FEDERAL EMERGENCY MANAGEMENT AGENCY FEMA 307/ May 1999 
FEMA 307 
EVALUATION OF EARTHQUAKE DAMAGED CONCRETE AND MASONRY WALL BUILDINGS 
Technical Resources Prepared by: LNTC The Applied Technology Council 555 Twin Dolphin Drive, Suite 550 Redwood City, California 94065 Prepared for: The Partnership for Response and Recovery Washington, D.C.
Funded by: Federal Emergency Management Agency 1998 
Applied Technology Council 
The Applied Technology Council (ATC) is a nonprofit, tax-exempt corporation established in 1971 through the efforts of the Structural Engineers Association of California.
ATC is guided by a Board of Directors consisting of representatives appointed by the American Society of Civil Engineers, the Structural Engineers Association of California, the Western States Council of Structural Engineers Associations, and four at-large representatives concerned with the practice of structural engineering. Each director serves a three-year term.
The purpose of ATC is to assist the design practitioner in structural engineering (and related design specialty fields such as soils, wind, and earthquake) in the task of keeping abreast of and effectively using technological developments. ATC also identifies and encourages needed research and develops consensus opinions on structural engineering issues in a nonproprietary format. ATC thereby fulfills a unique role in funded information transfer.
Project management and administration are carried out by a full-time Executive Director and support staff. Project work is conducted by a wide range of highly qualified consulting professionals, thus incorporating the experience of many individuals from academia, research, and professional practice who would not be available from any single organization. Funding for ATC projects is obtained from government agencies and from the private sector in the form of tax-deductible contributions.
1998-1999 Board of Directors 
Charles H. Thornton, President Edwin H. Johnson Edwin T. Dean, Vice President Kenneth A. Luttrell Andrew T. Merovich, Secretary/ Newland J. Malmquist Treasurer Stephen H. Pelham C. Mark Saunders, Past President Richard J. Phillips James R. Cagley Charles W. Roeder Arthur N. L. Chiu Jonathan G. Shipp Robert G. Dean 
Notice 
This report was prepared under Contract EMW-95-C-4685 between the Federal Emergency Management Agency and the Partnership for Response and Recovery.
Any opinions, findings, conclusions, or recommendations expressed in this publication do not necessarily reflect the views of the Applied Technology Council (ATC), the Partnership for Response and Recovery (PaRR), or the Federal Emergency Management Agency (FEMA). Additionally, neither ATC, PaRR, 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.
For further information concerning this document or the activities of the ATC, contact the Executive Director, Applied Technology Council, 555 Twin Dolphin Drive, Suite 550, Redwood City, California 94065+ADs- phone 650-595-1542+ADs-fax 650-593-2320+ADs- e-mail atc+AEA-atcouncil.org.
Preface 
Following the two damaging California earthquakes in 1989 (Loma Prieta) and 1994 (Northridge), many concrete wall and masonry wall buildings were repaired using federal disaster assistance funding. The repairs were based on inconsistent criteria, giving rise to controversy regarding criteria for the repair of cracked concrete and masonry wall buildings. To help resolve this controversy, the Federal Emergency Management Agency (FEMA) initiated a project on evaluation and repair of earthquake damaged concrete and masonry wall buildings in 1996. The project was conducted through the Partnership for Response and Recovery (PaRR), a joint venture of Dewberry +ACY- Davis of Fairfax, Virginia, and Woodward-Clyde Federal Services of Gaithersburg, Maryland. The Applied Technology Council (ATC), under subcontract to PaRR, was responsible for developing technical criteria and procedures (the ATC-43 project).
The ATC-43 project addresses the investigation and evaluation of earthquake damage and discusses policy issues related to the repair and upgrade of earthquake- damaged buildings. The project deals with buildings whose primary lateral-force-resisting systems consist of concrete or masonry bearing walls with flexible or rigid diaphragms, or whose vertical-load-bearing systems consist of concrete or steel frames with concrete or masonry infill panels. The intended audience is design engineers, building owners, building regulatory officials, and government agencies.
The project results are reported in three documents. The FEMA 306 report, Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings, Basic Procedures Manual, provides guidance on evaluating damage and analyzing future performance. Included in the document are component damage classification guides, and test and inspection guides. FEMA 307, Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings, Technical Resources, contains supplemental information including results from a theoretical analysis of the effects of prior damage on single-degree-of-freedom mathematical models, additional background information on the component guides, and an example of the application of the basic procedures. FEMA 308, The Repair of Earthquake Damaged Concrete and Masonry Wall Buildings, discusses the policy issues pertaining to the repair of earthquake damaged buildings and illustrates how the procedures developed for the project can be used to provide a technically sound basis for policy decisions. It also provides guidance for the repair of damaged components.
The project also involved a workshop to provide an opportunity for the user community to review and comment on the proposed evaluation and repair criteria.
The workshop open to the profession at large, was held in Los Angeles on June 13, 1997 and was attended by 75 participants.
The project was conducted under the direction of ATC Senior Consultant Craig Comartin, who served as Co- Principal Investigator and Project Director. Technical and management direction were provided by a Technical Management Committee consisting of Christopher Rojahn (Chair), Craig Comartin (Co- Chair), Daniel Abrams, Mark Doroudian, James Hill, Jack Moehle, Andrew Merovich (ATC Board Representative), and Tim McCormick. The Technical Management Committee created two Issue Working Groups to pursue directed research to document the state of the knowledge in selected key areas: (1) an Analysis Working Group, consisting of Mark Aschheim (Group Leader) and Mete Sozen (Senior Consultant) and (2) a Materials Working Group, consisting of Joe Maffei (Group Leader and Reinforced Concrete Consultant), Greg Kingsley (Reinforced Masonry Consultant), Bret Lizundia (Unreinforced Masonry Consultant), John Mander (Infilled Frame Consultant), Brian Kehoe and other consultants from Wiss, Janney, Elstner and Associates (Tests, Investigations, and Repairs Consultant). A Project Review Panel provided technical overview and guidance. The Panel members were Gregg Borchelt, Gene Corley, Edwin Huston, Richard Klingner, Vilas Mujumdar, Hassan Sassi, Carl Schulze, Daniel Shapiro, James Wight, and Eugene Zeller. Nancy Sauer and Peter Mork provided technical editing and report production services, respectively.
Affiliations are provided in the list of project participants.
The Applied Technology Council and the Partnership for Response and Recovery gratefully acknowledge the cooperation and insight provided by the FEMA Technical Monitor, Robert D. Hanson.
Tim McCormick PaRR Task Manager 
Christopher Rojahn ATC-43 Principal Investigator ATC Executive Director Technical Resources FEMA 307 Technical Resources ill 
Table of Contents 
Preface iii ix 
List of Figures.
List of Tables.x. xiii 
Prologue xv 1.
Introduction 1 
1.1 Purpose And Scope. 1 
1.2 Materials Working Group. 1 
1.2.1 Tests and Investigations. 1 
1.2.2 Component Behavior and Modeling. 1 
1.2.3 Repair Techniques. 2 
1.3 Analysis Working Group. 3 
1.4 References. 4 
2. Reinforced Concrete Components. 7 
2.1 Commentary and Discussion. 7 
2.1.1 Development of Component Guides and A-Factors. 7 
2.2 Typical Force-Displacement Hysteretic Behavior 10 
2.3 Tabular Bibliography 28 
2.4 Symbols for Reinforced Concrete.33 
2.5 References for Reinforced Concrete 35 
3. Reinforced Masonry 39 
3.1 Commentary and Discussion 39 
3.1.1 Typical Hysteretic Behavior.39 
3.1.2 Cracking and Damage Severity.39 
3.1.3 Interpretation of Tests.46 
3.2 Tabular Bibliography for Reinforced Masonry 46 
3.3 Symbols for Reinforced Masonry.53 
3.4 References for Reinforced Masonry 54 
4. Unreinforced Masonry.59 
4.1 Commentary and Discussion 59 
4.1.1 Hysteretic Behavior of URM Walls Subjected to In-Plane Demands.59 
4.1.2 Comments on FEMA 273 Component Force/Displacement Relationships 72 
4.1.3 Development of A-factors 75 
4.2 Tabular Bibliography for Unreinforced Masonry 77 
4.3 Symbols for Unreinforced Masonry.80 
4.4 References for Unreinforced Masonry 81 FEMA 307 Technical Resources v 
5. Infilled Frames.85 
5.1 Commentary And Discussion I 85 
5.1.1 Development of A-Factors for Component Guides. 85 
5.1.2 Development of Stiffness Deterioration-AK.85 
5.1.3 The Determination of XQ for Strength Deterioration 86 
5.1.4 Development of AD-Reduction in Displacement Capability +ADs- 87 
5.2 Tabular Bibliography for Infilled Frames 89 
5.3 References for Infilled Frames 91 
6. Analytical Studies 95 6.1 Overview 95 
6.2 Summary of Previous Findings 95 
6.2.1 Hysteresis Models 95 
6.2.2 Effect of Ground Motion Duration 98 
6.2.3 Residual Displacement 98 
6.2.4 Repeated Loading 98 
6.3 Dynamic Analysis Framework.99 
6.3.1 Overview 99 
6.3.2 Dynamic Analysis Approach 99 
6.3.3 Ground Motions 100 
6.3.4 Force/Displacement Models 120 
6.3.5 Undamaged Oscillator Parameters 122 
6.3.6 Damaged Oscillator Parameters 123 
6.3.7 Summary of Dynamic Analysis Parameters 125 
6.3.8 Implementation of Analyses 126 
6.4 Results Of Dynamic Analyses 126 
6.4.1 Overview and Nomenclature 126 
6.4.2 Response of Bilinear Models 127 
6.4.3 Response of Takeda Models 127 
6.4.4 Response Statistics 151 
6.5 Nonlinear Static Procedures 155 
6.5.1 Introduction 155 
6.5.2 Description of Nonlinear Static Procedures 156 
6.5.3 Comments on Procedures 159 
6.5.4 Application of Procedures to Undamaged and Damaged Oscillators 160 
6.6 Comparison of NSP and Dynamic Analysis Results 160 
6.6.1 Introduction 160 
6.6.2 Displacement Estimation 160 
6.6.3 Displacement Ratio Estimation 161 
6.7 Conclusions and Implications 177 
6.8 References 178 
7. Example Application 181 
7.1 Introduction 181 Technical Resources FEMA 307 
7.1.2 Organization.181 
7.2.1 Building Description.183 
7.2.2 Postearthquake Damage Observations.183 
7.2.3 Preliminary Classification (by Observation) of Component Types, Behavior Modes, and Damage Severity.189 
7.2.4 Final Classification (by Analysis) of Component Type, Behavior Mode and Damage Severity.190 
7.2.5 Other Damage Observations.195 
7.2.6 Summary of Component Classifications.195 7.3 Evaluation by the Direct Method 199 
7.3.1 Structural Restoration Measures.199 
7.3.2 Nonstructural Restoration Measures.201 
7.3.3 Restoration Summary and Cost.201 7.4 Evaluation by Performance Analysis 201 
7.4.1 Performance Objectives.202 
7.4.2 Nonlinear Static Analysis.203 
7.4.3 Force-Displacement Capacity (Pushover Analysis) Results.206 
7.4.4 Estimation of Displacement, de, Caused by Damaging Earthquake.209 
7.4.5 Displacement Demand 210 
7.4.6 Analysis of Restored Structure.212 
7.4.7 Performance Restoration Measures.214 
7.5 Discussion of Results 214 214
7.5.1 Discussion of Building Performance.
7.5.2 Discussion of Methodology and Repair Costs.215 
7.6 References 215 
Appendix A. Component Damage Records for Building Evaluated in Example Application.217 
ATC-43 Project Participants. 237 
Applied Technology Council Projects And Report Information.241 
181 7.1.1 Objectives.
183 7.2 Investigation.
FEMA 307 Technical Resources 
Figure 1-1 Component Force-Deformation Relationships 2 
Figure 1-2 Generalized Undamaged and Damaged Component Curves 3 
Figure 1-3 Effect of Damage on Building Response 4 
Figure 1-4 Global Load-Displacement Relationships 5 
Figure 2-1 Diagram of process used to develop component guides and component modification factors. 8 
Figure 4-1 Bed-joint sliding force/displacement relationship 73 
Figure 4-2 Relationship Between Toe Crushing and Bed-Joint Sliding 74 
Figure 4-3 Developing the initial portion of the damaged force/displacement relationship 76 
Figure 5-1 Energy-based damage analysis of strength reduction to define AQ 88 
Figure 6-1 Effect of Hysteretic Properties on Response to 1940 NS El Centro Record (from Nakamura, 1988).
97 
Figure 6-2 Characteristics of the WN87MWLN.090 (Mount Wilson) Ground Motion 102 
Figure 6-3 Characteristics of the BB92CIVC.360 (Big Bear) Ground Motion 103 
Figure 6-4 Characteristics of the SP88GUKA.360 (Spitak) Ground Motion 104 
Figure 6-5 Characteristics of the LP89CORR.090 (Corralitos) Ground Motion 105 
Figure 6-6 Characteristics of the NR94CENT.360 (Century City) Ground Motion 106 
Figure 6-7 Characteristics of the IV79ARY7.140 (Imperial Valley Array) Ground Motion 107 
Figure 6-8 Characteristics of the CH85LLEO.010 (Llolleo) Ground Motion 108 
Figure 6-9 Characteristics of the CH85VALP.070 (Valparaiso University) Ground Motion 109 
Figure 6-10 Characteristics of the IV40ELCN. 180 (El Centro) Ground Motion 110 
Figure 6-11 Characteristics of the TB78TABS.344 (Tabas) Ground Motion 111 
Figure 6-12 Characteristics of the LN92JOSH.360 (Joshua Tree) Ground Motion 112 
Figure 6-13 Characteristics of the MX85SCT1.270 (Mexico City) Ground Motion 113 
Figure 6-14 Characteristics of the LN92LUCN.250 (Lucerne) Ground Motion 114 
Figure 6-15 Characteristics of the IV79BRWY.315 (Brawley Airport) Ground Motion 115 
Figure 6-16 Characteristics of the LP89SARA.360 (Saratoga) Ground Motion 116 
Figure 6-17 Characteristics of the NR94NWHL.360 (Newhall) Ground Motion 117 
Figure 6-18 Characteristics of the NR94SYLH.090 (Sylmar Hospital) Ground Motion 118 
Figure 6-19 Characteristics of the KO95TTRI.360 (Takatori) Ground Motion 119 
Figure 6-20 Force-Displacement Hysteretic Models.
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Figure 6-21 Degrading Models Used in the Analyses 121 
Figure 6-22 Bilinear Model Used to Determine Strengths of Degrading Models 122 
Figure 6-23 Specification of the Pinching Point for the Takeda Pinching Model 122 
Figure 6-24 Specification of the Uncracked Stiffness, Cracking Strength, and Unloading Stiffness for the Takeda Models 123 
Figure 6-25 Construction of Initial Force-Displacement Response for Prior Ductility Demand +AD4- 0 and Reduced Strength Ratio +AD0- 1 123 
Figure 6-26 Construction of Initial Force-Displacement Response for PDD+AD4- 0 and RSR+ADw- 1 for Takeda5 and TakedalO Models 124 List of Figures FEMA 307 Technical Resources 
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Figure 6-49 Strength Degradation for Takeda Pinching Model 125 Construction of Initial Force-Displacement Response for PDD+AD4- 0 and RSR+ADw- 1 for Takeda Pinching Model 126 Response of Bilinear Oscillators to Short Duration Records (DDD+AD0- 8).
128 Response of Bilinear Oscillators to Long Duration Records (DDD+AD0- 8).
129 Response of Bilinear Oscillators to Forward Directive Records (DDD+AD0- 8).
130 Displacement Response of Takeda Models Compared with Elastic Response and Bilinear Response, for Short-Duration Records (DDD+AD0- 8 and RSR+AD0- 1).
131 Displacement Response of Takeda Models Compared with Elastic Response and Bilinear Response for Long-Duration Records (DDD+AD0- 8 and RSR+AD0- 1) 132 Displacement Response of Takeda Models Compared with Elastic Response and Bilinear Response for Forward Directive Records (DDD+AD0- 8 and RSR+AD0- 1) 133 Effect of Cracking Without and With Strength Reduction on Displacement Response of TakedaS Models, for Short-Duration Records (DDD+AD0- 8 and PDD+AD0- 1) 135 Effect of Cracking Without and With Strength Reduction on Displacement Response of Takeda5 Models, for Long-Duration Records (DDD+AD0- 8 and PDD+AD0- 1) 136 Effect of Cracking Without and With Strength Reduction on Displacement Response of TakedaS Models, for Forward Directive Records (DDD+AD0- 8 and PDD+AD0- 1) 137 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement Response of TakedaS Models, for Short Duration Records (DDD+AD0- 8 and PDD+AD0- 8) 138 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement Response of Takeda5 Models, for Long Duration Records (DDD+AD0- 8 and PDD+AD0- 8) 139 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement Response of Takeda5 Models, for Forward Directive Records (DDD+AD0- 8 and PDD+AD0- 8) 140 Effect of Damage on Response to El Centro (IV40ELCN. 180)for Takeda5, T+AD0-0.2 sec (DDD+AD0- 8) 141 Effect of Damage on Response to El Centro (IV40ELCN.180) for Takeda5, T+AD0-0.5 sec (DDD+AD0- 8) 142 Effect of Damage on Response to El Centro (IV40ELCN. 180) for Takeda5, T+AD0-1.0 sec (DDD+AD0- 8) 143 Effect of Damage on Response to El Centro (IV40ELCN.180) for TakedaS, T+AD0-1.5 sec (DDD+AD0- 8) 144 Effect of Damage on Response to El Centro (IV40ELCN.180) for Takeda5, T+AD0-2.0 sec (DDD+AD0- 8) I 145 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement Response of TakPinch Models, for Short Duration Records (DDD+AD0- 8 and PDD+AD0- 8) 146 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement Response of TakPinch Models, for Long Duration Records (DDD+AD0- 8 and PDD+AD0- 8) 147 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement Response of TakPinch, for Forward Directive Records (DDD+AD0- 8 and PDD+AD0- 8) 148 Effect of Damage on Response of TakPinch Model to El Centro (IV40ELCN.180) for Technical Resources FEMA 307 
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Figure 6-75 T+AD0-1.0 sec and RSR+AD0- 1 (DDD+AD0- 8) 149 Effect of Damage on Response of TakPinch Model to El Centro (IV40ELCN. 180) for T+AD0-1.0 sec and RSR +AD0- 0.6 (DDD+AD0- 8) 150 Effect of Cracking on Displacement Response of TakedalO Model for Short Duration Records (DDD+AD0- 8 and PDD+AD0-1).151Effect of Cracking on Displacement Response of TakedalO Model for Long-Duration Records (DDD+AD0- 8 and PDD+AD0-1).152Effect of Cracking on Displacement Response of TakedalO Model for Forward Directive Records (DDD+AD0- 8 and PDD+AD0-1).152Effect of Damage on Response of TakedalO Model to El Centro (IV40ELCN.180) for T+AD0-l.0 sec and RSR+AD0- 1 (DDD+AD0- 8).153 Mean and Standard Deviation Values of d'dIdd for TakedaS Model.154Mean and Standard Deviation Values of d'ddd for TakPinch Model. 155 Percent of TakedalO Oscillators that Collapsed.156Construction of Effective Stiffness for use with the Displacement Coefficient Method. 157 Initial Effective Stiffness and Capacity Curves Used in the Secant and Capacity Spectrum Methods.158Schematic Depiction of Secant Method Displacement Estimation.158Schematic Depiction of Successive Iterations to Estimate Displacement Response Using the Secant Method for Single-Degree-of-Freedom Oscillators.159Schematic Depiction of Successive Iterations to Estimate Displacement Response Using the Capacity Spectrum Method.159.Values of dd,NSPIdd for the'Takeda5 Model +ADs- 162Mean values of dd,NSP Idd for all ground motions for each NSP method, for short and long-period Takeda5 Models. See text in Section 6.6.3 t. 163 Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Short-Duration Records.163Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Long-Duration Records.164Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Forward Directive Records.164Secant Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Short-Duration Records.165Secant Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Long-Duration Records.165Secant Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Forward Directive Records.166Capacity Spectrum Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Short-Duration Records.166Capacity Spectrum Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Long-Duration Records.167Capacity Spectrum Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement Normalized by Computed Ratio, for Forward Directive Records.167Coefficient Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 Takeda5 Oscillators having DDD+AD0- 8 and PDD+AD0- 1.168 
Figure 6-50 Coefficient Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 Technical Resources FEMA 307 Technical Resources 
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Figure 7-15 Coefficient Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 Takeda5 Oscillators having DDD+AD0- 8 and PDD+AD0- 1.170173 Capacity Spectrum Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 TakedaS Oscillators having DDD+AD0- 8 and PDD+AD0- 1.174Capacity Spectrum Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 TakedaS Oscillators having DDD+AD0- 8 and PDD+AD0- 1.175Capacity Spectrum Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 Takeda5 Oscillators having DDD+AD0- 8 and PDD+AD0- 1.176Flowchart for Example.182Floor Plans.184Building Cross-section 185 Example Solid Wall Detail.185Example Coupled Wall Detail.186Solid Wall Example.187Coupled Wall Example I 188 Detail of Coupling Beam Replacement.202Response Spectra for Selected Performance Levels 203.
204Mathematical Model of Coupled Shear Wall.
Mathematical Model of Full Building.205Component Force-Displacement Curves for Coupling Beams.207Comparison of Pre-event and Post-event Pushover Curves.208Response Spectra from Damaging Earthquake.209Comparison of Pre-event and Repaired Pushover Curves.213FEMA 307 Technical Resources xii. Technical Resources FEIVA 307 169 TakedaS Oscillators having DDD- 8 and PDD+AD0- 1 I.
Secant Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 171 Takeda5 Oscillators having DDD+AD0- 8 and PDD+AD0- 1.
Secant Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 172 TakedaS Oscillators having DDD+AD0- 8 and PDD+AD0- 1.
Secant Method Estimates of Displacement Ratio of RSR+AD0-0.6 and RSR+AD0-1.0 Takeda5 Oscillators having DDD+AD0- 8 and PDD+AD0- 1.
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Table 7-8 Damage Patterns and Hysteretic Response for Reinforced Masonry Components 40 Ranges of Reinforced Masonry Component Displacement Ductility, 11A, Associated with Damage Severity Levels and A Factors ,. 47 Annotated Bibliography for Reinforced Masonry 48 Summary of Significant Experimental Research or Research Summaries 78 Tabular Bibliography for Infilled Frames 89 Recorded Ground Motions Used in the Analyses.101 Capacity of Potential Behavior Modes for Typical Solid Wall 191 Capacity of Potential Behavior Modes for Typical Coupling Beam 193 Shear Capacities for Potential Behavior Modes of Wall Pier (RC1) Components in Coupled Wall.194Summary of Component Type, Behavior Mode, and Damage Severity for Wall Components (North-South Direction) 200 Summary of Component Type, Behavior Mode, and Damage Severity for Wall Components (East-West Direction) 201 Restoration Cost Estimate by the Direct Method..202 Performance Indices for Pre-event and Post-event Structures.-212 Restoration Cost Estimate by the Relative Performance Method t 214 List of Tables+ACIAJQ- Ranges of Reinforced Concrete Component Displacement Ductility, pua,Associated 9 with Damage Severity Levels and AFactors.9.
29 Key References on Reinforced Concrete Wall Behavior. I.
Technical Resources FEMA 307 Technical Resources 
Prologue 
This document is one of three to result from the ATC-43 project funded by the Federal Emergency Management Agency (FEMA). The goal of the project is to develop technically sound procedures to evaluate the effects of earthquake damage on buildings with primary lateral- force-resisting systems consisting of concrete or masonry bearing walls or infilled frames. The procedures are based on the knowledge derived from research and experience in engineering practice regarding the performance of these types of buildings and their components. The procedures require thoughtful examination and review prior to implementation. The ATC-43 project team strongly urges individual users to read all of the documents carefully to form an overall understanding of the damage evaluation procedures and repair techniques.
Before this project, formalized procedures for the investigation and evaluation of earthquake-damaged buildings were limited to those intended for immediate use in the field to identify potentially hazardous conditions. ATC-20, Procedures for Postearthquake Safety Evaluation of Buildings, and its addendum, ATC- 20-2 (ATC, 1989 and 1995) are the definitive documents for this purpose. Both have proven to be extremely useful in practical applications. ATC-20 recognizes and states that in many cases, detailed structural engineering evaluations are required to investigate the implications of earthquake damage and the need for repairs. This project provides a framework and guidance for those engineering evaluations.
What have we learned? 
The project team for ATC-43began its work with a thorough review of available analysis techniques, field observations, test data, and emerging evaluation and design methodologies. The first objective was to understand the effects of damage on future building performance. The main points are summarized below.
+ACo- Component behavior controls global performance.
Recently developed guidelines for structural engineering seismic analysis and design techniques focus on building displacement, rather than forces as the primary parameter for the characterization of seismic performance. This approach models the building as an assembly of its individual components. Force-deformation properties (e.g., elastic stiffness, yield point, ductility) control the behavior of wall panels, beams, columns, and other components. The component behavior, in turn, governs the overall displacement of the building and its seismic performance. Thus, the evaluation of the effects of damage on building performance must concentrate on how component properties change as a result of damage.
+ACo- Indicators of damage (e.g., cracking, spalling) are meaningful only in light of the mode of component behavior.
Damage affects the behavior of individual components differently.Some exhibit ductile modes of post-elastic behavior, maintaining strength even with large displacements. Others are brittle and lose strength abruptly after small inelastic displacements. The post-elastic behavior of a structural component is a function of material properties, geometric proportions, details of construction, and the combination of demand actions (axial, flexural, shearing, torsional) imposed upon it. As earthquake shaking imposes these actions on components, the components tend to exhibit predominant modes of behavior as damage occurs. For example, if earthquake shaking and its associated inertial forces and frame distortions cause a reinforced concrete wall panel to rotate at each end, statics defines the relationship between the associated bending moments and shear force.
The behavior of the panel depends on its strength in flexure relative to that in shear. Cracks and other signs of damage must be interpreted in the context of the mode of component behavior. A one-eighth- inch crack in a wall panel on the verge of brittle shear failure is a very serious condition. The same size crack in a flexurally-controlled panel may be insignificant with regard to future seismic performance. This is, perhaps, the most important finding of the ATC-43 project: the significance of cracks and other signs of damage, with respect to the future performance of a building, depends on the mode of behavior of the components in which the damage is observed.
xv Technical Resources FEMA 307 Technical Resources xv Prologue 
+ACo- Damage may reveal component behavior that differs from that predicted by evaluation and design methodologies.
When designing a building or evaluating an undamaged building, engineers rely on theory and their own experience to visualize how earthquakes will affect the structure. The same is true when they evaluate the effects of actual damage after an earthquake, with one important difference. If engineers carefully observe the nature and extent of the signs of the damage, they can greatly enhance their insight into the way the building actually responded to earthquake shaking. Sometimes the actual behavior differs from that predicted using design equations or procedures. This is not really surprising, since design procedures must account conservatively for a wide range of uncertainty in material properties, behavior parameters, and ground shaking characteristics. Ironically, actual damage during an earthquake has the potential for improving the engineer's knowledge of the behavior of the building. When considering the effects of damage on future performance, this knowledge is important.
+ACo- Damage may not significantly affect displacement demand in future larger earthquakes.
One of the findings of the ATC-43 project is that prior earthquake damage does not affect maximum displacement response in future, larger earthquakes in many instances. At first, this may seem illogical.
Observing a building with cracks in its walls after an earthquake and visualizing its future performance in an even larger event, it is natural to assume that it is worse off than if the damage had not occurred. It seems likely that the maximum displacement in the future, larger earthquake would be greater than if it had not been damaged. Extensive nonlinear time- history analyses performed for the project indicated otherwise for many structures. This was particularly true in cases in which significant strength degradation did not occur during the prior, smaller earthquake. Careful examination of the results revealed that maximum displacements in time histories of relatively large earthquakes tended to occur after the loss of stiffness and strength would have taken place even in an undamaged structure. In other words, the damage that occurs in a prior, smaller event would have occurred early in the subsequent, larger event anyway.
What does it mean? 
The ATC-43project team has formulated performance- based procedures for evaluating the effects of damage.
These can be used to quantify losses and to develop repair strategies. The application of these procedures has broad implications.
+ACo- Performance-based damage evaluation uses the actual behavior of a building, as evidenced by the observed damage, to identify specific deficiencies.
The procedures focus on the connection between damage and component behavior and the implications for estimating actual behavior in future earthquakes. This approach has several important benefits. First, it provides a meaningful engineering basis for measuring the effects of damage. It also identifies performance characteristics of the building in its pre-event and damaged states. The observed damage itself is used to calibrate the analysis and to improve the building model. For buildings found to have unacceptable damage, the procedures identify specific deficiencies at a component level, thereby facilitating the development of restoration or upgrade repairs.
+ACo- Performance-based damage evaluation provides an opportunity for better allocation of resources.
The procedures themselves are technical engineering tools. They do not establish policy or prescribe rules for the investigation and repair of damage. They may enable improvements in both private and public policy, however. In past earthquakes, decisions on what to do about damaged buildings have been hampered by a lack of technical procedures to evaluate the effects of damage and repairs. It has also been difficult to investigate the risks associated with various repair alternatives. The framework provided by performance-based damage evaluation procedures can help to remove some of these roadblocks. In the long run, the procedures may tend to reduce the prevailing focus on the loss caused by damage from its pre-event conditions and to increase the focus on what the damage reveals about future building performance. It makes little Technical Resources FEMA 307 Prologue sense to implement unnecessary repairs to buildings seismic and structural design procedures. These will that would perform relatively well even in a take some time to be assimilated in the engineering damaged condition. Nor is it wise to neglect buildings in which the component behavior reveals serious hazards regardless of the extent of damage.
community. The same is true for building officials.
Seminars, workshops, and training sessions are required not only to introduce and explain the
+ACo- Engineering judgment and experience are essential to the successful application of the procedures.
procedures but also to gather feedback and to improve the overall process. Additionally, future materials-testing and analytical research will enhance the basic framework developed for this project. Current project documents are initial ATC-20 and its addendum, ATC-20-2, were editions to be revised and improved over the years.
developed to be used by individuals who might be somewhat less knowledgeable about earthquake In addition to the project team, a Project Review Panel building performance than practicing structural has reviewed the damage evaluation and repair engineers. In contrast, the detailed investigation of procedures and each of the three project documents.
damage using the performance-based procedures of This group of experienced practitioners, researchers, this document and the companion FEMA 306 report regulators, and materials industry representatives (ATC, 1998a) and FEMA 308 report (ATC, 1998b) reached a unanimous consensus that the products are must be implemented by an experienced engineer. technically sound and that they represent the state of Although the documents include information in knowledge on the evaluation and repair of earthquake- concise formats to facilitate field operations, they damaged concrete and masonry wall buildings. At the must not be interpreted as a +ACI-match the pictures+ACI- same time, all who contributed to this project exercise for unqualified observers. Use of these acknowledge that the recommendations depart from guideline materials requires a thorough traditional practices. Owners, design professionals, understanding of the underlying theory and building officials, researchers, and all others with an empirical justifications contained in the documents. interest in the performance of buildings during Similarly, the use of the simplified direct method to earthquakes are encouraged to review these documents estimate losses has limitations. The decision to use and to contribute to their continued improvement and this method and the interpretation of the results must enhancement. Use of the documents should provide be made by an experienced engineer. realistic assessments of the effects of damage and valuable insight into the behavior of structures during
+ACo- The new procedures are different from past damage evaluation techniques and will continue to evolve in the future.
earthquakes. In the long run, they hopefully will contribute to sensible private and public policy regarding earthquake-damaged buildings.
The technical basis of the evaluation procedures is essentially that of the emerging performance-based FEMIA 307 Technical Resources 
1. Introduction
1.1 Purpose And Scope 
The purpose of this document is to provide supplemental information for evaluating earthquake damage to buildings with primary lateral-force-resisting systems consisting of concrete and masonry bearing walls and infilled frames. This document includes background and theoretical information to be used in conjunction with the practical evaluation guidelines and criteria given in FEMA 306: Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings Basics Procedures Manual (ATC, 1998a). In both documents, concrete and masonry wall buildings include those with vertical-load-bearing wall panels, with and without intermediate openings. In these documents, shear wall buildings also include those with vertical-load-bearing frames of concrete or steel that incorporate masonry or concrete infill panels to resist horizontal forces. The FEMA 306 procedures for these building types address: 
a. The investigation and documentation of damage caused by earthquakes.
b. The classification of the damage to building components, according to mode of structural behavior and severity.
c. The evaluation of the effects of the damage on the performance of the building during future earthquakes.
d. The development of hypothetical measures that would restore the performance to that of the undamaged building.
Supplemental data in this document, FEMA 307, includes the results of the efforts of two issues working groups that focused on the key aspects of adapting and enhancing existing technology for the purposes of the evaluation and repair of earthquake-damaged buildings.
The general scope of work for each group is briefly outlined in the following two sections.
1.2 Materials Working Group 
The Materials Working Group effort was a part of the overall ATC-43 project. The primary objectives of the Materials Working Group were: 
a. To summarize tests and investigative techniques that can be used to document and evaluate existing structural conditions, particularly the effects of earthquake damage, in concrete and masonry wall buildings.
b. To recommend modifications to component force-deformation relationships currently used in nonlinear structural analysis, based on the documented effects of damage similar to that caused by earthquakes.
c. To describe the specification and efficacy of methods for repair of component damage in a coordinated format suitable for inclusion in the final document.
Figure 1-1 illustrates the idealization of the force- deformation relationships from actual structural component hysteretic data for use in nonlinear analysis.
The focus of the Materials Working Group was the generalized force-deformation relationship for structural components of concrete and masonry wall buildings, shown in Figure 1-2.
1.2.1 Tests and Investigations 
The scope included review of experimental and analytical research reports, technical papers, standards, and manufacturers' specifications. Practical example applications relating to the documentation, measurement, and quantification of the structural condition of concrete and masonry walls and in-fill frame walls were also reviewed. The reviews focused on tests and investigative techniques for identifying and evaluating cracking, crushing, deterioration, strength, and general quality of concrete or masonry and yielding, fracture, deterioration, strength, and location of reinforcing steel. Based on this review of existing information, practical guidelines for appropriate tests and investigative techniques were developed and are included in FEMA 306. These guidelines consist of outline specifications for equipment, materials, and procedures required to execute the tests, as well as criteria for documenting and interpreting the results.
1.2.2 Component Behavior and Modeling 
The members of the group reviewed experimental and analytical research reports, technical papers, and practical example applications relating to the force- deformation behavior of concrete and masonry walls and in-fill frame walls. Of particular interest were the effects of damage of varying nature and extent on the hysteretic characteristics of elements and components FEMA 307 Technical Resources Chapter 1: Introduction Force, F Backbone curve Actual hysteretic from MA 273 behavior Deformation i, D (a) Backbone curve from actual hysteretic behavior F F F Backbone curve C,D B.C,I D Idealized B B Do component+AFw-/ B./ E A N D 1A E DA A E D Ductile Semi-ductile Brittle (deformation controlled) (force controlled) (b) Idealized component behavior from backbone curves 
Figure 1-1 Component Force-Deformation Relationships subject to cyclic lateral loads. The types of damage investigated included cracking and crushing of concrete or masonry and yielding and fracture of reinforcing steel. Components included a wide variety of configurations for vertical-load-bearing and infilled- frame elements. Materials included reinforced concrete, reinforced masonry, and unreinforced masonry.
Based on the review, practical guidelines for identifying and modeling the force-deformation characteristics of damaged components were developed and included in FEMA 306. These consist of modifications (B', C', D', E') to the generalized force-deformation relationships for undamaged components, as shown in Figure 1-2.
Supplemental information on these modifications is included in this volume in Chapters 2 (Concrete), 3 (Reinforced Masonry), 4 (Unreinforced Masonry), and 5 (Infilled Frames).
1.2.3 Repair Techniques 
The Materials Group also reviewed experimental and analytical research reports, technical papers, standards, manufacturers' specifications, and practical example applications relating to the repair of damage in concrete and masonry walls and infilled-frame walls. The primary interest was the repair of earthquake damage to structural components. The review focused on materials and methods of installation and tests of the effectiveness of repair techniques for cracking, crushing, and deterioration of concrete or masonry and yielding, fracture, and deterioration of reinforcing steel.
Technical Resources FEIVA 307 Chapter 1: Introduction F A B 1i +ADw- Undamaged component Damaged component E A' A ADD' Figure 1-2 Generalized Undamaged and Damaged Component Curves Based on the review, practical guidelines for damage repair were developed and are contained in FEMA 308: The Repair of Earthquake Damaged Concrete and Masonry Wall Buildings (ATC, 1998b). These guidelines consist of outline specifications for equipment, materials, and procedures required to execute the repairs, as well as criteria for quality control and verification of field installations.
1.3 Analysis Working Group 
The work of the Analysis Working Group was a subproject of the overall ATC-43 project. The primary objectives of the group were:
+ACo- To determine whether existing structural analysis techniques are capable of capturing the global effects of previous earthquake damage on future seismic performance
+ACo- To formulate practical guidance for the use of these analysis techniques in design-oriented evaluation and repair of damaged masonry and concrete wall buildings.
Chapter 6 summarizes the results of the Analysis Working Group efforts. Work consisted primarily of analytical studies of representative single-degree-of- freedom (SDOF) oscillators subjected to a range of earthquake ground motions. The study was formulated so that the following question might be answered (see 
Figure 1-3): If a building has experienced damage in an earthquake (the damaging earthquake), and if that intermediate damage state can be characterized in terms of its effect on the global force-displacement relationship, how will the damage influence global response to a subsequent earthquake (the Performance Earthquake)? The SDOF oscillators had force-displacement relationships that represent the effects of earthquake damage on the global dynamic response of hypothetical buildings to earthquake ground motions. Types of global force-displacement relationships considered included those shown in Figure 1-4.
The results obtained using existing simplified analyses methods were compared to the time-history results. The group was particularly interested in understanding how nonlinear static analysis methods might be used to represent the findings. Regarding the nonlinear static methods, consideration was given to the applicability of the coefficient method, the capacity-spectrum method, and the secant method of analysis, as summarized in FEMA-273 NEHRP Guidelines for the Seismic Rehabilitation of Buildings (ATC, 1997a) and ATC-40 Seismic Evaluation and Retrofit of Concrete Buildings (ATC, 1996). The work included a study of the accuracy of the various methods in terms of predicting future performance. The study included an assessment of the FEIVA 307 Technical Resources Chapter 1: Introduction Performance Earthquake Pre-event Performance State Damage State Time a) Response of Pre-event Building Performance Earth quake Damage Pre-event VI Intermediate Performance Time State Damage State Damage State' b) Response of Damaged Building 
Figure 1-3 Effect of Damage on Building Response sensitivity of the predictions to variations in global load-deformation characteristics and to variations in ground motion characteristics. The results are reflected in the procedures presented in FEMA 306.
