

0

50

100

150

200

250

0 0.5 1 1.5 2

Elevation (ft)

Shear ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
F-12 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Figure F-12 20-story RC SW, irregular mass at Level 8, story moment ratios (ELF/MRSA). 

This figure is reproduced as Figure F-40 in the electronic Supporting 

Documentation for Appendix F: Additional Figures.

Figure F-13 20-story SMF, irregular mass at Level 8, story shear ratios (ELF/MRSA). This 

figure is reproduced as Figure F-87 in the electronic Supporting 

Documentation for Appendix F: Additional Figures.

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10

0

50

100

150

200

250

0 0.5 1 1.5 2

Elevation (ft)

Shear ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-13

Figure F-14 20-story SMF, irregular mass at Level 14, story shear ratios (ELF/MRSA). This figure 

is reproduced as Figure F-93 in the electronic Supporting Documentation for 

Appendix F: Additional Figures.

Figure F-15 20-story SMF, irregular mass at Level 14, story moment ratios (ELF/MRSA). This 

figure is reproduced as Figure F-94 in the electronic Supporting Documentation 

for Appendix F: Additional Figures.

0

50

100

150

200

250

0 0.5 1 1.5

Elevation (ft)

Shear ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10

0

50

100

150

200

250

0 0.5 1 1.5

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
F-14 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-16 20-story SMF, irregular mass at Level 14, mass ratio = 3. This figure is reproduced as Figure 

F-90 in the electronic Supporting Documentation for Appendix F: Additional Figures. 

 Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-17 20-story SMF, irregular mass at Level 14, mass ratio = 5. This figure is reproduced as Figure 

F-91 in the electronic Supporting Documentation for Appendix F: Additional Figures. 
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-15 

Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-18 20-story SMF, irregular mass at Level 14, mass ratio = 10. This figure is reproduced as Figure 

F-92 in the electronic Supporting Documentation for Appendix F: Additional Figures. 

Figure F-19 20-story RC SW, irregular mass at Level 14, story shear ratios (ELF/MRSA). This 

figure is reproduced as Figure F-45 in the electronic Supporting 

Documentation for Appendix F: Additional Figures. 

0

50

100

150

200

250

0 0.5 1 1.5 2

Elevation (ft)

Shear ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
F-16 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Figure F-20 20-story RC SW, irregular mass at Level 14, story moment ratios (ELF/MRSA). 

This figure is reproduced as Figure F-46 in the electronic Supporting 

Documentation for Appendix F: Additional Figures.

Figure F-21 10-story RC SW, irregular mass at Level 5, story shear ratios (ELF/MRSA). 

This figure is reproduced as Figure F-63 in the electronic Supporting 

Documentation for Appendix F: Additional Figures.

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10

0

20

40

60

80

100

120

140

0 0.5 1 1.5

Elevation (ft)

Shear ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-17 

Figure F-22 10-story RC SW, irregular mass at Level 5, story moment ratios (ELF/MRSA). 

This figure is reproduced as Figure F-64 in the electronic Supporting 

Documentation for Appendix F: Additional Figures. 

Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-23 20-story RC SW, irregular mass at Level 14, mass ratio = 3. This figure is reproduced as 

Figure F-42 in the electronic Supporting Documentation for Appendix F: Additional Figures. 

0

20

40

60

80

100

120

140

0 0.5 1 1.5

Elevation (ft)

Moment ratio (ELF/MRSA)

Baseline

Mass ratio = 3

Mass ratio = 5

Mass ratio = 10
F-18 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

 Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-24 20-story RC SW, irregular mass at Level 14, mass ratio = 5. This figure is reproduced as 

Figure F-43 in the electronic Supporting Documentation for Appendix F: Additional Figures. 

Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-25 20-story RC SW, irregular mass at Level 14, mass ratio = 10. This figure is reproduced as 

Figure F-44 in the electronic Supporting Documentation for Appendix F: Additional Figures.
FEMA P-2012 F: Global Behavior of Buildings with Mass Irregularity [V2] F-19 

Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-26 10-story RC SW, irregular mass at Level 5, mass ratio = 3. This figure is reproduced as 

Figure F-60 in the electronic Supporting Documentation for Appendix F: Additional Figures. 

 Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-27 10-story RC SW, irregular mass at Level 5, mass ratio = 5. This figure is reproduced as 

Figure F-61 in the electronic Supporting Documentation for Appendix F: Additional Figures. 
F-20 F: Global Behavior of Buildings with Mass Irregularity [V2] FEMA P-2012

Shear, V (kip) Moment, M (ft-kip) Max Drift, Δ (inch)

(a) (b) (c)

Elevation (ft)

Figure F-28 10-story RC SW, irregular mass at Level 5, mass ratio = 10. This figure is reproduced as 

Figure F-62 in the electronic Supporting Documentation for Appendix F: Additional Figures. 
FEMA P-2012 G: Story Stiffness and Strength Calculation G-1

Appendix G

Story Stiffness and Strength 

Calculation

This Appendix provides recommendations for the calculation of story 

stiffness and story strength. Such calculations are required to assess soft 

story and weak story vertical configuration irregularities [V1 and V5] and to 

determine the redundancy factor, ρ, in accordance with Table 12.3-3 of 

ASCE/SEI 7-16.

In addition to summarizing recommendations from the available literature, 

this appendix presents findings from analysis of a design space of 3-, 10-, 

and 20-story systems with shear-type response (typical of moment frames) 

and cantilever-type response (typical of shear walls) in a regular 

configuration (identical mass at all stories) and with a severe mass 

irregularity (mass ratio of 3.0, 5.0, or 10.0) at a single story. A few moment 

frame archetypes with unusual story heights were also investigated. Figure 

G-1 shows the design space used for these assessments. Archetypes were

developed for shear-type response (representative of moment frames) and 

cantilever-type response (representative of shear walls) for baseline 

conditions (uniform story heights and story masses). Additional archetypes 

have uniform story heights but irregular masses of 3, 5, and 10 times the 

standard mass separately at each location indicated. Other archetypes were

developed with uniform masses but with tall story height at an intermediate 

level. Appendix F provides the design details for each baseline archetype.
G-2 G: Story Stiffness and Strength Calculation FEMA P-2012

Figure G-1 Design space for story stiffness calculations.

G.1 Background

The equivalent lateral force (ELF) “procedure is based on an assumption of a 

gradually varying distribution of ... stiffness along the height” (ASCE, 

2017a). “Stiffness ... discontinuities may significantly affect the vertical 

distribution of forces and, for this reason, the modal analysis procedure, 

which can account for these discontinuities,” has been deemed necessary in 

such circumstances (SEAOC, 2013). The triggers provided in Table 12.3-2 

of ASCE/SEI 7-16 for soft story and extreme soft story irregularity reflect

stiffness ratios between adjacent stories that would not be considered

“gradually varying.” These judgment-based trigger values were established 

at a time when it was common for designers to use hand calculations for 

structures with simple configurations. Even for simple structures, the 

limitations of those calculations are quite severe, as discussed in Section 

G.2.1.

The R-factors used in ASCE/SEI 7-16 Chapter 12 design procedures are 

appropriate for structural configurations that will result in a reasonably 

uniform distribution of inelastic behavior in elements throughout the seismicforce-resisting system. “Buildings with a weak-story irregularity [V5] tend 

to develop all of their inelastic behavior and consequent damage at the weak 

story, possibly leading to collapse” (ASCE, 2017a). The triggers provided in 

Table 12.3-2 of ASCE/SEI 7-16 for weak story and extreme weak story 

irregularity reflect strength ratios where an undesirable concentration of 
FEMA P-2012 G: Story Stiffness and Strength Calculation G-3

inelastic response may be expected. As discussed in Section G.3, simple 

calculations are sufficient to identify this concern.

G.2 Calculation of Story Stiffness

Assessment of stiffness regularity requires computation of lateral stiffness for 

each story in each direction. “Generally, it is not practical to use stiffness 

properties unless these can be easily determined. There are many structural 

configurations where the evaluation of story stiffness is complex and is often 

not an available output from computer programs” (SEAOC, 2013).

Two methods to perform calculations for story stiffness comparisons are

described in Sections G.2.2 and G.2.3.

G.2.1 Simple Hand Calculations and Their Limitations

In recent decades use of the finite element method has become common for 

structural analysis. Prior to that time simple hand calculations were routinely 

used. The following expressions for lateral stiffness of moment frames and 

shear walls have a long history of use. Though not addressed here, simple 

expressions are also available for concentrically or eccentrically braced 

frames.

For a moment frame column at an intermediate story:

3

12EIc K

h = β

2

γ β

γ = +

b1 b2 b3 b4

1234

c

IIII

llll

I

h

γ

+++

=

where b1 and b2 are the beams above, and b3 and b4 are the beams below.

For an elastic, cantilevered shear wall:

2

4 3

E tc K

h h

L L

=         +

     

For an elastic wall fixed against rotation below and above:

2

3

E tc K

h h

L L

=         +

     
G-4 G: Story Stiffness and Strength Calculation FEMA P-2012

The expressions above are used for the “hand calculations” reported for the 

design space analyzed as part of this project. The shear wall calculations 

generally use the stiffness for a cantilevered wall and treat multiple stories as 

springs in series; for a bounding comparison the fixed-fixed expression is 

also used.

While these simple expressions have a long history of use, their 

shortcomings are numerous and include the following (Shultz, 1992; Eroglu 

and Akkar, 2010):

• By focusing on one story at a time, they neglect off-diagonal stiffness 

terms associated with global overturning and even shear and flexure in 

adjacent stories. Rigorous analysis yields stiffness matrices for frames 

that have contributions from adjacent minor diagonals and nonzero 

coefficients outside the tridiagonal band. Neglecting these terms tends to 

overpredict stiffness irregularities.

• Where story heights differ, the independent story-by-story approach 

breaks down. Adjustment factors in the literature for this effect are 

complex and not comprehensive.

• The expression for moment frames, being based on flexural flexibility, 

neglects the contribution of shear flexibility.

• While the expressions for shear walls include both shear and flexural 

deformations, they assume the same degree of cracking for both 

contributions and cannot reflect realistic conditions for multi-story walls 

that are between the pure cantilever and pure fixed-fixed conditions.

• These methods are not suitable to reflect abrupt changes in stiffness at 

boundary conditions (especially at top and bottom stories). Adjustment 

factors in the literature for these boundary effects are complex and not 

comprehensive.

• The expressions for shear walls do not reflect the effect of openings. 

There are several design aids compiled for practicing structural engineers 

that recommend a simplified hand procedure to account for openings in 

shear walls by treating them as a system of piers and spandrel beams. 

Neuenhofer (2006) reports that the recommended hand method is highly 

approximate and consistently underestimates the impact of the opening 

on the reduction of stiffness, thus producing a lateral stiffness larger than 

that obtained from detailed finite-element analysis.

Figure G-2 shows that when story stiffnesses for regular (baseline) moment 

frames are normalized, hand methods produce similar trends and may have 

reasonable correlation to results from the finite element method. The scatter 
FEMA P-2012 G: Story Stiffness and Strength Calculation G-5

introduced by the hand methods would only worsen for nonuniform 

conditions. For the design space analyzed as part of this project (which uses 

a typical story height of 12.5 ft.), hand calculations would identify a soft 

story for an unusual story with height of 14.5 ft. and an extreme soft story for 

an unusual story with height of 15.5 ft. By comparison, the rigorous finite 

element analyses identify triggering story heights of approximately 16 ft. and 

18 ft., respectively.