1.4 References ATC, 1996, 
The Seismic Evaluation and Retrofit of Concrete Buildings, Applied Technology Council, ATC-40 Report, Redwood City, California.
ATC, 1997a, NEHRP Guidelines for the Seismic Rehabilitation of Buildings, prepared by the Applied Technology Council (ATC-33 project) for the Building Seismic Safety Council, published by the Federal Emergency Management Agency, Report No. FEMA 273, Washington, D.C.
ATC, 1997b, NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, prepared by the Applied Technology Council (ATC-33 project) for the Building Seismic Safety Council, published by the Federal Emergency Management Agency, Report No. FEMA 274, Washington, D.C.
ATC, 1998a, Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings, Basic Procedures Manual, prepared by the Applied Technology Council (ATC-43 project) for the Partnership for Response and Recovery, published by the Federal Technical Resources FEMA 307+ADs- Chapter 1: Introduction F.+AF8- -I-1 I+AF8- a. Bilinear b. Stiffness degraded (positive post-yield stiffness) 
Figure 1-4 Global Load-Displacement Relationships Emergency Management Agency, Report No. FEMA 306, Washington D.C.
ATC,1998b,Repairof Earthquake Damaged Concrete and Masonry Wall Buildings, prepared by the Applied Technology Council (ATC-43 project) for FF d 1 c. Stiffness Degraded d. Stiffness and (negative post-yield strength degraded stiffness) the Partnership for Response and Recovery, published by the Federal Emergency Management Agency, Report No. FEMA 308, Washington D.C.
Technical Resources FEMA 307 Technical Resources FEIVA 2ma Reinforced Concrete Components s 2.1 Commentary and Discussion 2.1.1 Development of Component Guides and A Factors The Component Damage Classification Guides (Component Guides) and component modification factors (A factors) for reinforced concrete walls were developed based on an extensive review of the research.
The main references used are listed in the tabular bibliography of Section 2.3.
2.1.1.1 Identical Test Specimens Subjected to Different Load Histories As indicated in FEMA 306, the ideal way to establish A factors would be from structural tests designed specifically for that purpose. Two identical test specimens would be required for each structural component of interest. One specimen would be tested to represent the component in its post-event condition subjected to the performance earthquake+ADs- the second specimen would be tested to represent the component in its pre-event condition subjected to the performance earthquake. The A values would be derived from the differences in the force-displacement response between the two specimens.
Research to date on reinforced concrete walls does not include test programs as described above. There are only a few tests of identical wall specimens subjected to different loading histories, and typically this is only a comparison of monotonic versus cyclic behavior. For reinforced concrete columns, there are more studies of the effects of load history (El-Bahy et al., 1997+ADs- Kawashima and Koyama, 1988) but these studies have not focused on the specific problem of comparing previously damaged components to undamaged components.
2.1.1.2 Interpretation of Individual Tests In the absence of tests directly designed to develop At factors, the factors can be inferred from individual cyclic-static tests. This is done by examining the change in force-displacement response from cycle to cycle as displacements are increased. Initial cycles can be considered representative of the damaging earthquake, and subsequent cycles representative of the behavior of an initially damaged component. The general process of interpreting the test data is outlined in the diagram of Figure 2-1. Each structural test is considered according to the component type and behavior mode represented by the test. At intervals along the load-displacement history of the test the critical damage indicators, such as spalling, cracking, etc., are noted. The damage indicators at each interval are correlated with the displacement ductility reached at that point of the test and with the characteristics of subsequent cycles of the test. From the comparisons of initial and subsequent cycles, A values are estimated.
Critical damage indicators and the associated A factors are then discretized into different damage severity levels.
The ranges of component displacement ductility, /UA, associated with damage severity levels and A factors and for each Component Guide are given in Table 2-1. The range of ductility values are the result of the differences in test procedures, specimen details, and relative values of coincident loading (shear, moment, axial load). See the remarks column of Table 2-1 for specific factors affecting individual components. Typical force- displacement hysteresis loops from wall tests are given in Section 2.2. A discussion of the relationship between cracking and damage severity for reinforced masonry is given in Section 3.1.2. This discussion is largely applicable to reinforced concrete as well as reinforced masonry.
In estimating the A values, it was considered that some stiffness and strength degradation would occur in a structural component in the course of the Performance Earthquake, whether or not it was previously subjected to a damaging earthquake. As discussed in FEMA 306, the A factors refer to the difference in the stiffness, strength, and displacement capacity of the performance earthquake response, between a pre-event component and a post-event component.
2.1.1.3 Accuracy The X factors are considered accurate to one significant digit, as presented in the Component Damage Classification Guides. In the case of component types and behavior modes which are not well covered in the research, engineering judgment and comparisons to similar component types or behavior modes were used Technical Resources FEMA 307 Technical Resources Chapter 2: Reinforced Concrete Components Component Type and Behavior Mode Damage Indicators: Spalling, Bar Buckling, Bar Fracture, Residual Drift, Crack Type and Orientation, Crack Width.
+AHw- Displacement Ductility, uA Reached.
Characteristics of Subsequent Cycles.
Component Modification Values, A Damage Severity: Insignificant, Slight, Moderate, Heavy, Extreme.
Figure 2-1 Diagram of process used to develop component guides and component modification factors to establish X factors. In cases of uncertainty, the wall performance under load reversals is a function of recommended A factors and severity classifications are load history. The previous level of maximum designed to be conservative -that is, the factors and deformation is critical.+ACI- classifications may overestimate the effect of damage on future performance. For reinforced concrete columns, Mander et al. (1996) have shown a correlation between strength degradation Only limited research is available from which to infer and cumulative plastic drift. El-Bahy et al, (1997) have specific AD values. However, a number of tests support shown similar results. This research generally supports the general idea that ultimate displacement capacity can the AD values recommended for reinforced concrete, be reduced because of previous damaging cycles. which are 0.9 at moderate damage and 0.7 to 0.8 at Comparisons of monotonic to cyclic-static wall tests heavy damage.
show greater displacement capacities for monotonic loading, and Oesterle et al. (1976) conclude, +ACI-structural Technical Resources FEMA 307 Chapter 2: Reinforced Concrete Components Table 2-1 Ranges of reinforced concrete component displacement ductility, pF, associated with damage severity levels and A factors Component Damage Severity Remarks on Ductility Ranges Guide Insignif. Slight Moderate Heavy RC1A Ductile Flex- MA+ADw- 3 AK +AD0- 0.8 E +AD0-4 -8 AK +AD0- 0.6 Ma 3- 10 XK +AD0- +ALA- 5 Heavy not used , Slight category will only occur for low axial loads, where concrete does not spall until large ductilities develop ural Q+AD0- 1.0 AQ+AD0-.1 AQ +AD0- 0.8 AD+AD0-1.0 AD+AD0- 1.0 AD+AD0-0.9 RC1B A +ADw- 3 Slight not MA 2 6 MAd 2 8 Ductility depends on ratio of flexural to shear Flexure/ Diag-AK+AD0- 0.8 used AK +AD0- 0-5 AK+AD0- 0.2 strength. Lower ductility indicates behavior onal Tension AQ +AD0- 1.0 Q+AD0- 0.8 AQ +AD0- 0.3 similar to preemptive diagonal tension. Higher +AD0- 1.0 AD AD +AD0- 0,9 0.9 AD AD 0-7 0.7 ductility indicates behavior similar to ductile flexural.
RC1C MA+ADw- 3 Slight not A +AD0- 2 -6 MA 3 8 Ductility depends on ratio of flexural to web Flexure/ Web See RC1B used X +AD0- 0+ALA-5 AK +AD0- 0.2 crushing strength. Lower ductility indicates Crushing AQ +AD0- 0.8 AQ +AD0- 0.3 behavior similar to preemptive web crushing.
Higher ductility indicates behavior similar to 'DA+AD0- 0.9 AD+AD0- 0.7 ductile flexural.
RCID MA +ADw- 3 MA 4-6 Moderate MgA+AD0- 4 8 Ductility depends on ratio of flexural to sliding Flexure/ Slid-See RC1A See RC1A not used AK+AD0- 0.4 shear strength.
ing Shear AQ +AD0- 0.5 AD+AD0- 0.8 RC1E A +ADw- 3 MA 4 -6 MA 3 -6 MA 4 -8 Slight category will only occur for lower axial Flexure/ See RC1A See RC1A See RC1A +AD0- K 0.4 loads, where concrete does not spall until large Boundary ductilities develop. Lower ductility relates Compression AQ+AD0- 0.6 poorer confinement conditions. Higher ductil- AD 0.7 ity indicates behavior similar to ductile flexural RC2A -u +ADw- 3 M +AD0-4 -6 +AD0-3 -1 0 Heavy not See RClA Ductile Flex-See RC1A See RC1A AK +AD0- 0.5 used AQ+AD0- 0.8 AID+AD0- 0.9 RC2H MA+ADw- 1 Slight not MA+ADw- 1.5 M +ADw- 2 Force controlled behavior associated with low Preemptive AK+AD0- 0.9 used AK+AD0- 0.5 AK+AD0- 0.2 ductility levels.
Shear AQ+AD0- 1.0 AQ+AD0-0.8 AQ+AD0-0.3 AD+AD0- 1.0 AD+AD0-O-9 XD+AD0-007 A 2 -6 A2 -8 See RCIB RC3B A+ADw- 3 Slight not +AD0- Flexure/ Diag-See RC1B used See RC1B AK +AD0- 0.2 onal Tension AQ +AD0- 0.3 AD+AD0- 0.7 RC3D uA +ADw- 3 MAu+AD0- 4 -6 Moderate MA+AD0- 3 -8 Sliding shear may occur at lower ductility lev- Flexure/ Slid-See RC1D See RC1D not used AK +AD0- 0.2 els that RC ID because of less axial load.
ing Shear AQ +AD0- 0.3 AD +AD0- 0.7 FEMA 307 Technical Resources Chapter 2: Reinforced Concrete Components System: Reinforced Concrete Component Type: Isolated Wall or Stronger Wall Pier Example 1 of 1 Predominant Behavior Mode: Ductile Flexure Secondary Behavior Mode: - -1 Damage at in. deflection A +AD0- 3 in dh,, +AD0- 0.017 AQ +AD0- 1.o Lc0 v) VI Lal D a -0 m L 0 +AD4- m r a,.- rn a Damage at in. deflection A +AD0- 6 in dh, +AD0- 0.033 dQ+AD0- 1.o -I n m zY 1 YL Damage at in. deflection A +AD0- 8 in dh,, +AD0- 0.044 20 +AD0- 0.7 10 Technical Resources FEMA 307 Chapter 2: Reinforced Concrete Components System: Reinforced Concrete Component Type: Isolated Wall or Stronger Wall Pier -1 Example 1 of 2 Predominant Behavior Mode: Flexurel Diagonal Tension Secondary Behavior Mode:
4. Failure of a squat wall due to diagonal tension after reversed cyclic loading.
Hysteretic response of a squat wall that eventually failed in shear.
FEMA 307 Technical Resources

Chapter 2: Reinforced Concrete Components 
Component Type: 
System: Reinforced Concrete 
Isolated Wall or Stronger Wall Pier 
Example 2 of 2 
Predominant Behavior Mode: Flexurel Diagonal Tension 
Secondary Behavior Mode: Flexure Mleb Crushing 
Top Deflection, in. 
I in. * 25.4 mn 
I kip. 4.45 tN 
Crack pattern of specimen PW-1 at end of Phase II. 
1-80 
Load versus top deflection relationship for 
specimen PW-1. 
Specimen PW-1 at end of test. 
Technical Resources FEMA 307 
Chapter 2: Reinforced Concrete Components 
DAMAGE PATTERNS AND HYSTERETIC RESPONSE 
System: Reinforced Concrete 
Component Type: Isolated Wall or Stronger Wall Pier 
Example 1 of 3 
Predominant Behavior Mode: Flexure Mleb Crushing 
Secondary Behavior Mode: -
Damage at +3-in. deflection 
A = 3 in Ah, = 0.017 aQ= 1.0 
Load versus deflection relationship 
Damage prior to web crushing 
A = 4 in A/h, = 0.022 Ag = 1.0 
Damage after web crushing 
A = 5 in A/h, = 0.028 AQ = 0.3 
FEMA 307 Technical Resources Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: Isolated Wall or Stronger Wall Pier 
-1
Example 2 Of 3 
Predominant Behavior Mode: FlexurdSliding Shear 
Secondary Behavior Mode: -
Overall dimensions of typical test units. 
Splitting and Crushing of Concrete at Base of Wall 
Load-deflection relationshb for wall 1. 
Compression Toe 
FEMA 307 Technical Resources 
Chapter 2: Reinforced Concrete Components 
DAMAGE PATTERNS AND HYSTERETIC RESPONSE 
System: Reinforced Concrete 
Component Type: Isolated Wall or Stronger Wall Pier RC 1D I Example 3 of 3 
Predominant Behavior Mode: Flexure/Sliding Shear 
Secondary Behavior Mode: Reference: 
Paulay, Priestley, and Synge (1982)) 
Specimen: Wall 3 
Overall Dimensions for Walls 3 and 4. 
Load-Deflection Relationship for Flanged Wall 
Technical Resources FEMA 307 
Chapter 2: Reinforced Concrete Components 
DAMAGE PATTERNS AND HYSTERETIC RESPONSE 
System: Reinforced Concrete 
Component Type: 
Isolated Wall or Stronger Wall Pier 
Example 1 of 1 
Predominant Behavior Mode: Flexure Boundary Compression 
Secondary Behavior Mode: -
Damage at +3-in. deflection 
A=3in A/hw=0.017 Ag=l.O 
1-BO 
Load versus deflection relationship 
Buckled reinforcement after Load Cycle 30 
A = 4 in Ah, = 0.022 AQ = 0.9 
Damage during Load Cycle 34 
A = 6 in Ah, = 0.033 AQ = 0.6 
FEMA 307 Technical Resources 
Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: Isolated Wall or Stronger Wall Pier 
Example 1 of 2 
Predominant Behavior Mode: Flexure Out-of-Plane Wall Buckling 
Secondary Behavior Mode: -
Cracking pattern at +3 in. deflection for Specimen R2 
Inelastic instability of compression zone 
Cracking pattern at -3 in. deflection for Specimen R2 
Continuous load-deflection plot for Specimen R2 
Technical Resources FEMA 307 

Chapter 2: Reinforced Concrete Components 
DAMAGE PATTERNS AND HYSTERETIC RESPONSE 
System: Reinforced Concrete 
Component Type: Isolated Wall or Stronger Wall Pier Example 2 of 2 
Predominant Behavior Mode: Flexure/Out-of-Plane Wall Buckling 
Secondary Behavior Mode: -
Diagonal cracking and buckling in ;he plastic hinge region: structural wall (Gl). 
Stable hysteretic response of a ductile wall structure (Gl). 
FEMA 307 Technical Resources 
Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Example 1 of 2 
Predominant Behavior Mode: Preemptive Web Crushing 
Secondary Behavior Mode: -
Test specimen at conclusion of loading 
A = 3.0 in Nh;= 0.080 AQ = 0.2 
Hysteretic response 
Provided Information Calculated Values 
A Ah ;le
h, = 37.5 " 0.20 0.005 1.o 
f, = 60 ksi M, = 1700 k-1 0.23 0.006 0.9 
0.28 0.007 0.7 
f,' = 3920 psi V-corresponding 
to M, = 1810 psi 0.40 
0.80 
3.00 
0.011 
0.021 
0.080 
0.5 
0.3 
0.2 
Technical Resources FEMA 307 

Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: 
Isolated Wall or Stronger Wall Pier 
Example 2 of 2 
Predominant Behavior Mode: Preemptive Web Crushing 
Secondary Behavior Mode: -
1000 t 
V= -500
"0 I 2 3 
Deflection. in. 
Envelope of response 
Test specimen at ultimate load 
A = 0.2 in dlh, = 0.005 aQ= 1.0 
Test specimen at conclusion of loading
A = 3.0 in dh, = 0.040 AQ = 0.2 
Provided Information Calculated Values A fwv 42 
h,= 75 " P = 7.5 k 0.45 0.006 1.o 
0.60 0.008 0.9 
f,, = 71 ksi Mn= 2000 k-1 
0.80 0.01 1 0.7 
V 1.20 0.016 0.5
f,' = 3400 psi -corresponding to Mn = 1070 psi 1.70 0.023 0.3 
bJW 3.00 0.040 0.2 
FEMA 307 Technical Resources 
Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: Isolated Wall or Stronger Wall Pier 
Example 1 of 1 
Predominant Behavior Mode: Preemptive Sliding Shear 
Secondary Behavior Mode: Web Crushing 
Deflection. in. 
Envelope of response 
Test specimen at ultimate load 
A = 0.15 in Ah, = 0.008 3.e = 1.0 
-06 -04 -02 
04 06
Deflection. in 
Hysteretic response to 0.6in. 
Test specimen at conclusion of loading 
A = 3.0 in A/h, = 0.160 AQ = 0.4 'Oo0 /Envelope
Provided Information 
h, = 18.75 values from response plot hd 500 --
f,= 78 ksi 
f= 3730 psi 0.15 0.008 1.o 
Calculated Values 0.30 0.01 6 0.9 
P= 3.6 k 0.70 0.037 0.8. In 
Mn = 2180 k-1 1.80 0.096 0.6 
3.00 0.160 0.4 -corresponding to 
b>"L i
Mn = 4600 psi -1000 
Hysteretic response to 3.0 in. 
Technical Resources FEMA 307 

Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: Weaker Spandrel or Coupling Beam 
Example 1 of 1 
Predominant Behavior Mode: Ductile Flexure 
Secondary Behavior Mode: -
Radians x lom3 
Load-rotation relationship for Beam 316. 
FEMA 307 Technical Resources 
Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: Weaker Spandrel or Coupling Beam 
Example 1 of 1 
Predominant Behavior Mode: Flexure/Sliding Shear 
Secondary Behavior Mode: -
Theoretical: 
(b) Uncracked sections 
A 7, i fa) Cracked sections 
Load-rotation relationship for a conventional coupling beam. 
Technical Resources FEMA 307 
Chapter 2: Reinforced Concrete Components 
System: Reinforced Concrete 
Component Type: Weaker Spandrel or Coupling Beam Example 1 of 1 
Predominant Behavior Mode: Preemptive Diagonal Tension 
Secondary Behavior Mode: -
-1 
Beam 392 after being subjected to seismic-type Beam 392, Cycle 14. 
loading: Cycle 13. 
FEMA 307 Technical Resources 
Chapter 2: Reinforced Concrete Components 
2.3 Tabular Bibliography 
Table 2-2 contains a brief description of the key technical behavior 
modes are indicated The full references can be 
cal reports that address specific reinforced concrete found in Section 2.5. 
component behavior. The component types and their 
Technical Resources FEMA 307 
Table 2-2 Key References on Reinforced Concrete Wall Behavior. 
Reference Description Comp. Behavior modes Addressed 
Types A B C D E F G H I J K L 
EVALUATION AND DESIGN RECOMMENDANONS: 
ACI 318 (1995) Code provisions for the design of r/c walls. RC1 -
Distinct behavior modes are often not considered explicitly. RC4 
Paulay & Priestley Comprehensive recommendations for the design of r/c walls. RC 
(1992) Considers all component types and prevalent behavior modes. RC4 0 
Oesterle et al (1983) Development of a design equation for web crushing strength. RCI1 cD Strength is related to story drift and correlation with research results is shown. 
OVERVIEWS OF TEST RESULTS: 
N0 CD Wood (1991) Review of 27 specimens. 24 cyclic-static loading, 3 monotonic loading. RC1 CD k Do "Slender" walls: 1.1 < M/VL < 2.9, All specimens reached flexural yield. a. CD0 Wood (1990) 
Failure categorized as either "shear" or "flexure". 
Review of 143 specimens. 50 cyclic-static loading, 89 monotonic 
unidirectional loading. 
loading, 4 repeated RC1 0 0C) CD CD M 0 
"Short" walls: 0.23 < MIVL < 1.7. Review focuses on maximum strength. 0 
CD0 Failure modes and displacement capacity not addressed 00 
ATC-11(1983) Commentary on implications of r/c wall test results and design issues. RC 1, a RC3 C)03 Sozen & Moehle Review of wall test results applicable to nuclear power plant structures. Focused on RCI as 
(1993) predicting initial stiffness. 
1 Behavior modes: 
A Ductile Flexural Response F Flexure/Lap-Splice Slip K Preemptive Boundary Zone Compression Failure 
B Flexure/Diagonal Tension G Flexure/Out-of-Plane Wall Buckling L Preemptive Lap-Splice Failure 
C Flexure/Diagonal Compression (Web Crushing) H Preemptive Diagonal Tension M Global foundation rocking of wall 
D Flexure/Sliding Shear I. Preemptive Web Crushing N Foundation rocking of individual piers 
E Flexure/Boundary-Zone Compression J Preemptive Sliding Shear co CD 
Table 2-1 Key References on Reinforced Concrete Wall Behavior (continued) 
Reference Description Comp. Types 
DETAILED TEST RESULTS:: 
Behavior modes Addressed 
AB C D E FGHI IJ K L 0 0) CD M 0iD!Y M e SAD 
0a.0 0 C D 0 0 (0 Barda (1972) Barda, Hanson & 
8 test specimens: 6 cyclic-static loading, 2 monotonic loading, Small axial load. 
Approx. 1/3 scale, flanged walls. Low-rise: MIVL = 1.0, 0.5, 0.25. 
RC1 
Corley (1976) Wall vertical & horiz. reinf. and flange longit. reinf. varied 
(Lehigh Univ.) I specimen repaired by replacement of web concrete and tested. 
Oesterle et al (1976) 16 test specimens: 2 rectangular, 12 barbell, 2 flanged. M/VL = 2.4. RCI 
Oesterle et al (1979) Approx. 1/3 scale. Variables include boundary longit. and hoop reinf., wall horiz. reinf., 
(Portland Cement axial load, load history 
Association) 2 specimens repaired and tested. 
Shiu et al (1981) 2 test specimens. One solid wall and one wall with openings. Approx. 1/3 scale. RC1, (Portland Cement Association) 
Rectangular sections. Solid wall governed by sliding shear. Wall with openings was governed by diagonal compression in the piers. RC2, RC4 CD Coupling beams were not significantly damaged. 
C) Wang, Bertero & 10 test specimens: 6 barbell and 4 rectangular. 5 cyclic-static loading, 5 monotonic. RCI 
Popov (1975) Valle- 1/3 scale, modeled bottom 3 stories of 10-story barbell wall and 7-story rectangular wall. 0 0 C)
CDCI, Bertero & Popov (1979) (U.C. Berkeley) Iliya & Bertero 
5 specimens repaired with replacement of damaged rebar and crushed concrete. 
2 test specimens. Barbell-shaped sections. Combination of cyclic-static and monotonic RCI (1980) loading. 
(U.C. Berkeley) 1/3 scale, modeled bottom 3 stories of 10-story barbell wall. Specimens repaired with 
epoxy injection of cracks after minor damage then subsequently repaired (after major damage) with replacement of damaged rebar and crushed concrete. 
Behavior modes: 
A Ductile Flexural Response F Flexure/Lap-Splice Slip K Preemptive Boundary Zone Compression Failure 
B Flexure/Diagonal Tension G Flexure/Out-of-Plane Wall Buckling L Preemptive Lap-Splice Failure 
C Flexure/Diagonal Compression (Web Crushing) H Preemptive Diagonal Tension M Global foundation rocking of wall 
D Flexure/Sliding Shear I Preemptive Web Crushing N Foundation rocking of individual piers 
E Flexure/Boundary-Zone Compression J Preemptive Sliding Shear 

Table 2-1 Key References on Reinforced Concrete Wall Behavior (continued) 
00) 10 0 
Reference Description Comp. Behavior modes Addressed 
Types AB C D E F G H I J K L 
Mansur, Balendra, 4 successful test specimens, cyclic-static loading. RCI 
and H'ng (1991) Approx. 1/4 scale. Flanged section. Web reinforced with welded wire mesh or expanded 
metal. 
M/VL = 0.68. 
Saatcioglu (1991) 3 test specimens, cyclic-static loading RCI . . 
Approx. 1/3 scale. Rectangular section. Horizontal and sliding-shear dowel reinforcement 
varied. 
MIVL = 0.50. 
Aristizabal-Ochoa, 4 shake-table specimens. Approx. 1/12 scale. RCI 
Dario, & Sozen 10-story coupled walls, rectangular pier and beam sections. Discusses reduced stiffness of RC3 
D, -I (1976) (University of coupling beams resulting from bond slip, and redistribution of demands between wall 
-4 Illinois) piers. ED MLybas & Sozen 6 test specimens, 5 shake-table and I cyclic static. Approx. 1/12 scale. RCI C,O (1977) (University of 6-story coupled walls, rectangular pier and beam sections. RC3 CD Illinois) Azizinamini et al. Out-of-plane tests on tilt-up walls. 6 test specimens. RCI 
a,0 C 0CD CD 00 0 C,(1994) (Portland Approx. 3/5 scale. Monotonic out-of-plane loading. Cement Association) Report shows typical crack patterns resulting from out-of-plane forces. 
to ACI-SEAOSC Out-of-plane tests on tilt-up walls, 12 reinforced concrete specimens (Also, 18 reinforced RC1 
Task Force (1982) masonry specimens). Full scale monotonic out-of-plane loading and constant axial loading hit ratios of 30 to 60. 0 0CD -4 'Behavior modes: 
A Ductile Flexural Response F Flexure/Lap-Splice Slip K Preemptive Boundary Zone Compression Failure 
B Flexure/Diagonal Tension G Flexure/Out-of-Plane Wall Buckling L Preemptive Lap-Splice Failure 
C Flexure/Diagonal Compression (Web Crushing) H Preemptive Diagonal Tension M Global foundation rocking of wall 
D Flexure/Sliding Shear I Preemptive Web Crushing N Foundation rocking of individual piers 
E Flexure/Boundary-Zone Compression J Preemptive Sliding Shear 
0-. Chapter 2: Reinforced Concrete Components 
2.4 Symbols for Reinforced Concrete 
Symbols that are used in this chapter are defined below. hw = Height of wall or segment of wall considered 
Further information on some of the variables used (per ACI) 
(particularly those noted "per ACT") may be found by 
looking up the symbol in Appendix D of ACI 318-95. krc = Coefficient accounting the effect of ductility 
demand on V, per FEMA 306, Section A2.3.6.b 
Ach = Cross sectional area of confined core of wall 
Ip = Equivalent plastic hinge length, determined 
boundary region, measured out-to-out of confining 
reinforcement and contained within a according to FEMA 306, Section A2.3.3. 
length c' from the end of the wall, FEMA 306, IK= Unsupported length considered for wall buck-
Section A2.3.7 ling, determined according to FEMA 306, 
ACV= Net area of concrete section bounded by web Section A2.3.9 
thickness and length of section in the direction In = Beam clear span (per ACI) 
of shear force considered, in2 (per ACI) 
1W = Length of entire wall or segment of wall considered 
Ag = Gross cross sectional area of wall boundary in direction of shear force (per ACI). 
region, taken over a length c' from the end of (For isolated walls and wall piers equals horizontal the 
wall, FEMA 306, Section A2.3.7 length, for spandrels and coupling beams 
equals vertical dimension i.e., overall depth)
Ash = Total cross-sectional area of transverse reinforcement 
(including crossties) within spacing s Mcr = Cracking moment (per ACI) 
and perpendicular to dimension h,. (per ACI) Me = Expected moment strength at section, equal to 
b = Width of compression face of member, in (per nominal moment strength considering expected 
ACI) material strengths. 
bw = Web width, in (per ACI) M, = Nominal moment strength at section (per ACI) 
c = Distance from extreme compressive fiber to Mu = Factored moment at section (per ACI) 
neutral axis (per ACI) 
M/V= Ratio of moment to shear at a section. When 
c' = Length of wall section over which boundary moment or shear results from gravity loads in 
ties are required, per FEMA 306, addition to seismic forces, can be taken as 
Section A2.3.7 M. /V. 
db = Bar diameter (per ACI) No = Factored axial load normal to cross section 
dbt = Bar diameter of tie or loop occurring simultaneously with Vu; to be taken 
as positive for compression, negative for tension fc 
= Specified compressive strength of concrete, psi (per ACI) 
(per ACI) s = Spacing of transverse reinforcement measured 
fy = Specified yield strength of nonprestressed rein-along the longitudinal axis of the structural reinforcement, psi. (per ACI) member (per ACI) 
fyh = Specified yield strength of transverse reinforcement -s, = spacing of vertical reinforcement in wall (per, psi (per ACI) ACI) 
hc = Cross sectional dimension of confined core of Vc = Nominal shear strength provided by concrete 
wall boundary region, measured out-to-out of (per ACI) 
confining reinforcement V, = Nominal shear strength (per ACI) 
hd = Height over which horizontal reinforcement VP = Nominal shear strength related to axial load per 
contributes to V, per FEMA 306, 
Section A2.3.6.b 33 
Technical Resources
FEMA 307 Technical Resources 33 
Chapter 2: Reinforced Concrete Components 
V, = Nominal shear strength provided by shear reinforcement -ILA = Displacement ductility demand for a component 
(per ACI), used in FEMA 306, Section A2.3.4, as 
Vu = Factored shear force at section (per ACI) 
discussed in Section 6.4.2.4 of FEMA-273. 
Equal to the component deformation corresponding 
VwC= Web crushing shear strength per FEMA 306, 
Section A2.3.6.c 
to the global target displacement, 
divided by the effective yield displacement of 
the component (which is defined in Section 
a = Coefficient accounting for wall aspect ratio 6.4.1.2B of FEMA-273). 
effect on V, per FEMA 306, Section A2.3.6.b 
Pg = Ratio of total reinforcement area to cross-sectional -
/3 = Coefficient accounting for longitudinal reinforcement 
area of wall. 
effect on V, per FEMA 306, 
Section A2.3.6.b 
pt = Local reinforcement ratio in boundary region of 
wall according to FEMA 306, Section A2.3.7 
8 = Story drift ratio for a component, corresponding 
to the global target displacement, used in 
the computation of V.c, FEMA 306, 
pn = Ratio of distributed shear reinforcement on a 
plane perpendicular to plane of A,, (per ACI). 
= Section A2.3.6.c 
Coefficient of friction (per ACI) 
(For typical wall piers and isolated walls indicates 
amount of horizontal reinforcement.) 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 2: Reinforced Concrete Components 
2.5 References for Reinforced Concrete
This list contains references from the reinforced 
concrete chapters of both FEMA 306 and 307. 
ACI, 1995,Building Code Requirements for Reinforced 
Concrete, American Concrete Institute, Report ACI 
318-95, Detroit, Michigan. 
ACI-SEAOSC, 1982, Test Report on Slender Walls, 
Task Committee on slender Walls, American Concrete 
Institute, Southern California Chapter, and 
Structural Engineers of Southern California. 
Alexander, C.M., Heidebrecht, A.C., and Tso, W.K., 
1973, "Cyclic Load Tests on Shear Wall Panels, 
Proceedings," Fifth World Conference on Earthquake 
Engineering, Rome, pp. 1116-1119. 
Ali, Aejaz and Wight, J. K., 1991, "R/C Structural 
Walls with Staggered Door Openings," Journal of 
Structural Engineering, ASCE, Vol. 117, No. 5, 
pp. 1514-1531. 
Antebi, J., Utku, S., and Hansen, R.J., 1960, The 
Response of Shear Walls to Dynamic Loads, MIT 
Department of Civil and Sanitary Engineering, 
Report DASA-1160, Cambridge, Massachusetts. 
Aristizabal-Ochoa, D., J., and Sozen, M.A., 1976, 
Behavior of Ten-Story Reinforced Concrete Walls 
Subjected to Earthquake Motions, Civil Engineering 
Studies Structural Research Series No. 431, 
Report UILU-ENG-76-2017, University of Illinois, 
Urbana, Illinois. 
ASCE/ACI Task Committee 426, 1973, "The Shear 
Strength of Reinforced Concrete Members," ASCE 
Journal of Structural Engineering, Vol. 99, No. 
ST6, pp 1091-1187. 
ATC, 1983, Seismic Resistance of Reinforced Concrete 
Shear Walls and Frame Joints: Implication of 
Recent Research for Design Engineers, Applied 
Technology Council, ATC-11Report, Redwood 
City, California. 
ATC, 1996, The Seismic Evaluation and Retrofit of 
Concrete Buildings, Applied Technology Council, 
ATC-40 Report, Redwood City, California. 
ATC, 1997a, NEHRP Guidelines for the Seismic Rehabilitation 
of Buildings, prepared by the Applied 
Technology Council (ATC-33 project) for the 
Building Seismic Safety Council, published by the 
Federal Emergency Management Agency, Report 
No. FEMA 273, Washington, D.C. 
ATC, 1997b, NEHRP Commentary on the Guidelines 
for the Seismic Rehabilitation of Buildings, prepared 
by the Applied Technology Council (ATC-33 
project) for the Building Seismic Safety Council, 
published by the Federal Emergency Management 
Agency, Report No. FEMA 274, Washington, D.C. 
Azizinamini, A., Glikin, J.D., and Oesterle, R.G., 1994, 
Tilt-up Wall Test Results, Portland Cement Association, 
Report RP322D, Skokie, Illinois. 
Barda, Felix, 1972, Shear Strength of Low-Rise Walls 
with Boundary Elements, Ph.D. University, Lehigh 
University, Bethlehem, Pennsylvania. 
Barda, Felix, Hanson, J.W., and Corley, W.G., 1976, 
Shear Strength of Low-Rise Walls with Boundary 
Elements, Research and Development Bulletin 
RD043.01D, preprinted with permission from ACI 
Symposium Reinforced Concrete Structures in 
Seismic Zones, American Concrete Institute. 
Barney, G.B., Shiu, K.N., Rabbat, B.G., Fiorako, A.E., 
Russell, H.G., and Corley, W.G., 1978, Earthquake 
Resistant Structural Walls-Test of Coupling 
Beams, Report to National Science Foundation, 
Portland Cement Association, Skokie, Illinois. 
Benjamin, J.R., and Williams, H.A., 1958a, "The 
Behavior of One-Story Reinforced Concrete Shear 
Walls," Journal of the Structural Division, ASCE, 
Vol. 83, No. ST3. 
Benjamin, J.R., and Williams, H.A., 1958b, Behavior of 
One-Story Reinforced Concrete Shear Walls Containing 
Openings, ACI Journal, Vol. 55, pp. 605618. 
BSSC, 1992, NEHRP Handbook for the Seismic Evaluation 
of Existing Buildings, prepared by the Building 
Seismic Safety Council for the Federal 
Emergency Management Agency, Report No. 
FEMA-178, Washington, D.C. 
BSSC, 1997, NEHRP Recommended Provisions for 
Seismic Regulations for New Buildings and Other 
Structures, prepared by the Building Seismic Safety 
Council for the Federal Emergency Management 
Agency, Report No. FEMA 302, Composite Draft 
Copy, Washington, D.C. 
Cardenas, Alex E., 1973, "Shear Walls --Research and 
Design Practice," Proceedings, Fifth World Conference 
on Earthquake Engineering, Rome Italy. 35 
Technical Resources 
FEMA 307 Technical Resources 35 
Chapter 2: Reinforced Concrete Components 
Corley, W.G., Fiorato, A.E., and Oesterle, R.G., 1981, 
Structural Walls, American Concrete Institute, Publication 
SP-72, Detroit, Michigan, pp. 77-131. 
CRSI, No publication date given, Evaluation of Reinforcing 
Steel in Old Reinforced Concrete Structures, 
Concrete Reinforcing Steel Institute, 
Engineering Data Report No. 11, Chicago, Illinois. 
CSI, 1997, SAP2000, Computers and Structures, Inc., 
Berkeley, California. 
El-Bahy, A., Kunath, S.K., Taylor, A.W., and Stone, 
W.C., 1997, Cumulative Seismic Damage of Reinforced 
Concrete Bridge Piers, Building and Fire 
Research Laboratory, National Institute of Standards 
and Technology (NIST), Draft Report, Gaithersburg, 
Maryland. 
Hill, James A, 1997, "Summary of Finite Element Studies 
of Walls," oral communication 
ICBO, 1994, 1997, Uniform Building Code, International 
Conference of Building Officials, Whittier, 
California. 
Iliya, R., and Bertero, V.V., 1980, Effects of Amount and 
Arrangement of Wall-Panel Reinforcement on 
Behavior of Reinforced Concrete Walls, Earthquake 
Engineering Research Center, University of California 
at Berkeley, Report UCB-EERC-82-04. 
Kawashima, K., and Koyama, T., 1988, "Effect of 
Number of Loading Cycles on Dynamic Characteristics 
of Reinforced Concrete Bridge Pier Columns," 
Proceedings of the Japan Society of Civil 
Engineers, Structural Eng./Earthquake Eng., Vol. 
5,No. 1. Lybas, J.M. and Sozen, M.A., 1977, Effect of Beam 
Strength and Stiffness on Dynamic Behavior of 
Reinforce Concrete Coupled Walls, University of 
Illinois Civil Engineering Studies, Structural 
Research Series No. 444, Report UILU-ENG-77-
2016 (two volumes), Urbana, Illinois. 
Maier, Johannes, 1991, "Shear Wall Tests," Preliminary 
Proceedings, International Workshop on Concrete 
Shear in Earthquake, Houston Texas. 
Mander, J.B., Mahmoodzadegan, B., Bhadra, S., and 
Chen, S.S.,1996, Seismic Evaluation of a 30-Year-
Old Highway Bridge Pier and Its Retrofit, Department 
of Civil Engineering, State University of New 
York, Technical Report NCEER-96-0008, Buffalo NY 
Mansur, M.A., Balendra, T., and H'Ng, S.C., 1991, 
"Tests on Reinforced Concrete Low-Rise Shear 
Walls Under Cyclic Loading," Preliminary Proceedings, 
International Workshop on Concrete 
Shear in Earthquake, Houston Texas. 
Oesterle, R.G., Fiorato, A.E., Johal, L.S., Carpenter, 
J.E., Russell, H.G., and Corley, W.G., 1976, Earthquake Resistant Structural Walls- Tests of Isolated 
Walls, Report to National Science Foundation, Portland 
Cement Association, Skokie, Illinois, 315 pp. 
Oesterle, R.G., Aristizabal-Ochoa, J.D., Fiorato, A.E., 
Russell, H.G., and Corley, W.G., 1979, Earthquake 
Resistant Structural WallsTests of Isolated Walls 
--Phase11,Report to National Science Foundation, 
Portland Cement Association, Skokie, Illinois. 
Oesterle, R.G., Aristizabal, J.D., Shiu, K.N., and Corley, W.G., 1983, Web Crushing of Reinforced Concrete 
Structural Walls, Portland Cement 
Association, Project HR3250, PCA R&D Ser. No. 