Figure G-2 Stiffness comparisons and correlations for steel moment frames.

Figure G-3 shows that trends for normalized story stiffnesses for regular 

(baseline) shear walls and their correlations to results from the finite element 
G-6 G: Story Stiffness and Strength Calculation FEMA P-2012

method are reasonable for the 3-story archetype, but are unreliable for the 

taller archetypes.

Figure G-3 Stiffness comparisons and correlations for concrete shear walls.

G.2.2 SEAOC Story Drift Ratio Method

According to SEAOC (2013), “recognizing that the basic intent of this 

irregularity check is to determine if the lateral-force distribution will differ 

significantly from the pattern prescribed by Section 12.8.3, which assumes a 

prescribed shape for the first dynamic mode of response, this type of 

irregularity can also be determined by comparing values of drift ratios due to 

the prescribed lateral forces. To compare displacements rather than stiffness, 
FEMA P-2012 G: Story Stiffness and Strength Calculation G-7

it is necessary to use the reciprocal of the limiting percentage ratios of 70 and 

80 percent as they apply to story stiffness, or reverse their applicability to the 

story or stories above.” To use this method, story drifts and story drift ratios 

are determined, where the story drift ratio is the story drift divided by story 

height. Comparison of these ratios identifies changes in the slope of the 

displaced shape.

While this method has some merit, it suffers from at least two weaknesses:

1. “Using the story-drift ratios (drift based) to determine whether a soft 

story exists may result in the discovery of soft stories in the upper stories 

of multistory buildings that may not be correct” (SEAOC, 2013). For the 

design space analyzed as part of this project, the story drift ratio method 

produces a false soft-story positive at Level 17 of the 20-story baseline 

SMF even though that story has greater stiffness than the stories above

based on either simple hand calculations or the apparent story stiffness 

method; the natural displaced shape of structures with shear-type 

response produces decreasing story drift ratios up the height, even where 

story stiffness is constant.

2. Since differences in story mass affect story drift, the story drift ratio 

method can produce false positives for soft story irregularity, as 

compared to explicit stiffness calculations. For the design space 

analyzed as part of this project, the story drift ratio method produces 

false soft-story positives at stories with mass irregularities in the top half 

of the SMF archetypes.

G.2.3 Apparent Story Stiffness Method

“The lateral stiffness of a story is generally defined as the ratio of story shear 

to story drift” (Shultz, 1992). Since story drift is affected by vertical

distribution of lateral loads, the lateral stiffness of a story is not a stationary 

property, but an apparent one that depends on lateral load distribution. The 

ELF procedure uses “regular” loads—acting in the same direction on all 

floors, and varying from floor to floor in a controlled manner.

Shultz (1992) reports on analyses using three distributions of lateral load 

designated as constant, linear, and parabolic. These lateral load distributions 

have lateral loads on each floor that are of equal magnitude, are proportional 

to the height, or are proportional to the square of the height of each floor 

from the base of the frame, respectively. Shultz finds that the apparent story 

stiffnesses are not affected much by the type of lateral load distribution, and 

that the concept of a single-valued story stiffness is quite accurate if the 

distribution is regular.
G-8 G: Story Stiffness and Strength Calculation FEMA P-2012

For the design space analyzed as part of this project, significant mass 

irregularities were considered at various levels (with mass ratios of 3.0, 5.0, 

and 10.0). As may be seen in the top frames of Figures G-2 and G-3, even 

such substantial variations in story force have only minor impact on the 

apparent story stiffness, so the use of a single-value apparent story stiffness 

based on the ELF load distribution is judged to be sufficiently accurate.

G.3 Calculation of Story Strength

Assessment of strength regularity requires computation of lateral strength for 

each story in each direction. The intent “is to use a simple measure (elastic 

or plastic) to determine” the “total strength of all seismic-force-resisting 

elements sharing the story shear for the direction under consideration” 

(ASCE, 2017a; SEAOC, 2013). Where compliance with Table 12.3-3 of 

ASCE/SEI 7-16 is being assessed for determination of the redundancy factor, 

the summation excludes the strength of the element whose removal is being 

considered. This calculation does not require a rigorous 3-dimensional 

plastic analysis; instead, it is acceptable simply to sum the shear 

contributions of seismic-force-resisting elements in each of two orthogonal 

directions as follows:

• Brace members: The shear contribution is the horizontal component of 

the lower of the brace capacity (in tension or compression, depending on 

the direction of load application), or the connection capacity. Where 

uplift of a shallow foundation, column capacity, or the capacity of an 

element supporting a discontinuous frame controls the response, the 

computed strength should reflect that limit state.

• Moment frame columns: The shear contribution is that corresponding 

to the least lateral capacity. For frame columns with weakcolumn/strong-beam conditions, the shear contribution is the lower of 

that developed when the top and bottom of the column are at flexural 

capacity, or the column shear capacity. For frame columns with a 

strong-column/weak-beam condition, the shear contribution is the lower 

of the shear corresponding to development of flexural yielding at each 

end of the column (from adjoining beam yield hinges or column base 

connection capacity), or the column shear capacity.

• Shear wall piers: The shear contribution is the lower of either the shear 

at development of the flexural strength, or the shear strength. Where 

wall flexure controls the response, both the 1.2D and 0.9D axial load 

cases should be considered. Where the capacity of an element 

supporting a discontinuous wall controls the response, the computed 

strength should reflect that limit state.
FEMA P-2012 G: Story Stiffness and Strength Calculation G-9

G.4 Recommendations

G.4.1 Calculation of Story Stiffness

Section 12.7.3 of ASCE/SEI 7-16 requires use of a mathematical model of 

the structure for “determining member forces and structure displacements 

resulting from applied loads,” which must “include the stiffness and strength 

of elements that are significant to the distribution of forces and deformations 

in the structure and represent the spatial distribution of mass and stiffness 

throughout the structure.” Not only is such a model, which is suitable for 

application of the apparent story stiffness method described in Section G.2.3, 

consistent with the state of the practice and standard of care, it is required for 

code compliance. There is no reason to use “simple” hand calculations for 

story stiffness determinations; as described in Section G.2.1 those methods 

have serious flaws and actually require greater effort on the part of the 

designer than simply assessing the results from the more rigorous analytical 

model that is required for code compliance. Since the results of the analysis 

include both story shears and story drifts, there is no reason to use the story 

drift ratio method, which can produce erroneous results.

For assessment of soft story vertical configuration irregularities [V1], lateral 

forces from the ELF procedure should be applied to the mathematical model 

and the apparent story stiffness of each story should be determined in each 

direction. The apparent story stiffness should be computed as:

Kx = Vx / (δx – δx-1)

where:

Vx = the story shear at level x determined by an elastic analysis using 

the forces defined in Section 12.8.3; and

δx = the deflection at level x determined by an elastic analysis using the 

forces defined in Section 12.8.3.

G.4.2 Calculation of Story Strength

Unlike the determination of story stiffness, calculation of story strength does 

not require use of a single, rigorous mathematical model. Instead, for 

assessment of weak story vertical configuration irregularities [V5], a simple 

summation of the shear contributions of seismic-force-resisting elements as 

recommended in Section G.3 is most meaningful and effective.

FEMA P-2012 H: Steel Systems Not Specifically Detailed H-1

for Seismic Resistance

Appendix H

Steel Systems Not Specifically 

Detailed for Seismic Resistance

ASCE/SEI 7 identifies a class of seismic-force-resisting systems entitled, 

“Steel Systems Not Specifically Detailed for Seismic Resistance, Excluding 

Cantilever Column Systems.” These systems have no height limit in Seismic 

Design Categories (SDC) B and C, but are not permitted in SDC D, E, and F. 

Seismic forces are obtained using Response Modification Factor (R) of 3 and 

the members are designed and detailed following the requirements of AISC 

360, Specification for Structural Steel Buildings. In other words, because the 

design is based on smaller R-factors and the resulting seismic design forces 

are larger, the requirements found in AISC 341, Seismic Provisions for 

Structural Steel Buildings, need not be followed.

R = 3 systems were not specifically studied for this report; nevertheless, it 

may be possible to draw some general conclusions regarding the sensitivity 

of R = 3 systems to irregularities by examining the behavior of the steel 

buildings designed for SDC B. While wind drift limits governed the design 

of all the SDC B buildings, the difference between wind and seismic forces 

was not large for the 3-story building. On the other hand, the wind force on 

the 9-story and 20-story buildings was approximately three times larger. 

Thus, for SDC C it is likely that the 9-story and 20-story buildings also 

would be governed by wind while the 3-story building might or might not be 

depending on many design factors (e.g., building proportion, mass, total 

height). 

H.1 Background

The premise behind the so-called “R = 3 systems” is that use of a low Rfactor makes nearly elastic response more likely while still recognizing the 

inherent seismic resistance of these structures. The assumed lack of required 

inelastic deformation capability renders the ductile detailing and member 

proportioning requirements in AISC 341 unnecessary. Often, member sizes 

for these systems are governed by wind rather than seismic loads. It is 

assumed that choosing such a system in areas of low- to moderate-seismicity 

may be more cost-effective due to fabrication, erection and inspection 

savings compared to systems designed following AISC 341.
H-2 H: Steel Systems Not Specifically Detailed FEMA P-2012

for Seismic Resistance

The following sections highlight key differences in design requirements 

between R = 3 designs and AISC 341 designs.

H.2 Configuration

AISC 360 places no significant configurational constraints on R = 3 seismic 

systems. AISC 341, on the other hand, addresses a number of configuration 

issues. For example, AISC 341 does not permit K-braced frames, where the 

brace delivers load to beam and column away from the column and beam 

centerline work point. The general concern is that column demands in Kbraced frames may exceed column strength, particularly where the column is 

designed for code-based forces rather than the force the brace can deliver to 

the column. Given the importance of columns in carrying both gravity and 

seismic demands, increased column vulnerability is likely to increase the 

probability of collapse. The presence of irregularities found to be of 

significance likely exacerbates R = 3 system vulnerability.

H.3 Proportioning

H.3.1 Strong-Column/Weak-Beam Requirement

In R = 3 designs, beams would be sized to be as stiff as possible to satisfy 

drift demands consistent with any depth restrictions, as this is usually the 

most cost-effective approach. Columns would typically be designed for the 

moments caused by wind or seismic forces and associated axial loads due to 

gravity and lateral demands. It is likely that beams would be stronger in 

flexure than the columns, possibly by a significant margin. 

The consequences of failing to meet strong-column/weak-beam requirements 

include the potential for collapse due to column-driven story mechanisms 

occurring prior to mobilization of beam plastic hinging on multiple floors. 

Based on comparisons of collapse probabilities between the ELF and MRSA

methods used to design similar buildings described in this report, assuming 

that the appropriate limit states have been identified and correctly modeled, 

the consistently lower probabilities of collapse for the ELF-based designs 

suggest using higher base shears can minimize the consequences of certain 

design deficiencies. 

H.3.2 Panel Zone Proportioning

AISC 360 requires that panel zones be designed to resist the panel zone shear 

developed by the governing force demands, most likely wind. AISC 341, on 

the other hand, requires that the panel zones be designed to resist the shear 

developed by the yielding of the frame beams. Thus, the R = 3 designs are 

likely to have weaker panel zones, particularly in the designs governed by 
FEMA P-2012 H: Steel Systems Not Specifically Detailed H-3

for Seismic Resistance

wind. The concern would be that excessive panel zone deformation delays 

beam hinging to the point that only the panel zone yields and the resulting 

local column flange deformation would lead to column flange fracture or 

beam flange-to-column flange weld fracture. 