1714, Draft Copy, Skokie, Illinois. 
Ogata, K., and Kabeyasawa, T., 1984, "Experimental 
Study on the Hysteretic Behavior of Reinforced 
Concrete Shear Walls Under the Loading of Different 
Moment-to-Shear Ratios," Transactions, Japan 
Concrete Institute, Vol. 6, pp. 274-283. 
Park, R., 1996, "A Static Force-Based Procedure for the 
Seismic Assessment of Existing R/C Moment 
Resisting Frames," Proceedings of the Annual 
Technical Conference, New Zealand National Society 
for Earthquake Engineering. 
Park, R. and Paulay, T., 1975, Reinforced Concrete 
Structures, John Wiley & Sons, New York. 
Paulay, T., 1971a, "Coupling Beams of Reinforced-
Concrete Shear Walls," Journal of the Structural 
Division, ASCE, Vol. 97, No. ST3, pp. 843-862. 
Paulay, T., 1971b, "Simulated Seismic Loading of 
Spandrel Beams," Journal of the Structural Division, 
ASCE, Vol. 97, No. ST9, pp. 2407-2419. 
Paulay, T., 1977, "Ductility of Reinforced Concrete 
Shearwalls for Seismic Areas," Reinforced Concrete 
Structures in Seismic Zones, American Concrete 
Institute, ACI Publication SP-52, Detroit, 
Michigan, pp. 127-147. 
Paulay, T., 1980, "Earthquake-Resisting Shearwalls -New 
Zealand Design Trends," ACI Journal, pp. 144-152. FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 2: Reinforced Concrete Components 
Paulay, T., 1986, "A Critique of the Special Provisions 
for Seismic Design of the Building Code Requirements 
for Reinforced Concrete," ACI Journal, pp. 274-283. 
Paulay, T., and Binney, J.R., 1974, "Diagonally Reinforced 
Coupling Beams of Shear Walls," Shear in 
Reinforced Concrete, ACI Publication SP-42, 
American Concrete Institute, Detroit, Michigan, pp. 579-598. 
Paulay, T. and Priestley, M.J.N., 1992, Seismic Design 
of Reinforced Concrete and Masonry Buildings, 
John Wiley & Sons, New York. 
Paulay, T., and Priestley, M.J.N., 1993, "Stability of 
Ductile Structural Walls," ACI Structural Journal, 
Vol. 90, No. 4. 
Paulay, T., Priestley, M.J.N., and Synge, A.J., 1982, 
"Ductility in Earthquake Resisting Squat Shear 2 6 9
walls," ACI Journal, Vol. 79, No. 4, pp.2 5 7-. 
Paulay, T., and Santhakumar, A.R., 1976, "Ductile 
Behavior of Coupled Shear Walls," Journal of the 
Structural Division, ASCE, Vol. 102, No. ST1, pp. 93-108. 
Priestley M.J.N., Evison, R.J., and Carr, A.J, 1978, 
"Seismic Response of Structures Free to Rock on 
their Foundations," Bulletin of the New Zealand 
National Society for Earthquake Engineering, Vol. 
11, No. 3, pp. 141-150. 
Priestley, M.J.N., Seible, F., and Calvi, G.M., 1996, 
Seismic Design and Retrofit of Bridges, John Wiley 
& Sons, New York, 686 pp. 
Saatcioglu, Murat, 1991, "Hysteretic Shear Response of 
Low-rise Walls," Preliminary Proceedings, International 
Workshop on Concrete Shear in Earthquake, 
Houston Texas. 
SANZ, Standards Association of New Zealand, 1995, 
Code of Practice for the Design of Concrete Structures, 
NZS3101. SEAOC, 1996, Recommended Lateral Force Requirements 
and Commentary ("Blue Book"), 6th Edition, 
Seismology Committee, Structural Engineers Association 
of California, Sacramento, California. 
Shiga, Shibata, and Takahashi, 1973, "Experimental 
Study on Dynamic Properties of Reinforced Concrete 
Shear Walls," Proceedings, Fifth World Conference 
on Earthquake Engineering, Rome, pp. 
107-117 
Shiga, Shibata, and Takahashi, 1975, "Hysteretic 
Behavior of Reinforced Concrete Shear Walls," 
Proceedings of the Review Meeting, US-Japan 
Cooperative Research Program in Earthquake Engineering 
with Emphasis on the Safety of School 
Buildings, Honolulu Hawaii, pp. 1157-1166 
Shiu, K.N., Daniel, J.I., Aristizabal-Ochoa, J.D., A.E. 
Fiorato, and W.G. Corley, 1981, Earthquake Resistant 
Structural Walls --Tests of Wall With and Without 
Openings, Report to National Science 
Foundation; Portland Cement Association, Skokie, 
Illinois. 
Sozen, M.A., and Moehle, J.P., 1993, Stiffness of Reinforced 
Concrete Walls Resisting In-Plane Shear, 
Electric Power Research Institute, EPRI TR102731, 
Palo Alto, California. Vallenas, J.M., Bertero, V.V., Popov, E.P., 1979, Hysteretic 
Behavior of Reinforced Concrete Structural 
Walls, Earthquake Engineering Research Center, 
University of California, Report No. UCB/EERC-
79/20, Berkeley, California, 234 pp. 
Wallace, J. W., 1996, "Evaluation of UBC-94 Provisions 
for Seismic Design of RC Structural Walls," 
Earthquake Spectra, EERI, Oakland, California. 
Wallace, J. W. and Moehle, J.P., 1992, "Ductility and 
Detailing Requirements for Bearing Wall Buildings," 
Journal of Structural Engineering, ASCE, 
Vol. 118, No. 6, pp. 1625-1644. 
Wallace, J. W. and Thomsen IV, J.H., 1995, "Seismic 
Design of RC Shear Walls (Parts I and II)," Journal 
of Structural Engineering, -ASCE, pp. 75-101. 
Wang, T.Y., Bertero, V.V., Popov, E.P., 1975, Hysteretic 
Behavior of Reinforced Concrete Framed Walls, 
Earthquake Engineering Research Center, University 
of California at Berkeley, Report No. UCB/ 
EERC-75/23, Berkeley, California, 367 pp. 
Wight, James K. (editor), 1985, Earthquake Effects on 
Reinforced Concrete Structures, US-Japan 
Research, ACI Special Publication SP-84, American 
Concrete Institute, Detroit Michigan. 
Wiss, Janney, Elstner and Associates, 1970, Final 
Report on Bar Tests, for the Committee of Concrete 
Reinforcing Bar Producers, American Iron and 
Steel Institute (Job #70189), Northbrook, Illinois. 
Wood, S. L, 1990, "Shear Strength of Low-Rise Reinforced 
Concrete Walls," ACI Structural Journal, Vol. 87, No. 1, pp 99-107. 37 
Technical Resources
FEMA 307 -Technical Resources 37 
Chapter 2: Reinforced Concrete Components 
Wood, S. L., 1991, "Observed Behavior of Slender Publication SP-127, S.K. Ghosh, Editor, American Reinforced Concrete Walls Subjected to Cyclic Concrete Institute, Detroit Michigan, pp. 453-478
Loading," Earthquake-Resistant Concrete Structures, 
Inelastic Response and Design, ACI Special 
FEMA 307
Technical Resources
Technical Resources FEMA 307
Chapter 3: Reinforced Masonry 
Reinforced Masonry
3 
3.1 Commentary and Discussion 
Several topics that are relevant to the development of 
the reinforced masonry component guides are addressed 
in this chapter. 
3.1.1 Typical Hysteretic Behavior 
The behavior modes described for reinforced masonry 
in FEMA 306, Section A3.2 are based on experimental 
research and field observation of earthquake damaged 
masonry buildings. Typical damage patterns and 
hysteretic response representative of different 
components and behavior modes are presented in 
Table 3-1 
3.1.2 Cracking and Damage Severity 
Cracks in a structural wall can provide information 
about previous displacements and component response. 
Aspects of cracking that relate to component behavior 
include: 
* The orientation of cracks 
* The number (density) of cracks 
* The spacing of cracks 
* The width of individual cracks 
* The relative size of crack widths 
In reinforced masonry with a flexural behavior mode, 
flexural cracks generally form in the mortar bed joints. 
At the base of a tall cantilever wall, flexural cracks may 
propagate across the entire length of the wall. Following 
an earthquake, flexural cracks tend to close due to 
gravity loads, and they may be particularly hard to 
locate in mortar joints. They are generally associated 
with ductile response and the natural engagement of 
vertical reinforcement; as a result, they do not provide a 
good measure of damage. When such cracks are visible, 
they are only used to identify behavior modes, not to 
assess the severity of damage. 
Diagonal cracks reflect associated shear stresses, but 
they may be a natural part of ductile flexural action. In 
fully-grouted hollow brick or block masonry, diagonal 
cracks typically propagate through the units with short 
deviations along the mortar joints. Stair-step diagonal 
cracks are rare, and would indicate partial grouting and 
low-strength mortar. In plastic-hinge zones undergoing 
flexural response, diagonal cracks propagate from the 
ends of flexural cracks. In shear-dominated panels, 
diagonal cracks are more independent of flexural 
cracks. 
In a flexurally-controlled wall, diagonal cracks are well-
distributed and of uniform, small width. In a wall 
undergoing the transition from flexural response to 
shear response, one or two diagonal cracks, typically at 
the center of the wall, will grow wider than the others, 
dominating the response and concentrating shear 
deformations in a small area. A poorly-detailed wall 
undergoing preemptive shear behavior may have very 
few cracks until a critical, single diagonal crack opens. 
In the investigation of earthquake-damaged concrete 
and masonry wall structures, cracks are the most visible 
evidence of damage. Because cracks are a striking and 
easily observed indication of the effect of earthquakes 
on walls, there is a strong temptation to overemphasize 
the relationship between crack width and the associated 
decrease (if any) in the strength and deformation 
capacity of a wall. Hanson (1996), has made the case 
that crack width alone is a poor indicator of damage 
severity. In recognition of this, the Component Damage 
Classification Guides in FEMA 306 do not rely on 
crack width as the only description of damage-
numerous indicators of damage severity in reinforced 
masonry walls are described, among which crack width 
is only one. Cracking patterns can provide a wealth of 
information about the performance of a structural wall, 
but the location, orientation, number, and distribution of 
the cracks must be considered as important as, if not 
more important than, the crack width. 
With the understanding that crack width must be 
considered in the context of all of the other parameters 
that can affect the behavior mode and damage severity 
of a wall, a rational approach is required to understand 
the influence of crack width on damage. This section 
outlines the basis of crack width limits specified in the 
Component Damage Classification Guides. 
39 
Technical Resources
Technical Resources 39
FEMA 307 
Table 3-1 Damage Patterns and Hysteretic Response for Reinforced Masonry Components Component and Reference Crack I Damage Pattern Hysteretic Response 
Behavior Mode RM 1 Shing et al., 100. 
DIAGONAL CRACK ,TOE CRUSHING
80.0 Flexure Specimen 12 See Guide RMlA 
2 0.009 $ -20.0 w' I -40.0 -60.0 
DIAGONAL CRACK 
-80.0 TOE CRUSHING' 7 
-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2M 
LATERAL DKPLACNENT [IN] 
RM 1 Priestley and 3der 1982 Flexure See Guide RMlA -c
80 ra0 

Table 3-1 Damage Patterns and Hysteretic Response for Reinforced Masonry Components (continued) 
RM1 ; Shing et al., 125. 
Flexure I Shear Specimen 7 75.0 1 
DIAGONAL CRACK 
See Guides RMlB 
2nd RM2B 
-75.0 DIAGONAL CRACK 
-100. 7 FIRST YIELD 
-2.m -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 
LATERAL DISPLACEMENT [IN] 
RM1 Priestley and 
Elder 1982 
Flexure I Shear 
See Guides RMIB 
and RM2B 
Table 3-1 Damage Patterns and Hysteretic Response for Reinforced Masonry Components (continued) 
RM 1 ; Shing et al., 100 F 1 
99 1 
Flexure I Sliding specimen 8 
Shear 
See Guide RMl C 
'FIRST YIELD
-60.0 
'TOE CRUSHING 
-80 0 
-2.00 -1.50 -1.00 -0.50 0.M) 0.50 1.W 1.50 2.00 
LATERAL DISPLACEMENT [IN] 
RM1 Shing et al., 
1991 /DIAGONAL CRACK 
Flexure I Shear I specimen 6 
600 
Sliding Shear 
See Guides RMl B 
and RMI C 
-80 0 
DIAGONAL CRACK 
-200 -1 50 -1 00 -0.50 0.00 0.50 l. W 1.50 2.00 
Lateral DISPLACEMENT [IN] 
3-1 Damage Patterns and Hysteretic Response for Reinforced Masonry Components (continued) 
Flexure /lap splice 
slip 
See Guide RMIE 
Shing et al., 
1991 
Specimen 19 
125 
100 
75 0 
50.0 
25 0 
0 00 
-25 0 
-50 0 
-75 0 
-100 IFIRST YIELD 
FIRST YIELD 
-125. I
-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 
Lateral DISPLACEMENT [IN] 
d0 
RMl or RM2 Shing et al., 
1991 
125. 
100. DIAGONAL CRACK -=r 
0 
3. 
E 
Preemptive Shear Specimen 9 
P See Guide RM2G 
v)
05tD 
0 00 
-25 0 
fJY -50 0 
-75 0 
first YIELD-I1 DIAGONAL CRACK 

Table 3-1 Damage Patterns and Hysteretic Response for Reinforced Masonry Components (continued) 
RM1 or RM2 Shing et al., 1991 
Preemptive Shear Specimen 14 
See Guide RM2G 2
3 0.00 
3 25.0 w
4 50.0 
-75.0 
-100. 
DIAGONAL 
-2.00 1.50 1.M) 0.50 0.00 0.50 1.m 1.50 2.02 
LATERN DISPLACEMENT flN1 3 
0 RM3 Priestley and 
5 Hon, 1985 
3. 0
2 Flexure a (D v)
0 See Guide RM3A: (D0) n m z
D W 0 4 
I Table 3-1 Damage Patterns and Hysteretic Response for Reinforced Masonry Components (continued) 
RM1 or RM2 with Priestley and 
0 flange. He, 1990 I 
Flexure / Shear 
See Guides RMJA, 
RMIB, and/or 4,@,
RM2G 
S.C 5.5 s. C (ml 
M g km a
0 I I l 
C;M 0 
0. 0) M . 0k 
R0 00 0. 0 a0)0 I 01b 
Chapter 3: Reinforced Masonry 
Research has been conducted to evaluate the 
relationship between crack width, crack spacing, and 
reinforcing bar strain. A partial review of the literature 
on crack width is provided by Noakowski, (1985). 
Research indicates that the width of a crack crossing a 
reinforcing bar at first yield of the reinforcement 
depends on the bar diameter, the reinforcement yield 
stress, the reinforcement ratio, the reinforcement elastic 
modulus, and on the characteristics of the bond stress-
slip relationship. However, most research in this area 
has focused on nearly elastic systems (prior to yield in 
reinforcement), and flexural cracking in beams and 
uniaxial tension specimens. It is difficult to extrapolate 
quantitative expressions for crack width and spacing 
prior to yield to reinforced masonry specimens with 
sufficient damage to reduce strength or deformation 
capacity. 
Sassi and Ranous (1996) have suggested criteria to 
relate crack width to damage, but they have not 
provided sufficient information to associate crack 
patterns with specific behavior modes, which is 
essential when determining damage severity. 
In the guides for reinforced masonry components, the 
crack width limits for each damage severity level have 
been determined empirically, using crack widths 
reported in the literature and photographs of damaged 
specimens. Consideration has been given to the 
theoretical crack width required to achieve yield of 
reinforcement under a variety of conditions. A 
fundamental presumption is that the width of shear 
cracks is related to damage severity, while flexural 
crack widths are not closely related to damage severity. 
3.1.3 Interpretation of Tests 
Interpretation of test results for reinforced masonry was 
similar to that for reinforced concrete as described in 
Section 2.1.1.2. The ranges of component ductility and 
1-factors are presented in Table 3-2. 
3.2 Tabular Bibliography for 
Reinforced Masonry 
Table 3-3 contains a brief description of the key 
technical reports which address specific reinforced 
masonry component behavior. The component types 
and their behavior modes are indicated. The full 
references can be found in Section 3.4. 
Technical Resources FEMA 307 
Chapter 3: Reinforced Masonry 
Table3-2-Ranges of reinforced masonry component displacement ductility, A, associated with 
damage severity levels and A factors 
Damage Severity 
Guide Insignificant Slight Moderate Heavy 
RM1A t <3 P =2-4 ud=3-8 Heavy not used 
Ductile Flexural AK = 0.8 AK = 0.6 ; K = 0.4 
AQ=1.0 AQ=l.0 AQ=0.9 
AD= 1-0 AD= 1.0 AD= 1.0 
RM1B < 2 / =2-3 y=3-5 
Flexure/Shear AK = 0.8 AK= 0.6 AK = 0.4 
AQ=1.0 AQ=1.0 AQ =0.8 
A4= 1.0 AD=1.0 AD=0.9 
RMIC See RM1A /I2-2-4 3-8 
Flexure/ Sliding Shear AK = 0.5 AK = 0.2 
AQ=0.9 AQ=0.8 
AD=1.0 AD=0.9 
RM1D See RM1A See RMIA SeeRM1A PA 8-10 
Flexure/ Out-of-Plane AK = 0.4 
Instability AQ = 0.5 
AD = 0.5 
RM1E SeeRM1A See RM1A 3-4 
Flexure/ Lap Splice Slip or RM1B or RM1B AK = 0.4 
AQ = 0.5 
AD = 0.8 
RM2B 2 a2-3 A<yA 3 5 
Heavy not used 
Flexure/Shear AK = 0.8 AK = 0.6 AK = 0.4 
AQ= 1.0 AQ=1.0 AQ=0.8 
_D= 1.0 AD= 1.0 AD=0.9 
RM2G MAIl I-2 ua=I-2 2-3 
Preemptive Shear AK = 0.9 AK = 0.8 AK = 0.5 AK = 0.3 
AQ= 1.0 AQ=1.0 AQ=0.8 AQ= 0.4 
AD= 1.0 AD= 1.0 AD=0.9 AD=0.5 
RM3A < 2 4 <3 ya=6 
Flexure AK = 0.9 AK= 0.8 AK = 0.6 
AQ=1.0 AQ=0.9 AQ=0.8 
AD=1.0 AD= 1.0 AD= 1.0 
RM3G AK= 0.9 AK= 0.8 AK= 0.3 
Preemptive Shear AQ = 1.0 AQ = 0.8 AQ = 0.5 
(No ,u values for RM3G) AD = 1.0 AD = 1.0 AD = 0-9 
FEMA 307 Technical Resources 
Table 3-3 Annotated Bibliography for Reinforced Masonry 
Reference(s) Description Comp. Behavior modes 
Type(s) Addressed 
E f a b c d e f g 
EVALUATIONANDDESIGNRECOMMENDATIONS: 
Paulay and Priestley Overview of capacity-design principles Description of RIM component RMI 9 o 
(1992) for reinforced concrete and response in terms of dis- RM2 
masonry structures. Thorough placement and ductility. RM3 
description of R/C failure modes, RM4 
and, to a lesser extent, R/M failure 
modes. 
OVERVIEWS OF EXP ELTEST RESULTS
Drysdale, Hamid, and Textbook for design of masonry RM1 0:)
W t5A) 
Baker (1994) structures. Includes complete bibliography 
and selected results RM2 RM4 9. 0(D00 C) from experimental EXPERIMENTAL TEST RESULTS research. 0 C)0 0.Q 0_In0 Abrams (1989) and Paulson 2 specimens 
1/4-scale model RM2 0 (D Abrams and Paulson (1990) 
Foltz and Yancy 10 Specimens No vertical reinforcement Many damage photos. No hysteresis RM2 
(1993) 8" CMU Pv = 0.0% curves. 
56" tall by 48" wide Ph = 0.024% 0.22% Joint reinforcement improved 
D Axial load 200+ psi ultimate displacement from g-=l 
Axial load increased w/ displacement to ;i3. 
Clear improvement in displacement 
and crack distribution w/ ,n. increased horizontal reinforcement. 
0 4 I "I m Table 3-3 Annotated Bibliography for Reinforced Masonry (continued) 
0 4 Ghanem et al. (1993) 
Hammons et al. (1994) 
Hidalgo et al. (1978) 
Chen et al. (1978) 
Hidalgo et al. (1979) 
14 Specimens 
1/3 scale concrete block 
124 specimens 
Hollow concrete and clay masonry 
63 specimens: 
28 8" hollow clay brick 
18 2-wythe clay brick 
17 8" hollow concrete block Monotonic tests only reported 
here. Monotonic testing of lap splices. 
Only #4 in 8" units fail by classical pull-out. 
Others fail in tensile splitting. 
Aspect ratios: 0.5, 1.0, 2.0 
High axial loads, increasing 
with lateral displacement. RM2 
Tensile splitting failure likely N/A 
regardless of lap splice length 
for: 
#4 in 4 inch units 
#6 in 6 inch units 
#8 in 8 inch units 
All failures in shear or flexure/ RM2 
shear 0 0 Hon & Priestley 
(1984) 2 fully-grouted specimens 
8" hollow concrete block 
Full-scale, fully-reversed cyclic loading. Stable hysteresis up to displacement ductility of 4 at first crush RM3 
Priestley & Hon One specimen tested in New 2nd specimen purposely violated ing. I 0(1985) Zealand, and a second later at UC proposed design criteria, Achieved ductility of 10 with 
0so Hart & Priestley San Diego. and performed in a ductile minor load degradation. 0tD. 
(1989) Priestley (1990) manner. 
(D 0CD0 Igarashi et al. (1993) 1 fully grouted 3-story wall specimen pv = 0.15% Flexural response to 0.3% drift RM1 
6" hollow concrete block 
3 story full-scale cantilever wall 
P = 0.22% 
Ph = 0.22% 
followed by lap-splice slip at 
base and stable rocking to 1% 
drift at approx. 1/3 of max. load. 
Kubota and 5 cmu wall specimens Sudden loss of strength associated Vertical splitting at lap RM2 
Murakami (1988) Investigated effect of lap splices w/ lap-splice failure. Test 
stopped following lap-splice failure 
Kubota et al. (1985) 5 wall specimens Minimum vertical reinf RM2 
Hollow clay brick Ph = 0.17% 0.51% 
Matsumura (1988) Includes effect of grout flaws on 
damage patterns and shear strength. 
Missing or insufficient grout 
causes localized damage and 
inhibits uniform distribution of 
RM2 cracks. Q00
Table 3.3 Annotated Bibliography for Reinforced Masonry(continued) 
Matsuno et al. (1987) 1 grouted hollow clay specimen Limited ductility, significant Flexure response in long wall RM1 
3-stories strength degradation associated (RM1) RM2 
3-coupled flanged walls w/ preemptive shear failure Flexure/shear in short walls RM4 of coupling beams. (RM2) 
Merryman et al 6 fully-grouted. 2-story wall specimens Flexural design by 1985 UBC. Stable flexural response in RM1 
(1990) Shear design to ensure flexure pled walls, limited by compression 
Leiva and Klingner 2-story walls with openings hinging. toe spalling, fracture of (1991) 2-story pairs of wall coupled by pv = 0.22% reinforcement, and sliding. No slab only Ph = 0.22% 0.44% significant load degradation even 
2-story pairs of walls coupled by at end of test. 
slab and R/M lintel One specimen inadvertently 
loaded to 60% of max base shear 
in single pulse prior to test, with I D 
Okada and Concrete block beams Similar to concrete. 
no clear effect on response. 
Damage for lap splices limited to RM4 0 I 
Kumazawa (1987) 32"x90" Rotation capacity of 1/100 splice zone. More distributed 
without laps. 
5. 00 CI Priestley and Elder (1982) RM1 C). 0. 
CD Co Schultz, (1996) 6 partially-grouted specimens Minimum vertical reinf Drift = 0.3%-1% at 75% of max RM2 Ca concrete masonry Ph = 05% .12% strength. 0 I 
Moderately ductile response w/ Behavior characterized by vertical initial 
peak and drop to degrading cracks at junction of grouted 
plateau at approx. 75% of and ungrouted cells. Few if any 
max. diagonal cracks except in one specimen. n m 0 
Table 3-3 I Annotated Bibliography for Reinforced Masonry (continued) 
Seible et al. (1994) 1 fully grouted. 5-story building Flexural design by 1991 Ductile flexural response with RM1 Seible et al. (1995) specimen NEHRP Recommended Provisions some sliding to i=6 and 9, (drift 
Kingsley (1994) 6" hollow concrete block for the Development of = 1% and 1.5%). 
Kingsley et al. (1994) 5-story full-scale flanged walls Seismic Regulations for New Distributed cracking. Kurkchubasche et al. coupled by topped, precast plank Buildings. Significant influence of flanges 
(1994) floor system Shear design to ensure flexural and coupling slabs. 
Pv = 0.23%-0.34% hinging. Ph = 0.11% 0.44% 
Shing et al. (1990a) 24 fully-grouted test specimens: Full-scale walls, 6-ft square, 2 specimens with lap splices at RM1 
Shing et al. (1990b) 6 6-inch hollow clay brick loaded in single curvature. base, others with continuous RM2 
Shing et al. (1991) 18 6-inch hollow concrete block M/VL = 1 reinforcement. 
1 specimen w/ confinement 0 0 2 monotonic loading 
22 cyclic-static loading. Uniformly distributed vertical 
& horizontal reinforcement. comb at wall toe. 
.5 cD 5. D tn F 4 levels of axial load 
p, = 0.38% 0.74% Ph = 0.14% 0.26% 
Most comprehensive tests on 
reinforced masonry wall components 
to date 
CD 0 ao o 0 C) 
Tomazevic and Zarnic (1985) 
32 wall specimens 
Concrete block walls and complete 
= 0.26% 0.52% 
Ph = 0.00% 0.52% 
RM2 2. 0. CA CD Cl Tomazevic and Lutman (1988) 
structures 
Static and shaking table 0 
Tomazevic and Modena (1988) 
Tomazevic et al. (1993) 
Yamazaki et al. 1 fully-grouted 5-storv building First damage in masonry lintel Flexural modes degraded to RM1 
(1988a) specimen beams of many different geometries shear failing modes at 0.75% RM2 
Yamazaki et al. 8" hollow concrete block. building drift (1.4% first story RM4 
(1988b) 5-story full-scale flanged walls drift). 
coupled by cast-in-place 6" and 8" 
R/C floor slabs 
0n Table 3-3 Annotated Bibliography for Reinforced Masonry (continued) 
EXPERIMENTAL TEST RESULTS REPAIRED OR RETROFITTED WALLS 
Innamorato (1994) 3 fully-grouted test specimens Tested in "original" and Repair by epoxy injection and RMI
Designed to match Shing (1991) "repaired" condition carbon fiber overlay RM2 
Preemptive shear failure Flexure failure Laursen et al. (1995) 2 in-plane specimens Tested in "original," Repair by epoxy injection and RM1 
Designed to match Shing (1991) "repaired," and "retrofit" con-carbon fiber overlays in horizon- RM2 specimen preemptive shear failure. figurations. tal or vertical direction to 2 out-of-plane specimens enhance ductility or strength 
Weeks et al. (1994) 5-story building tested previously Repair by epoxy injection and RM1 by Seible et al. (1994) repaired carbon fiber overlay 
and retested. 
-Behavior modes: c Flexure/Sliding Shear f Foundation rocking of individual piers CI) F
E a Ductile Flexural Response: d Flexure/Out-of-Plane Wall Buckling g Preemptive Diagonal Shear Failure (D 
CDb Flexure/Diagonal Shear e Flexure/Lap-Splice Slip 0
Chapter 3: Reinforced Masonry 
3.3 Symbols for Reinforced Masonry 
Ag = Gross crossectional area of wall s = Spacing of reinforcement 
Asi = Area of reinforcing bar i t = Wall thickness 
AV Avf a 
= Area of shear reinforcing bar VI 
= Area of reinforcement crossing perpendicular V 
to the sliding plane m 
= Depth of the equivalent stress block V 
= Expected shear strength of a reinforced 
masonry wall 
= Portion of the expected shear strength of a 
wall attributed to masonry 
= Portion of the expected shear strength of a 
c = Depth to the neutral axis wall attributed to steel 
Cm = Compression force in the masonry VP = Portion of the expected shear strength of a 
fie = Expected compressive strength of masonry wall attributed to axial compression effects 
fye = Expected yield strength of reinforcement Vse 
= Expected sliding shear strength of a masonry 
wall 
he = Effective height of the wall (height to the 
resultant of the lateral force) = M/V xi = Location of reinforcing bar i 
id = Lap splice development length 
1p = Effective plastic hinge length Ap 
= Maximum inelastic displacement capacity 
1w = Length of the wall 
= Displacement at first yield 
M/V = Ratio of moment to shear (shear span) at a 
section = Maximum inelastic curvature of a masonry 
section Me = Expected moment capacity of a masonry section BY = Yield curvature of a masonry section P = Displacement ductility 
PU = Wall axial load, = Coefficient of friction at the sliding plane 
FEMA 307 Technical Resources 
Chapter 3: Reinforced Masonry 
3.4 References for Reinforced Masonry
This list contains references from the reinforced 
masonry chapters of both FEMA 306 and 307. 
Abrams, D.P., and Paulson, T.J., 1989, "Measured Nonlinear 
Dynamic Response of Reinforced Concrete 
Masonry Building Systems," Proceedings of the 
Fifth Canadian Masonry Symposium, University of 
British Columbia, Vancouver, B.C., Canada. 
Abrams, D.P., and Paulson, T.J., 1990, "Perceptions and 
Observations of Seismic Response for Reinforced 
Masonry Building Structures," Proceedings of the 
Fifth North American Masonry Conference, University 
of Illinois at Urbana-Champaign. 
Agbabian, M., Adham, S, Masri, S., and Avanessian, V., 
Out-of-Plane Dynamic Testing of Concrete 
Masonry Walls, U.S. Coordinated Program for 
Masonry Building Research, Report Nos. 3.2b-1 
and 3.2b-2. 
Anderson, D.L., and Priestley, M.J.N., 1992, "In Plane 
Shear Strength of Masonry Walls," Proceedings of 
the 6th Canadian Masonry Symposium, Saskatoon, 
Saskatchewan. 
Atkinson, R.H., Amadei, B.P., Saeb, S., and Sture, S., 
1989, "Response of Masonry Bed Joints in Direct 
Shear," American Society of Civil Engineers Journal 
of the Structural Division, Vol. 115, No. 9. 
Atkinson, R.H., and Kingsley, G.R., 1985, A Comparison 
of the Behavior of Clay and Concrete Masonry 
in Compression, U.S. Coordinated Program for 
Masonry Building Research, Report No. 1.1-1. 
Atkinson, R.H., Kingsley, G.R., Saeb, S., B. Amadei, 
B., and Sture, S., 1988, "A Laboratory and In-situ 
Study of the Shear Strength of Masonry Bed 
Joints," Proceedings of the 8th International Brick! 
Block Masonry Conference, Dublin. 
BIA, 1988, Technical Notes on Brick Construction, No. 
17, Brick Institute of America, Reston, Virginia. 
Blakeley, R.W.G., Cooney, R.C., and Megget, L.M., 
1975, "Seismic Shear Loading at Flexural Capacity 
in Cantilever Wall Structures," Bulletin of the New 
Zealand National Society for Earthquake Engineering, 
Vol. 8, No. 4. 
Calvi, G.M., Macchi, G., and Zanon, P., 1985, "Random 
Cyclic Behavior of Reinforced Masonry Under 
Shear Action," Proceedings of the Seventh International 
Brick Masonry Conference, Melbourne, Australia. 
Chen, S.J., Hidalgo, P.A., Mayes, R.L., and Clough, 
R.W., 1978, Cyclic Loading Tests of Masonry Single 
Piers, Volume2 Height to Width Ratio of 1, 
Earthquake Engineering Research Center Report 
No. UCB/EERC-78/28, University of California, 
Berkeley, California. 
Drysdale, R.G., Hamid, A.A., and Baker, L.R., 1994, 
Masonry Structures, Behavior and Design, Prentice 
Hall, New Jersey. 
Fattal, S.G., 1993, Strength of Partially-Grouted 
Masonry Shear Walls Under Lateral Loads, 
National Institute of Standards and Technology, 
NISTIR 5147, Gaithersburg, Maryland. 
Foltz, S., and Yancy, C.W.C., 1993, "The Influence of 
Horizontal Reinforcement on the Shear Performance 
of Concrete Masonry Walls", Masonry: 
Design and Construction, Problems and Repair, 
ASTM STP 1180, American Society for Testing 
and Materials, Philadelphia, Pennsylvania. 
Ghanem, G.M., Elmagd, S.A., Salama, A.E., and 
Hamid, A.A., 1993, "Effect of Axial Compression 
on the Behavior of Partially Reinforced Masonry 
Shear Walls," Proceedings of the Sixth North American 
Masonry Conference, Philadelphia, Pennsylvania. 
Hamid, A., Assis, G., and Harris, H., 1988, Material 
Modelsfor Grouted Block Masonry, U.S. Coordinated 
Program for Masonry Building Research, 
Report No. 1.2a-1. 
Hamid, A., Abboud, B., Farah, M., Hatem, K., and Harris, 
H., 1989, Response of Reinforced Block 
Masonry Walls to Out-of-Plane Static Loads, U.S. 
Coordinated Program for Masonry Building 
Research, Report No. 3.2a-1. 
Hammons, M.I., Atkinson, R.H., Schuller, M.P., and 
Tikalsky, P.J., 1994, Masonry Research for Limit-
States Design, Construction Productivity Advancement 
Research (CPAR)U.S. Army Corps of Engineers 
Waterways Experiment Station, Program 
Report CPAR-SL-94-1, Vicksburg Mississippi. 
Hanson, R.D., 1996, "The Evaluation of Reinforced 
Concrete Members Damaged by Earthquakes", 
Earthquake Spectra, Vol. 12, No. 3, Earthquake 
Engineering Research Institute. 
Technical Resources FEMA 307 
Chapter 3: Reinforced Masonry 
Hart, G.C., and Priestley, M.J.N., 1989, Design Recommendations 
for Masonry Moment-Resisting Wall 
Frames, UC San Diego Structural Systems 
Research Project Report No. 89/02. 
Hart, G.C., Priestley, M.J.N., and Seible, F., 1992, 
"Masonry Wall Frame Design and Performance," 
The Structural Design of Tall Buildings, John Wile 
& Sons, New York. 
He, L., and Priestley, M.J.N., 1992, Seismic Behavior of 
Flanged Masonry Walls, University of California, 
San Diego, Department of Applied Mechanics and 
Engineering Sciences, Report No. SSRP-92/09. 
Hegemier, G.A., Arya, S.K., Nunn, R.O., Miller, M.E., 
Anvar, A., and Krishnamoorthy, G., 1978, A Major 
Study of Concrete Masonry Under Seismic-Type 
Loading, University of California, San Diego 
Report No. AMES-NSF TR-77-002. 
Hidalgo, P.A., Mayes, R.L., McNiven, H.D., and 
Clough, R.W., 1978, Cyclic Loading Tests of 
Masonry Single Piers, Volume I Height to Width 
Ratio of 2, University of California, Berkeley, 
Earthquake Engineering Research Center Report 
No. UCB/EERC-78/27. 
Hidalgo, P.A., Mayes, R.L., McNiven, H.D., and 
Clough, R.W., 1979, Cyclic Loading Tests of 
Masonry Single Piers, Volume 3 Height to Width 
Ratio of 0.5, University of California, Berkeley, 
Earthquake Engineering Research Center Report 
No. UCB/EERC-79/12. 
Hon, C.Y., and Priestley, M.J.N., 1984, Masonry Walls 
and Wall Frames Under Seismic Loading, Department 
of Civil Engineering, University of Canterbury, 
Research Report 84-15, New Zealand. 
Igarashi, A., F. Seible, and Hegemier, G.A., 1993, 
Development of the Generated Sequential Displacement 
Procedure and the Simulated Seismic 
Testing of the TCCMAR 3-Story In-plane Walls, 
U.S. Coordinated Program for Masonry Building 
Research Report No. 3.1(b)-2. 
Innamorato, D., 1994, The Repair of Reinforced Structural 
Masonry Walls using a Carbon Fiber, Polymeric 
Matrix Composite Overlay, M.Sc. Thesis in 
Structural Engineering, University of California, 
San Diego. 
Kariotis, J.C., Rahman, M. A., El-mustapha, A. M., 
1993, "Investigation of Current Seismic Design 
Provisions for Reinforced Masonry Shear Walls," 
The Structural Design of Tall Buildings, Vol. 2, 
163-191. 
Kingsley, G.R., 1994, Seismic Design and Response of 
a Full-scale Five-Story Reinforced Masonry 
Research Building, Doctoral Dissertation, University 
of California, San Diego, School of Structural 
Engineering. 
Kingsley, G.R., Noland, J.L., and Atkinson, R.H., 1987, 
"Nondestructive Evaluation of Masonry Structures 
Using Sonic and Ultrasonic Pulse Velocity Techniques," 
Proceedings of the Fourth North American 
Masonry Conference, University of California at 
Los Angeles. 
Kingsley, G.R., Seible, F., Priestley, M.J.N., and Hegemier, 
G.A., 1994, The U.S.-TCCMAR Full-scale 
Five-Story Masonry Research Building Test, Part 
11: Design, Construction, and Test Results, Structural 
Systems Research Project, Report No. SSRP-94/02, University of California at San Diego. 
Kubota, T., and Murakami, M., 1988, "Flexural Failure 
Test of Reinforced Concrete Masonry Walls Effect 
of Lap Joint of Reinforcement," Proceedings 
of the Fourth Meeting of the U.S.-Japan Joint Technical 
Coordinating Committee on Masonry 
Research, San Diego, California. 
Kubota, T., Okamoto, S., Nishitani, Y., and Kato, S., 
1985, "A Study on Structural Behavior of Brick 
Panel Walls," Proceedings of the Seventh International 
Brick Masonry Conference, Melbourne, Australia. 
Ktirkchuibasche, A.G., Seible, F., and Kingsley, G.R., 
1994, The U.S.-TCCMAR Five-story Full-scale 
Reinforced Masonry Research Building Test: Part 
114Analytical Models, Structural Systems Research 
Project, Report No. TR 94/04, University of California 
at San Diego. 
Laursen, P. T., Seible, F., and Hegemier, G. A., 1995, 
Seismic Retrofit and Repair of Reinforced Concrete 
with Carbon Overlays, Structural Systems Research 
Project, Report No. TR 95/01, University of California 
at San Diego. 
Leiva, G., and Klingner, R.E., 1991, In-Plane Seismic 
Resistance of Two-story Concrete Masonry Shear 
Wallswith Openings, U.S. Coordinated Program for 
Masonry Building Research, Report No. 3.1(c)-2. 