While the influence of weak panel zones was not an area of systematic study 

for this report, designs of taller buildings that had strong panel zones did not 

perform as well as those with panel zones more closely matched to the 

demand generated by the frame beams. This suggests that sharing energy 

dissipation and inelastic deformation between beam hinging and column 

panel zone yielding is desirable and concentrating deformation in either the 

beams or the column panel zones may negatively impact overall 

performance.

H.3.3 Connection Design Philosophy

Connection designs in R = 3 systems use the calculated demand from the 

governing lateral demand (i.e., wind or seismic) based on building code 

forces. On the other hand, most connections in seismic systems designed 

using ASIC 341 are proportioned using the expected strength produced by 

the member delivering forces to the connection. The difference in 

connection strength between R = 3 systems and those designed using AISC 

341 can be significant, particularly for braced frames. Generally, AISC 341 

requires brace connections to be designed to develop the expected strength of 

the brace in tension or using the code-derived forces multiplied by the 

overstrength factor. Given the potentially large difference in connection 

strength, it is suspected that R = 3 systems governed by seismic demands, 

and, perhaps even those governed by wind, may be unacceptably more prone 

to collapse than those designed using AISC 341. It is expected that 

irregularities found to be of significance for systems designed using AISC 

341 would also prove to increase the probability of collapse in R = 3 systems.

H.4 Member Local Buckling and Lateral Bracing 

Requirements

As wind drift would govern in most cases for R = 3 designs, stiffness, not 

strength, would drive the selection of frame beams. For Fy = 50 ksi, 

effectively all wide flanges are considered compact sections and can develop 

the plastic flexural strength, Mp, of the beam before local buckling occurs. 

Local buckling, when it occurs after multiple cycles of yield-level 

displacements, effectively limits the demand placed on beam-to-column 

connections. The primary concern due to local buckling is strength 

degradation and low-cycle fatigue fracture. 
H-4 H: Steel Systems Not Specifically Detailed FEMA P-2012

for Seismic Resistance

Lateral torsional bracing for the frame beams designed to satisfy drift 

demands most likely could be spaced further apart than would be needed to 

develop Mp because the demand is not expected to be that high. Columns, on 

the other hand, being sized essentially for strength, would need to develop 

something on the order of Mp, adjusted for the axial load demand. The 

consequence of lateral torsional buckling of the frame beams is reduced 

frame strength and stiffness coupled with less effective local bracing of the 

columns in the area of high moment demand.

For braced frames, the more stringent local bucking requirements found in 

AISC 341 would not apply to members in the R = 3 frames. Experimental 

testing and post-earthquake damage assessments suggest that relatively thin 

member proportions, especially in HSS sections, can lead to premature brace 

fracture when local buckling occurs. This behavior may render an R = 3

braced frame significantly more vulnerable to collapse than a braced frame 

designed using the requirements of AISC 341 because load redistribution 

cannot occur. It is not known whether the higher seismic force used to 

design R = 3 braced frames provide a sufficient margin of safety against 

collapse. Given the relatively small difference in seismic force obtained for 

R = 3 designs and R = 3.5 ordinary braced frames, it is suspected that R = 3

braced frames governed by seismic demands, rather than by wind, would be 

relatively more prone to collapse. It is expected that irregularities found to 

be of significance for systems designed using AISC 341 would also prove to 

increase the probability of collapse in R = 3 braced frames.

H.5 Less Stringent Material Specifications and 

Inspection Requirements

AISC 360 does not limit the yield strength as does AISC 341, nor does it 

require that welding filler metals achieve a minimum Charpy V-notch 

toughness. In addition, many of the design provisions in AISC 341 are based 

on a mechanism approach that requires use of the expected member strength 

rather than its nominal strength. Although inspection requirements in AISC 

360 have been more explicitly detailed in the relatively new Chapter N, 

AISC 341 requires significantly more stringent inspection requirements, with 

an emphasis on visual inspection rather than nondestructive testing (NDT). 

As the 1994 Northridge earthquake pointed out, over-reliance on NDT can 

produce a false sense of competency and reliability. 
FEMA P-2012 Symbols I-1

Symbols

The following is a list of key symbols referenced in the document, but it is not a

comprehensive list. Many symbols in the list are defined in other standards and 

reports referenced in this document, including FEMA P695 and ASCE/SEI 7-16. 