Leiva, G., and Klingner, R.E., 1994, "Behavior and 
Design of Multi-Story Masonry Walls under In-
Technical Resources 
FEMA 307 Technical Resources 
Chapter 3: Reinforced Masonry 
plane Seismic Loading," The Masonry Society 
Journal, Vol. 13, No. 1. 
Matsumura, A., 1988, "Effectiveness f Shear Reinforcement 
in Fully Grouted Hollow Clay Masonry 
Walls," Proceedings of the Fourth Meeting of the 
U.S.-Japan Joint Technical Coordinating Committee 
on Masonry Research, San Diego, California. 
Matsuno, M., Yamazaki, Y, Kaminosono, T., Teshigawara, 
M., 1987, "Experimental and Analytical 
Study of the Three Story Reinforced Clay Block 
Specimen," Proceedings of the ThirdMeeting of the 
U.S.-Japan Joint Technical Coordinating Committee 
on Masonry Research, Tomamu, Hokkaido, 
Japan. 
Mayes, R.L., 1993, Unpublished study in support of the 
U.S. Coordinated Program for Masonry Building 
Research Design and Criteria Recommendations 
for Reinforced Masonry. 
Merryman, K.M., Leiva, G., Antrobus, N., and Klingner, 
1990, In-plane Seismic Resistance of Two-story 
Concrete Masonry Coupled Shear Walls, U.S. 
Coordinated Program for Masonry Building 
Research, Report No. 3. 1 (c)- I. 
Modena, C., 1989, "Italian Practice in Evaluating, 
Strengthening, and Retrofitting Masonry Buildings,"
Proceedings of the International Seminaron 
Evaluating, Strengthening, and Retrofitting 
Masonry Buildings, University of Texas, Arlington, 
Texas. 
Noakowski, Piotr, 1985, Continuous Theory for the 
Determination of Crack Width under the Consideration 
of Bond, Beton-Und Stahlbetonbau, 7 u. 
Noland, J.L., 1990, "1990 Status Report: U.S. Coordinated 
Program for Masonry Building Research," 
Proceedings of the Fifth North American Masonry 
Conference, Urbana-Champaign, Illinois. 
Ohkubo, M., 1991, Current Japanese System on Seismic 
Capacity and Retrofit Techniques for Existing 
Reinforced Concrete Buildings and Post-Earthquake Damage Inspection and Restoration Techniques, University of California, San Diego 
Structural Systems Research Project Report No. 
SSRP-91/02. 
Okada, T., and Kumazawa, F., 1987, "Flexural Behavior 
of Reinforced Concrete Block Beams with Spirally-
Reinforced Lap Splices," Proceedings of the Third 
Meeting of the U.S.-Japan Joint Technical Coordinating 
Committee on Masonry Research, Tomarnu, 
Hokkaido, Japan. 
Park, R. and T. Paulay, 1975, Reinforced Concrete 
Structures, John Wiley & Sons, New York. 
Paulay T., and Priestley, M.J.N, 1992, Seismic Design of 
Reinforced Concrete and Masonry Structures, John 
Wiley & Sons, New York. 
Paulay, T., and Priestley, M.J.N, 1993, "Stability of 
Ductile Structural Walls," ACI Structural Journal, 
Vol. 90, No. 4. 
Paulay, T., Priestley, M.J.N., and Synge, A.J., 1982, 
"Ductility in Earthquake Resisting Squat Shear-
walls," A CI Journal, Vol. 79, No. 4, pp.257-269. 
Priestley, M.J.N., 1977, "Seismic Resistance of Reinforced 
Concrete Masonry Shear Walls with High 
Steel Percentages," Bulletin of the New Zealand 
National Society for Earthquake Engineering, Vol. 
10, No. 1, pp.1-16. 
Priestley, M.J.N., 1986, "Flexural Strength of Rectangular 
Unconfined Shear Walls with Distributed 
Reinforcement," The Masonry Society Journal, Vol. 
5, No. 2. 
Priestley, M.J.N., 1990, Masonry Wall-Frame Joint 
Test, Report No. 90-5, Sequad Consulting Engineers, 
Solana Beach, California. 
Priestley, M.J.N. and Elder, D.M., 1982, Seismic Behavior 
of Slender Concrete Masonry Shear Walls, Dept. 
of Civil Engineering, University of Canterbury, 
Christchurch, Research Report ISSN 0110-3326, 
New Zealand. 
Priestley M.J.N., Evison, R.J., and Carr, A.J., 1978, 
"Seismic Response of Structures Free to Rock on 
their Foundations," Bulletin of the New Zealand 
National Society for Earthquake Engineering, Vol. 
11, No. 3, pp. 141-150. 
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the Period of Vibration of Masonry 
Wall Buildings, Structural Systems Research 
Project, Report No. SSRP 89/05, University of California 
at San Diego. 
Priestley, M.J.N., and Hon, C.Y., 1985, "Seismic 
Design of Reinforced Concrete Masonry Moment Resisting 
Frames," The Masonry Society Journal, 
Vol. 4., No. 1. 
Technical Resources FEMA 307 
Chapter 3: Reinforced Masonry 
Priestley, M.J.N., and Limin, He, 1990, "Seismic 
Response of T-Section Masonry Shear Walls," The 
Masonry Society Journal, Vol. 9, No. 1. 
Priestley, M.J.N., Verma, R., and Xiao, Y., 1994, "Seismic 
Shear Strength of Reinforced Concrete Columns,"
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Concrete Walls," From Experience, Structural 
Engineers Association of Southern California, 
Whittier, California. 
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1994, "Injection Grouting for Repair and Retrofit of 
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Advances in Structural Concrete and Masonry, 
A.E. Schultz and S.L. McCabe, Eds., American 
Society of Civil Engineers, New York. 
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M., 1987, "The Japanese 5-story Full Scale Reinforced 
Concrete Masonry Test Design and Construction 
of the Test Specimen," The Masonry 
Society Journal, Vol. 6, No. 2. 
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Kuirkchubasche, A.G., 1991, Flexural coupling of 
Topped Hollow Core Plank Floor Systems in Shear 
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at San Diego. 
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Kuirkchibasche, A.G., 1994b, "Seismic Response 
of a Five-story Full-scale RM Research Building", 
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of Shear Strength of Reinforced Masonry 
Walls," Proceedings of the Sixth North American 
Masonry Conference, Philadelphia, Pennsylvania. 
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and Schuller, M.P., 1991, Response of Single Story 
Reinforced Masonry Shear Walls to In-plane Lateral 
Loads, TCCMAR Report No. 3.1 (a)-2. 
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Division, Vol 116, No. 3. 
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Concrete Masonry," Proceedings Fourth North 
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Elsevier Applied Science, London. 
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"The Influence of Lateral Load Time-history on the 
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Shear," Proceedings of the Sixth North American 
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Behavior of Mixed, Reinforced Concrete, Reinforced 
Masonry Structural Systems," Brick and 
Block Masonry, J.W. DeCourcy, Ed., Elsevier 
Applied Science, London. 
307 Resources
FEMA Technical 
FEMA 307 Technical Resources 57 
Chapter 3: Reinforced Masonry 
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Horizontal Reinforcement on the Strength and Ductility 
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of the Seventh International Brick Masonry 
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for Predicting the Lateral Response of RC Shear 
Walls, University of California, UCB/EERC Report 
No. 87-19, Berkeley, California. 
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M.J.N., 1994, The U.S.-TCCMAR Full-scale Five-
story Masonry Research Building Test, Part V Repair 
and Retest, University of California Structural 
Systems Research Project Report No. SSRP-
94/05. 
Yamamoto, M., and Kaminosono, T., 1986, "Behavior 
of Reinforced Masonry Walls with Boundary 
Beams," Proceedings of the Second Meeting of the 
Joint Technical Coordinating Committee on 
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T., Teshigawara, M., 1988b, "The Japanese 5-story 
Full Scale Reinforced Concrete Masonry Test Forced 
Vibration and Cyclic Load Test Results," 
The Masonry Society Journal, Vol. 7, No. 1. 
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Seible, F., 1988a, "The Japanese 5-story Full Scale 
Reinforced Concrete Masonry Test Pseudo 
Dynamic and Ultimate Load Test Results," The 
Masonry Society Journal, Vol. 7, No. 2. 
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Stress Distribution of Grouted Hollow Clay 
Masonry Under Stain Gradient, U.S. Coordinated 
Program for Masonry Building Research, Report 
No. 1.2b-1. 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Unreinforced Masonry
4. 4.1 Commentary and Discussion 
4.1.1 Hysteretic Behavior of URM 
Walls Subjected to In-Plane 
Demands 
A search of the available literature was performed to 
identify experimental and analytical research relevant to 
unreinforced masonry bearing-wall damage. Because 
URM buildings have performed poorly in past 
earthquakes, there is an extensive amount of anecdotal 
information in earthquake reconnaissance reports; there 
have also been several studies that took a more 
statistical approach and collected damage information 
in a consistent format for a comprehensive population 
of buildings. These studies help to confirm the 
prevalence of the damage types listed in FEMA 306, 
and they help to indicate the intensity of shaking 
required to produce certain damage types. 
The proposed methodology for this document, however, 
requires moving beyond anecdotal and qualitative 
discussions of component damage and instead obtaining 
quantitative information on force/displacement 
relationships for various components. The focus of 
research on URM buildings has been on the in-plane 
behavior of walls. Most of the relevant research has 
been done in China, the former Yugoslavia, Italy, and 
the United States. This stands in contrast to the 
elements in URM buildings that respond to ground 
shaking with essentially brittle or force-controlled 
behavior: parapets, appendages, wall-diaphragm ties, 
out-of-plane wall capacity, and, possibly, archaic 
diaphragms such as brick arch floors. While there has 
been very little research on most of these elements, it is 
less important because performance of these elements is 
not deformation-controlled. 
Unfortunately, research on in-plane wall behavior is 
rarely consistent-materials, experimental techniques, 
modes of reporting, and identified inelastic mechanisms 
all vary widely. Placing the research in a format 
consistent with FEMA 273 and this project s emphasis 
on components, damage types, hysteresis curves, 
nonlinear force/displacement relationships, and 
performance levels is difficult. Almost no experimental 
tests have been done on damaged URM walls; typically, 
tests were done on undamaged walls and stopped. In 
some cases, the damaged wall was repaired and 
retested. Most of the research does not provide simple 
predictive equations for strength and stiffness 
(particularly post-elastic stiffness); when analysis has 
been done, it has usually used fairly sophisticated finite 
element modeling techniques. 
Hysteresis loops for in-plane wall behavior are shown 
on the following pages, Sections 4.1.1.1 to 4.1.1.6, 
organized by behavior mode. Research shows that the 
governing behavior mode depends upon a number of 
variables including material properties, aspect ratio, and 
axial stress. To aid in comparing the curves, basic data 
given in the research report are provided, including the 
average compressive strength of prism tests and the 
masonry unit, the pier aspect ratio, the nominal axial 
stress, and whether the specimen was free to rotate at 
the top (cantilever condition) or was fixed (double curvature 
condition). For many of the specimens, 
independent calculations have been carried out for this 
document to allow comparison between the evaluation 
procedure predictions in Section 7.3 of FEMA 306 and 
the actual experimental results. Predictions using 
FEMA 273 are also noted. In several cases, engineering 
judgment has been exercised to make these calculations, 
since not all of the necessary information is available. 
Material properties that were assumed for the purposes 
of the calculation are identified. It is expected that 
predicted results could vary significantly if different 
assumptions are made. In addition, the experimental 
research in URM piers is difficult to synthesize for 
several reasons: 
* Some researchers do not report a measure of bed-
joint sliding-shear strength. Others use triplet tests 
rather than in-place push tests to measure bed-joint 
sliding capacity. Comparisons between triplet tests 
and in-place push tests are not well established. 
Several different assumptions were investigated for 
this project, and the approach shown below was 
found to correlate best with the data. 
* Descriptions of cracking can be inconsistent and 
overly vague. Diagonal cracking, for example, is 
often reported, but it can be unclear if the report 
refers to diagonal tension cracking, toe crushing 
with diagonally-oriented cracks, or stair-stepped 
bed-joint sliding. 
* Observed damage is often not linked to points on the 
force/displacement hysteresis loops. 
* Final drift values are not always given; when they 
are, it is often unclear why the test was stopped and 
Technical Resources 
FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
whether additional stable deformation capacity 
remained. 
In many tests, the applied axial load varies 
significantly from the desired nominal value at 
different times during the test. Thus, lateral 
capacities can be affected. 
4.1.11 Rocking 
Reference: Anthoine et al. (1995) 
Specimen: High wall, first run 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 
Prism f m=6.2 MPa, brick f M=16 MPa 
Lleff =lml2m= 0.5 
Nominal fa=0.60 MPa 
Fixed-fixed end conditions 
Assumed Values: 
Vmei=(0.75/l 5)*(0.23+0.57fa)
MPa 
Vme2=(0.75/l.5)*(0.57fa)MPa 
Calculated Values (kN): 
Vr=68 Vt,=65 
Vbjsl=73 Vbjs2=43 
Vdtl=8 5 Vdt2=130 
FEMA 273 Predicted Mode: Toe crushing 
ATC-43 Predicted Behavior: Rocking at 68 kN 
with drift "d"=0.8% 
Actual Behavior: Rocking at 72 kN with test 
stopped at 0.6%. Slight cracks at mid-pier. Axial 
load increased for second run (see below). 
* There is no direct test for fdt,. FEMA 273 equations 
use vme for f This gives the value for Vdtl. As an 
additional check, 1/30th of the value of flat-wise 
compressive strength of the masonry units was also 
used; this results in the value for Vdt2. 
Hysteretic response of the high wall, first run. 
Technical Resources FEM2A 307 
Chapter 4: Unreinforced Masonry 
Reference: Anthoine et al. (1995) 
Specimen: High wall, second run 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 
Prism f m=6.2 MPa, brick f M=16 MPa 
Lhelml2m=0.5 
Nominal fa= 0.80 MPa 
Fixed-fixed end conditions 
Assumed Values: 
Vme1=(0.75/1.5)*(0.23+0.57fa) MPa 
Vme2=(0.75/1.5)*(0.57fa) MPa 
Calculated Values (kN): 
Vr=90 Vt,=82 
Vbjs1 =85 Vbj 32=5 8 
Vdtl=10 4 Vdt2=14l 
FEMA 273 Predicted Mode: Toe crushing 
ATC-43 Predicted Behavior: Same as FEMA 273 Hysteretic response of the high wall, second run. 
Actual Behavior: Rocking, then stair-stepped bed-
joint sliding at a drift of 0.75% 
Reference: Magenes & Calvi (1995) 
Specimen: 3, runs 7-12 
Material: Brick 
Loading: Shaketable 
Provided Information: 
Prism f m=8.6 MPa, brick f M=18.2 MPa 
Lheff =lml2m = 0.5 
Nominal fa= 0.63 MPa 
Fixed-fixed end conditions 
Assumed Values: 
Vmei=(O.751l.5)*(115+0.57fa) MPa 
Vme2=(0.75/1,5)*(0.57fa) MPa 
Calculated Values (kN): 
Vr=71 Vt,=70 
Vbjs1=1 8 9 Vbjs2= 4 5 
Vdtl=171 Vdt2=14 5 Shear-displacement curve characterized 
by rocking (wall 3, run 10). The figure 
FEMA 273 Predicted Mode: Toe crushing does not show final runs 11and 12. 
ATC-43 Predicted Behavior: Rocking at 71 kN with 
drift "d" = 0.8%. 
Actual Behavior: Rocking at 87 kN with drift of 
1.3% in run 10. 
Technical Resources 
FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
Reference: Costley & Abrams (1996) 
Specimen: SI Door Wall 
Material: Brick 
Loading: 3/8th-scale building on shaketable 
.C 
Provided Information: 
Prism f m=1960 psi, brick f M=6730 psi 
Assumed Values: II 
Vme1=(0.75/ 5)*(0.75*361+fa) psi 
Fixed-fixed end conditions I 
Vme2=(0.75/I.5)*(f,) psi 4.
Outer Piers: 
L/hef1I.44ft/2.67ft =0.54 
Nominal fa= 33 psi 
Door-wall shear vs. first-level door-wall
Calculated Values (kips): displacement from Test Run 14 
V,=l 0 Vt,=1.1 
7
VbjsI=9. Vbjs2=I 1 
VdtI=7.2 Vdt2=10.3 
Inner Pier: 
Lhef0.79ft/1.50ft=0.53 
Nominal fa= 40 psi 
Calculated Values (kips): 
V,=2.7 Vt,=2.9 
VbjI=1 5.3 Vbjs2=I 8 a
Vdtl=14.3 Vdt2=2 0.4 
FEMA 273 Predicted Behavior of Wall Line: Rocking 1 2 
at 4.7 kips with inner-pier drift "d"=0.5% Zib N 
ATC-43 Predicted Behavior of Wall Line: Same as 
FEMA 273 
Actual Behavior of the Wall Line: 
40. 0.0 0.0 020 10 0.00 0.00 020 0.00 0.40 O0
Run 14: Rocking up to 8 kips, then stable at 4-6 kips. 
Drift up to 1.1%. Door-wall shear vs. first-level door-wall
Run 15: Rocking at 4-6 kips with drift up to 1.3% displacement from Test Run 15 
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Reference: Costley & Abrams (1996) 
Specimen: S2 Door Wall 
Material: Brick 
Loading: 3/8th-scale building on shake table 
Provided Information: 
Prism f m=1960 psi, brick f M=6730 psi I 
Fixed-fixed end conditions 
Assumed Values: Vme
1 =(0.75l 5)*(0.75*36l+fa) pSi 
Vme2=(0.75/1.5)*(fa) psi 
Outer Piers: 
0106 4.10 d.05. 00 0.01 0.10 0.15 
041 00)
LAe0.79ft/2.67ft =0.30 
Nominal fa= 40 psi Door-wall shear vs. first-level door-wall 
Calculated Values (kips): displacement from Test Run 22 
V,0.4 Vt-0.4 
Vbjsl=5.5 Vbjs2=0.7 
7
Vdtl=4 1 Vdt2=5. 
Inner Piers: 
Lhehft=1.12ft/2.67ft =0.42 
4 
Nominal f = 4 8 psi 
Calculated Values (kips): 
Vr O.9 Vt=1.0 I 
Vbjsl=7.9 Vbjs2=1l2 I 
Vdtl=6.1 Vdt2=8. 
FEMA 273 Predicted Behavior of Wall Line: Rocking 
at 2.6 kips with inner-pier drift "d"=1.0% 
l
45 d20 . 10 d.00 d0. 0.00 0.0 01. 0.1$ 0d1 0020 
C)
ATC-43 Predicted Behavior of Wall Line: Same as to 
FEMA 273 Door-wall shear vs. first-level door-wall 
Actual Behavior of the Wall Line: displacement from Test Run 23 
Run 22: Rocking at 4 kips, up to a 0.3% drift 
Run 23: Rocking at 4 kips, up to a 0.8% drift 
Run 24: Rocking at 4 kips, up to a 1.1%drift 
Door-wall shear vs. first-level door-wall 
displacement from Test Run 24 
IFEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
4.1.1.2 Bed-joint Sliding 
Reference: Magenes & Calvi (1992) 
Specimen: MI4 
Material: Brick 
Loading: Reversed quasi static cyclic 
Provided Information: 
Prism f m=7.9 MPa, brick f M=19.7 MPa 
300.00 
L fe=1.5mI3m = 0.5 
-200.00
Nominal fa= 0.69 MPa >1I LH L1_
Fixed-fixed end conditions 4 WIBEE. Lz
100.00
Assumed Values: 
Vme 1 =(0.75/1.5)*(0.206+0.8l3fa) MPa a 0.00
Vme2=(0.75/1.5)*(0.8I3fa) MPa 
6-1 
Calculated Values (kN): 
0 _V,=177 Vt,=172 
Vbjsl=219 Vbjs2=160 
Vdtl=2 4 5 Vdt2=3 6 0 =iiwd LCO:
Id-1 Jidko 2b K6b 3J0 Iso 20.ao
Horiz. displacement 6 (mm)
FEMA 273 Predicted Behavior: Toe crushing at 172 
kN Specimen M14 
ATC-43 Predicted Behavior: Rocking at 177kN 
with drift "d" = 0.8% 
Actual Behavior: Stair-stepped bed-joint sliding at 
153 kN with a final drift of 0.6% 
Reference: Abrams & Shah (1992) 
Specimen: WI 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 100 
Prism f m=911 psi, brick f 0M=3480 psi 1,-L
IL so
lhef I12ftl6ft = 2 
Nominal fa= 75 psi 
-9 0 Y/1/ 
Cantilever conditions 
Assumed Values: 
Vmel=(0.75/1.5)*(0.75*100+fa) pSi "t</1 
0 0 VAD a. la Li 210
Vme2=(0.75/1 5)*(fa) psi D C be 
Calculated Values (kips): Test Wall W1 
V,=76 Vtc=74 3 1=8 4 VbjVbjs2=4 2 
Vdtl=14 9 Vdt2=16 7 
FEMA 273 Predicted Behavior: Toe crushing at 74 kips 
ATC-43 Predicted Behavior: Flexural cracking/toe 
crushing/bed-joint sliding with a peak load of 74 
kips with "d" drift of 0.4% 
Actual Behavior: Bed-joint sliding at 92 kips with 
test stopped at a drift of 2.4%. 
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Reference: Magenes & Calvi (1995) 
Specimen: 5 
Material: Brick 
Loading: Shaketable 
Provided Information: 
Prism f m=6.2 MPa, brick f M=16 MPa 
LA/helm/l.35m = 0.74 
Nominal fa= 0.63 MPa 
Fixed-fixed end conditions z 
Assumed Values: V
Vmei=(0.75/1.5)*(0.23+0.57fa)MPa 
uS Vme2=(0.75/1.5)*(0.57fa) MPa 
En Calculated Values (kN): 
V4=105 Vt,=102 
Vbjsl=7 4 Vbjs2=45 
Vdtl=9 7 Vdt2=1 6 0 
FEMA 273 Predicted Behavior: Bed-joint sliding at Horiz. displ. (cm) 
74 kN with "d" drift of 0.4% Shear-displacement curve characterized 
ATC-43 Predicted Behavior: Same as FEMA 273 by rocking and sliding (wall 5, runs 2-6). 
The figure does not show final run 7. 
Actual Behavior: Flexural cracking then horizontal 
and stepped bed-joint sliding with peak load of 114 
kN Reference: Magenes & Calvi (1992) 
Specimen: M12 
Material: Brick 
Loading: Reversed quasistatic cyclic 
3W.00 Provided Information: 
Prism f m-=7.9 MPa, brick f m=19.7 MPa *A 
;1UU.UU
L hefl.5mr2m = 0.74 zW 
Nominal fa= 0.67 MPa I 
W2 
jt A; I 
> :O.OO 
Fixed-fixed end conditions 
Assumed Values: 
0.00
Vmei=(0.75/1.5)*(0.206+0.813fa) MPa 0d 
Vme2 =(0.7511.5)*(0.813fa) MPa 
3E:E F
Calculated Values (kN): 100.00 
I Ar A4
0
V1 =257 Vt,= 2 51 Y_
Vbjs1=213 Vbjs2=155 
Vdtl= 2 67 Vdt2=3 9 9 =UDaWv
a* MaA I I I I I-.-.-.L
FEMA 273 Predicted Behavior: Bed-joint sliding at swdw 006-io 
Wo DD 0. O s O. b- sbo 20.bo 
213 kN with "d" drift of 0.4%. Hori2. displacement 6 (mm) 
ATC-43 Predicted Behavior: Same as FEMA 273 
Actual Behavior: Horizontal bed-joint sliding at top Specimen M12 
course, then stair-stepped bed-joint sliding with a 
peak load of 227 kN and drift of 0.7% 
FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
4.1.1.3 Rocking/Toe Crushing 
Reference: Abrams & Shah (1992) 
Specimen: W3 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 
Prism f m= 911 psi, brick f M= 3480 psi so 
Nominal fa= 50 psi 
IAherf6ft/6ft=1.0 Cantilever conditions Je 
Assumed Values: 
Vel=(0.75/1.5)*(0.75*100+fa) psi 321 
Vme2 =(0.75115)*(f,) psi 50 
Calculated Values (kips): 0.6 )4 02 0.0 02 OA 06 
V,= 12.6 Vt,=12.9 Deflection inches
Vbj =35 Vbjs2=14 Test Wall W3: Measured relation between 
lateral force and deflection. 
Vdtl=6 9 Vdt2=7 8 
FEMA 273 Predicted Behavior: Rocking at 12.6 
kips with drift "d"=0.4% 
ATC-43 Predicted Behavior: Same as FEMA 273 
Actual Behavior: Rocking at 20 kips then toe crushing 
at drift of 0.8% 
4.1.1.4 Flexural Cracking/Toe Crushing/Bed-Joint Sliding 
Reference: Manzouri et al. (1995) 
Specimen: WI 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 160.0 
Prism f m= 2000 psi, brick f M= 3140 psi 
LSkea=8.5ft/5ft =1.7 800 
Nominal fa= 150 psi 
Cantilever conditions 0.0 
Assumed Values: 
Vme=(0.7511.5)*(0.75*85+fa)psi 80.0 
Vme2=(0.75/1l 5)*(fa) psi 
Calculated Values (kips):. 
Vr-152 Vt,=151 160.8 OA 0.0 0. 
Vbjsl=156 Vbjs2=9 9 Lateral Displacement (in) 
Vdtl=2 35 Vdt2=17 2 Specimen W1 
FEMA 273 Predicted Behavior: Toe crushing at 151 
kips. 
ATC-43 Predicted Behavior: Flexural cracking/toe 
crushing/bed-joint sliding with a 151 kip peak load, 
99 kip load for "c" and a "d" drift of 0.4%. 
Actual Behavior: Flexural cracking at 88 kips, toe 
crushing then bed-joint sliding at 156 kips, with a 
final drift of 1.3% 
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Reference: Manzouri et al. (1995) 
Specimen: W2 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 
Prism f m-2200 psi, brick f M- 3140 psi 00.0 
Liheff 8.5ftlsft =1.7 
Nominal fa-55 psi 
Cantilever conditions 
Assumed Values: 3 0// 
Vme1=(0.75/1.5)*(0.75*85+fa) psi 
Vme2=(0.75/1.)5fa) psi 
Calculated Values (kips): 5 0 
Vr= 56 Vt,=60 
Vbjs1=9 3 Vbjs2=3 6 . 0. 
Vdtl=12 4 Vdt2=171 a Disp4oeo, e.4 (ons 
FEMA 273 Predicted Behavior: Rocking at 56 kips. 
ATC-43 Predicted Behavior: Flexural cracking/toe 
crushing at 60 kips. Specimen W2 
Actual Behavior: Flexural cracking at 31 kips, toe 
crushing at 68 kips, diagonal cracking at 62 kips, 
then bed-joint sliding at 52 kips and below, with a 
final drift of 1.2% 
Reference: Manzouri et al. (1995) 
Specimen: W3 
Material: Brick 
Loading: Reversed quasistatic cyclic i. 
Provided Information: 
Prism f m= 2600 psi, brick f M= 3140 psi 
Llhefic 8.5ft/Sft =1.7 Sa,om 
Nominal fa= 85 psi 
Cantilever conditions 
Assumed Values: 
Vmel=(0.751l.5)*(0.75*85+fa)psi 
Vme2=(0.75/1l.5)*(f)psi 
Calculated Values (kips): 40/0 
V,= 86 Vt,=9 l 
Vbjsl=l 13 Vbjs2=56 
Vdtl=l 5 9 Vdt2= 187 l400 A 0.0 OA Ox 
FEMA 273 Predicted Behavior: Rocking at 86 kips. Lateral Displacement (I) 
ATC-43 Predicted Behavior: Flexural cracking/toe 
crushing/bed-joint sliding with a 91 kip peak load, Specimen W3 
56 kip load for "c" and a "d" drift of 0.4%. 
Actual Behavior: Flexural cracking at 55 kips, toe 
crushing at 80 kips, then bed-joint sliding at 80 kips, 
reducing to 56-62 kips, with some final toe crushing 
up to final drift of 0.8% 
FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
4.1.1.5 Flexural Cracking/Diagonal Tension 
Reference: Anthoine et al. (1995) 
Specimen: Low Wall 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 
Prism f m=6.2 MPa, brick f M=16 MPa 
L2etcfflni1l.35m= 0.74 
Nominal f 0= 0.60 MPa 
Fixed-fixed end conditions 
Assumed Values: 
Vme1=(0.75/1.5)*(0.23+0.57fa) MPa 
Vme2=(0.75/l.5)*(0.57fa) MPa 
Calculated Values (kN): 
V,=100 Vtc=96 
Vbj$1=73 Vbjs2=4 3 
Vdtl=9 4 Vdt2=144 
FEMA 273 Predicted Behavior: Bed-joint sliding at 
73 kips with "d" drift of 0.4% 
ATC-43 Predicted Behavior: Same as FEMA 273 Hysteretic response of the low wall. 
Actual Behavior: Flexural cracking then diagonal 
tension cracking with a peak load of 84 kN and a 
final drift of 0.5% 
Reference: Magenes & Calvi (1992) 
Specimen: MI3 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 300.00 
Prism f m=7.9 MPa, brick f M=19.7 MPa 
LUhet1.5n/3m = 0.5 
Nominal fa= 1.245 MPa > 100.00 
Fixed-fixed end conditions 
--T A, 
Assumed 
Values: as 0.00 
vel =(0.75/1.5)*(0.206+0.8l3fa) MPa 
4 I 00.00 
V.,e 2=(0.75/1.5)*(0.813fa) MPa 0 
m 
Calculated Values (kN): z-200,00 
Vtc=2 7 5
Vr-319 
d.d -0 0.60 5.60 1O.b0is.bo 20.00
Vbjs1=3 4 7 Vbjs2= 2 8 8 20.00-1 w.66. 
Horiz. displacement 6 (mm) 
Vdtl=4 06 Vdt2=4 2 7 
FEMA 273 Predicted Behavior: Toe crushing 
ATC-43 Predicted Behavior: Flexural cracking! Specimen M13 
diagonal tension at 275 kN 
Actual Behavior: Flexural cracking then diagonal 
tension cracking with a peak load of 185 kN and a 
final drift of 0.5% 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Reference: Magenes & Calvi (1995) 
Specimen: 8 
Material: Brick 
Provided Information: 
Prism f m=6.2 MPa, brick f M=16 MPa 
L/ehflm/2m = 0.5 
Nominal fa= 1.11 MPa 
Fixed-fixed end conditions z
Assumed Values: 
Vme1=(0.75/1.5)*(0.23+0.57fa) MPa 0 C
Vme2=(0.75/l.5)*(0.57fa) MPa fi
Calculated Values (kN): 
Vr-125 Vyt=109 
Vbjsl=108 Vbjs2=79 
Vdtl=13 7 Vdt2=171 Horiz. displ. (cm) 
FEMA 273 Predicted Behavior: Bed-joint sliding or 
Brittle collapse due to diagonal cracking
toe crushing. 
ATC-43 Predicted Behavior: Bed-joint sliding or (wall 8, runs 5-9) 
flexural cracking/diagonal tension at 108-109 kN 
Actual Behavior: Flexural cracking then diagonal 
tension cracking with a peak load of 129 kN and a 
final drift of 0.8-1.3% 
Reference: Magenes & Calvi (1992) 
Specimen: MI1 
Material: Brick 
Loading: Reversed quasistatic cyclic , 300.00 
Provided Information: 
Prismf =7.9 MPa, brick f M=19.7 MPa _zoo 
L/hefy<l.5m/2m= 0.75 Jbl-_6 I yaA I"II-
Nominal fa= 1.123 MPa P_100.00 
4 
II
la
Fixed-fixed end conditions 0 ono 
Assumed Values: 
" b Vmel=(0.75/1.5)*(0.206+0.813fa) MPa 
0 SW Vme2=(0.75/l.5)*(0.813fa) MPa mi;
V Calculated Values (kN): 200.00
4, F iF Vr=432 Vt,=383. oDc I. L.1._LL 
-0.0r.0 5. 00 0.60 5.00 0.00 15.00z0.0
Vbjsl=319 Vbjs2=2 60 Hori7. displacement (5 (mm) 
Vdtl=4 15 Vdt2=46 2 
Teston wall MIl and Mllm 
FEMA 273 Predicted Behavior: Bed-joint sliding at (dashed line); h = 2m. 
319 kN with drift "d"=0.4% 
ATC-43 Predicted Behavior of Wall Line: Same as 
FEMA 273 
Actual Behavior: Flexural cracking then diagonal 
tension at 259 kN, with maximum drift of 0.6% 
Technical Resources 
Technical Resources
FEMA 307 

Chapter 4: Unreinforced Masonry 
4. 1. 1. 6 Flexural Cracking Toe Crushing 
Reference: Abrams & Shah (1992) 
Specimen: W2 
Material: Brick 
Loading: Reversed quasistatic cyclic 
Provided Information: 
Prism f m= 911 psi, brick f M=3480 psi 
5o 
Llhefj= 9ft 6ft = 1. 5 1, 
Nominal fa= 50 psi 
& 2S 
Cantilever conditions. 
Assumed Values: 
Vnzei= (0. 75 1. 5) (0. 75 100 + fa) psi 10, 
Vme2= (0. 75 l 5) (f) psi. 3 25 
Calculated Values (kips): 4 0
V, =28 Vtc=29 
Vbjs
1. 0 O. 5 O 0. 3 1. 0 1. 5 2. 0
1 =53 Vbjs2=2 l 
Vdtl= 155 Vdt2= 175 Dekcdm wb 
FEMA 273 Predicted Behavior: Rocking at 28 kips Test Wall W2
with drift d =0. 3% 
ATC 43 Predicted Behavior: Flexural cracking toe 
crushing at 29 kips 
Actual Behavior: Flexural cracking toe crushing, 
with a maximum capacity of 43 45 kips. 
Reference: Epperson and Abrams (1989) 
Specimen: El 
Material: Brick 
Loading: Monotonic 
Provided Information: 
Prism f m= 1740 psi, brick f M=8280 psi 
LhIheff 7. 83ft 6ft = 1. 31 0. 
Nominal fa= 126 psi U) 
Cantilever conditions VI 
Assumed Values: IrJ I 
Vmel= (0. 75 l. 5) (0. 75 l86+fa) psi 
V. e 2= (0. 75 l. 5) (fa) psi La 
Calculated Values (kips): in 
Vr =118 VtC=118 
Vbjs=250 Vbjs2=1ll1 
Vdtl= 336 Vdt2= 533. 0 0. o0 0. 20 
TOP DISPLACEMENT (in) 
FEMA 273 Predicted Behavior: Rocking or toe 
crushing Summary of measured top level 
displacement of the Test Walls
ATC 43 Predicted Behavior: Flexural cracking toe vs shear stress 
crushing at 118 kips 
Actual Behavior: Flexural cracking toe crushing, 
with a maximum capacity of 120 kips and final drift 
of 0. 3% 
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Reference: Epperson and Abrams (1989) 
Specimen: E3 
Material: Brick 
Loading: Monotonic 
Provided Information: 
Prism f m= 1740 psi, brick f M=8280 psi 
lh7eff 9. 5ft 6ft = 1. 58 
Nominal fa= 141 psi 
Cantilever conditions 
Assumed Values: 
Vme1= (0. 75 1. 5) (0. 75 186+fa) pSi 
Vme2 = (0. 75 l 5) (f) psi 
Calculated Values (kips): 
Vr=190 1t, =l86 
Vbjsl=3 0 7 Vbjs2=133 
Vdtl= 4 20 Vdt2= 6 3 5 
FEMA 273 Predicted Behavior: Toe crushing at 186 
kips 
ATC 43 Predicted Behavior: Flexural cracking toe 
crushing at 186 kips 
Actual Behavior: Flexural cracking toe crushing, 
with a maximum capacity of 164 kips and final drift of 
0. 4% 
Reference: Epperson and Abrams (1989) 
Specimen: E6 
Material: Brick 
Loading: Monotonic 
Provided Information: 
Prism f m= 1740 psi, brick f M=8280 psi 
IJheff 11. 42ft 6ft= 1. 90 
Nominal fa= 76 psi 
Cantilever conditions 
Assumed Values: 
Vmei= (0. 75 l. 5) (0. 75 186+fa) psi 
Vme2= (0. 75 l. 5) (fa) psi 
Calculated Values (kips): 
V, =141 Vt, =147 
Vbj, =284 Vbjs2=8 2 
Vdtl= 3 5 7 Vdt2= 6 7 5 
FEMA 273 Predicted Behavior: Rocking at 141kips 
with d drift of 0. 2% 
ATC 43 Predicted Behavior: Flexural cracking toe 
crushing at 147 kips 
Actual Behavior: Flexural cracking toe crushing, 
with a maximum capacity of 150 kips and final drift of 
0. 2% Reference: Epperson and Abrams (1989) 
Specimen: E5 
Material: Brick 
Loading: Monotonic 
Provided Information: 
Prism f m= 1740 psi, brick f M=8280 psi 
lJhJef=11. 42ft 6ft = 1. 90 
Nominal fa= 81 psi 
Cantilever conditions 
Assumed Values: 
Vmei= (0. 751. 5) (0. 75 186+fa) psi 
Vme2= (0. 75 l 5) (f,) psi 
Calculated Values (kips): 
Vr=150 Vt, =156 
Vbjs1=2 8 9 Vbjs2=8 8 
Vdtl= 36 7 Vdt2=6 8 0 
FEMA 273 Predicted Behavior: Rocking at 150 kips 
with d drift of 0. 2% 
ATC 43 Predicted Behavior: Flexural cracking toe 
crushing at 156 kips 
Actual Behavior: Flexural cracking toe crushing, with a 
maximum capacity of 154 kips and final drift of 0. 4% 
Reference: Epperson and Abrams (1989) 
Specimen: E7 
Material: Brick 
Loading: Monotonic 
Provided Information: 
Prism f m= 1740 psi, brick f M=8280 psi 
Llhef 11. 42ft 6ft= 1. 90 
Nominal fa= 93 psi 
Cantilever conditions 
Assumed Values: 
Vmej= (0. 75 1. 5) (0. 75 186+fa) psi 
Vme2 = (0. 75 l. 5) (fa) psi 
Calculated Values (kips): 
V, 173 Vt, =177 
Vbjsl=302 Vbjs2=1l0 
Vdtl= 3 90 Vdt2=6 9 2 
FEMA 273 Predicted Behavior: Rocking at 173 kips 
with d drift of 0. 2% 
ATC 43 Predicted Behavior: Flexural cracking toe 
crushing at 177 kips 
Actual Behavior: Flexural cracking toe crushing, with a 
maximum capacity of 157 kips and final drift of 0. 4% 
Technical FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
4. 1. 2 Comments on FEMA 273 
Component Force Displacement Relationships 
4. 1. 2. 1 Conclusions from Review of the 
Research and Their Impact on the 
Evaluation Methodology 
As the previous sections indicate, the FEMA 273 
methodology leads to successful predictions in certain 
cases. In other cases, the predictions did not match the 
observed behavior. To help address this issue, some 
modifications were made in the Section 7. 3 
methodology in FEMA 306. Some of these issues and 
their resolution include: 
Rocking and toe crushing equations often yield very 
similar values; when they do differ, the lower value 
does not necessarily predict the governing mode. 