ACMR = adjusted collapse margin ratio

Cd = deflection amplification factor per Table 12.2-1 of ASCE/SEI

7-16

Cs = seismic response coefficient per Section 12.8.1.1 of ASCE/SEI

7-16

Cu = upper-limit period coefficient per Table 12.8-1 of ASCE/SEI

7-16

CMR = collapse margin ratio

D = effect of dead load for use in load combinations per Section 

2.3.6 of ASCE/SEI 7-16

EIg = gross cross-sectional moment of inertia

Fa = short-period site coefficient (at 0.2-second period) per Section 

11.4.4 of ASCE/SEI 7-16

Fv = long-period site coefficient (at 1.0-second period) per Section 

11.4.4 of ASCE/SEI 7-16

Fy = yield strength of material

′

cf = compressive strength of unconfined concrete, based on standard 

cylinder test

fy = yield stress of longitudinal reinforcement 

g = constant acceleration due to gravity

hn = vertical distance from the base to the highest level of the seismic 

force-resisting system of the structure, per Section 11.3 of 

ASCE/SEI 7-16

k = exponent used in the vertical distribution of seismic forces for 

the ELF procedure, which is intended to approximate the effect 

of higher modes per Section 12.8.3 of ASCE/SEI 7-16
I-2 Symbols FEMA P-2012

L = effect of live load for use in load combinations of Section 2.3.6

of ASCE/SEI 7-16

P = axial load

R = response modification coefficient per Table 12.2-1 of ASCE/SEI

7-16

RC = reinforced concrete

S = snow load per Chapter 2 of ASCE/SEI 7-16

SDS = design, 5% damped, spectral response acceleration parameter at 

short periods per Section 11.4.5 of ASCE/SEI 7-16

SD1 = design, 5% damped, spectral response acceleration parameter at 

a period of 1 second per Section 11.4.5 of ASCE/SEI 7-16

SMS = the MCER, 5% damped, spectral response acceleration parameter 

at short periods adjusted for site class effects per Section 11.4.4

of ASCE/SEI 7-16

SM1 = the MCER, 5% damped, spectral response acceleration parameter 

at a period of 1 second adjusted for site class effects per Section 

11.4.4 of ASCE/SEI 7-16

SS = mapped MCER, 5% damped, spectral response acceleration 

parameter at short periods per Section 11.4.2 and Section 11.4.4 

of ASCE/SEI 7-16

Sa = spectra acceleration, g

Sa(T) = the spectral acceleration at the period, T

SMF = special moment frame

SSF = spectral shape factor

T = the fundamental period of the building, in seconds, based on the 

limits per Section 12.8.2 of ASCE/SEI 7-16 and the approximate 

fundamental period, Ta

T1 = the fundamental period of the building, as determined by 

eigenvalue analysis of the structural model (seconds)

Ta = the approximate fundamental period of the building, in seconds,

as determined in Section 12.8.2.1 of ASCE/SEI 7-16

TIR = torsional irregularity ratio, defined as the ratio of the maximum 

drift at a building’s edge to the average drift given a lateral force 

with 5% eccentricity, as shown in Figure 4-1 in this report
FEMA P-2012 Symbols I-3

Ts = short-period transition period of the building, in seconds, equal 

to SD1/SDS per Section 11.3 of ASCE/SEI 7-16

V = total design lateral force or shear at the base per ASCE/SEI 7-16

Vc = nominal shear strength provided by concrete per ACI 318-14

Vn = nominal shear strength including contributions from concrete 

and steel per ACI 318-14

Vs = nominal shear strength provided by shear reinforcement per ACI 

318-14

Vu = shear demand

W = effective seismic weight of the building as defined in Section 

12.7.2 of ASCE/SEI 7-16

wx = portion of W that is located at or assigned to Level x

x = parameter of Equation 12.8-7 given in Table 12.8-2 of 

ASCE/SEI 7-16

δu = roof displacement used to approximate the ultimate 

displacement capacity of the seismic force-resisting system, as 

derived from pushover analysis

φ = strength reduction factor

μT = period-based ductility of an index archetype model

θp = plastic hinge rotation (radians)

ρ = redundancy factor based on the extent of structural redundancy 

present in a building as defined in Section 12.3.4 of ASCE/SEI 

7-16

ρ (or ρtot) = ratio of total area of longitudinal reinforcement (for columns) or 

ratio of tensile longitudinal reinforcement (for beams)

ρ′ = ratio of compressive longitudinal reinforcement (for beams)

ρsh = area ratio of transverse reinforcement in column hinge region 

Ω = calculated overstrength of an index archetype analysis model

Ω0 = overstrength factor appropriate for use in the load combinations 

of Section 12.4 of ASCE/SEI 7-16 (current values of Ω0 are 

given in Table 12.2-1 of ASCE/SEI 7-16)

FEMA P-2012 Glossary J-1

Glossary

Definitions

Archetype: A prototypical representation of a seismic-force-resisting 

system.

Base Shear: Total design lateral force or shear at the base (ASCE/SEI

7-16).

Building: Any structure whose intended use includes shelter of human 

occupants (ASCE/SEI 7-16).

Collapse Level Earthquake Ground Motions: The level of earthquake 

ground motions that cause collapse of the seismic force-resisting system 

of interest.

DBE: Displacement-based beam-column element used in OpenSees.

Design Earthquake Ground Motions: The earthquake ground motions 

that are two-thirds of the corresponding MCER ground motions 

(ASCE/SEI 7-16).

ELF: Equivalent lateral force procedure for seismic design per Section 12.8 

of ASCE/SEI 7-16.

FBE: Force-based beam-column element used in OpenSees.

GILD: Gravity induced lateral demand.

Incremental Dynamic Analysis: Series of nonlinear response history 

analyses using an input ground motion that is incrementally scaled to 

increasing intensities until collapse is detected in the analysis.

Maximum Considered Earthquake (MCE) Ground Motions: The most 

severe earthquake effects considered, as defined by Section 11.4 of 

ASCE/SEI 7-16. 

Modeling Uncertainty: Collapse uncertainty associated with the quality of 

the index archetype models. 
J-2 Glossary FEMA P-2012

MRSA: Modal response spectrum analysis procedure for seismic design per 

Section 12.9.1 of ASCE/SEI 7-16.

Nonbuilding Structure: A structure, other than a building, constructed of a 

type included in Chapter 15 of ASCE/SEI 7-16.

Non-Simulated Collapse: Structural collapse caused by collapse modes 

that are not represented in the analytical model. Non-simulated collapse 

occurs when a component limit state is exceeded, as defined by 

component fragility functions. 

OMF: Ordinary moment frame.

Seismic Design Category: A classification assigned to a structure based on 

its Risk Category and the severity of design earthquake ground motions 

at the site per Section 11.4 of ASCE/SEI 7-16.

Seismic-Force-Resisting System (SFRS): That part of the structural 

system that is considered to provide the required resistance to seismic 

forces prescribed in ASCE/SEI 7-16.