Section 7. 3 in FEMA 306 thus identifies which 
mode will occur on the basis of aspect ratio, unless 
the axial stress is very high, since there have been no 
reported instances of rocking in stocky piers. The 
itheff> 1. 25 is a somewhat arbitrary threshold based 
simply on a review of test results. 
Stable rocking generally exceeds the proposed d 
drift value of 0. 4helfL. Thus, this value is 
conservative (see Costley and Abrams, 1996 and 
Anthoine et al., 1995). 
Rocking does not appear to exhibit the FEMA 273 
drop to the c capacity value in the above two tests 
nor, apparently, in the Magenes and Calvi (1995) 
tests. The only exception is Specimen W3 of 
Abrams and Shah (1992), which, after rocking for 
ten cycles at drifts of up to 0. 5% (0. Sheff L), was 
then pushed to 0. 8% drift (0. 8heff L) where it 
experienced toe crushing. The test was stopped at 
that point. Given the limited number of specimens, 
it is difficult to determine if this represents the drop 
from initial load to the c level, or a special, 
sequential mode. For simplicity, this case was 
combined with the rocking cases, and the d drift 
level was set to account for this level of toe crushing. 
In most cases, though, rocking capacities will not 
drop off significantly. The d drift value of 0. 4hefL 
was set based on Costley and Abrams (1996), with 
some conservatism (Abrams, 1997) to account for 
Specimen W3. The c drift value was 
conservatively set at 0. 6, because of the limited test 
data (Abrams, 1997), but aside from Specimen W3, 
higher c values are probably likely. 
There are few pure bed joint sliding tests. Specimen 
WI of Abrams and Shah (1992) is one example, and 
Specimens M12 and M14 of Magenes and Calvi 
(1992) appear to be examples as well. The drop in 
lateral strength appears to occur at about 0. 3 0. 4% 
drift in Wi and MI4, so the proposed d value of 
0. 4 seems reasonable. The c of 0. 6 also seems 
reasonable. The capacity for bed joint sliding is 
based on the bond plus friction strength. After 
cracking, the bond capacity will be eroded, and the 
strength is likely to be based simply on the friction 
portion of the equation. Cyclic in place push tests 
show this behavior; so does Specimen Wi of. 
Abrams and Shah (1992). One could argue that the 
second cycle backbone curve of FEMA 273 (which, 
by definition, goes into the nonlinear, post cracking 
range) should be limited only to the frictional 
capacity. But in many cases, other modes will be 
reached before the full bed joint sliding capacity is 
reached. In some of these cases, interestingly, bed 
joint sliding occurs after another mode has occurred. 
Manzouri et al. (1995), for example, show sequences 
such as initial toe crushing that progresses to bed 
joint sliding at higher drift values. One explanation 
is that toe crushing degenerated into bed joint 
sliding because the toe crushing and initial bed joint 
sliding values were quite close. See Section 4. 1. 2. 2 
for further explanation. 
Mixed modes or, more accurately, sequences of 
different behavior modes are common in the 
experiments. 
4. 1. 2. 2 The Bed Joint Sliding and Flexural 
Cracking Toe Crushing Bed Joint 
Sliding Modes 
The model of bed joint sliding used in this document is 
shown in Figure 4 1. For estimating the strength and 
deformation capacity of the undamaged bed joint 
sliding mode, FEMA 273 was used. The idealized 
relationship has a plateau at the bed joint capacity VbjS1, 
which includes the bond and friction components. 
After bond is lost, the residual strength is limited to 
60% of Vbjs1 The actual backbone curve is likely to be 
smoother than the idealized model, since the loss of 
bond does not occur all at once in the entire masonry 
section. Instead, more heavily stressed portions crack, 
and shear demand is redistributed to the remaining 
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Insignificant Moderate Heavy Extreme 
A B C D V 
VbIS TWR bjs 
0. 6 Vbjs1 
Vbjs2 Actual undamaged 
backbone curve 
1 FEMA 273 Idealized 
Tvz force displacement 
relation 
Loss of bond 
Insignificant damage curve 
Moderate damage curve 
Heavy damage curve 
d= 0. 4% e 0. 8% heff 
Figure4 1 Bed joint sliding force displacement relationship 
sections. The actual residual strength could be higher 
or lower than 0. 6Vbj31. One measure of the residual 
capacity is VbJ32. 
Figure 4 1 also shows the assumed changes to the force 
displacement relationship following the damaging 
event. Insignificant damage is characterized by 
displacement during the damaging event that is between 
points A and B. Loss of bond is limited. Following the 
damaging event, the dashed Insignificant Damage 
Curve represents the force displacement relationship. 
For damaging events that reach levels of initial 
displacement beyond point B, greater loss of bond 
occurs, and the subsequent damage curve achieves a 
lower strength. Eventually, with initial displacements 
beyond point C, the entire bond is lost and only friction 
remains. Thus, future cycles will no longer be able to 
achieve the original Vbjsl level, reaching only the Vbis2 
level. With significant cyclic displacements, some 
erosion of the crack plane and deterioration of the wall 
is likely to lead to a small reduction in capacity below 
the Vbj, 2 level. 
The varying level of bed joint sliding strength is 
assumed in this document to be a possible explanation 
for some of the observed testing results in stocky walls, 
in particular results such as (1) Specimen W1 of 
Abrams and Shah (1992), in which bed joint sliding 
was the only mode observed; (2) Manzouri et al. (1995), 
in which toe crushing behavior was followed by bed 
joint sliding; and (3) Epperson and Abrams (1989), in 
which toe crushing was not followed by sliding. 
Figure 4 2 helps to explain the hypothesis. 
In the top set of curves, toe crushing strength 
substantially exceeds the Vbpl level. As displacement 
occurs, the bed joint sliding capacity is reached first, 
and it becomes the limit state. If displacement is such 
that heavy damage occurs, then in subsequent cycles, 
the strength will be limited to the Vbj 32 level. 
Technical Resources 73
FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
l. 25VbJB1< V.: 
1. 25 Vbmst< Vt,: 
Bed joint sliding 
Toe crushing k 
Vt VbjSl A 3 Bed joint
sliding Bed joint sliding 
VbAS 
Initial Force Displacement Relationship Heavy Damage 
Vbls2 < 0. 75 Vbj, I< Vt, < VbS1: 
Flexural yield Toe crushing Bed joint sliding 
Toe crushing 
Vbjs1 I Bed joint sliding 
Vtl ec < Bed joint sliding 
VbiSE Heavy Damage 
0. 7 5 Vbjs < Vtc: Toe crushing A4hh Toe crushing Vbjs I E Bed joint sliding I,  Toe crushing 
Vbj. 12 Composite curve Wh Initial Force Displacement Relationship Heavy Damage 
Figure 4 2 Relationship Between Toe Crushing and Bed Joint Sliding 
In the second set of curves, toe crushing and initial bed will be limited to the Vbj, 2 level. This is one possible 
joint sliding strengths are similar. As displacement explanation for the Manzouri et al. (1995) tests. 
occurs, the toe crushing strength is reached first, 
cracking and movement occur within the wall, some of In the third set of curves, toe crushing strength is 
the bond is lost, and the wall begins to slide. The initial substantially lower than initial bed joint sliding strength
force displacement curve is thus similar to that for bed and the ductile mechanism of sliding is not achieved. 
joint sliding, except that the peak is limited by the toe This is one possible explanation for the Epperson and 
crushing strength. If displacement is such that Heavy Abrams (1989) results, in which mortar shear strength
damage occurs, then in subsequent cycles, the strength was much higher and ductility was lower. 
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Section 7. 3. 2 in FEMA 306 makes use of the above 
hypotheses; cutoff values for the middle set of curves 
were based in part on review of the results shown in 
Section 4. 1. 1. Results are promising, but additional 
testing and verification of other tests should be done. 
4. 1. 2. 3 Out of Plane Flexural Response 
The most comprehensive set of testing done to date on 
the out of plane response of URM walls was part of the 
ABK program in the 1980s, and it is documented in 
ABK (1981c). Input motions used in the ABK (1981c) 
were based on the following earthquake records: Taft 
1954 N21E, Castaic 1971 N69E, Olympia 1949 S04E, 
and El Centro 1940 SOOE. They were scaled in 
amplitude and were processed to represent the changes 
caused by diaphragms of varying stiffness to produce 
the final series of 22 input motion sets. Each set has a 
motion for the top of the wall and the bottom of the 
wall. Peak velocities range up to 39. 8 in sec; 
accelerations, up to 1. 42g; and displacements, up to 
9. 72 inches. In ABK (1984), the mean ground input 
velocity for UBC Seismic Zone 4 was assumed to be 12 
in sec. For buildings with crosswalls, diaphragm 
amplification would increase this about 1. 75 fold, to 21 
in sec. For buildings without crosswalls, wood roofs 
were assumed to have a velocity of about 24 in sec and 
floors about 27 in sec. 
Since 1981, a significant number of ground motion 
records have been obtained, including a number of near 
field records. In several instances, recent recordings 
substantially exceed the 12 in sec value and even exceed 
the maximum values used by ABK (1981c). Of 
particular concern are near field pulse effects and 
whether they were adequately captured by the original 
testing. When site specific spectra and time histories 
that incorporate these effects are available, it may be 
possible to address this issue using the original 
research. 
4. 1. 3 Development of A factors 
One of the central goals of this document is to develop a 
method for quantitatively characterizing the effect of 
damage on the force displacement relationship of wall 
components. Ideally, the most accurate approach would 
be to have two sets of cyclic tests for a component. One 
test would be of an initially undamaged wall displaced 
to failure. The second set would include walls initially 
displaced to various levels of damage (to represent the 
damaging event) and then retested to failure. This 
would allow for direct determination of the X factors 
contained in the Component Guides in FEMA 306. 
Unfortunately, as noted in Section 4. 1. 1 there have been 
almost no experimental tests done on damaged URM 
walls; typically, tests were done on undamaged walls 
and either stopped or continued only after the damaged 
wall was repaired. 
In the absence of test results on damaged walls, 
hysteresis curves of initially undamaged walls were 
reviewed. In reviewing these tests, the goal was to 
characterize how force displacement relationships 
changed from cycle to cycle as displacement was 
increased. Early cycles were considered to represent 
damaging events, and subsequent cycles represented 
the behavior of an initially damaged component. 
Particular attention was given to tests in which multiple 
runs on a specimen were performed. In these cases, 
initial runs (representing not just a damaging cycle, but 
a damaging earthquake record) were compared with 
subsequent runs to determine the extent of strength and 
stiffness deterioration. 
Using these tests, the following general approaches 
were used to estimate X factors for this project. The 
reloading stiffnesses (i. e., the stiffness observed moving 
from the fourth quadrant to the first) at different cycles 
or different runs were compared to the initial stiffness to 
determine AK. This variable is estimated to be the ratio 
of stiffness at higher cycles to the initial stiffness. The 
assumption made is that if testing had been stopped and 
the displacement reset to zero and then restarted, the 
stiffness of the damaged component would have been 
similar to the reloading stiffness. See Figure 4 3 for an 
example. 
For determining AQ, the approach shown in Figure 4 1 
and discussed in the previous section is applied where 
appropriate to determine AQ, the ratio of strength at 
higher cycles to initial strength. The loss of strength is 
roughly equal to the capacity at high drift levels divided 
by the peak capacity. FEMA 273 describes both 
deformation controlled and force controlled modes. In 
a purely force controlled mode, there is, by definition, 
little or no ductility. Deformation progresses until a 
brittle failure results. Thus, there are few, if any, 
damage states between Insignificant and Extreme, and 
there would be little, if any, post cracking strength. 
Further, until a brittle mode occurs, the component 
would be expected to be minimally affected by previous 
displacement. Review of available hysteresis curves 
shows, though, that even modes defined as force 
FEMA 307 Technical Resources 
Chapter 4: Unreinforced Masonry 
Initial backbone 
Negative curve 
residual set on 
cycle () de 
Example Hysteresis Curve 
Size of initial Shift for Residual Set 
reduction depends 
on de on de Beyond dhjft 
curves assumed Initial 
Damaged Idealized Force Initial vs. Damaged Backbone Curves Deflection Relations 
Figure 4 3 Developing the initial portion of the damaged force displacement relationship controlled by FEMA 273 (such as diagonal tension) do 
have some residual strength. 
There is little available information for determining 1., 
because retesting of damaged components to failure has 
not been done. Values were estimated using 
engineering judgment. In most cases, less ductile 
modes are assumed to have higher A values, even at 
higher damage levels. The basis of this assumption is 
the idea that in more ductile modes, Ais assumed to be 
somewhat more dependent on cumulative inelastic 
deformation. In more ductile modes, the available 
hysteretic energy has been dissipated in part by the 
damaging earthquake, and there is less available in the 
subsequent event. The result is the final displacement 
that can be achieved is reduced. 
Values for XKAQ and AA are based, where possible, 
on tests of repaired walls. The values in URM1F, for 
example, are set at 1. 0 because the hysteresis curves of 
repaired walls were equal to or better than those of the 
original walls. In most other cases, repairs typically 
involve injection of cracks, but since micro cracking can 
never be fully injected, it may not be possible to restore 
Technical Resources FEM2A 307 
Chapter 4: Unreinforced Masonry 
complete initial stiffness. In the bed joint sliding modes 
without tests, it was assumed that the strength could not 
be fully restored by injection, because the horizontal 
crack planes are closed and bond cannot be restored in 
these locations. It is important to recognize that 
injection of walls with many cracks or unfilled collar 
joints and cavities, may enhance strength, but it may 
also lead to less ductile behavior, because other modes 
may then occur prior to bed joint sliding. 
Values for cut are based on a review of the ABK 
(1981c) document, the model proposed in Priestley 
(1985), and engineering judgment. At low levels of 
damage, the portions of wall between the crack planes 
are essentially undamaged, and the effective thickness, 
remains unchanged. At higher levels of damage, 
deterioration, crushing, and spalling of the corners of 
the masonry at crack locations reduces the effective 
thickness and the ability of the wall to resist movements 
imparted by the diaphragm. 
4. 2 Tabular Bibliography for Unreinforced Masonry 
Table 4 1 contains a brief description of the key 
technical reports that address specific reinforced 
masonry component behavior. The component types 
and their behavior modes are indicated. The full 
references can be found in Section 4. 4. 
Technical Resources 
FEMA 307 Technical Resources 77 
4 Table 4 1 Summary of Significant Experimental Research or Research Summaries 
29 
Behavior Modes Addressed 1 
Reference Specimen Loading Aspect Axial Predictive Repair Component a b c d e f g h i j k I m n 
Ratio Stress Equations 
(LI, ff) (pin Type psi) 
Abrams (1992) Based on Abrams and Strength None URM1 
Shah (1992) and Epperson 
and Abrams (1989) 
Abrams and Shah 3 cantilever brick piers 2 75 Strength None URM1 
(1992) with reversed static 1. 5 50 cyclic loading 1 50 
ABK (1981c) 22 specimens with hit from 2 23 None Ferrocement surface URMI 
dynamic out of plane 14. 0 25. 2 coating on 2 specimens 
loading, including brick, 
grouted and ungrouted 
clay and concrete block 
C.) 0 0 CD:D 0 0 8ID 
Anthoine et al. (1995) 
Costley and Abrams (1996b) 
3 brick piers in double 
curvature with reversed 
static cyclic loading 
2 3 8th scale brick buildings
on shake table, each 
0. 5 0. 5 0. 74 0. 54 0. 84 0 53 0. 74 
87 87 116 33 36 40 48 None Strength 
None None URM2 URM2 a a C 3 TCD 5. 0 
with two punctured walls 0. 30 0. 40 40 48 a a. 
Cn lines in the in plane 0. 96 1. 50 33 36 
direction 0 Epperson and Abrams (1989) 
5 cantilever brick piers with monotonic loading 
1. 31 1. 58 126 143 Strength None URMI1 1 
1. 90 81 1. 90 76 1. 90 93 I 0 Kingsley (1996) 
et al. 1 2 story, full scale brick 
building with reversed 
na na None None URM2 
static cyclic loading 
Magenes and Calvi 4 brick piers in double 0. 75 163 Strength None URM2 
(1992) curvature with reversed 0. 75 97 
static cyclic loading 0. 5 181 e 
0. 5 100 rn n E Table 4 1 Summary of Significant Experimental Research or Research Summaries (continued) 
(a0 Reference Specimen Loading Aspect Axial Predictive Repair Com a b c 
Behavior Modes Addressed 
d e f g h i j k 1 m n 
Ratio Stress Equations component
(Liheff) (fa in Type psi) 
Magenes and Calvi 8 brick piers in double 0. 74 59 None URM2
(1995) curvature tested on a 0. 74 68
shake table, some run 0. 74 152. 
4 multiple times with varying 0. 5 62 0 
axial load 0. 50. 50. 5 
9114901600 
0. 74 91 
0. 74 161 
0. 5 91 
0. 5 173 
0. 5 161 
M Manzourzi et. al. 4 virgin brick piers with 1. 7 150 Sophisticated Repair techniques URM1 0 (1995) reversed static cyclic 
loading, 3 cantilever and 
1. 7 
1. 7 
55 
85 
finite element include grout injection pinning, and URMI. URMI 
CD00 1 pair of piers with spandrels 
1. 27 70 modeling addition of rebar filled chases 
URM2 C Rutherford & Chekene Contains extensive set of Uses Grout and epoxy 
tD (1997) research summaries of FEMA 273 injection, surface 
URM enhancement and pro coatings, adhered 
vides equations fabrics, shotcrete, 
for reinforced and post enhanced tensioned cores, 
walls infilled openings, 
enlarged openings, 
and steel bracing 
Tomasevic and 4 1 4 scale brick build None Compares effective 
Weiss (1996) on shake table ness of various wall diaphragm ties 
Behavior Mode: 
a Wall pier rocking f Flexural cracking toe crushing bed joint sliding k Preemptive diagonal tension 
b Bed joint sliding g Flexural cracking diagonal tension I Preemptive toe crushing 
c Bed joint sliding at wall base h Flexural cracking toe crushing m Out of plane flexural response 
d Spandrel joint sliding i Spandrel unit cracking n Other: Includes complex modes and those reported as having 
e Rocking toe crushing j Corner damage diagonal cracking 
Chapter 4: Unreinforced Masonry 
4. 3 Symbols for Unreinforced Masonry 
Symbols used in the unreinforced masonry sections of 
FEMA 306 and 307 are the same as those given in 
Section 7. 9 of FEMA 273 except for the following 
additions and modifications. 
C Resultant compressive force in a spandrel, lb 
Lsp Length of spandrel, in. 
Mspcr Expected moment capacity of a cracked spandrel, 
lb in. MsPun Expected moment capacity of an uncracked 
spandrel, lb in. Vspcr Expected diagonal tension capacity of a 
cracked spandrel, lb VspUn Expected diagonal tension capacity of an 
uncracked spandrel, lb 
NB Number of brick wythes in a spandrel 
NR Number of rows of bed joints in a spandrel 
T Resultant tensile force in a spandrel, lb 
Vbjsl Expected shear strength of wall or pier based on 
bed joint shear stress, including both the bond 
and friction components, lb 
Vbjs2 Expected shear strength of wall or pier based on 
bed joint shear stress, including only the friction 
component, lb 
Vp Shear imparted on the spandrel by the pier, lb 
Vdt Expected shear strength of wall or pier based on 
diagonal tension using vineforf dt, lb 
Vtc Expected shear strength of wall or pier based on 
toe crushing using vie forf dt, lb 
Ww Expected weight of a wall, lb 
beffcr Effective length of interface for a cracked spandrel, 
in. 
beffun Effective length of interface for an uncracked 
spandrel, in. 
bh Height of masonry unit plus bed joint thickness, 
in. 
b1 Length of masonry unit, in. 
bw Width of brick unit, in. 
dp Depth of spandrel, in. 
deffer Distance between resultant tensile and compressive 
forces in a cracked spandrel, in. 
defAn Distance between resultant tensile and compressive 
forces in an uncracked spandrel, in. 
f dt Masonry diagonal tension strength, psi 
Vbjcr Cracked bed joint shear stress, psi 
Vbjun Uncracked bed joint shear stress in a spandrel, 
psi vccr Cracked collar joint shear stress in a spandrel, 
psi vcun Uncracked collar joint shear stress in a spandrel, 
psi, 6 =0. 67 when L heff<0. 67, =Llheff when 
0. 67Llheff<1. O, and = 1. 0 when Llhf >1 
As Average slip at cracked spandrel (can be estimated 
as average opening width of open head 
joint), in. 
e Factor for estimating the bond strength of the 
mortar in spandrels 
Factor for coefficient of friction in bed joint 
sliding equation for spandrels 
77 Factor to estimate average stress in uncracked 
spandrel. Equal to NRI2 or, for more sophistication, 
use 7 i NR [ (dp 2 bh (i)) (d 5p 2 bhA) ] 
At Factor used to estimate the loss of out of plane 
wall capacity to damaged URM walls 
uAL Displacement ductility demand for a component, 
used in FEMA 306, Section 5. 3. 4, and 
discussed in Section 6. 4. 2. 4 of FEMA 273. 
Equal to the component deformation corresponding 
to the global target displacement, 
divided by the effective yield displacement of 
the component (which is defined in Section 
6. 4. 1. 2B of FEMA 273). 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
4. 4 References for Unreinforced Masonry
ABK, 1981a, Methodology for Mitigation of Seismic 
Hazards in Existing Unreinforced Masonry Buildings: 
Categorization of Buildings, A Joint Venture 
of Agbabian Associates, S. B. Barnes and Associates, 
and Kariotis and Associates (ABK), Topical 
Report 01, c o Agbabian Associates, El Segundo, 
California. 
ABK, 1981b, Methodology for Mitigation of Seismic 
Hazards in Existing Unreinforced Masonry Buildings: 
Diaphragm Testing, A Joint Venture of Agbabian 
Associates, S. B. Barnes and Associates, and 
Kariotis and Associates (ABK), Topical Report 03, 
c o Agbabian Associates, El Segundo, California. 
ABK, 1981c, Methodology for Mitigation of Seismic 
Hazards in Existing Unreinforced Masonry Buildings: 
Wall Testing, Out of Plane, A Joint Venture of 
Agbabian Associates, S. B. Barnes and Associates, 
and Kariotis and Associates (ABK), Topical Report 
04, c o Agbabian Associates, El Segundo, California 
ABK, 1984, Methodology for Mitigation of Seismic 
Hazards in Existing Unreinforced Masonry Buildings: 
The Methodology, A Joint Venture of Agbabian 
Associates, S. B. Barnes and Associates, and 
Kariotis and Associates (ABK), Topical Report 08, 
Cdo Agbabian Associates, El Segundo, California. 
Abrams, D. P., 1992, Strength and Behavior of Unreinforced 
Masonry Elements, Proceedings of Tenth 
World Conference on Earthquake Engineering, 
Balkema Publishers, Rotterdam, The Netherlands, 
pp. 3475 3480. 
Abrams, D. P., 1997, personal communication, May. 
Abrams, D. P., and Epperson, G. S, 1989, Evaluation of 
Shear Strength of Unreinforced Brick Walls Based 
on Nondestructive Measurements, 5th Canadian 
Masonry Symposium, Department of Civil Engineering, 
University of British Columbia, Vancouver, 
British Columbia., Volume 2. 
Abrams, D. P., and Epperson, G. S, 1989, Testing of 
Brick Masonry Piers at Seventy Years, The Life of 
Structures: Physical Testing, Butterworths, London. 
Abrams, D. P., and Shah, N., 1992, Cyclic Load Testing 
of Unreinforced Masonry Walls, College of Engineering, 
University of Illinois at Urbana, Advanced 
Construction Technology Center Report #92 26 10. 
Adham, S. A., 1985, Static and Dynamic Out of Plane 
Response of Brick Masonry Walls, Proceedings of 
the 7th International Brick Masonry Conference, 
Melbourne, Australia. 
Anthoine, A., Magonette, G., and Magenes, G., 1995, 
Shear Compression Testing and Analysis of Brick 
Masonry Walls, Proceedings of the 10th European 
Conference on Earthquake Engineering, Duma, 
editor, Balkema: Rotterdam, The Netherlands. 
ATC, 1997a, NEHRP Guidelines for the Seismic Rehabilitation 
of Buildings, prepared by the Applied 
Technology Council (ATC 33 project) for the 
Building Seismic Safety Council, published by the 
Federal Emergency Management Agency, Report 
No. FEMA 273, Washington, D. C. 
ATC, 1997b, NEHRP Commentary on the Guidelines 
for the Seismic Rehabilitation of Buildings, prepared 
by the Applied Technology Council (ATC 33 
project) for the Building Seismic Safety Council, 
published by the Federal Emergency Management 
Agency, Report No. FEMA 274, Washington, D. C. 
BSSC, 1992, NEHRP Handbook for the Seismic Evaluation 
of Existing Buildings, prepared by the Building 
Seismic Safety Council for the Federal 
Emergency Management Agency, Report No. 
FEMA 178, Washington, D. C. 
Calvi, G. M., Kingsley, G. R., and Magenes, G., 1996, 
Testing of Masonry Structures for Seismic Assessment, 
Earthquake Spectra, Earthquake Engineering 
Research Institute, Oakland, California, Vol. 12, 
No. 1, pp. 145 162. 
Calvi, G. M, and Magenes, G., 1994, Experimental 
Results on Unreinforced Masonry Shear Walls 
Damaged and Repaired, Proceedings of the 10th 
International Brick Masonry Conference, Vol. 2, 
pp. 509 518. 
Calvi, G. M., Magenes, G., Pavese, A., and Abrams, 
D. P., 1994, Large Scale Seismic Testing of an 
Unreinforced Brick Masonry Building, Proceedings 
of Fifth U. S. National Conference on Earthquake 
Engineering, Chicago, Illinois, July 1994, 
pp. 127 136. 
City of Los Angeles, 1985, Division 88: Earthquake 
Hazard Reduction in Unreinforced Masonry Buildings, 
City of Los Angeles Building Code, Los 
Angeles, California. 
City of Los Angeles, 1991, Seismic Reinforcement Seminar 
Notes, City of Los Angeles Department of 
Building and Safety. 
Technical Resources 
FEMA 307 Technical Resources 81 
Chapter 4: Unreinforced Masonry 
Costley, A. C., Abrams, D. P., and Calvi, G. M., 1994, 
Shaking Table Testing of an Unreinforced Brick 
Masonry Building, Proceedings of Fifth U. S. 
National Conference on Earthquake Engineering, 
1 3 6
Chicago, Illinois, July 1994, pp. 1 2 7 Costley, A. C., and Abrams, D. P, 1996a, Response of 
Building Systems with Rocking Piers and Flexible 
Diaphragms, Worldwide Advances in Structural 
Concrete and Masonry, Proceedings of the Committee 
on Concrete and Masonry Symposium, ASCE 
Structures Congress XIV, Chicago, Illinois. 
Costley, A. C., and Abrams, D. P., 1996b, Dynamic 
Response of Unreinforced Masonry Buildings with 
Flexible Diaphragms, National Center for Earthquake 
Engineering Research, Technical Report 
NCEER 96 0001, Buffalo, New York. 
Epperson, G. S., and Abrams, D. P., 1989, Nondestructive 
Evaluation of Masonry Buildings, College of 
Engineering, University of Illinois at Urbana, 
Advanced Construction Technology Center Report 
No. 89 26 03, Illinois. 
Epperson, G. S., and Abrams, D. P., 1992, Evaluating 
Lateral Strength of Existing Unreinforced Brick 
Masonry Piers in the Laboratory, Journal of The 
Masonry Society, Boulder, Colorado, Vol. 10, No. 2, 
pp. 86 93. 
Feng, Jianguo, 1986, The Seismic Shear Strength of 
Masonry Wall, Proceedings of the US PRC Joint 
Workshop on Seismic Resistance of Masonry Structures, 
State Seismological Bureau, PRC and 
National Science Foundation, USA, Harbin, China. 
Gambarotta, L. and Lagomarsino, S., 1996, A Finite 
Element Model for the Evaluation and Rehabilitation 
of Brick Masonry Shear Walls, Worldwide 
Advances in Structural Concrete and Masonry, Proceedings 
of the Committee on Concrete and 
Masonry Symposium, ASCE Structures Congress 
XIV, Chicago, Illinois. 
ICBO, 1994, Uniform Code for Building Conservation, 
International Conference of Building Officials, 
Whittier, California. 
Kariotis, J. C., 1986, Rule of General Application Basic Theory, 
Earthquake Hazard Mitigation of 
Unreinforced Pre 1933 Masonry Buildings, Structural 
Engineers Association of Southern California, 
Los Angeles, California. 
Kariotis, J. C., Ewing, R. D., and Johnson, A. W., 1985a, 
Predictions of Stability for Unreinforced Brick 
Masonry Walls Shaken by Earthquakes, Proceedings 
of the 7th International Brick Masonry Conference, 
Melbourne, Australia. 
Kariotis, J. C., Ewing, R. D., and Johnson, A. W., 1985b, 
Strength Determination and Shear Failure Modes 
of Unreinforced Brick Masonry with Low Strength 
Mortar, Proceedings of the 7th International Brick 
Masonry Conference, Melbourne, Australia. 
Kariotis, J. C., Ewing, R. D., and Johnson, A. W., 1985c, 
Methodology for Mitigation of Earthquake Hazards 
in Unreinforced Brick Masonry Buildings, 
Proceedings of the 7th International Brick Masonry 
Conference, Melbourne, Australia. 
Kingsley, G. R., 1995, Evaluation and Retrofit of Unreinforced 
Masonry Buildings, Proceedings of the 
Third National Concrete and Masonry Engineering 
Conference, San Francisco, California, pp. 709 728. 
Kingsley, G. R., Magenes, G., and Calvi, G. M., 1996, 
Measured Seismic Behavior of a Two Story 
Masonry Building, Worldwide Advances in Structural 
Concrete and Masonry, Proceedings of the 
Committee on Concrete and Masonry Symposium, 
ASCE Structures Congress XIV, Chicago, Illinois. 
Magenes, G., 1997, personal communication, May. 
Magenes, G., and Calvi, G. M., 1992, Cyclic Behavior 
of Brick Masonry Walls, Proceedings of the Tenth 
World Conference, Balkema: Rotterdam, The Netherlands. 
Magenes, G. and Calvi, G. M., 1995, Shaking Table 
Tests on Brick Masonry Walls, 10th European 
Conference on Earthquake Engineering, Duma, 
editor, Balkema: Rotterdam, The Netherlands. 
Manzouri, T., Shing, P. B., Amadei, B., Schuller, M., 
and Atkinson, R., 1995, Repair and Retrofit of 
Unreinforced Masonry Walls: Experimental Evaluation and 
Finite Element Analysis, Department of 
Civil, Environmental and Architectural Engineering, 
University of Colorado: Boulder, Colorado, 
Report CU SR 95 2. 
Manzouri, T., Shing, P. B., Amadei, B., 1996, Analysis 
of Masonry Structures with Elastic Viscoplastic 
Models, 1996, Worldwide Advances in Structural 
Concrete and Masonry, Proceedings of the Committee 
on Concrete and Masonry Symposium, ASCE 
Structures Congress XIV, Chicago, Illinois. 
Priestley, M. J. N, 1985, Seismic Behavior of Unreinforced 
Masonry Walls, Bulletin of the New 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 4: Unreinforced Masonry 
Zealand National Society for Earthquake Engineering, 
Vol. 18, No. 2. 
Proposal for Change G7 7, 1997, proposal to change the 
in plane URM wall provisions of FEMA 273 (1996). 
Rutherford & Chekene, 1990, Seismic Retrofitting 
Alternatives for San Francisco s Unreinforced 
Masonry Buildings: Estimates of Construction Cost 
And Seismic Damage for the San Francisco Department 
of City Planning, Rutherford and Chekene 
Consulting Engineers: San Francisco, California. 
Rutherford & Chekene, 1997, Development of Procedures 
to Enhance the Performance of Rehabilitated 
Buildings, prepared by Rutherford & Chekene Consulting 
Engineers, published by the National Institute 
of Standards and Technology as Reports NIST 
GCR 97 724 1 and 97 724 2. 
SEAOC CALBO, 1990, Commentary on the SEAOCCALBO 
Unreinforced Masonry Building Seismic 
Strengthening Provisions, Evaluation and 
Strengthening of Unreinforced Masonry Buildings, 
1990 Fall Seminar, Structural Engineers Association 
of Northern California, San Francisco, California. 
SEAOSC, 1986, RGA (Rule of General Application) 
Unreinforced Masonry Bearing Wall Buildings 
(Alternate Design to Division 88), Earthquake 
Hazard Mitigation of UnreinforcedPre 1933 
Masonry Buildings, Structural Engineers Association 
of Southern California: Los Angeles, California. 
Sheppard, P. F. and Tercelj, S., 1985, Determination of 
the Seismic Resistance of an Historical Brick 
Masonry Building by Laboratory Tests of Cut Out 
Wall Elements, Proceedings of the 7th International 
Brick Masonry Conference, Melbourne, Australia. 
Tena Colunga, A., and Abrams, D. P., 1992, Response of 
an Unreinforced Masonry Building During the 
Loma Prieta Earthquake, Department of Civil 
Engineering, University of Illinois at Urbana 
Champaign, Structural Research Series No. 576. 
Tomazevic, M., and Anicic, 1989, Research, Technology 
and Practice in Evaluating, Strengthening, and 
Retrofitting Masonry Buildings: Some Yugoslavian 
Experiences, Proceedings of the International 
Seminar on Evaluating, Strengthening and Retrofitting 
Masonry Buildings, The Masonry Society: 
Boulder, Colorado. 
Tomazevic, M., Lutman, M., and Weiss, P., 1996, Seismic 
Upgrading of Old Brick Masonry Urban 
Houses: Tying of Walls with Steel Ties, Earthquake 
Spectra, EERI: Oakland, California, Volume 
12, No. 3. 
Tomazevic, M., and Weiss, P., 1990, A Rational, 
Experimentally Based Method for the Verification 
of Earthquake Resistance of Masonry Buildings, 
Proceedings of the Fourth U. S. National Conference 
on Earthquake Engineering, EERI: Oakland, 
California. 
Turnsek, V., and Sheppard, P., 1980, The Shear and 
Flexural Resistance of Masonry Walls, Proceedings 
of the International Research Conference on 
Earthquake Engineering, Skopje, Yugoslavia. 
Willsea, F. J., 1990, SEAOC CALBO Recommended 
Provisions, Evaluation and Strengthening of Unreinforced 
Masonry Buildings, 1990 Fall Seminar, 
Structural Engineers Association of Northern California, 
San Francisco, California. 
Xu, W., and Abrams, D. P., 1992, Evaluation of Lateral 
Strength and Deflection for Cracked Unreinforced 
Masonry Walls, U. S. Army Research Office, Report 
ADA 264 160, Triangle Park, North Carolina. 
Zsutty, T. C., 1990, Applying Special Procedures, 
Evaluation and Strengthening of Unreinforced 
Masonry Buildings, 1990 Fall Seminar, Structural 
Engineers Association of Northern California, San 
Francisco, California. 
Technical Resources 
FEMA 307 Technical Resources 83 
Infilled Frames
5. 5. 1 Commentary And Discussion 
There is a wealth of experimental data reported in the 
literature on infilled frames. Unfortunately, only a 
limited amount of the research has been performed 
under cyclic loading and conducted on specimens that 
reflect U. S. construction practice. For these test results, 
it is evident that infilled frames can possess stable 
hysteresis loops and continue to carry substantial lateral 
loads at significant interstory drifts. This is true in spite 
of the highly damaged appearance and even complete 
loss of some of the masonry units within an infill panel. 
Most experimental results on infilled frame systems 
show a mixture of behavior modes that take place at 
various stages of loading. At low interstory drift levels 
(0. 2% 0. 4%), corner crushing and some diagonal 
cracking in the panel tend to occur first. This is 
followed by frame yielding (0. 5% 1. 0% interstory 
drift) and possible bed joint sliding. As the drift 
amplitude increases beyond about 1%, cracking in the 
infill panel becomes more extensive, along with further 
frame damage. The frame damage takes the form of 
cracking, crushing, and spalling of concrete in the case 
of reinforced concrete frames or prying damage to 
bolted semi rigid connections in steel frames. The 
coexistence of several behavior modes makes it difficult 
to determine what A factors should be used for 
quantitative strength and deformation analysis. 
Therefore, it is necessary to resort to individual 
component tests to assess A values. The results of 
experiments conducted by Aycardi et al. (1994) are 
illustrative of the performance of nonductile reinforced 
concrete frames. These tests give results for each of the 
failure modes (except column shear). 
In the experimental studies on infilled frames by 
Mander et al. (1993a, b), steel frames were used and 
were instrumented with numerous strain gauges so the 
behavior of the frame could be uncoupled from the 
behavior of the infill panel. It was, therefore, possible 
to plot the net lateral load drift capacity of the brick 
masonry infill panel. These results were helpful in 
identifying the A factors for corner crushing, diagonal 
cracking and general shear failure behavior modes for 
masonry. The bed joint sliding behavior mode tends to 
occur mostly in steel frames with ungrouted 
unreinforced masonry infill with low panel height to 
length aspect ratios. The experimental results of 
Gergely et al. (1994) were useful for identifying A 
factors for this behavior mode. 
When investigating the out of plane behavior of infilled 
frame panels, it is difficult to enforce a complete failure, 
as evidenced by recent tests by Angel and Abrams 
(1994). It should be noted that these investigators first 
loaded their specimens in plane before conducting their 
out of plane tests. Results of this study indicate that 
lateral strength capacity is generally well in excess of 
200 psf. Thus, it is unlikely that out of plane failure 
should occur for normal infill height to thickness aspect 
ratios. These results suggest that if an out of plane 
failure is observed in the field, then some other (inplane) 
behavior mode has contributed to the failure of 
the infill. 
Dealing with infill panels with openings is difficult due 
to the many potential types of openings that may occur 
in practice. Evidently, when openings are present, the 
strength capacity is bounded by that of bare frame 
(lower bound) and that of a system with solid infill 
panels (upper bound). Although these results are 
derived from monotonic tests, they suggest that the 
deformation capacity is not impaired if openings exist. 