SFI-MVLEM: Shear-flexure-interaction multi-vertical line-element model 

used in OpenSees.

Simulated Collapse: Structural collapse caused by collapse modes that are 

directly represented in the analytical model. 

Site Class: A classification assigned to a site based on the types of soils 

present and their engineering properties, as defined in Chapter 20 of 

ASCE/SEI 7-16.

SMF: Special moment frame.

Structure: That which is built or constructed and limited to buildings and 

nonbuilding structures per ASCE/SEI 7-16.
FEMA P-2012 References K-1

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FEMA P-2012 References K-3

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developments in FEMA P-58 Seismic Risk Assessment of Wood 

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K-4 References FEMA P-2012

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the Federal Emergency Management Agency, Washington, D.C.

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Development of Seismic Regulations for New Buildings, FEMA 95, 

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the Federal Emergency Management Agency, Washington, D.C.

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FEMA, 2012a, Seismic Evaluation and Retrofit of Multi-Unit Wood-Frame 

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FEMA P-2012 References K-5

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Technology, Caracas, Venezuela.

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Gupta, A., and Krawinkler, H., 1999, Seismic Demands for the Performance 

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Haselton, C.B., Liel, A.B., Lange, S.T., and Deierlein, G.G., 2008, BeamColumn Element Model Calibrated for Predicting Flexural Response 

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Haselton, C.B., Liel, A.B., Deierlein, G.G., Dean, B.S., and Chou, J.H., 

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IDIEM, 2010, Peritaje Estructural Edificio Alto Río, Ciudad de Concepción, 

Informe Final, Descripción de Caida y Factores Asociados al 

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Estructural en La República de Panamá, Ministry of Public Works, 

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shear-flexure interaction in reinforced concrete structural walls. Part 

I: Theory,” Journal of Structural Engineering, Vol. 141, No. 5.

Kolozvari, K., Tran, T.A., Orakcal, K., and Wallace, J.W., 2015b, “Modeling 

of cyclic shear-flexure interaction in reinforced concrete structural 

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FEMA P-2012 References K-7

Kolozvari, K., Orakcal, K., and Wallace, J.W., 2018, “New OpenSees

models for simulation of nonlinear flexural and shear-flexural 

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torsion,” Proceedings, 2016 SEAOC Convention, Maui, Hawaii.

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Lignos, D.G., Krawinkler, H., and Whittaker, A.S., 2011, “Prediction and 

validation of sidesway collapse of two scale models of a 4-story steel 

moment frame,” Earthquake Engineering & Structural Dynamics, 

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MacRae, G., and Deam, B., 2009, Building Regularity for Simplified 

Modeling, EQC Project No. 06/514, University of Canterbury, 

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seismic code provisions for vertically irregular frames,” 

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K-8 References FEMA P-2012

Marius, M., 2013, “Seismic behaviour of reinforced concrete shear walls 

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McKenna, F., Fenves, G.L., Scott, M.H., and Jeremie, B., 2000, Open System 

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Michalis, F., Dimitrios, V., and Manolis, P., 2006, “Evaluation of influence 

of vertical irregularities on the seismic performance of a nine-storey 

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Quality Supervision and Quarantine Bureau, 2001, Code for Seismic 

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Moehle, J., Lehman, D., and Lowes, L., 2006, “Beam-column connections,”

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Earthquake Engineering Research Institute (EERI) Technical 

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McGraw-Hill, New York, New York.

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FEMA P-2012 References K-9

NISEE, 1971b, Karl V. Steinbrugge Collection, NISEE/PEER/UCB, 

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NISEE, 1987, Karl V. Steinbrugge Collection, NISEE/PEER/UCB, National 

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NISEE, 1989, Loma Prieta Collection, NISEE/PEER/UCB, National 

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K-10 References FEMA P-2012

NIST, 2010, Evaluation of the FEMA P-695 Methodology for Quantification 

of Building Seismic Performance Factors, NIST GCR 10-917-8, 

prepared by NEHRP consultants Joint Venture, a partnership of the 

Applied Technology Council and the Consortium of the Universities 

for Research in Earthquake Engineering, for the National Institute of 

Standards and Technology, Gaithersburg, Maryland.

NIST, 2011, Seismic Design of Cast-in-Place Concrete Special Structural 

Walls and Coupling Beams: A Guide for Practicing Engineers, NIST 

GCR 11-917-11REV-1, prepared by NEHRP consultants Joint 

Venture, a partnership of the Applied Technology Council and the 

Consortium of the Universities for Research in Earthquake 

Engineering, for the National Institute of Standards and Technology, 

Gaithersburg, Maryland. Revised 2012.

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Design Criteria for New Buildings, NIST GCR 12-917-20, prepared 

by NEHRP consultants Joint Venture, a partnership of the Applied 

Technology Council and the Consortium of the Universities for 

Research in Earthquake Engineering, for the National Institute of 

Standards and Technology, Gaithersburg, Maryland. 

NIST, 2013, Development of NIST Measurement Science R&D Roadmap: 

Earthquake Risk Reduction in Buildings, NIST GCR 13-917-23,

prepared by the National Institute of Building Sciences for the 

National Institute of Standards and Technology, Gaithersburg, 

Maryland. 

NIST, 2014, Recommendations for Seismic Design of Reinforced Concrete 

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the Consortium of the Universities for Research in Earthquake 

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FEMA P-2012 References K-11

Obayashi, 1995, Preliminary Report on the 1995 Southern Hyogo Prefecture 

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K-12 References FEMA P-2012

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FEMA P-2012 References K-13

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FEMA P-2012 Project Participants L-1 

Project Participants

FEMA Oversight

Michael (Mai) Tong (Project Officer)

Federal Emergency Management Agency

400 C Street, SW, Suite 313 

Washington, D.C. 20472 

Farzad Naeim (Subject Matter Expert) 

Farzad Naeim, Inc.

100 Spectrum Center Drive, Suite 900 

Irvine, California 92618

ATC Management and Oversight

Jon A. Heintz (Program Executive, Program Manager)

Applied Technology Council

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

Veronica Cedillos (Project Manager)

Applied Technology Council

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

Ayse Hortacsu (Project Manager)

Applied Technology Council

201 Redwood Shores Parkway, Suite 240 

Redwood City, California 94065 

Project Technical Committee

Michael Valley (Project Technical Director)

Magnusson Klemencic Associates

1301 Fifth Avenue, Suite 3200 

Seattle, Washington 98101 

Curt Haselton 

Haselton Baker Risk Group, LLC

728 Cherry Street, Suite C 

Chico, California 95928 

Charles A. Kircher

Kircher & Associates

1121 San Antonio Road, Suite D-202 

Palo Alto, California 94303 

Laura N. Lowes 

University of Washington

233C More Hall, 352700 

Seattle, Washington 98195 

Rafael Sabelli

Walter P Moore

595 Market Street, Suite 2130

San Francisco, California 94105 

Thomas A. Sabol 

Englekirk Structural Engineers

888 South Figueroa Street, Eighteenth Floor 

Los Angeles, California 90017 

Project Review Panel

Gregory G. Deierlein

Stanford University

318 Parkside Drive 

Palo Alto, California 94306 

Larry A. Fahnestock

University of Illinois

620 Pittsfield Drive 

Champaign, Illinois 61822 
L-2 Project Participants FEMA P-2012

James R. Harris

J. R. Harris & Company

1175 Sherman Street, Suite 2000

Denver, Colorado 80203

Conrad Hohener

Degenkolb Engineers

300 South Grand Avenue, Suite 3850

Los Angeles, California 90071

John Hooper

Magnusson Klemencic Associates

1301 Fifth Avenue, Suite 3200

Seattle, Washington 98101

Ryan A. Kersting

Buehler & Buehler Structural Engineers

600 Q Street, Suite 200

Sacramento, California 95814

Roberto Leon*

Virginia Tech 

102D Patton Hall (0105)

Blacksburg, Virginia 24061

*ATC Board Contact

Working Group

Kamal Ahmed

University of Washington

Box 352700

Seattle, Washington 98195

Dustin Cook

Haselton Baker Risk Group, LLC

728 Cherry Street, Suite C

Chico, California 95928

D. Jared DeBock

California State University, Chico

400 West 1st Street

Chico, California 95929

Sara Essila

Haselton Baker Risk Group, LLC

728 Cherry Street, Suite C

Chico, California 95928

Katie Fitzgerald

Haselton Baker Risk Group, LLC

728 Cherry Street, Suite C

Chico, California 95928

Heavenz Kaur

Englekirk Structural Engineers

888 South Figueroa Street, Eighteenth Floor

Los Angeles, California 90017

Kristijan Kolozvari

California State University, Fullerton

800 N. State College Boulevard

Fullerton, California 92834

Dawn Lehman

University of Washington

214B Moore Hall, Box 352700

Seattle, Washington 98195

Nasser Marafi

University of Washington

2209 North 38th Street

Seattle, Washington 98103

Diane Nishi

Englekirk Structural Engineers

888 South Figueroa Street, Eighteenth Floor

Los Angeles, California 90017

Josh Pugh

Department of Civil and Environmental Engineering

Seattle University

901 12th Avenue, ENGR 525

Seattle, Washington 98122

Ricardo Roldan

Englekirk Structural Engineers

888 South Figueroa Street, Eighteenth Floor

Los Angeles, California 90017

Negin A. Tauberg

University of California, Los Angeles

405 Hilgard Avenue

Los Angeles, California 90024
FEMA P-2012 Project Participants L-3

Tsenguun Tsoqbadrakh

University of Washington

2209 North 38th Street

Seattle, Washington 98103

Workshop Participants

David Bonneville

Degenkolb

1300 Clay Street, 9th Floor

Oakland, California 94612

Dan Dolan

Washington State University

405 Spokane Street, Sloan 101

Pullman, Washington 99164

Anindya Dutta

Simpson Gumpertz & Heger, Inc.

100 Pine Street, Suite 1600

San Francisco, California 94111

Ken Elwood

The University of Auckland

Dept. of Civil and Environmental Engineering

3 Grafton Road

Auckland, New Zealand

Michael Gannon

American Institute of Steel Construction

1 E Upper Wacker Drive

Chicago, Illinois 60601

S. K. Ghosh

S. K. Ghosh Associates Inc.

334 East Colfax Street, Unit E

Palatine, Illinois 60067

Ronald O. Hamburger

Simpson Gumpertz & Heger, Inc.

100 Pine Street, Suite 1600

San Francisco, California 94111

Robert D. Hanson

Federal Emergency Management Agency

500 C Street, SW

Washington, DC 20472

Bret Lizundia

Rutherford + Chekene

375 Beale Street, Suite 310

San Francisco, California 94105

James O. Malley

Degenkolb Engineers

375 Beale Street, Suite 500

San Francisco, California 94105

Justin Moresco

Applied Technology Council

201 Redwood Shores Parkway, Suite 240

Redwood City, California 94065

Kevin Wong

National Institute of Standards and Technology

Engineering Laboratory

100 Bureau Drive

Gaithersburg, Maryland 20899

Noelle Yuen

Maffei Structural Engineering

98 Battery Street, Suite 300

San Francisco, California 94111

Farzin Zareian

University of California, Irvine

The Henry Samueli School of Engineering

Irvine, California 92697


FEMA P-2012 

Catalog No. 18166-1