5. 1. 1 Development of A Factors for 
Component Guides 
The Component Damage Classification Guides and 
component modification factors (A factors) for infilled 
frames were based on an extensive review of research in 
the area of both nonductile reinforced concrete frames, 
as well as masonry structures. The principal references 
used in this work are listed in the tabular bibliography 
presented in Section 5. 2. For each component behavior 
mode, three types of A factors are used: stiffness 
reduction factors (AK), strength reduction factor (AQ) 
and a displacement reduction factor (AD). Description 
of how each of these A factors were derived from 
experimental evidence and theoretical considerations is 
presented in what follows. 
5. 1. 2 Development of Stiffness 
Deterioration AK 
As the displacement ductility of a member 
progressively increases, the member also softens. Even 
though the strength may be largely maintained at a 
nominal yield level, softening is manifest in the form of 
stiffness reduction. The degree of softening is generally 
related to the maximum displacement ductility the 
member has previously achieved. 
Technical Resources 
FEMA 307 Technical Resources 85 
Chapter 5: Infilled Frames 
There are several analytical models that can be used to shown that the reduced strength F1 = AQFn can be 
give guidance on how one can assess the degree of evaluated through 
softening in an element. For example, Chang and 
Mander (1994) describe several computational F M MlO. 0, 
hysteretic models calibrated for reinforced concrete AQ = i = 1 c E 
c, 1 (5 2) F Mn MMXOE3PC 
components. Utilizing their information obtained from 
a calibrated modified Takeda model, the AK factor for in which 1DCi = accumulated damage, Yci = stiffness reduction can be related by the following cumulative plastic drift, Mn = nominal moment 
relationship: capacity, Mc = the moment generated by the eccentric 
concrete stress block and Y 6pC = cumulative plastic 
rotation capacity considering concrete fatigue alone. 
AK (= (5 1) = (IA) Using energy concepts where it is assumed that the 
finite energy reserve of an unconfined concrete section 
where Amax = maximum displacement in the is gradually consumed to resist the concrete displacement history, Ay = yield displacement, 
yUA= displacement ductility factor, and a = an 
experimentally calibrated factor that is material or 
specimen dependent. 
Strictly, a should be established on a component by 
component basis. However, for reinforced concrete 
components there is a range of values from a = 0. 25 to 
a = 1 that may be applicable, a = 0. 5 being typical for 
most specimens. Well detailed members tend to have 
low a values, whereas higher a values are common for 
poorly detailed members. Although specific research on 
infill panels is not developed to the same extent, it 
seems reasonable that similar trends would be found for 
these components. 
5. 1. 3 The Determination of AQ for 
Strength Deterioration 
In structural elements not specifically designed for 
seismic resistance, there is generally a lack of adequate 
transverse reinforcement necessary to provide adequate 
confinement and shear resistance. As a result, under 
reversed cyclic loading the strength of such elements 
deteriorates progressively. Furthermore, if the non 
seismically designed frame elements have inadequate 
anchorage for the reinforcing steel, there can be a 
gradual loss in strength and then a sudden drop in 
strength when the anchorage zone or lap splice zone 
fails. An energy approach can be used to assess the loss 
of strength in a reinforced concrete column or beam 
element where inadequate transverse reinforcement is 
found. The energy based approach advanced by 
Mander and Dutta (1997) has been used in developing 
this process. A summary of the underlying theoretical 
concepts is given below. 
Assuming the moment capacity contributed by the 
concrete is gradually consumed by the propagating level 
of damage, then at the end of the cycle it can be 
compression force, a work expression can be 
formulated as 
EWD = IWD (5 3) 
where EWD = external work done on the section by the 
concrete compression force defined by the left hand 
side of the equation below, and IWD = internal work or 
energy absorption capacity of the section defined by the 
right hand side of the following equation Cccx= (5 4) 
CC (, X C=A, jfcdE
2) 0 in which Cc = concrete compression force, Up = plastic 
curvature, c = neutral axis depth, 2Nc = total number of 
reversals and Ag = gross area of the concrete section. 
The integral in the above expression actually denotes 
the finite energy capacity of an unconfined concrete 
section which in lieu of a more precise analysis, can be 
approximated as 0. 008 fc. Note also that the term in 
brackets in the above equation denotes the plastic strain 
at the location of the concrete compression force. 
Assuming that in a cantilever column the plastic 
rotation is entirely confined to the plastic hinge zone (of 
length Lp), using the moment area theorem and 
rearranging terms in the above equation, it is possible to 
solve for the cumulative plastic drift capacity as 
0. 016 (P) (5 5) Y (PC ) D (
where X0p = 2NCOp is the cumulative plastic drift 
defined as the sum of all positive and negative drift 
amplitudes up to a given stage of loading; and D = 
overall depth diameter of the column. 
Technical Resources FEMA 307 
Chapter 5: Infilled Frames 
The concrete damage model described so far is 
generally applicable to beam and or column elements 
with adequate bonding between the longitudinal 
reinforcement and the surrounding concrete. Thus 
following Equation 5 2, the concrete strength continues 
to decay until the moment capacity of the eccentric 
concrete block is fully exhausted. At this point the 
residual moment capacity entirely consists of the steel 
contribution. This is schematically portrayed in 
Figure 5 la. However, more often than not, older 
buildings possess lap splice zones at their column bases. 
Such splices are not always equipped with adequate lap 
length to ensure proper development of bond strength. 
The lap splice thus becomes the weak point in the 
column which shows a drastic reduction in the strength 
almost immediately following the lap splice failure. 
This is depicted in Figure 5 lb where the bond failure 
in the lap splice is assumed to occur over one complete 
cycle. The residual strength immediately after Fi is 
determined by the extent of confinement around the lap 
splice, if any. Subsequently the lateral strength is 
entirely dependent on the performance of pure concrete 
which continues to decay following the same 
Equation 5 2 until the residual rocking strength Fr is 
obtained. 
This theory has been validated with experimental results 
as shown in Figures 5 ic and 5 id. In Figure 5 ic, the 
lateral strength envelope is compared with test results 
with instances of unconfined concrete failure only. In 
Figure 5 id, the strength envelope is plotted for column 
specimen with a clear indication of lap splice failure. 
Satisfactory agreement between theory and experiment 
is observed. 
Therefore, with the mechanism of failure and the 
progression of strength deterioration clearly identified 
and quantified, it is possible to assess, analytically, kQ 
factors for reinforced concrete elements with specific 
detailing. The research has not been developed to the 
same extent for infill panels, although an examination 
of test results indicates that similar trends are present. 
5. 1. 4 Development of AD Reduction 
in Displacement Capability 
The reduction in displacement capability is more 
difficult to ascertain from traditional, quasi static, 
reversed cyclic loading, laboratory tests on members. 
Generally such tests are conducted using two cycles at 
previous loading history that is, the amount of energy 
absorbed with respect to the total energy absorption 
capacity. Strictly this cannot be ascertained without 
resorting to fatigue type of testing. 
Mander et al. (1994, 1995) and Mander and Dutta 
(1997) have shown that the displacement capability of 
structural concrete and steel elements follows a well 
known Manson Coffin fatigue relationship that can be 
written in displacement ductility terms as follows: 
(5 6) MA =mN. N 
where Nf= number of equi amplitude cycles required to 
produce failure at ductility amplitude tA; Mm,7
= monotonic ductility capacity; and c = fatigue exponent. 
Typical values of the latter are c = 1 3 for steel failure 
and c = 1 2 for nonductile reinforced concrete. 
The above equation can be written in terms of a 
damage fraction (D = nd Nf) that can be sustained 
for nd cycles of loading in the damaging earthquake: 
DN=nd) A (5 7) Nf P 
The remaining fatigue life then is (1 D). The 
displacement based AD factor can thus be defined as 
(5 8) A=P. M 
In the above two equations superscripts d and r refer to 
the damaging earthquake and remaining life, 
respectively. 
Thus for nonductile reinforced concrete failure taking 
c = 1 2 gives 1 PAI) (5 9) AD=Y 
For frictional or sliding behavior modes such as lap 
splice failure of masonry infill panels, there is no limit 
to the displacement capability. Therefore, for these two 
behavior modes, AD = 1 at all times. 
each ductility factor (or drift angle percentages) of  1, Although specific research on infill components is less
2, 6. until failure occurs. The reduction in developed, it is reasonable to assume that similar trends 
displacement capacity depends on the severity of the 
would be observed. 
Technical Resources 
FEMA 307 Technical Resources 
Chapter 5: Infilled Frames 
(a) (b) 4 I ID 1. 0 Nominal Flexural Strength I Nominal Flexural Strength 
F F I F F. F. I 2; VP 2a P 
(C) (d). 2 SPECIMEN TESTED BY 
IMANDER at. (1993b) 
0. S EXPERIMENTALLY C 0BSERVED STRENGTH r a: ENERY. DAZED 
DAMAGE MODEL 
0. 4 0. G 1. 2 1. n 
CUMULATWIPLASTICDRIFT 
z IL 6 IC. 4 I0 01 I 5I J 0 
Uj 02 TOTAL COLUMN DRIFT 
I Figure 5 1 Energy based damage analysis of strength reduction to define Ao 
Do00 Technical Resources FEMA307 
Chapter 5: Infilled Frames 
5. 2 Tabular Bibliography for Infilled Frames 
Table 5 1 Tabular Bibliography for Infilled Frames 
References Categories Remarks 
A B C D E F G H I 
Abrams, 1994 
Al Chaaretal., 1994 
Aycardietal., 1992 Nonductile concrete frame performance 
Aycardietal., 1994 Nonductile concrete frame performance 
Axely and Berteto, 1979 Experiments on multistory frames 
Benjamin and Williams, 1958 $ Classic brick infilled steel frame experiments 
Betemo and Brokken, 1983 
Bacci et al, 1995 Emphasis on nonductile frame performance 
Brokken and Berteso, 1981 
Cou, 1966 
Crisaffllyetal., 1995 
Dawe and McBride, 1985 Steel frame with pierced brick infills 
Dhanasekaretal., 1985 
Flanagan and Bennett, 1994 Steel frame clay tile infill 
Focardi and Manzini, 1984 
Gegelyet al., 1993 Steel frame clay tile infill
Hambuger and Charadeo, 1993
Hill, 1994 
Holmes, 1961 
Kadir, 1974 
Kahn and Hanson, 1977 
Klingner and Berttew, 1976 Multistory infilled frame performance 
Klingner and Berttew, 1978 Multistory infilled frame performance
Kaduretal., 1995 
Liauw and Lee, 1977 I 
Liauw, 1979 Multistory infilled frame performance
Liauw and Kwan, 1983a Steel frame concrete infill plastic failure modes 
Liauw and Kwan, 1983b Plastic strength theory 
Maghaddamn and Dowling, 1987 Geneva treatise on infilled frame behavior 
Mainstone and Weeks, 1970 
A= Modes of Failure, B = Strength, C =Stiffness, D= Ductility, E= Hysteretic Performance, F =Openings, G= Repairs, 
H =Experimental Performance of Walled Frames, I =Steel and Concrete Frame Behavior 
FEMA 307 FEMA 
Technical Resources Technical Resources 
Chapter 5: Infilled Frames 
Table 5 1 Tabular Bibliography for Infilled Frames (continued) 
References CategoriesRemarks 
A B C D E F G H I 
Mainstone, 1971 work on strut methods of analysis 
Mallick and Garg, 1971 
Mander and Nair, 1993a Steel frames brick infills under cyclic loading 
Mander et al., 1993b Effect of ferrocement repairs 
Manderet al., 1994 Low cycle fatigue of steel flame connections 
Mander et al., 1995 
Mehrabieta]., 1996 Cont flame block infill experiments 
Mosalarnet al., 1994 Steel frame brick infills finite element analysis 
Parducci and Mezzi, 1980 
Paulay and Priestley, 1992 Classical text on design 
Polyakov, 1956 Earliest work on infills translated from Russian 
Prawel and Lee, 1994 ferrocement repairs for masonry 
Priestley, 1996 Most recent work on RC in shear 
Priestley et al., 1996 Most recent work on RC in shear 
Reinhom et al., 1995 Advanced analysis methods for infills 
Riddingtonand Stafford Smith, 1977 Early work on strut methods of analysis 
Riddington, 1984 V V Emphasis on gap effects 
Sachanski, 1960 
Saneinejadand Hobbs, 1995 Most up to date reference on analysis methods 
Shapiroetal., 1994 
Shen and Zhu, 1994 Pseudo dynamic tests 
Shing et al., 1994 
Stafford Smith, 1966 Early experimental work 
Stafford Smith and Carter, 1969 Pioneering work on analysis using strut methods 
Thomas, 1953 Emphasis on brick work 
Wood, 1978 Early work on plastic methods of analysis 
Yoshimura and Kikuchi, 1995 
Zamic and Tomazevic, 1984 
Zamic and Tomazevic, 1985a 
Zamic and Tomazevic, 1985b 
A = Modes of Failure, B = Strength, C= Stiffness, D= Ductility, E= Hysteretic Performance, 
F= Openings, G = Repairs, 
H = Experimental 
Performance of Infilled Frames, I = Steel and Concrete Frame Behavior 
Technical Resources FEIVA 307 
Chapter 5: Infilled Frames 
5. 3 References for Infilled Frames a 
This list contains references from the infilled frames 
chapters of both FEMA 306 and 307. 
Abrams, D. P. (Ed.), 1994, Proceedings of the NCEER 
Workshop on Seismic Response of Masonry Infills, 
National Center for Earthquake Engineering 
Research, Technical Report NCEER 94 0004. 
Al Chaar, G., Angel, R. and Abrams, D., 1994, 
Dynamic testing of unreinforced brick masonry 
infills, Proc. of the Structures Congress 94, 
Atlanta, Georgia., ASCE, 1: 791 796. 
Angel R., and Abrams, D. P., 1994, Out Of Plane 
Strength evaluation of URM infill Panels, Proceedings 
of the NCEER Workshop on Seismic 
Response of Masonry Infills, D. P. Abrams editor, 
NCEER Technical Report NCEER 94 0004. 
Aycardi, L. E., Mander, J. B., and Reinhorn, A. M., 1992, 
Seismic Resistance of RC Frame Structures 
Designed only for Gravity Loads, Part II: Experimental 
Performance of Sub assemblages, National 
Center for Earthquake Engineering Research, Technical 
Report NCEER 92 0028. 
Aycardi, L. E., Mander, J. B., and Reinhorn, A. M., 1994, 
Seismic resistance of reinforced concrete frame 
structures designed only for gravity loads: Experimental 
performance of sub assemblages, ACI 
Structural Journal, (91) 5: 552 563. 
Axely, J. W. and Bertero, V. V., 1979, Infill panels: their 
influence on seismic response of buildings, Earthquake 
Eng. Research Center, University of California 
at Berkeley, Report No. EERC 79 28. 
Benjamin, J. R., and Williams, H. A., 1958, The behavior 
of one story shear walls, Proc. ASCE, ST. 4, 
Paper 1723: 30. 
Bertero, V. V. and Brokken, S. T., 1983, Infills in seismic 
resistant building, Proc. ASCE, 109 (6). 
Bracci, J. M., Reinhorn, A. M., and Mander, J. B., 1995, 
Seismic resistance of reinforced concrete frame 
structures designed for gravity loads: Performance 
of structural system, ACI Structural Journal, 
(92) 5: 597 609. 
Brokken, S. T., and Bertero, V. V., 1981, Studies on 
effects of infills in seismic resistance RIC construction, 
Earthquake Engineering Research Centre, 
University of California at Berkeley, Report No. 
EERC 81 12. 
Chang, G. A., and Mander, J. B., 1994, Seismic Energy 
Based Fatigue Damage Analysis of Bridge Columns: 
Part I Evaluation of Seismic Capacity, 
Technical Report NCEER 94 0006, and Part II 
Evaluation of Seismic Demand, Technical Report 
NCEER 94 0013, National Center for Earthquake 
Engineering Research, State University of New 
York at Buffalo. 
Cheng, C. T., 1997, New Paradigms for the Seismic 
Design and Retrofit of Bridge Piers, Ph. D. Dissertation, 
Science and Engineering Library, State University 
of New York at Buffalo, Buffalo, New York. 
Chrysostomou, C. Z., Gergely, P, and Abel, J. F., 1988, 
Preliminary Studies of the Effect of Degrading Infill 
Walls on the Nonlinear Seismic Response of Steel 
Frames, National Center for Earthquake Engineering 
Research, Technical Report NCEER 88 0046. 
Coul, A., 1966, The influence of concrete infilling on 
the strength and stiffness of steel frames, Indian 
Concrete Journal. 
Crisafulli, F. J., Carr, A. J., and Park, R., 1995, Shear 
Strength of Unreinforced Masonry Panels, Proceedings 
of the Pacific Conference on Earthquake 
Engineering; Melbourne, Australia, Parkville, Victoria, 
3: 77 86. 
Dawe, J. L. and McBride, R. T., 1985, Experimental 
investigation of the shear resistance of masonry 
panels in steel frames, Proceedings of the 7th 
Brick Masonry Conf., Melbourne, Australia. 
Dawe, J. L. and Young, T. C., 1985, An investigation of 
factors influencing the behavior of masonry infill in 
steel frames subjected to in plane shear, Proceedings 
of the 7th International. Brick Masonry Conference, 
Melbourne, Australia. 
Dhanasekar, K., Page, A. W., and Kleeman, P. W., 1985, 
The behavior of brick masonry under biaxial stress 
with particular reference to infilled frames, Proceedings 
of the 7th International. Brick Masonry 
Conference, Melbourne, Australia. 
Durrani, A. J., and Luo, Y. H., 1994, Seismic Retrofit of 
Flat Slab Buildings with Masonry Infills, in Proceedings 
of the NCEER Workshop on Seismic 
Response of Masonry Infills, D. P. Abrams editor, 
National Center for Earthquake Engineering 
Research, Technical Report NCEER 94 0004. 
Flanagan, R. D. and Bennett, R. M., 1994, Uniform Lateral 
Load Capacity of Infilled Frames, Proceedings
FEMA 307 Technical Resources 
Chapter 5: Infilled Frames 
of the Structures Congress 94, Atlanta, 
Georgia, ASCE, 1: 785 790. 
Focardi, F. and Manzini, E., 1984, Diagonal tension 
tests on reinforced and non reinforced brick panels, 
Proceedings of the 8th World Conference on 
Earthquake Engineering, San Francisco, California, 
VI: 839 846. 
Freeman S. A., 1994 The Oakland Experience During 
Loma Prieta Case Histories, Proceedings of the 
NCEER Workshop on Seismic Response of Masonry 
Infihls, D. P. Abrams editor, National Center for 
Earthquake Engineering Research, Technical 
Report NCEER 94 0004. 
Gergely, P., White, R. N., and Mosalam, K. M., 1994, 
Evaluation and Modeling of Infilled Frames, Proceedings 
of the NCEER Workshop on Seismic 
Response of Masonry Infills, D. P. Abrams editor, 
National Center for Earthquake Engineering 
Research, Technical Report NCEER 94 0004, pp. 
1 51 to 1 56. 
Gergely, P., White, R. N., Zawilinski, D., and Mosalam, 
K. M., 1993, The Interaction of Masonry Infill and 
Steel or Concrete Frames, Proceedings of the 1993 
National Earthquake Conference, Earthquake Hazard 
Reduction in the Central and Eastern United 
States: A Time for Examination and Action; Memphis, 
Tennessee, II: 183 191. 
Hamburger, R. O. and Chakradeo, A. S., 1993, Methodology 
for seismic capacity evaluation of steel frame 
buildings with infill unreinforced masonry, Proceedings 
of the 1993 National Earthquake Conference, 
Earthquake Hazard Reduction in the Central 
and Eastern United States: A Time for Examination 
and Action; Memphis, Tennessee, II: 173 182. 
Hill, James A., 1994, Lateral Response of Unreinforced 
Masonry Infill Frame, Proceedings of the 
Eleventh Conference (formerly Electronic Computation 
Conference) held in conjunction with ASCE 
Structures Congress 94 and International Symposium 
94, Atlanta, Georgia, pp. 77 83. 
Holmes, M., 1961, Steel frames with brickwork and 
concrete infilling, Proceedings of the Institute of 
Civil Engineers, 19: 473. 
Kadir, M. R. A., 1974, The structural behavior of 
masonry infill panels in framed structures, Ph. D. 
thesis, University of Edinburgh. 
Kahn, L. F. and Hanson, R. D., 1977, Reinforced concrete 
shear walls for a seismic strengthening, Proceedings 
of the 6th World Conf on Earthquake 
Engineering, New Delhi, India, III: 2499 2504. 
Klingner, R. E. and Bertero, V. V., 1976, Infilled frames 
in earthquake resistant construction, Earthquake 
Engineering Research Centre, University of California 
at Berkeley, Report No. EERC 76 32. 
Klingner, R. E. and Bertero, V. V., 1978, Earthquake 
resistance of infilled frames, Journal of the Structural 
Division, Proc. ASCE, (104) 6. 
Kodur, V. K. R., Erki, M. A., and Quenneville, J. H. P., 
1995, Seismic design and analysis of masonry 
infilled frames, Journal of Civil Engineering, 22: 
576 587. 
Liauw, T. C. and Lee, S. W., 1977, On the behavior and 
the analysis of multi story infilled frames subjected 
to lateral loading, Proceedings of the Institute of 
Civil Engineers, 63: 641 656. 
Liauw, T. C., 1979, Tests on multi storey infilled 
frames subject to dynamic lateral loading, ACI 
Journal, (76) 4: 551 563. 
Liauw, T. C. and Kwan, K. H., 1983a, Plastic theory of 
infilled frames with finite interface shear strength, 
Proceedings of the Institute of Civil Engineers, 
(2) 75: 707 723. 
Liauw, T. C. and Kwan, K. H., 1983b, Plastic theory of 
non integral infilled frames, Proceedings of the 
Institute of Civil Engineers, (2) 75: 379 396. 
Maghaddam, H. A. and Dowling, P. J., 1987, The State of 
the Art in Infilled Frames, Civil Engineering 
Department, Imperial College, ESEE Research 
Report No. 87 2, London. 
Mainstone, R. J. and Weeks, G. A., 1970, The influence 
of bounding frame on the racking stiffness and 
strength of brick walls, 2nd International Brick 
Masonry Conference. 
Mainstone, R. J., 1971, On the stiffness and strength of 
infilled frames, Proceedings of the Institute of 
Civil Engineers Sup., pp. 57 90. 
Mallick, D. V. and Garg, R. P., 1971, Effect of openings 
on the lateral stiffness of infilled frames, Proceedings 
of the Institute of Civil Engineers, 49: 193 209. 
Mander J. B., Aycardi, L. E., and Kim, D K, 1994, 
Physical and Analytical Modeling of Brick Infilled 
Steel Frames, Proceedings of the NCEER Workshop 
on Seismic Response of Masonry Infills, D. P. 
Abrams editor, National Center for Earthquake 
Engineering Research, Technical Report NCEER 
94 0004. 
Technical Resources FEMA 307 
Chapter 5: Infilled Frames 
Mander, J. B., Chen, S. S., and Pekcan, G., 1994, Low cycle 
fatigue behavior of semi rigid top and seat 
angle connections, AISC Engineering Journal, 
(31) 3: 111 122. 
Mander, J. B., and Dutta, A., 1997, How Can Energy 
Based Seismic Design Be Accommodated In Seismic 
Mapping, Proceedings of the FHWA IVCEER 
Workshop on the National Representation of Seismic 
Ground Motion for New and Existing Highway 
Facilities, Technical Report, National Center for 
Earthquake Engineering Research, NCEER 97 0010, pp 95 114. 
Mander, J. B., and Nair, B., 1993a, Seismic Resistance 
of Brick Infilled Steel Frames With and Without 
Retrofit, The Masonry Society Journal, 12 (2): 2437. 
Mander, J. B., Nair, B., Wojtkowski, K., and Ma, J., 
1993b, An Experimental Study on the Seismic Performance 
of Brick Infilled Steel Frames, National 
Center for Earthquake Engineering Research, Technical 
Report NCEER 93 0001. 
Mander, J. B., Pekcan, G., and Chen, S. S., 1995, Low cycle 
variable amplitude fatigue modeling of top 
and seat angle connections, AISC Engineering 
Journal, American Institute of Steel Construction, 
(32) 2: 54 62. 
Mander, J. B., Waheed, S. M., Chaudhary, M. T. A., and 
Chen, S. S., 1993, Seismic Performance of Shear 
Critical Reinforced Concrete Bridge Piers, 
National Center for Earthquake Engineering 
Research, Technical Report NCEER 93 0010. 
Mehrabi, A. B., Shing, P. B., Schuller, M. P. and Noland 
J. L., 1996, Experimental evaluation of masonry 
infilled RC frames, Journal of Structural Engineering. 
Mosalam, K. M., Gergely, P., and White, R., 1994, Performance 
and Analysis of Frames with URM 
Infills, Proceedings of the Eleventh Conference 
(formerly Electronic Computation Conference) 
held in conjunction with ASCE Structures Congress 
94 and International Symposium 94, Atlanta, 
Georgia, pp. 57 66. 
Parducci, A. and Mezzi, M., 1980, Repeated horizontal 
displacement of infilled frames having different 
stiffness and connection systems Experimental 
analysis, Proceedings of the 7th World Conference 
on Earthquake Engineering, Istanbul, Turkey, 7: 
193 196. 
Paulay, T. and Priestley, M. J. N., 1992, Seismic Design 
Of Reinforced Concrete and Masonry Buildings, 
John Wiley & Sons, New York. 
Polyakov, S. V., 1956, Masonry in framed buildings, 
pub. by Gosudarstvennoe Izdatelstvo po Stroitelstvu 
I Arkhitekture (Translation into English by 
G. L. Cairns). 
Prawel, S. P. and Lee, H. H., 1994, Research on the 
Seismic Performance of Repaired URM Walls, 
Proc. of the US Italy Workshop on Guidelines for 
Seismic Evaluation and Rehabilitation of Unreinforced 
Masonry Buildings, Department of Structural 
Mechanics, University of Pavia, Italy, June 2224, 
Abrams, D. P. et al. (eds.) National Center for 
Earthquake Engineering Research, SUNY at Buffalo, 
pp. 3 17 3 25. 
Priestley, M. J. N., 1996, Displacement based seismic 
assessment of existing reinforced concrete buildings, 
Bulletin of the New Zealand National Soc. for 
Earthquake Eng., (29) 4: 256 271. 
Priestley, M. J. N., Seible, F., and Calvi, G. M., 1996, 
Seismic Design and Retrofit of Bridges, John Wiley 
& Sons, New York, 686 pp. 
Reinhorn, A. M., Madan, A., Valles, R. E., Reichmann, 
Y., and Mander, J. B., 1995, Modeling of Masonry 
Infill Panels for Structural Analysis, National Center 
for Earthquake Engineering Research, Technical 
Report NCEER 95 0018. 
Riddington, J. and Stafford Smith, B., 1977, Analysis 
of infilled frames subject to racking with design 
recommendations, Structural Engineers, (52) 6: 
263 268. 
Riddington, J. R., 1984, The influence of initial gaps on 
infilled frame behavior, Proceedings of the Institute 
of Civil Engineers, (2) 77: 259 3 10. 
Sachanski, S., 1960, Analysis of earthquake resistance 
of frame buildings taking into consideration the car 
ring capacity of the filling masonry, Proceedings 
of the 2nd World Conference on Earthquake Engineering, 
Japan, 138: 1 15. 
Saneinejad, A and Hobbs, B., 1995, Inelastic design of 
infilled frames, Journal of Structural Engineering, 
(121) 4: 634 650. 
Shapiro, D., Uzarski, J., and Webster, M., 1994, Estimating 
Out of Plane Strength of Cracked Masonry 
Infills, University of Illinois at Urbana Champaign, 
Report SRS 588, 16 pp. 93 
Technical Resources 
FEMA 307 Technical Resources 93 
Chapter 5: Infilled Frames 
Shen, J. and Zhu, R., 1994, Earthquake response simulation 
of reinforced concrete frames with infilled 
brick walls by pseudo dynamic test, Proc. of the 
Second International Conference on Earthquake 
Resistant Construction and Design, Berlin, A. 
Balkema, Rotterdam, pp. 955 962. 
Shing, P. B., Mehrabi, A. B., Schuller, M. and Noland 
J. D., 1994, Experimental evaluation and finite element 
analysis of masonry infilled R C frames, 
Proc. of the Eleventh Conference (formerly Electronic 
Computation Conference) held in conjunction 
with ASCE Structures Congress 94 and 
International Symposium 94, Atlanta, Georgia., 
pp. 84 93. 
Stafford Smith, B. S., 1966, Behavior of square infilled 
frames, ASCE (92) 1: 381 403. 
Stafford Smith, B. and Carter, C., 1969, A method of 
analysis for infilled frames, Proceedings of the 
Institute of Civil Engineers, 44: 31 48. 
Thiruvengadam, V., 1985, On the natural frequencies 
of infilled frames, Earthquake Engineering and 
Structural Dynamics, 13: 401 419. 
Thomas, F. G., 1953, The strength of brickwork, J. 
Instnt. Struct. Engrs., (31) 2: 35 46. 
Wood, R. H., 1978, Plasticity, composite action and 
collapse design of unreinforced shear wall panels in 
frames, Proceedings of the Institute of Civil Engineers, 
2: 381 411. 
Yoshimura, K. and Kikuchi, K., 1995, Experimental 
study on seismic behavior of masonry walls confined 
by R C frames, Proceedings of the Pacific 
Conference on Earthquake Engineering, Melbourne, 
Australia, Parkville, Victoria, 3: 97 106. 
Zarnic, R. and Tomazevic, M., 1984, The behavior of 
masonry infilled reinforced concrete frames subjected 
to seismic loading, Proceedings of the 8th 
World Conference on Earthquake Engineering, California, 
VI: 863 870. 
Zarnic, R. and Tomazevic, M., 1985a, Study of the 
behavior of masonry infilled reinforced concrete 
frames subjected to seismic loading, Proc. 7th Intl. 
Brick Masonry Conf., Melbourne, Australia. 
Zarnic, R. and Tomazevic, M., 1985b, Study of the 
behavior of masonry infilled reinforced concrete 
frames subjected to seismic loading, Part 2. A 
report to the research community of Slovenia, 
ZRMK IKPI 8502, Ljubljana. 
Technical Resources FEMA 307 
6 Analytical Studies 
6. 1 Overview 
Analytical studies were conducted as part of this project 
to serve two broad objectives: (1) to assess the effects of 
damage from a prior earthquake on the response of 
single degree of freedom oscillators to a subsequent, 
hypothetical performance level earthquake, and (2) to 
evaluate the utility of simple, design oriented methods 
for estimating the response of damaged structures. 
Previous analytical studies were also reviewed. 
To assess the effects of prior damage on response to a 
performance level earthquake, damage to a large 
number of single degree of freedom (SDOF) oscillators 
was simulated. The initially damaged oscillators were 
then subjected to an assortment of ground motions. The 
response of the damaged oscillators was compared with 
that of their undamaged counterparts to identify how the 
damage affected the response. 
The oscillators ranged in initial period from 0. 1 to 2. 0 
seconds, and the strength values were specified such 
that the oscillators achieved displacement ductility 
values of 1, 2, 4, and 8 for each of the ground motions 
when using a bilinear force displacement model. The 
effects of damage were computed for these oscillators 
using several Takeda based force displacement models. 
Damage was parameterized independently in terms of 
ductility demand and strength reduction. 
Ground motions were selected to represent a broad 
range of frequency characteristics in each of the 
following categories: Short duration (SD) records were 
selected from earthquakes with magnitudes less than 
about 7, while long duration (LD) records were 
generally selected from stronger earthquakes. A third 
category, forward directivity (FD), consists of ground 
motions recorded near the fault rupture surface for 
which a strong velocity pulse may be observed very 
early in the S wave portion of the record. Six motions 
were selected for each category, representing different 
frequency characteristics, source mechanisms, and 
earthquakes occurring in locations around the world 
over the last half century. 
The utility of simple, design oriented methods for 
estimating response was evaluated for the damaged and 
undamaged SDOF oscillators. The displacement 
coefficient method is presented in FEMA 273 (FEMA, 
1997a) and the capacity spectrum and secant stiffness 
methods is presented in ATC 40 (ATC, 1996). 
Estimates of peak displacement response were 
determined according to these methods and compared 
with computed values obtained in the dynamic analyses 
for the damaged and undamaged structures. In addition, 
the ratio of the peak displacement estimates of damaged 
and undamaged structures was compared with the ratio 
obtained from the displacements computed in the 
nonlinear dynamic analyses. 
This chapter summarizes related findings by previous 
investigators in Section 6. 2. The dynamic analysis 
framework is described in detail in Section 6. 3, and 
results of the nonlinear dynamic analyses are presented 
in Section 6. 4. The design oriented nonlinear static 
procedures are described in Section 6. 5, and the results 
of these analyses are compared with the results 
computed in the dynamic analyses in Section 6. 6. 
Conclusions and implications of the work are presented 
in Section 6. 7. 
6. 2 Summary of Previous 
I Findings 
Previous studies have addressed several issues related to 
this project. Relevant analytical and experimental 
findings are reviewed in this section. 
6. 2. 1 Hysteresis Models 
Studies of response to recorded ground motions have 
used many force displacement models that incorporate 
various rules for modeling hysteretic response. By far, 
the most common of these are the bilinear and stiffness 
degrading models, which repeatedly attain the strengths 
given by the monotonic or envelope force displacement 
relation. The response of oscillators modeled using 
bilinear or stiffness degrading models is discussed 
below. 
6. 2. 1. 1 Bilinear and Stiffness Degrading 
Models 
Many studies (for example, Iwan, 1977; Newmark and 
Riddell, 1979; Riddell, 1980; Humar, 1980; Fajfar and 
Fischinger, 1984; Shimazaki and Sozen, 1984; and 
Minami and Osawa, 1988) have examined the effect of 
the hysteresis model on the response of SDOF 
structures. These studies considered elastic perfectly 
plastic, bilinear (with positive post yield stiffness), and 
stiffness degrading models such as the Takeda model 
Technical Resources
FEMA 307 Technical Resources 95 
Chapter 6: Analytical Studies 
and the Q model, as well as some lesser known models. 
For the nonlinear models used in these studies, the post 
yield stiffness of the primary curve ranged between 0 
and 10% of the initial stiffness. It is generally found that 
for long period structures with positive post yield 
stiffness, peak displacement response tends to be 
independent of the hysteresis model, and it is 
approximately equal to the peak displacement of linear 
elastic oscillators having the same initial stiffness. For 
shorter period structures, however, peak displacement 
response tends to exceed the response of linear elastic 
oscillators having the same initial stiffness. The 
difference in displacement response is exacerbated in 
lower strength oscillators. Fajfar and Fischinger (1984), 
found that for shorter period oscillators, the peak 
displacements of elastic perfectly plastic models tend 
to exceed those of degrading stiffness models (the Q 
model), and these peak displacements tend to exceed 
those of the bilinear model. Riddell (1980), reported 
that the response of stiffness degrading systems tends to 
go below the peaks and above the troughs of the 
spectra obtained for elastoplastic systems. 
The dynamic response of reinforced concrete structures 
tested on laboratory shake tables has been compared 
with the response computed using different hysteretic 
models. The Takeda model was shown to give good 
agreement with measured response characteristics 
(Takeda et al., 1970). In a subsequent study, the Takeda 
model was shown to match closely the recorded 
response; acceptable results were obtained with the 
less complicated Q Hyst model (Saiidi, 1980). Time 
histories computed by these models were far more 
accurate than those obtained with the bilinear model. 
Studies of a seven story reinforced concrete moment 
resisting frame building damaged in the 1994 
Northridge earthquake yield similar conclusions. 
Moehle et al. (1997) reported that the response 
computed for plane frame representations of the 
structure most nearly matched the recorded response 
when the frame members were modeled using stiffness 
degrading models and strength and stiffness degrading 
force displacement relationships; dynamic analysis 
results obtained using bilinear force displacement 
relationships were not sufficiently accurate. 
Iwan (1973) examined the effect of pinching and 
yielding on the response of SDOF oscillators to four 
records. It was found that the maximum displacement 
response of oscillators having an initial period equal to 
one second was very nearly equal to that computed for 
bilinear systems having the same initial stiffness and 
yield strength. For one second oscillators having 
different system parameters and subjected to different 
earthquake records, the ratio of mean degrading system 
peak displacement response to bilinear system response 
was 1. 06, with standard deviation of 0. 14. Iwan noted 
that for periods appreciably less than one second, the 
response of degrading systems was significantly greater 
than that for the corresponding bilinear system, but 
these effects were not quantified. 
Iwan (1977) reported on the effects of a reduction in 
stiffness caused by cracking. Modeling the uncracked 
stiffness caused a reduction in peak displacement 
response for shorter period oscillators with 
displacement ductility values less than four, when 
compared with the response of systems having initial 
stiffness equal to the yield point secant stiffness. 
Humar (1980) compared the displacement ductility 
demand calculated for the bilinear and Takeda models 
for SDOF and multi degree of freedom (MDOF) 
systems. For the shorter period SDOF oscillators, the 
displacement ductility demands exceeded the strength 
reduction factor, particularly for the Takeda model. 
Five and ten story frames were designed with girder 
strengths set equal to 25% of the demands computed in 
an elastic analysis, and column strengths were set 
higher than the values computed in an elastic analysis. 
The Takeda model, which included stiffness 
degradation, generally led to larger interstory drifts and 
girder ductility demands than were computed with the 
bilinear model. 
The studies described above considered hysteretic 
models for which the slope of the post yield portion of 
the primary curve was greater than or equal to zero. 
Where negative post yield slopes are present, peak 
displacement response is heightened (Mahin, 1980). 
The change in peak displacement response tends to be 
significantly larger for decreases in the post yield slope 
below zero than for similar increases above zero. Even 
post yield stiffness values equal to negative 1 % of the 
yield stiffness were sufficient to cause collapse. These 
effects were found to be more pronounced in shorter 
period systems and in relatively weak systems. 
Rahnama and Krawinkler (1995) reported findings for 
SDOF structures subjected to 15 records obtained on 
rock sites. They found that higher lateral strength is 
required, relative to elastic demands to obtain target 
displacement ductility demands, for oscillators with 
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Chapter 6: Analytical Studies 
negative post yield stiffness. The decrease in the 6. 2. 
1. 2 Strength Degrading Models 
strength reduction factor is relatively independent of 
The response of structures for which the attainable 
vibration period and is more dramatic with increases in 
target displacement ductility demand. These effects 
strength is reduced with repeated cyclic loading is 
discussed below. 
depend on the hysteresis model; the effect of negative 
post yield stiffness on the strength reduction factor is 
much smaller for stiffness degrading systems than for Parducci and Mezzi (1984) used elasto plastic force displacement models to examine the effects of strength 
bilinear systems. They note that stiffness degrading degradation. Yield strength was modeled as decreasing 
systems behave similarly to bilinear systems for linearly with cumulative plastic deformation. Using
positive post yield stiffness, and they are clearly accelerograms recorded in Italian earthquakes, The
superior to systems with negative values of post yield authors found that strength degradation causes an 
stiffness. 
increase in displacement ductility demand for the 
stronger, shorter period oscillators. For weaker 
Palazzo and DeLuca (1984) found that the strength oscillators, strength degradation amplifies ductility
required to avoid collapse of SDOF oscillators demand over a broader range of periods. The more rapid
subjected to the Irpinia earthquake increased as the degradation of strength, the greater the increase in
post yield stiffness of the oscillator became ductility demand. An analogy can be made with the 
increasingly negative. Xie and Zhang (1988) compared 
the response of stiffness degrading models (having zero 
findings of Shimazaki and Sozen (1984): when strength 
post yield stiffness) with the response of models having degradation occurs, the increase in ductility demand can 
a negative post yield stiffness. The SDOF oscillators be kept small for shorter period structures if sufficient 
were subjected to 40 synthetic records having duration 
strength is provided. 
varying from 6 to 30 seconds. It appears that Xie and 
Zhang found that for shorter period structures, negative Nakamura and Tanida (1988) examined the effect of 
strength degradation and slip on the response of SDOF 
post yield stiffness models were more likely to result in 
oscillators to white noise and to the 1940 NS El Centro
collapse than were the stiffness degrading models for motion. Figure 6 1 plots the force displacement 
all durations considered. 
response curves obtained in this study for various 
combinations of hysteresis parameters for oscillators 
with a 0. 2 sec period. The parameter D controls the 
r +1OZ D C . 0 D C 0. 2 Q D C 0. 4 D C 0X. 6
r 0 DC 0. 0ram D C . O2 D C 0. 6 D C 0. 0 D C 0. 2 D C O. 4 D C0. 6 
0 t +D C 0. 4 + r 0 0 X r 10% 0 2J
D 0. 6 l0. 0 SeC, 0. 75 (E D. C. tr C. O. 6 DUO DSC 0. 0 IDC UX2 DEC ot. r C 0. 6 D 0. 6 Tt. 0. 2 see C 0. 375 (El Centro NS. D 0. T. 0. 2se, C 0. 375 (El Ceotro NlS) a e. S. a 02 C E o
Effect of Load Degradation on Response under El Centro Wave. 
Figure 6 1 Effect of Hysteretic Properties on Response to 1940 NS El Centro Record (from Nakamura, 1988) 
FEMA 307 Technical Resources 
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amount of slip, C controls the degraded loading 
stiffness, and as and a, control the unloading stiffness 
for the slip and degrading components of the model. It 
is clear that peak displacement response tends to 
increase as slip becomes more prominent, as post yield 
stiffness decreases or even becomes negative, and as 
loading stiffness decreases. 
Rahnama and Krawinkler (1995) modeled strength 
degradation for SDOF systems as a function of 
dissipated hysteretic energy. Strength degradation may 
greatly affect the response of SDOF systems, and the 
response is sensitive to the choice of parameters by 
which the strength degradation is modeled. Results of 
such studies need to be tied to realistic degradation 
relationships to understand the practical significance of 
computed results. 
6. 2. 2 Effect of Ground Motion Duration 
As described previously, Xie and Zhang (1988) 
subjected a number of SDOF oscillators to 40 synthetic 
ground motions, which lasted from 6 to 30 seconds. For 
stiffness degrading and negative post yield stiffness 
models, the number of collapses increased, as ground 
motion duration increased. The incidence of collapse 
tended to be higher for shorter period structures than 
longer period structures. Shorter duration ground 
motions that were just sufficient to trigger the collapse 
of short period structures did not trigger the collapse of 
any longer period structures. 
Mahin (1980) reported on the evolution of ductility 
demand with time for SDOF oscillators subjected to 
five synthetic records, each having a 60 second 
duration. Peak evolutionary ductility demands were 
plotted at 10 second intervals for bilinear oscillators; 
ductility demand was found to increase asymptotically 
toward the peak values obtained at 60 seconds. This 
implies that increases in the duration of ground motion 
may cause relatively smaller increases in ductility 
demand. 
Sewell (1992) studied the effect of ground motion 
duration on elastic demand, constant ductility strength 
reduction factors, and inelastic response intensity, using 
a set of 262 ground motion records. He found that the 
spectral acceleration of elastic and inelastic systems is 
not correlated with duration, and that strength reduction 
factors can be estimated using elastic response 
ordinates. These findings suggest that the effect of 
duration on inelastic response is contained within 
representations of elastic response quantities. 
6. 2. 3 Residual Displacement 
Kawashima et al. (1994) studied the response of bilinear 
systems with periods between 0. 1 and 3 seconds that 
were subjected to Japanese ground motion records. 
According to this study, residual displacement values 
are strongly dependent on the post yield stiffness of the 
bilinear system; that is, systems with larger post yield 
stiffness tend to have significantly smaller residual 
displacements, and systems with zero or negative post 
yield stiffness tend to have residual displacements that 
approach the peak response displacement. They also 
found that the magnitude of residual displacement, 
normalized by peak displacement, tends to be 
independent of displacement ductility demand, based 
on displacement ductility demands of two, four, and six. 
The results also indicated that the magnitude of residual 
displacement is not strongly dependent on the 
characteristic period of the ground motion, the 
magnitude of the earthquake, or the distance from the 
epicenter. 
In shake table tests of reinforced concrete wall and 
frame wall structures, Araki et al. (1990) reported that 
residual drifts for all tests were less than 0. 2% of 
structure height. These tests included wall structures 
exhibiting displacement ductility demands up to about 
12 and frame wall structures exhibiting displacement 
ductility demands up to about 14. The small residual 
drifts in this study were attributed to the presence of 
restoring forces (acting on the mass of the structure), 
which are generated as the wall lengthens when 
displaced laterally. Typical response analyses do not 
model these restoring forces. These results appear to be 
applicable to systems dominated by flexural response. 
However, larger residual displacements have been 
observed in postearthquake reconnaissance. 
6. 2. 4 Repeated Loading 
In the shake table tests, Araki et al. (1990) also 
subjected reinforced concrete wall and frame wall 
structures to single and repeated motions. It appears that 
a synthetic ground motion was used. It was found that 
the low rise structures subjected to repeated shake table 
tests displaced to approximately twice as much as they 
did in a single test. For the mid rise and high rise 
structures, repeated testing caused peak displacements 
that were approximately 0 to 10% larger than those 
obtained in single tests. 
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Wolschlag (1993) tested three story reinforced concrete 
walls on a shake table. In one test series, an undamaged 
structure was subjected to repeated ground motions of 
the same intensity. In the repeat tests, the peak 
displacement response at each floor of the damaged 
specimen hardly differed from the response measured 
for the initially undamaged structure. 
Cecen (1979) tested two identical ten story, three bay, 
reinforced concrete frame models on a shake table. The 
two models were subjected to sequences of base 
motions of differing intensity, followed by a final test 
using identical base motions. When the structures were 
subjected to the repeated base motion, the peak 
displacement response at each story was only slightly 
affected by the previous shaking of the same intensity. 
When the two structures were subjected to the same 
final motion, peak displacement response over the 
height of the two structures was only slightly affected 
by the different prior sequences. Floor acceleration 
response, however, was prone to more variation. 
Mahin (1980) investigated the analytical response of 
SDOF oscillators to repeated ground motions. He 
reported minor to moderate increases in displacement 
ductility demand across all periods, and weaker 
structures were prone to the largest increases. For 
bilinear models with negative post yield stiffness, 
increased duration or repeated ground motions tended 
to cause significant increases in displacement ductility 
demand (Mahin and Boroschek, 1991). 
6. 3 Dynamic Analysis 
Framework 
6. 3. 1 Overview 
This section describes the dynamic analyses determining 
the effects of damage from prior earthquakes on 
the response to a subsequent performance level 
earthquake. In particular, this section describes the 
ground motion and hysteresis models, the properties of 
the undamaged oscillators, and the assumptions and 
constructions used to establish the initially damaged 
oscillators. Results of the dynamic analyses are 
presented in Section 6. 4. 
6. 3. 2 Dynamic Analysis Approach 
The aim of dynamic analysis was to quantify the effects 
of a damaging earthquake on the response of a SDOF 
oscillator to a subsequent, hypothetical, performance 
event earthquake. Two obvious approaches may be 
taken: the first simulates the damaging earthquake, and 
the second simulates the damage caused by the 
damaging earthquake. 
To simulate the damaging earthquake, oscillators can be 
subjected to an acceleration record that is composed of 
an initial, damaging ground motion record, a quiescent 
period, and a final ground motion record specified as 
the performance level event. This approach appears to 
simulate reality well, but it is difficult to determine a 
priori how to specify the intensity of the damaging 
ground motion. One rationale would be to impose 
damaging earthquakes that cause specified degrees of 
ductility demand. This would result in oscillators 
having experienced prior ductility demand and residual 
displacement at the start of the performance level 
ground motion. 
In the second approach, taken in this study, the force 
displacement curve of the oscillator is modified 
prescriptively to simulate prior ductility demand, and 
these analytically damaged oscillators are subjected 
to only the performance level ground motion. To 
identify the effects of damage (through changes in 
stiffness and strength of the oscillator force 
displacement response), the possibility of significant 
residual displacements resulting from the damaging 
earthquake was neglected. Thus, the damaging 
earthquake is considered to have imposed prior ductility 
demands (PDD), possibly in conjunction with strength 
reduction or strength degradation, on an initially 
undamaged oscillator. Initial stiffness, initial unloading 
stiffness, and strength of the oscillators at the start of the 
performance level ground motion may be affected. 
Response of the initially damaged structure is 
compared with the response of the undamaged structure 
under the performance level motion. This approach 
presumes that an engineer will be able to assess changes 
in lateral stiffness and strength of a real structure based 
on the nature of damage observed after the damaging 
earthquake. 
While a number of indices may be used to compare 
response intensity, peak displacement response is 
preferred here because of its relative simplicity, its 
immediate physical significance, and its use as the basic 
parameter in the nonlinear static procedures (described 
in Section 6. 5). The utility of the nonlinear static 
procedures is assessed vis  vis their ability to estimate 
accurately the peak displacement response. 
It should be recognized that predicting the capacity of 
wall and infill elements may be difficult and prone to 
uncertainty, whether indexed by displacement, energy, 
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Chapter 6: Analytical Studies 
or other measures. When various modes of response 
may contribute significantly to an element s behavior, 
existing models may not reliably identify which mode 
will dominate. Uncertainty in the dominant mode 
necessarily leads to uncertainty in estimates of the 
various capacity measures. 
6. 3. 3 Ground Motions 
Several issues were considered when identifying ground 
motion records to be used in the analyses. First, the 
relative strength of the oscillators and the duration of 
ground motion are thought to be significant because 
these parameters control the prominence of inelastic 
response. Second, it is known that ground motions rich 
in frequencies just below the initial frequency of the 
structure tend to exacerbate damage, because the period 
of the structure lengthens as yielding progresses. Third, 
information is needed on the characteristics of structural 
response to near field motions having forward 
directivity effects. 
The analyses were intended to identify possible effects 
of duration and forward directivity on the response of 
damaged structures. Therefore, three categories of 
ground motions were established: short duration (SD), 
long duration (LD), and Forward Directivity (FD). The 
characteristics of several hundred ground motions were 
considered in detail in order to select the records used in 
each category. Ground motions within a category were 
selected to represent a broad range of frequency 
content. in addition, it was desired to use some records 
that were familiar to the research community, and to use 
some records obtained from the Loma Prieta, 
Northridge, and Kobe earthquakes. Within these 
constraints, records were selected from a diverse 
worldwide set of earthquakes in order to avoid 
systematic biases that might otherwise occur. Six time 
series were used in each category to provide a statistical 
base on which to interpret response trends and 
variability. Table 6 1 identifies the ground motions that 
compose each category, sorted by characteristic period. 
Record duration was judged qualitatively in order to 
sort the records into the short duration and long duration 
categories. The categorization is intended to 
discriminate broadly between records for which the 
duration of inelastic response is short or long. Because 
the duration of inelastic response depends 
fundamentally on the oscillator period, the relative 
strength, and the force displacement model, a suitable 
scalar index of record duration is not available. 
The physical rupture process tends to correlate ground 
motion duration and earthquake magnitude. It can be 
observed that earthquakes with magnitudes less than 7 
tended to produce records that were categorized as 
short duration motions, while those with magnitudes 
greater than 7 tended to be categorized as long duration 
motions. 
Ground motions recorded near a rupturing fault may 
contain relatively large velocity pulses if the fault 
rupture progresses toward the recording station. 
Motions selected for the forward directivity category 
were identified by others as containing near field pulses 
(Somerville et al., 1997). Recorded components aligned 
most nearly with the direction perpendicular to the fault 
trace were selected for this category. 
The records shown in Table 6 1 are known to come 
from damaging earthquakes. The peak ground 
acceleration values shown in Table 6 1 are in units of 
the acceleration of gravity. The actual value of peak 
ground acceleration does not bear directly on the results 
of this study, because oscillator strength is determined 
relative to the peak ground acceleration in order to 
obtain specified displacement ductility demands. 
Identifiers in Table 6 1 are formulated using two 
characters to represent the earthquake, followed by two 
digits representing the year, followed by four characters 
representing the recording station, followed by three 
digits representing the compass bearing of the ground 
motion component. Thus, IV40ELCN. 180 identifies the 
South North component recorded at El Centro in the 
1940 Imperial Valley earthquake. Various magnitude 
measures are reported in the literature and repeated here 
for reference: ML represents the traditional local or 
Richter magnitude, Mw represents moment magnitude, 
and Ms represents the surface wave magnitude. 
Detailed plots of the ground motions listed in Table 6 1 
are presented in Figures 6 2 through 6 19. The plots 
present ground motion acceleration, velocity, and 
displacement time series data, as well as spectral 
response quantities. In all cases, ground acceleration 
data were used in the response computations, assuming 
zero initial velocity and displacement. For most records, 
the ground velocity and displacement data presented in 
the figures were prepared by others. For the four records 
identified with an asterisk ( ) in Table 6 1, informal 
integration procedures were used to obtain the ground 
velocity and displacement values shown. 
(Text continued on page 120) 
100 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Table6 1 Recorded Ground Motions Used in the Analyses 
Identifier Earthquake Mag. Station T Component PGA Epic. Char. 
Date (g) Dist. Period 
l m (k) (sec) 
Short Duration (SD) 
WN87MWLN. 090 Whittier Narrows ML= 6. 1 Mount Wilson 90 0. 175 18 0. 20 
1Oct 87 Caltech Seismic Station 
BB92CIVC. 360 Big Bear Ms=6. 6 Civic Center Grounds 360 0. 544 12 0. 40 
28 Jun 92 
SP88GUKA. 360 Spitak Ms=6. 9 Gukasyan, Armenia 360 0. 207 57 0. 55 
7 Dec 88 
LP89CORR. 090 Loma Prieta Ms=7. 1 Corralitos 90 0. 478 8 0. 85 
17 Oct 89 Eureka Canyon Rd. 
NR94CENT. 360 Northridge MW=6. 7 Century City 360 0. 221 19 1. 00 
17 Jan 94 
IV79ARY7. 140 Imperial Valley ML=6. 6 Array #7 14 140 0. 333 27 1. 20 
15 Oct79 
Long Duration (LD) 
CH85LLEO. 010 Central Chile Ms=7. 8 Llolleo Basement of 1 010 0. 711 60 0. 30 
3 Mar 85 Story Building: 
CH85VALP. 070 Central Chile Ms=7. 8 Valparaiso University of 070 0. 176 26 0. 55 
3 Mar 85 Santa Maria 
IV40ELCN. 180 Imperial Valley ML=6. 3 El Centro 180 0. 348 12 0. 65 
18 May 40 Irrigation District 
TB78TABS. 344 Tabas M=7. 4 Tabas 344 0. 937 <3 0. 80 
16 Sep 78 
LN92JOSH. 360 Landers M=7. 5 Joshua Tree 360 0. 274 15 1. 30 
28 Jun 92 
MX85SCTI. 270 Michoacan MS=8. 1 SCTI Secretary of Communication 270 0. 171 376 2. 00 
19 Sep 85 and Transportation 
Forward Directivity (FD): 
LN92LUCN. 250 Landers M=7. 5 Lucerne 250 0. 733 42 0. 20 
28 Jun 92 
6
IV79BRWY. 315 Imperial Valley ML=6. Brawley Municipal Airport 315 0. 221 43 0. 35 
15 Oct 79 
LP89SARA. 360 Loma Prieta Ms=7. 1 Saratoga 360 0. 504 28 0. 40 
17 Oct 89 Aloha Avenue 
NR94NWHL. 360 Northridge MW=637 Newhall 360 0. 589 19 0. 80 
17 Jan 94 LA County Fire Station 
NR94SYLH. 090 Northridge MW=6. 7 Sylmar County Hospital 090 0. 604 15 0. 90 
17 Jan 94 Parking Lot 
KO95TTRI. 360 Hyogo Ken Nambu ML= 7. 2 Takatori kisu 360 0. 617 11 1. 40 
17 Jan 95 
Indicates that informal integration procedures were used to calculate the velocity and displacement histories 
shown in Figures 6 2 through 6 19. 
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WN87MWLN. 090
0 10 2 0 30 40 so 60 
10 20304 50 50
0 10 20 30 40 
0 10 2 0 3 0 40 50 60
Time (sec) Equivalent Velocity (cm sec) Pseudo Acceleration (cm sec2 
1200 I I I2 Damping 2% Damping
5 0 1000. 10% Damping 20% Damping. 
40 800 30 60 0 2 0 400 10 200 0 0 L . 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 
Period, (eec) Period, (eec) 
Figure 6 2 Characteristics of the WN87MWLN. 090 (Mount Wilson) Ground Motion 
Technical FM 0
102 102 Resources FEMA 307 
Chapter 6: Analytical Studies 
SP88GUJKA 360 2 00
I 1 2 
150 Ground. Acceleration (cm see 
100
50
I 0
5 0 
100 
15 0 
2 00
250L I I II I 
0 10 2 0 3 0 40 50 60 
15 1 0 Ground Velocity (cm sec) 
5 0 5 1 0 
1 5 20 
O 10 20 30 4 0 50 60
3 Ground Displacement (cm) 
2 1
0
1
2
3
0 10 2 0 3 0 40 5 0 60
Time (sec) 
Equivalent Velocity (cm sec) Pseudo Acceleration (cm sec2
9 0 900 
2% Damping 2% Damping
80. 5% Damping 800 z 5% Damping 10% 
Damping 10% Damping 
7 0 20% Dam ing 700 20% Damping
6 0 600 
50 500 j. 
40 4 0 0. 
I 3 0 0 3 
20 200. 
10 100. 
0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 I. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 
Period, (sec) Period, (sec) 
Figure 6 4 Characteristics of the SP88GUKA. 360 (Spitak) Ground Motion 
104 104 Resources FEMA 307 
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Chapter 6: Analytical Studies 
H85VALP. 070
CH85VALP. 070
200
150 
100 
50 
50 
100 
150 
200
0 10 20 30 40 5060
15 
10 
5
0
5
10 
15 
10 2030 40 50 60 
4. Displacement (cm) | Ground 
10 203040 50 60
Time (see) 
Equivalent Velocity (cm sec) Pseudo Acceleration (cm sec2) 
120. 1000 II 
2% Damping
900. 5% Damping 100 
10% Damping 800 
20% Damping. 
7 0 0. 80. 600 8 4 1 60 
500 400 A 
40 2 0 0. 200 
20 100 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 
Period, (sec) Period, (sec) 
Figure 6 9 Characteristics of the CH85VALP. 070 (Valparaiso University) Ground Motion 
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Chapter 6: Analytical Studies 
TB78TABA. 344
1000 
400 
600 
600 
0 10 20 30 40 50 60 
150 
Ground Velocity (cm sec) 
100 
50
0
50 
100
150 10 20 30 40 5 
I0 10 20 30 40 50 646
80 
60. 
40 
60. 
80. 
100 
0 10 20 30 40 50 60 
Time (sec) 
Equivalent Velocity (cm sec) Pseudo Acceleration (cm sec2) 
5000 I 1 1 1
450 I I T I I 
2% Damping 500 2%Damping 
400: 5%
Dampin 4500 5% Damping 10% 
Damping 10% Damping 350 p 20%
Damping 4000. 20% Damping. 
300 1. 1 3500
3000. 
250 
2500 I. 
200
2000., 
150. 1500, y. i
100 
1000. 
500. 
L I 
0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0
Period, (sec) Period, (sec) 
Figure 6 11 Characteristics of the TB78TABS. 344 (Tabas) Ground Motion 
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Chapter 6:. Analytical Studies 
LN92LUCN. 250
800
600 (cm (sec4
era&t1on. 
400 200 0
200 I I. I. I 
400
600
800I
D 10 20 30 40 50 61
Ground 
40
20
20
40
60
80. 1 111, 
100. 
120. 
140
1I0 20 30 40 50 6 
40
20nd Displacement
20.
40.
60. 
80 
100
120
140
160
0 10 20 30 40 50 60
Time (sec) Equivalent Velocity (cm sec) Pseudo Acceleration (cm sec2
180 4000
2% Dpi I 2% Damping 
160. 5% Damping  2% Damping 
10% Damping: 3500 10% Damping 
140 fl
3000 
20% Damping. 
120:. 
I 2500
100
2000
80. I IT 
1500
: 
60 I. 1000
40 
500
:.:. 
20
I I 
0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 
Period, (sec) Period, (sec) 
Figure 6 14 Characteristics of the LN92LUCN. 250 (Lucerne) Ground Motion 
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LP89SARA. 360
300
200. Ground Acceler. & Ion. (CM. SeC2. 
100
0
10 0 
200 
300
400
500
I) 10 20 30 40 50 63 
30
Velocity
20. J. Ground. (cm/sec) 
10
0 r 11 
1 0 
20
30
40
50
0 10 20 30 40 50 6 (
20
Ground Displacement (cm) 
15
10
5
0
5
10
0 102030405060
Time (sec) 
Equivalent Velocity (cm sec) Pseudo Acceleration (cm seC2
200 1 1 I. 2000 I 1I I 
2% D ping Damping 
5%Dampin
180 5% ng 1800 2% 10% 
Damping 160 
20% g. 1600. 20% Damping. 140 
L. 1400. 
120 12000
100. 7. 
80. 
20 
0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 
Period, (sec) Period, (sec) 
Figure6 16 Characteristics of the LP89SARA. 360 (Saratoga) Ground Motion 
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NR94NWHL. 360 
600
Ground Acceleration (cm sec
400
200
0
200
400
600
0 10 20 30 40 50 6 D 
60
40. Ground. Velocity. I. cm sec 
20
I 0
20
40
60
80
100 
0 10 20 30 40 50 60 
40 
Ground Disp ac t (cm) 
I 
30
,. 
20 
10
0. 
10 
20,. 
30
0 10 20 3040 50 60 Time (sec) 
Equivalent Velocity (cm sec) Pseudo Acceleration (cm seC2) 450 3000
2% Damping 400 5% Damping 10% Damping 
2500 350
Po 20Da>V, 5w mpi. 
300 t 2000 r
250, 2w 
1500 
200
150 1000 
I I 1 100 
I. I I. 500
I. 50
O, 0 L 
0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0
Period, (sec) Period, (sec) 
Figure 6 17 Characteristics of the NR94NWHL. 360 (Newhall) Ground Motion 
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Chapter 6: Analytical Studies 
NR94SYLM. 090 
600 
500 lrat o 
400 
300 
200 
100 
100 
200 
300. 
400 
0 10 20 30 40 50 60 
60 
1 
20. 
0 
20 
40 
60 
80 
20 30 40 50 60 
15 
0 10 0 >Ground Displacement (m
1 
10 5
1 I. 
0 
I I I. I 
5 
10 
15 
20 
0 102030405060 
Time (sec) 
Equivalent Velocity (cm sec) Pseudo Acceleration (cm sec2) 
250 2000 1 I I 
2% Damping
1800. 5% Damping 
10% Damping 200 
1600. 20% Damping 1400 
150. 1200 + 
1000.I
j. 
9. 
100. 800 800 
600 
50 400. 
200
00. 0 
0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 
Period, (sec) Period, (sec) 
Figure 6 18 Characteristics of the. 090 (Sylmar Hospital) Ground Motion 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
The characteristic period, Tg, of each ground motion 
was established assuming equivalent velocity spectra 
and pseudo acceleration spectra for linear elastic oscillators 
having 5% damping. The equivalent velocity, Vm, 
is related to input energy, Em, and ground acceleration 
and response parameters by the following expression: 
I mV = Em =m cXidt (6 1) 
2 m 
where m= mass of the single degree of freedom 
oscillator, xg = the ground acceleration, and k = the 
relative velocity of the oscillator mass (Shimazaki and 
Sozen, 1984). The spectra present peak values 
calculated over the duration of the record. 
The characteristic periods were determined according to 
engineering judgment to correspond approximately to 
the first (lowest period) peak of the equivalent velocity 
spectrum, and, at the same time, the period at which the 
transition occurs between the constant acceleration and 
constant velocity portions of a smooth design spectrum 
fitted to the 5% damped spectrum (Shimazaki and 
Sozen, 1984; Qi and Moehle, 1991; and Lepage, 1997). 
Characteristic periods were established prior to the 
dynamic analyses. 
Other criteria are available to establish characteristic 
periods. For example, properties of the site, 
characterized by variation of shear wave velocity with 
depth, may be used to establish Tg. Alternatively, the 
characteristic period may be defined as the lowest 
period for which the equal displacement rule applies, 
and thus becomes a convenient reference point to 
differentiate between short and long period systems. 
6. 3. 4. Force Displacement Models 
The choice of force displacement model influences the 
response time history and associated peak response 
quantities. Ideally, the force displacement model should 
represent behavior typical of wall buildings, including 
strength degradation and stiffness degradation. 
Actual response depends on the details of structural 
configuration and component response, which in turn, 
depend on the material properties, dimensions, and 
strength of the components, as well as the load 
environment and the evolving dynamic load history 
(which can influence the type and onset of failure). The 
objective of the dynamic analyses is to identify basic 
trends in how prior damage affects system response in 
future earthquakes. Fulfilling this objective does not 
require the level of modeling precision that would be 
needed to understand the detailed response of a 
particular structure or component. For this reason, we 
selected relatively simple models that represent a range 
of behaviors that might be expected in wall buildings. 
Three broad types of system response can be 
distinguished: 
Type A: Stiffness degrading systems with positive 
post yield stiffness (Figure 6 20a). 
Type B: Stiffness degrading systems with negative 
post yield stiffness (Figure 6 20b). 
Type C: Pinched systems exhibiting strength and 
stiffness degradation Figure 6 20c). 
(a) Stiffness Degrading (b) Stiffness Degrading (c) Stiffness and Strength 
(positive post yield stiffness) (negative post yield stiffness) Degrading (with pinching) 
Figure 6 20 Force Displacement Hysteretic Models 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Type A behavior typically represents wall systems 
dominated by flexural response. Type B behavior is 
more typical of wall systems that exhibit some 
degradation. In response with increasing displacement; 
degradation may be due to relatively brittle response 
modes. Type C behavior is more typical of wall systems 
that suffer degradation of strength and stiffness, 
including those walls in which brittle modes of response 
may predominate. 
Type A behavior was represented in the analyses using 
the Takeda model (Takeda et al., 1970) with post yield 
stiffness selected to be 5% of the secant stiffness at the 
yield point (Figure 6 21a). Previous experience 
(Section 6. 2. 1) indicates that this model represents 
stiffness degradation in reinforced concrete members 
exceptionally well. In addition, it is widely known by 
researchers, and it uses displacement ductility to 
parameterize stiffness degradation. The Takeda model 
features a trilinear primary curve that is composed of 
uncracked, cracked, and yielding portions. After 
yielding, the unloading stiffness is reduced in 
proportion to the square root of the peak displacement 
ductility. Additional rules are used to control other 
aspects of this hysteretic model. This model is 
subsequently referred to as Takeda5 . 
Type B behavior was represented in the analyses using 
the Takeda model with post yield stiffness selected to 
be 10% of the yield point secant stiffness 
(Figure 6 21b). This model is subsequently referred to 
as TakedalO. 
F 4 k 0. 05k F 
Type C behavior was represented in the analyses by a 
modified version of the Takeda model (Figure 6 21c). 
The behavior is the same as for Type A, except for 
modifications to account for pinching and cyclic 
strength degradation. The pinching point is defined 
independently in the first and third quadrants 
(Figure 6 22). The pinching point displacement is set 
equal to 30% of the current maximum displacement in 
the quadrant. The pinching point force level is set equal 
to 10% of the current maximum force level in the 
quadrant. Cyclic strength degradation incorporated in 
this model is described in Section 6. 3. 6. This model is 
subsequently referred to as TakPinch. 
Collectively, the Takeda5, TakedalO, and TakPinch 
models are referred to as degrading models in the body 
of this section. For these models, dynamic analyses 
were used to identify the effects of prior damage on 
response to future earthquakes. The analyses covered a 
number of relative strength values, initial periods of 
vibration, damage intensities, and performance level 
earthquakes. For all dynamic analyses, damping was set 
equal to 5% of critical damping, based on the period of 
vibration that corresponds to the yield point secant 
stiffness. 
In addition, a bilinear model (Figure 6 23) was selected 
to establish the strength of the degrading oscillators, 
which were set equal to the strength required to achieve 
bilinear displacement ductility demands of 1 (elastic), 2, 
4, and 8 for each reference period and for each of the 18 
ground motions. The bilinear model does not exhibit 
stiffness or strength degradation. Besides establishing 
Ak Yield Point F 4k 0. 10k A (a) Takeda Model (+5%) (b) Takeda Model ( 10%) (c) Takeda Pinching Model (Takeda5 ) (TakedalO) (TakPinch) 
Figure 6 21 Degrading Models Used in the Analyses 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies k Yield Point A 0. 05k 
Figure 6 22 Bilinear Model Used to Determine Strengths of Degrading Models 
Maximum prior displacement cycle I 0. 3A., g
Figure 6 23 Specification of the Pinching Point for the Takeda Pinching Model 
the strength of the oscillators, this model serves two 
additional purposes. First, results obtained in this study 
with the bilinear model can be compared with those 
obtained by other researchers to affirm previous 
findings and, at the same time, to develop confidence in 
the methods and techniques used in this study. Second, 
the bilinear model provides a convenient point of 
departure from which the effects of stiffness and 
strength degradation can be compared. 
6. 3. 5 Undamaged Oscillator Parameters 
To identify effects of damage on response, it is first 
necessary to establish the response of initially 
undamaged oscillators to the same ground motions. The 
response of the undamaged oscillators is determined 
using the degrading models of Figure 6 21 for the 
performance level ground motions. 
The yield strength of all degrading models is set equal 
to the strength required to achieve displacement 
ductility demands (DDD) of 1 (elastic), 2, 4, and 8 
using the bilinear model. This is done at each period 
and for each ground motion. For any period and ground 
motion considered, the yield strength of the initially 
undamaged models is the same, but only the bilinear 
model achieves the target displacement ductility 
demand. Where the same target displacement ductility 
demand can be achieved for various strength values, the 
largest strength value is used, as implemented in the 
computer program PCNSPEC (Boroschek, 1991). 
The initial stiffness of the models is established to 
achieve initial (reference) vibration periods of 0. 1, 0. 2, 
0. 3, 0. 4, 0. 5, 0. 6, 0. 8, 1. 0, 1. 2, 1. 5, and 2. 0 seconds. 
These periods are determined using the yield point 
secant stiffness for all the models considered. 
For the undamaged Takeda models, the cracking 
strength is set equal to 50% of the yield strength, and 
the uncracked stiffness is set equal to twice the yield 
point secant stiffness (Figure 6 24). 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Yield Point
F 0. 5FY 
Cracking Point 
A Aax A y 
Specification of the Uncracked Stiffness, Cracking Strength, and Unloading Stiffness for the Takeda
Figure 6 24 Models 6. 3. 6 Damaged Oscillator Parameters 
Damage is considered by assuming that the force 
displacement curves of the oscillators are altered as a 
result of previous inelastic response. Reduction in 
stiffness caused by the damaging earthquake is 
parameterized by prior ductility demand. Strength 
degradation is parameterized by the reduced strength 
ratio. 
Each of the initially undamaged degrading oscillators is 
considered to have experienced prior ductility demand 
(PDD) equal to 1, 2, 4, or 8 as a result of the damaging 
earthquake. The construction of an initially damaged 
oscillator force displacement curve is illustrated for a 
value of PDD greater than zero in Figure 6 25. The 
prior ductility demand also regulates the unloading 
stiffness of the Takeda model until larger displacement 
ductility demands develop. 
The analytical study considered damaging earthquakes 
of smaller intensity than the performance level 
earthquake. Consequently, the PDD values considered 
must be less than or equal to the design displacement 
ductility (DDD). Thus, an oscillator with strength 
established to achieve a displacement ductility of 4 is 
analyzed only for prior displacement ductility demands 
of 1, 2, and 4. The undamaged Takeda oscillators 
sometimes had ductility demands for the performance 
level earthquake that were lower than their design 
values (DDD). Again, because the damaging earthquake 
is considered to be less intense than the performance 
level event, oscillators having PDD in excess of the 
undamaged oscillator response were not considered, 
further. 
The Takeda models of the undamaged oscillators 
represent cracking behavior by considering the 
uncracked stiffness and the cracking strength. The 
effects of cracking in a previous earthquake were 
assessed by comparing the peak displacement response 
Undamaged Damaged 
Figure 6 25 Construction of Initial Force Displacement Response for Prior Ductility Demand > 0 and Reduced 
Strength Ratio = 1 123 
FEMA 307 Technical Resources Technical Resources 123 
Chapter 6: Analytical Studies 
Initially Undamaged 
I Initially Damaged 
Figure 6 26 Construction of Initial Force Displacement Response for PDD> 0 and RSR< 1 for Takeda5 and TakedalO Models 
of initially uncracked oscillators to the response of should more closely approximate the response of oscillators that are initially cracked; that is, Takeda the ideal model. oscillators having a PDD of one. When larger PDD 
values are considered, the reductions in initial loading 2. TakPinch Oscillators: Rather than begin with a 
and unloading stiffness are determined in accordance reduced strength, a form of cyclic strength degradation 
was explicitly modeled for the Takeda Pinching
with the Takeda model. 
oscillators. A trilinear primary curve was established 
It is not obvious what degree of strength degradation is (Figure 6 27), identical to the envelope curve consistent with the PDDs, nor just how the degradation used in the Takeda5 model. The curve exhibits of strength should be modeled to represent real cracking, a yield strength determined from the 
structures. We used two approaches to gauge the extent response of the bilinear models, and a post yield 
to which strength degradation might affect the response: stiffness equal to 5% of the yield point secant stiffness. A secondary curve is established, having the 
1. Takeda5 and TakedalO Oscillators: The initial same yield displacement and post yield stiffness as 
strength of the damaged models was reduced to try the primary curve, but having yield strength equal 
to capture the gross effects of strength degradation to the reduced strength ratio (RSR) times the prion response. The initial response of the damaged mary yield strength. For displacements less than the 
oscillator was determined using the construction of current maximum displacement in the quadrant, a 
Figure 6 26. The resulting curve may represent a reduced strength point is defined at the maximum 
backbone curve that is constructed to approximate displacement at 0. 54 (l RSR) Fy above the secondary 
the response of a strength degrading oscillator. For curve strength, where n is the number of cycles 
example, a structure for which repeated cycling approaching the current maximum displacement. 
causes a 20% degradation in strength relative to the The oscillator may continue beyond this displace 
primary curve may be modeled as having an initial ment, and once it loads along the primary curve, n
strength equal to 80% of the undegraded strength. is reset to one, to cause the next cycle to exhibit 
If the backbone curve is established using the strength degradation. The term (1 RSR) Fyis simply 
expected degraded strength asymptotes, then the strength difference between the primary and 
modeled structure tends to have smaller initial secondary curves, and the function O. 5 represents
stiffness and larger displacement response relative an asymptotic approach toward the secondary curve 
to the ideal degrading structure. Consequently, the with each cycle. In each cycle, the strength is 
modeled response is expected to give an upper reduced by half the distance remaining between the 
bound to the displacement response expected from current curve and the secondary curve. Pinching
the ideal model. If, instead, the backbone curve is and strength degradation are modeled independently selected 
to represent an average degraded response, in the first and third quadrants. 
using typical degraded strength values rather than 
the lower asymptotic values, the computed response 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
(RSR) Fy YiC 
Figure 6 27 Strength Degradation for Takeda Pinchir 
For the TakPinch models, strength degradation is 
modeled with and without PDD. When PDD is 
present, the oscillator begins with n equal to one. 
This represents a single previous cycle to the PDD 
displacement, and corresponds to initial loading 
towards a reduced strength point halfway between 
the primary and secondary curves at the PDD 
displacement (Figure 6 28). 
For the other degrading models, strength reduction is 
considered possible only for PDDs greater than zero. 
The parameter RSR is used to describe strength. 
degradation in the context of the Takeda Pinching 
models and strength reduction in the context of the 
other degrading models. For this study, values of RSR 
were arbitrarily set at 100%, 80%, and 60%. 
Oscillators were referenced by their initial, undamaged 
vibration periods, determined using the yield point 
secant stiffness, regardless of strength loss and PDDs. 
Note that changes in strength further affect the initial 
stiffness of the damaged oscillators. 
While the values of the parameters used to model Type 
A, B, and C behaviors, as well as the hysteresis rules 
themselves, were chosen somewhat arbitrarily, they 
were believed to be sufficiently representative to allow 
meaningful conclusions to be made regarding the 
effects of prior damage on response characteristics of 
various wall structures. Values of RSR and PDD were 
selected to identify trends in response characteristics, 
not to represent specific structures. 
0. 5 (l RSR) Fy Prior maximum displacement cycle 
Current cycle A. A ig Model 6. 3. 7 Summary of Dynamic Analysis
Parameters 
Nonlinear dynamic analyses were conducted for SDOF 
systems using various force displacement models, 
various initial strength values, and for various degrees 
of damage. The analyses were repeated for the 18 
selected ground motion records. The analysis 
procedures are summarized below. 
1. Initially undamaged oscillators were established at 
eleven initial periods of vibration, equal to 0. 1, 0. 2, 
0. 3, 0. 4, 0. 5, 0. 6, 0. 8, 1. 0, 1. 2, 1. 5, and 2. 0 seconds. 
At these periods, the strength necessary to obtain 
design displacement ductilities (DDDs) of 1 (elastic), 
2, 4, and 8 were obtained using the bilinear 
model for each earthquake. This procedure establishes 
44 oscillators for each of 18 ground motions. 
2. The responses of the oscillators designed in step 1 
were computed using the three degrading models 
(Takeda5, TakedalO, and TakPinch). The yield 
strength of the degrading oscillators in this step is 
identical to that determined in the previous step for 
the bilinear model. The period of vibration of the 
degrading oscillators, when based on the yield 
point secant stiffness, matches that determined in 
the previous step for the bilinear model. 
3. Damage is accounted for by assuming that the 
force displacement curves of the oscillators are 
altered as a result of previous inelastic response. 
The extent of prior damage is parameterized by 
PDD. For some cases, the strength of the oscillators 
is reduced as well. Each of the initially undamaged, 
degrading oscillators was considered to have experienced 
a PDD equal to 1, 2, 4, or 8, but not in 2 
excess of the ductility demand for which the oscillators 
Technical Resources 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
Primary Curve 
Pinching Point 
Reduced Strength Point 
5 0c5 (1 RSR) Fy 
Initial Damaged Response 
Ay 0. 3 (PDD) A (PDD) Ay A 
Figure 6 28 Construction of Initial Force Displacement 
Response for PDD> 0 and RSR< 1 for Takeda Pinching Model 
was designed. The effects of cracking on 6. 4 Results Of Dynamic 
response were determined by considering a PDD of Analyses
one. Where larger PDDs are considered, reductions 
in the initial loading and unloading stiffness were 
determined in accordance with the Takeda model. 6. 4. 1 Overview and Nomenclature 
4. Strength degradation was modeled explicitly in the This section describes results obtained from the 
TakPinch model. In the Takeda5 and TakedalO dynamic analyses. Section 6. 4. 2 characterizes the 
models, strength degradation was approximated by ground motions in terms of strength and displacement 
reducing the initial strength of the damaged demand characteristics for bilinear oscillators, in order 
Takeda5 and TakedalO models. RSRs equal to to establish that the ground motions and procedures 
100%, 80%, and 60% were considered. Although used give results consistent with previous studies. 
the strength reduction considered in the Takeda 5 Section 6. 4. 3 discusses the response of the Takeda 
and TakedalO models does not model the evolution models in some detail, for selected values of 
of strength loss, it suggests an upper bound for the parameters. Section 6. 4. 4 presents summary response 
effect of strength degradation on response characteristics statistics for the Takeda models for a broader range of 
parameter values. 
6. 3. 8 Implementation of Analyses Several identifiers are used in the plots, as follows: 
Over 22, 000 inelastic SDOF analyses were conducted Records:
using a variety of software programs. The strength of 
the oscillators was determined using constant ductility SD= Short duration ground motions. 
iterations for the bilinear oscillators using the program LD= Long duration ground motions. 
PCNSPEC (Boroschek, 1991), a modified version of FD= Forward directivity ground motions. 
NONSPEC (Mahin and Lin, 1983). Response of the 
Takeda models was computed using a program DDD: Design Displacement Ductility. Strength 
developed by Otani (1981). This program was modified was determined to achieve the specified 
at the University of Illinois to include the effects of DDD response for bilinear oscillators having PDD, pinching, and strength degradation and to identify post yield stiffness equal to 5% of the collapse states for models with negative post yield initial stiffness. Values range from 1 to 8. stiffness. 
PDD: Prior Ductility Demand. This represents a 
modification of loading and unloading 
stiffness, to simulate damage caused by 
126 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
previous earthquakes. Values range from 1 
to 8, but not in excess of DDD. 
RSR: Reduced Strength Ratio. This represents a 
reduction or degradation of strength and 
associated changes in stiffness. Values 
ranges from 100% to 60%, as detailed in 
Figures 6 26, 6 27, and 6 28. 
Displacements: 
dd = Peak displacement response of 
undamaged oscillator 
d d=Peak displacement response of damaged 
oscillator 
de = Peak displacement response of elastic 
oscillator having stiffness equal to the 
yield point secant stiffness of the corresponding 
Takeda oscillator 
Space constraints limit the number of included figures. 
Selected results for oscillators designed for a 
displacement ductility of 8 are presented below. Elastic 
response characteristics are presented as part of the 
ground motion plots in Figures 6 2 to 6 19
6. 4. 2 Response of Bilinear Models 
Figures 6 29 to 6 31 present the response of bilinear 
models to the SD, LD, and FD ground motions, 
respectively. The ratio of peak displacement of the 
inelastic model to the peak displacement response of an 
elastic oscillator having the same initial period, 
ddlde, is presented in the upper plot of each figure. The 
lower plot presents the ratio of elastic strength demand 
to the yield strength provided in order to attain the 
specified DDD, which in this case equals 8. 
When the strength reduction factor, R, has a value of 8, 
the inelastic design strength is 1 8 of the elastic 
strength. For DDD = 8, an R = 8 means that the reduced 
inelastic design strength and the resulting oscillator 
ductility are equal. If R is greater than 8, say 12, for 
DDD = 8, then the reduced inelastic design strength of 
the structure can be 1 12 of the expected elastic strength 
to achieve an oscillator ductility of 8. That is, for any R, 
the structure can be designed for 1IR times the elastic 
needed strength to achieve a ductility of DDD. 
Response to each ground motion is indicated by the 
plotted symbols, which are ordered by increasing 
characteristic period, Tg. It was found that the 
displacement and strength data are better organized 
when plotted against the ratio T Tg instead of the 
reference period, T The plots present data only for 
T Tg < 4 in order to reveal sufficient detail in the range 
T Tg < 1. The trends shown in Figures 6 29 through 6 31 
resemble those reported by other researchers, for 
example, Shimazaki and Sozen (1984), Miranda (1991), 
and Nassar and Krawinkler (1991). However, it can be 
observed that the longer period structures subjected to 
ground motions with forward directivity effects show a 
peak displacement response in the range of 
approximately 0. 5 to 2 times the elastic structure 
response, somewhat in excess of values typical of the 
other classes of ground motion. Additionally, strength 
reduction factors, R, tend to be somewhat lower for the 
FD motions, representing the need to supply a greater 
proportion of the elastic strength demand in order to 
maintain prespecified DDDs. 
6. 4. 3 Response of Takeda Models 
The Takedamodels were provided with lateral strength 
equal to that determined to achieve specified DDDs of 
1, 2, 4, and 8 for the corresponding bilinear models, 
based on the yield point secant stiffness. 
Prior damage was parameterized by prior ductility 
demand (PDD), possibly in conjunction with strength 
reduction or strength degradation, which is 
parameterized by RSR. PDD greater than zero (damage 
present) and RSR less than one (strength reduced or 
degrading) both cause the initial period of the oscillator 
to increase. When previous damage has caused 
displacements in excess of the yield displacement 
(PDD>1), even small displacements cause energy 
dissipation through hysteretic response. No further 
attention is given to those oscillators for which the 
imposed PDD exceeds the response of the undamaged 
oscillator, and these data points are not represented on 
subsequent plots. 
6. 4. 3. 1 Response of the Takeda5 Model 
It is of interest to observe how structures proportioned 
based on the bilinear model respond if their force 
displacement response is represented more accurately 
by a Takeda model. This interest is based in part on the 
widespread use of the bilinear model in developing 
current displacement based design approaches. 
Figures 6 32 through 6 34 present the response of 
Takeda5 models in which the oscillator strength was set 
to achieve a bilinear displacement ductility demand of 
8. The upper plot of each figure shows the ratio of peak 
displacement response to the peak response of an elastic 
(Text continued on page 134) 
Technical Resources 
Technical Resources
FEMA 307 
Chapter 6: Analytical Studies 
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Figure 6 29 Response of Bilinear Oscillators to Short Duration Records (DDD= 8) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 129 
Chapter 6: Analytical Studies 
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Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Records LD; DDD=8; PDD=O; RSR=1; Model=Takeda5 
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Period Ratio, TIT, Figure 6 33 Displacement Response of Takeda Models Compared with Elastic Response ahd Bilinear Response for 
Long Duration Records (DDD= 8 and RSR= 1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 132 Technical Resources FEMA307 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=O; RSR=1; Model=Takeda5 10 
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Period Ratio, TIT, 
Figure 6 34 Displacement Response of Takeda Models Compared with Elastic Response and Bilinear Response for 
Forward Directive Records (DDD= 8 and RSR= 1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
07 Technical Resources 13
FEMA 307 Technical Resources 133 
Chapter 6: Analytical Studies analog, dd de. The upper plots of Figures 6 32 through 6 34 are analogous to those presented in Figures 6 29 
through 6 3 1. 
The lower plots of Figures 6 32 through 6 34 show the 
ratio of the Takeda5 and bilinear ultimate displacements, 
dd Takeda5 Bilinear It is clear that peak displacements 
of the Takeda model may be several times 
larger or smaller than those obtained with the corresponding 
bilinear model. 
The effect of damage on the Takeda5 model is shown in 
Figures 6 35 through 6 40, for Takeda5 oscillators that 
were initially designed for a bilinear DDD of 8. The 
upper plot of each figure shows the response without 
strength reduction (RSR = 1); the lower plot shows 
response for RSR = 0. 6. 
Figures 6 35 through 6 37 show the effect of cracking 
on response. The displacement response, dd, of 
Takeda5 oscillators subjected to a PDD of one is 
compared with the response of the corresponding 
undamaged Takeda5 oscillators, dd. Where no strength 
degradation occurs (RSR = 1), cracking rarely causes an 
increase in displacement demand; for the vast majority 
of oscillators, cracking is observed to cause a slight 
decrease in the peak displacement response. Reductions 
in strength typically cause a noticeable increase in 
displacement response, particularly for low T Tg. 
Figures 6 38 through 6 40 show the effect of a PDD of 
8 on peak displacement, d d, relative to the response of 
the corresponding undamaged oscillators. Prior damage 
is observed to cause modest changes in displacement 
response where the strength is maintained (RSR = 1); 
displacements may increase or decrease. Where 
displacements increase, they rarely increase more than 
about 10% above the displacement of the undamaged 
oscillator for the short duration and long duration 
motions. For the forward directivity motions, they 
rarely increase more than about 30% above the 
displacement of the undamaged oscillator. The largest 
displacements tend to occur more frequently for T<Tg. 
The above discussion concerned oscillators for which 
the strength is maintained. When strength is reduced 
(RSR = 0. 6), prior ductility demand may cause 
displacements to increase or decrease, but the tendency 
for displacements to increase is more prominent than 
for RSR = 1. Furthermore, the increase in displacement 
tends to be larger than for RSR = 1. Reduction in 
strength, as represented in Figure 6 26, also causes 
reduction in stiffness, and both effects contribute to the 
tendency for displacements to increase. 
To understand the effects of prior damage on the 
response of the Takeda5 models, it is helpful to consider 
several oscillators exposed to the IV40ELCN. 180 (El 
Centro) record. Figures 6 41 to 6 45 plot the response 
of oscillators having initial (reference) periods of 0. 2, 
0. 5, 1. 0, 1. 5, and 2. 0 sec, respectively, to this ground 
motion. The oscillators have yield strength equal to that 
required to obtain displacement ductility demands of 8 
for the bilinear model. Oscillators having PDD of 0 
(undamaged), 1, 4, and 8 are considered. Displacement 
time histories (40 sec) of the oscillators are plotted at 
the top of each figure. Details of the first 10 seconds of 
response are shown below these. The solid lines 
represent the response of the initially undamaged 
oscillators, and the dashed and dotted lines represent 
oscillators with PDD > 0. Force displacement plots for 
the first 10 sec of response of each oscillator are 
provided in the lower part of the figure, using the same 
PDD legend. It can be observed that even though the 
undamaged oscillators initially have greater stiffness, 
their displacement response tends to converge upon the 
response of the initially damaged oscillators within a 
few seconds. The displacement response of the 
damaged oscillators tends to be in phase with that of the 
initially undamaged oscillators, and maximum values 
tend to be similar to and to occur at approximately the 
same time as the undamaged oscillator peaks. Thus, it 
appears that prior ductility demands have only a small 
effect on oscillator response characteristics and do not 
cause a fundamentally different response to develop. 
6. 4. 3. 2 Response of the TakPinch Model 
Figures 6 46 to 6 48 plot the ratio, d dldd, of damaged 
and undamaged displacement response for the TakPinch 
models having DDD = 8 and PDD = 8, for RSR = 1 and 
0. 6. Figure 6 49 plots the displacement time history of 
TakPinch oscillators subjected to the NS component of 
the 1940 El Centro record, and Figure 6 50 plots results 
for oscillators having cyclic strength degradation given 
by RSR = 0. 6. These oscillators have a reference period 
of one second, DDD = 8, and various PDDs. 
By comparison with the analogous figures for the 
Takeda5 model (Figures 6 38 to 6 40 and 6 43), it can 
be observed that: (1) for RSR = 1 (no strength 
degradation), the effect of PDD on displacement 
response is typically small for the Takeda5 and 
TakPinch oscillators, and (2) the effect of cyclic 
strength degradation, as implemented here, is also 
relatively small. Thus, the observation that prior 
(Text continued on page 151) 
Technical Resources FEIVA 307 
Chapter 6: Analytical Studies 
I I Records=SD; DDD=8; PDD=1; RSR=1; Model=Takeda5 
Excludescases where pnor damage (PDD) exceeds undamaged 
3 WN87MWLN. 090 
O BB92CIVC. 360 
A SP88GUKA. 360 
1. 5 C. 1. I. 11 1. 1. 1. 1. I I ll I ll. I I l:1 v LP89CORR. 090 
O NR94CENT. 360 
IV79ARY7. 140 
0t 
1 A A. A t A 0 AI V a A, A I. I. A 
M A, Q: b 
0. 5 
C 
0 l 2 3 4 
Period Ratio, T T, 
5 
Records=SD; DDD=8; PDD=1; RSR=0. 6; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds undamaged response 
O WN87MWLN. 090 
O BB92CIVC. 360 
4 A SP88GUKA. 360 
V LP89CORR. 090 
| NR94CENT. 360 
3 IV79ARY7. 140 
0 2 o. s. 
e 0 i 
0 
0 
0 I 2 3 4 
Period Ratio, T Tg 
Figure 6 35 Effect of Cracking Without and With Strength Reduction on Displacement Response of Takeda5 Models, 
for Short Duration Records (DDD= 8 and PDD= 1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
Records=LD; DDD=8; PDD=1; RSR=1; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds undamaged response: 
O CH85LLEO. 010 
O CH85VALP. 070 
A IV40ELCN. 180 
1. 5. V TB78TABS. 344 
O LN92JOSH. 360 
A MX85SCT1. 270 
1 r 6. iE 0 5>fiSo. A v
b 1 i oo
s o 0 0 1 2 3 4 
Period Ratio, TIT, 
Records=LD; DDD=8; PDD=1; RSR=0. 6; Model=Takeda5 
Excludes cases where prior damage (PDP) exceeds undamaged response 
CH85LLEO. 010 A 0 CH85VALP. 070 
A IV40ELCN. 180
4. A. V TB78TABS. 344 
LN92JOSH. 360 
3. A. MX85SCT1. 270 V
VA 0 0 1 2 3 4 
Period Ratio, T IT 
Figure 6 36 Effect of Cracking Without and With Strength Reduction on Displacement Response of Takeda5 Models, 
for Long Duration Records (DDD= 8 and PDD= 1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
136 Technical Resources FEMA 307 
136 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=1; RSR=1; Model=Takeda5 
2 Excludes cases where prior damage (PDD) exceeds undamaged response 
3 LN92LUCN. 250 
O IV79BRWY. 315 
A LP89SARA. 360 
1. 5 V NR94NWHL. 36 
NR94SYLH. 090 
KO95TTRI. 360 
A. 1 o D O a 0 A 
0. 5 I 0 0 1 2. 3 4I 
Period Ratio, TI T 
Records=FD; DDD=8; PDD=1, RSR=0. 6; Model=Takeda5 
5 Excludes cases where prior damage (PDD) exceeds undamaged responses 
Ol LN92LUCN. 250 
O IV79BRWY. 315 
4 A LP89SARA. 360 
V NR94NWHL. 360 
NR94SYLH. 090 
KO95TTRI. 360
II. 3 2 A D
VA 0 00 
vOV Ev 0 v. 
V4 V. O 0. So. X OA 4 A; V sQ; 
0 I 0 1 2 34 
Period Ratio, T T 
Figure 6 37 Effect of Cracking Without and With Strength Reduction on Displacement Response of Takeda5 Models, 
for Forward Directive Records (DDD= 8 and PDD= 1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 137 

Chapter 6: Analytical Studies 
Records=SD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
2 Excludes: cases response:
Where prior damage (PDD) exceeds undamaged 
C WN87MWLN.090 
O BB92CIVC.360 
A SP8BGUKA.360 
1.5 I. I I I I 1 I l 
V LP89CORR.090 
0 NR94CENT.360 
IV79ARY7.140 
V E, I I I. V I W s a 0 0 0 I I 
V V 0.5 1 I I S.I
0 1 2 3 z I 
Period Ratio, TIT, 
Records=SD; DDD=8; PDD=8; RSR=0.6; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds 
O WN87MWLN.090 
O BB92CIVC.360 
4 A SP88GUKA.360 
V LP89CORR.090 
NR94CENT.360 
I. A IV79ARY7.140
bt 2 A, A A A Va A o 0 
I VD A 0 i 0 1 2 34 Period Ratio, T T, 
Figure 6 38 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement 
Response of Takeda5 Models, for Short Duration Records (DDD= 8 and PDD= 8) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio Technical Resources FEMA 307 
Chapter6: Analytical Studies 
Records=LD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds undamaged response. 
o CH85LLEO.010 
O CH85VALP.070 
A IV40ELCN.180 
1.5 v TB78TABS. 344 
0 LN92JOSH. 360
A v MX85SCT1. 270 
t 1 V 0tA 0e 00 I 9 o I 
0.5 0 0 l2 34 I 
Period Ratio, TIT, 
Records=LD; DDD=8; PDD=8; RSR=0.6; Model=Takeda5 
5 Excludes cases where prior damage (PDD) exceeds undamaged response 
o CH85LLEO.010 
O CH85VALP.070 
4 A IV40ELCN.180 
v TB78TABS.344 
LN92JOSH.360 
MX85SCT1.270
3 0. 01 A 2 v 0
v 0i5, v 0 vY A 0 0. v. 03. 0.
1 A, PAAkA 0 0 0 1 234 
Period Ratio, T Tg 
Figure 6 39 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement 
Response of Takeda5 Models, for Long Duration Records (DDD= 8 and PDD= 8) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=8; RSR=1; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds undamaged response. 
o LN92LUCN.250 
O IV79BRWY.315 
A LP89SARA.360 
1.5 V NR94NWHL.360 
A a v r NR94SYLH.090 
0 0 K095TTRI.360 
1va0. 1 A 0 0 A 
0.5 0.5 0 
0 1 2 3 4 
Period Ratio, TIT, 
Records=FD; DDD=8; PDD=8; RSR=0.6; Model=Takeda5 
Excludes cases where prior damage (PDD) exceeds undamaged response 
El LN92LUCN.250 
O IV79BRWY.315 
4 A LP89SARA.360 
V NR94NWHL.360 
NR94SYLH.090 
A 095TTR 360
3 9.3.6.0 
2 0 OVO E 
0 0 0 1 2 3 4 
Period Ratio, TIT, 
Figure 6 40 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement 
Response of Takeda5 Models, for Forward Directive Records (DDD= 8 and PDD= 8) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
IV40ELCNDDD 8 T 1.5 sec. TakedaS 
Displacement (cm) 
15 pd 10, g1
S 0 n < d8
5 10, 1
15 20 0 5 10 15 20 25 30 35 40C 
15 p. pddO10 1ps; 
d + 5
0 5 10 15 j I J I I I j
L I I 2 0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 
Time (sec) 
Force (N) Force (N) 
40 r, r 40 
30; 
30. 40 
20 
10 
0 
10 
01 1.
4 
20 j r 
20 30 
40 T i I I I I 
20 15 10 5 0 10 15 20 15 10 5 0 5 10 15 
Displacement (cm) Displacement (cm 
Force (N) Force (N) 
40 40 
L 30, 1 iS.
30 
20 20 
10 10 
L, 0
0 
X. 5. 
10 10 
20. 20
30 
30
4A
An 20 15 10 5 0 5 10 15 20 15 10 5 0 5 10 15 
Displacement (cm) Displacement (cm) 
Figure 6 44 Effect of Damage on Response to El Centro (IV40ELCN. 180) for Takeda5, T=1.5 sec (DDD= 8) 
DOD = Design Displacement Ductility 
FEMA 307 
Technical Resources 
144 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
IV40913CNDDD 8 T 2.0 sea, Takeda5 
Displacement (cm) 
15 
10 
5
I R I I I pdd8 
0
5
10 
15 
0 5 10 15 20 25 30 35 41D 
15 I 
pddO
10 i T pddlpdd4 
p d.
2 j.
0 5 
paS
5, y.
10. I
15 
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 
Time (sec) 
Force (N) Force (N) 
25 25 
20 I 20
15 15
10 
10.I. 10.
5 S1, 
x. 
15 4; i0 
10
15 
I. 205. X f.
20 
25 
0
15 10 5 O 5 10 15 15 10 5 0 5 10 15 
Displacement (cm) Displacement (cm) 
Force (N) Force (N) 
25 
20.
15 iI 
 ; 15 X
f
20. 
20 
5 X 
10 15 10 
15. 
20 15; 10 5. 
25
25 
15 10 5 0 5 10 15 0 5 10 15 
Displacement (cm) Displacement (cm) 
Figure 6 45 Effect of Damage on Response to El Centro (IV40ELCN. 180) for Takeda5, T=2.0 sec (DDD= 8) 
DDD = Design Displacement Ductility 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
Records=SD; DDD=8; PDD=8; RSRM1; Model=TakPinch 5 
Excludes cases where prior damage (PDD) exceeds undamaged
response 
3 WN87MWLN.090 
O BB92CIVC.360 
A SP88GUKA.360
4 v LP89CORR.090 
O NR94CENT.360 
3 IV79ARY7.140 
2 
0 
I I AC A 
V 
A 0O A 13 A AI & 
0 
0 1 2 3 4I 
Period Ratlo, T IT 
Records=SD; DDD=8; PDD=8; RSR=0.6; Model=TakPinch 
Excludes cases where prior damage (PDD) exceeds undamaged
response. WN87MWLN.090 
O BB92CIVC.360 
A SP88GUKA.360
4 V LP89CORR.090 4
I O NR94CENT.360 
IV79ARY7.140 
3 0 2 0 
: A 0 A 
I 0 1 2 34 
Period Ratio, T T 
Figure 6 46 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement 
Response of TakPinch Models, for Short Duration Records (DDD= 8 and PDD= 8) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
146 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
5Records=LD; DDD=8; PDD=8; RSR=1; Model=TakPinch 
Excludes cases where prior damage (PDD) exceeds undamaged response 
0 CH85LLEO.010 
0 CH85VALP.070 
A IV40ELCN.180 
v TB78TABS.344 
LN92JOSH.360 b E
MX85SCT1.270 
vo o 1 a 0t 0sOo A 
o+0 0a; i0 
0 l2 3 4 
Period Ratio, T T Records=LD; DDD=8; PDD=8; RSR=0.6; Model=TakPinch 
Excludes cases where prior damage (PDD) exceeds undamaged response 11C8LE.1 OCH85VALP.4 A IV
40ELCN.180 
v TB78TABS.344 
O LN92JOSH.360 
@; MXESSCT1.270
AO V v e++v v o V, V.
ow4 : 003 
0C8VL.70 El 
0 1 2 3 4 
Period Ratio, TIT, 
Figure 6 47 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement 
Response of TakPinch Models, for Long Duration Records (DDD= 8 and PDD= 8) DDD 
= EDesign
Displacement Ductility; PDD= Prior Ductility Demands RM Reduced Strength Ratio 
FEMA 307 Technical Resources 147 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=8; RSR=1; Model=TakPinch 
Excludes cases where prior damage (PDD) exceeds undamaged response OLN92WCN.250 
o IV79BRWY.315 
A LP89SARA.360
4 V NR94NWHL.360 
: NR94SYLH.090 
K095TTRI.360
3 
2 
V 0 
I Y pO0 O
V cW A 00; A
b 
0 
0 
o 2 3 4
0 
Period Ratio, T T, 
Records=FD; DDD=8; PDD=8; RSR=0.6; Model=TakPinch 
Excludes cases where prior damage (PDD) exceeds undamaged response O LN92LUCN250 
O IV79BRWY.315 
4 A LP89SARA.360 
V NR94NWHL.360 
NR94SYLH.090 
3 A KO95TTRI.360 @
3 06 Ao AV O0 
0 I I 
0 1 2 3 4 
Period Ratio, TITg 
Figure 6 48 Effect of Large Prior Ductility Demand Without and With Strength Reduction on Displacement 
Response of TakPinch, for Forward Directive Records (DDD= 8 and PDD= 8) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
14 ehia 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
IV40ELCNDDD=8 T l.0 sec, Takeda Pinching RSR 1 
Displacement (cm)
15
A 10
S
:t g.
0
5
10
15
0 5 10 15 20 25 30 35 4 (1 
15 2 
10
5
0 i i i ip
d 
5
I 10
1 r 
0.0 2.0 4.0 6.0 8.0 10.0 
Time (sec) 
Force (N) Force (N) 
80. 80
60. 60.
40 40; 
20.
1. 0
O20, 20
40 40. 
60 60 I. 
80 i i i i. 80 
15 10 5 0 5 10 15 15 10 5 0 5 10 15 
Displacement (cm) Displacement (cm) 
Force (N) Force (N) 
80 80 I I I I 
60 40.40 
z. 0 
+. 
20 
20 
0, 
20, 
20O i. 
40 40 I.
60, 
60
80
1.5 10 5 0 5 10 15 15 10 5 0 5 10 15 
Displacement (cm) I Displacement (cm) 
Figure 6 49 Effect of Damage on Response of TakPinch Model to El Centro (IV40ELCN. 180) for 
T=1.0sec and RSR= I (DDD=8) 
DDD = Design Displacement Ductility 
FEMVA 307 Technical Resources 149 
Chapter 6: Analytical Studies 
IV40ELCNDDD 8T 1.O sec, Takeda Pinching RSR 0.6
Displacement (cm) 15 10 5 0 10d
5 10
0 5 10 15 25. 30 35 4D
F i t" 20, v 15 10 5
0, I i 5 10 15 
0.0 2.0 4.0 6.0 8.0 10.0 
Time (sec) 
Forrce (N) Force (N) 
80 80 1
60. 60 40 
40, 7C; 4 
20 20 0
20 20
40 40 
60. 
60. 
80 1 80 i i II 
5 10 5 0 5 10 15 15 10 5 0 5 10 15 
Displacement (cm) Displacement (cm) 
Force (N) Force (N) 
80 80 I 
60 60
40 i 40
20
20 0
0 1 
20 20.r
40 40
60
80 80
I15 
10 5 0 5 10 15 1.5 10 5 0 5 10 15 
Displacement (cm) Displacement (cm) 
Figure 6 50 Effect of Damage on Response of TakPinch Model to El Centro (IV40ELCN. 180) for 
T=1.0 sec and RSR = 0.6 (DDD= 8) 
DDD = Design Displacement Ductility 
Technical Resources FEMVA 307 
Chapter 6: Analytical Studies 
ductility demand has, in general, only a small effect on TakedalO oscillators having DDD = 2. Collapse of the 
displacement demand applies equally to the standard damaged oscillators (whether the corresponding 
Takeda oscillator and to Takeda oscillators that exhibit undamaged oscillator collapsed or not) is indicated by a 
pinching. The Takeda5 oscillators with initially reduced ratio equal to six, and collapse of the undamaged 
strength, given by RSR = 0.6, tended to have a response oscillators is indicated by a ratio equal to zero. 
amplified to a much greater extent than is observed for Approximately 10% of the oscillators having DDD = 2 
the TakPinch model, reflecting the more dramatic form collapsed with no prior damage. This indicates that 
of strength degradation that was implemented in the structures characterized by negative post yield 
Takeda5 model. stiffnesses must remain nearly elastic if collapse is to be 
avoided. Prior ductility demand may cause 
6.4.3.3 Response of TakedalO Model displacement response to either increase or decrease for 
The TakedalO model is a Takeda model having post those oscillators that do not collapse. 
yield stiffness equal to 10% of the yield point secant 
Figure 6 54 plots the displacement time history of a
stiffness. As has been found previously by others, mod one second oscillator having DDD = 8 and PDD
with negative post yield stiffness are prone to collapse 
ranging from 0 (undamaged) to 8, subjected to the NS, where collapse is defined as the point at which component of the 1940 El Centro record. It can be
the displacement is large enough that the force resisted observed that prior ductility demand helps to avoid
by the oscillator decreases to zero. Comparisons of peak collapse in some cases, and may cause collapse in
displacement response are of limited value when collapse 
occurs. Instead, the likelihood of collapse is used others. 
to assess the impact of prior damage on response for the 6.4.4 Response Statistics
TakedalO models. 
Summary response statistics were prepared to identify 
Figures 6 51 to 6 53 plot the ratio, d dldd, of damaged general trends in the data. 
and undamaged peak displacement response for the 
Records=SD; DDD=2; PDD=1; RSR=1; Model=Takedal0 
oscillator
6 Amplitude of 6 identifies collapse of damaged oscillator; 0 identifies collapse of only the undamaged Excludes cases where prior damage (PDD) exceeds undamaged response 5 S. A SP88GUKA.360 
4 V LP89CORR.090 
NR94CENT.360 
IV79ARY7.140 
br 3 e V 00 Vzh & nV 
0 O 4 0 I2 3 4 
Period Ratio, TIT, 
Figure 6 51 Effect of Cracking on Displacement Response of TakedalO Model for Short Duration Records (DDD= 8 and PDD=1) 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 151 
Technical Resources 
FEMA 307 Technical Resources 151 
Chapter 6: Analytical Studies 
Mean (d d dd), TakPinch, RSR=1 
S.a a. Mean + SD (d dldd), TakPinch, RSR=1 
8 116 rv 6 6Ea) 
a 4 E 4. 1:2 115 
4 727. 
1 
0 
0 
0 
2 
0 
8 
1 I 1:0 0.9 b O09 
l; D00 o i1; 0 i i.E 1 2 3 4 5 6 7 8DesignDisplacementDuctility (
DDD) Mean (d dldd), TakPinch, RSR=0.8, 
0 a. a. 
2 1.43 1.22 1:16 
1:23 1 22.11 1101 
00 10 0 100 10 
1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Mean + SD (d dldd), TakPinch, RSR=0.8 
86 0 6. E 
0) a 4 E 0a 
j.44 ll5 
2 2 1S4 1.l I. 
a 0 1:071.O8.100 0.98 
0e M; 37 1.40 1 17 > z1 
0 II 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 
a. Design Displacement Ductility (DDD) Design Displacement Ductility (DDD) 
EL E, 8 
Mean (d d dd), TakPinch, RSR=0.6 
S a Mean + SD (dd dd), TakPinch, RSR=0.6 
8. 1:24 a r0 6 4 0 
1.0. `4 4, 111 s1, 02 
Ca E0 a 6 4 a. i.i < 1.45. 1; 20 
a) 2 I1.21 1.08 1.04 
11ii1 1:17 10; 7 1.. 03 
2 1.<72 1A2; 1.55 
1:48h6 64; 1A3 1.26 
0 0 0 1 2 3 4 5 6 7 8 A. 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) Design Displacement Ductility (DDD) 
Figure 6 56 Mean and Standard Deviation Values of d d dd for TakPinch Model. 
damaged structure to a given earthquake varies relative 
to the response in the initially undamaged state. 
However, this variability is insignificant in the context 
of variability arising from other sources. For example, 
the hysteresis model and earthquake ground motion 
have a greater effect on response displacements than the 
variability arising due to prior damage. Figures 6 32 to 
6 34 indicate how different the peak displacement 
response of undamaged Takeda and bilinear models can 
be to a given earthquake. 
Figure 6 57 shows the percentage of TakedalO 
oscillators that reached their collapse displacement. It 
can be observed that 10% or more of those structures 
designed to achieve a displacement ductility of two 
collapsed. This indicates the need to ensure that 
structures having negative post yield stiffnesses remain 
nearly elastic if collapse is to be avoided. Strength 
reduction tends to increase the tendency of the 
oscillators to collapse. No clear trend emerges as to the 
effect of PDD on the tendency of these oscillators to 
collapse. 
6.5 Nonlinear Static Procedures 
6.5.1 Introduction 
Nonlinear static analysis is used to estimate inelastic 
response quantities without undertaking the effort 
required for inelastic dynamic analyses. Several 
methods are presently in use. No consensus has 
emerged as to the applicability and relative accuracy of 
the methods, which are collectively known as nonlinear 
static procedures (NSP) These procedures each focus 155 
Technical Resources 
FEMA 307 Technical Resources 155 
Chapter 6: Analytical Studies 
Collapse Percentage for RSR=1 
X 8, v > 8O2 6 6; E.
O 4. 65% 869 
I ?. 2 21% 58% 909M 
0% 10% 55% 859% 
0 070l% 5, %, i 9s 
0. 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Collapse Percentage for RSR=0.8 
0. 8: 
I E. 6j. 4. 
7 1 9 4n.
2242%: 
69%G. 9 6% 
a0.66% 98
I 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Collapse Percentage for RSR=0.6 
8 6.>4. s pt sa E o 2 9. 
n4t t 8X% 6
A 98% c.
j j t I
O 1 2 3 4 5 6 7 8 
Design Displacement Ductility (DDD) 
Figure 6 57 Percent of Takeda10 Oscillators that Collapsed 
on different parameters for determining estimates of NSP are compared with values computed from dynamic 
peak displacement response. Consequently, NSP analyses in Section 6.6. 
displacement estimates may be affected to different 
degrees by differences in hysteretic model, initial 6.5.2 Description of Nonlinear Static 
stiffness, lateral strength, and post yield stiffness. Procedures 
Section 6.5.2 describes three nonlinear static methods; The methods are briefly described in this section for 
displacement coefficient, secant, and capacity spectrum cases assumed to correspond most closely to the 
methods. Differences among the methods and the dynamic analysis framework of Section 6.3.3, 
implications for estimating displacements are discussed representing wall buildings at the collapse prevention 
in Section 6.5.3. Assumptions made to extend the performance level. The reader is referred to FEMA 273 
methods to cases with prior damage are discussed in for greater detail on the displacement coefficient 
Section 6.5.4. Displacement estimates obtained using method, and to ATC 40 for greater detail on the secant 
and capacity spectrum methods. The displacement 
FEMA307 
Technical Resources
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
coefficient method described here is the same as in 
FEMA 273. 
6.5.2.1 Displacement Coefficient Method 
The displacement coefficient method estimates peak 
inelastic displacement response as the product of a 
series of coefficients and the elastic spectral 
displacement. The peak displacement estimate, dd, is 
given by dd = COCIC2C3Sa@); (6 2) 
where coefficients C0 through C3 modify the spectral 
displacement, given by the product of the elastic 
spectral acceleration, Sa, and (Te 21t) 2, where T, is an 
effective period based on the effective stiffness 
determined using the construction of Figure 6 58. 
In the above, C0 relates the spectral displacement and 
the expected roof displacement, and is set at 1 for 
SDOF systems. The coefficient C1 accounts for the 
amplification of peak displacement for short period 
systems, is set at 1 for T, > Tg, and is computed as 
follows for T, < Tg: 
Cl = 1 + (1 1 Tg (6 33 
where R = the strength reduction factor, given by the 
ratio of the elastic base shear force and the effective 
Fye Fye 0.6 Fye 
Pushover ye yI Displacement 
yield strength, Fyes illustrated in Figure 6 58. An 
optional limit of 2 on C1 was not applied in the analyses 
described here. 
The coefficient C2 accounts for the type of hysteretic 
response. At the collapse prevention performance level, 
C2 varies linearly between 1.5 at 0.1 sec and 1.2 at Tg. 
and remains at 1.2 for T, greater than Tg. 
The coefficient C3 accounts for increases in 
displacements that arise when P A effects are significant. 
Because the dynamic analyses did not include 
second order effects, C3 was assigned a value of 1. 
However, the Takeda 10 models had a negative post 
yield stiffness of 10 percent, which approximates P A 
effects 
6.5.2.2 Secant Method 
The secant method assumes that the peak displacement 
response of a nonlinear system can be estimated as the 
peak response of an elastic system having increased 
period. An idealized lateral force displacement curve 
for the structure is developed using a static pushover" 
analysis. The elastic response of the structure is 
computed using a response spectrum analysis, using 
initial component stiffness values. The resulting elastic 
displacements are used to obtain revised stiffness values 
for the components, set equal to the secant stiffness 
defined at the intersections of the component force 
displacement curves and the elastic displacements 
obtained from the response spectrum analysis. Using 
these revised stiffness values, another response 
spectrum analysis is performed, and iterations continue 
Force I y PDDAy 
Displacement 
Figure 6 58 Construction of Effective Stiffness for use with the Displacement Coefficient Method 
FEMVA 307 Technical Resources 
Chapter 6: Analytical Studies 
Force Ax PDDAy Displacement 
Figure 6 59 Initial Effective Stiffness and Capacity Curves Used in the Secant and Capacity Spectrum Methods 
Force or Spectral 
Pseudo Acceleration 
5% Damped 
Elastic Spectrum 
Pushover Curve Peak Displacement Estimate 
Displacement or Spectral 
Displacement 
Figure 6 60 Schematic Depiction of Secant Method Displacement Estimation 
until the displacements converge. All response stiffness. This stiffness may be used to obtain a revised spectrum analyses are made for 5% damping in the estimate of peak displacement response. These secant method, as described in ATC 40. iterations continue until satisfactory convergence 
For SDOF structures, the secant method can be occurs. This is shown schematically in Figure 6 61. 
implemented in spectral pseudo acceleration spectral 
displacement space, much like the capacity spectrum 6.5.2.3 Capacity Spectrum Method 
method. The force displacement curve may be Like the secant method, the capacity spectrum method 
determined using the constructions of Figure 6 59 for assumes that the peak displacement response of a 
both the undamaged and damaged oscillators. This nonlinear system can be estimated by an elastic system 
curve is plotted together with the elastic response having reduced stiffness. The difference is that the 
spectrum for 5% damping in Figure 6 60. An estimate elastic spectral response values are modified to reflect 
of peak displacement is indicated in the figure. For the increases in damping associated with inelastic response. 
undamaged oscillators, an initial estimate of peak A lateral force pushover" curve is developed for the 
displacement response is the peak response of an elastic structure and plotted on spectral pseudo acceleration 
oscillator having stiffness equal to the initial stiffness of spectral displacement coordinates. The structure is 
the oscillator. The intersection of the previous assumed to displace until it reaches an elastic demand 
displacement estimate with the idealized force curve that has damping that corresponds to a value 
displacement curve of the structure defines a new secant based on the current displacement estimate. 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
5% Damped 
Elastic Spectrum 
Pushover Curve 
Peak Displacement Estimate 
10. 
Displacement or Spectral 
Displacement 
Figure 6 61 Schematic Depiction of Successive Iterations to Estimate Displacement Response Using the Secant 
Method for Single Degree of Freedom Oscillators 
The method may be implemented by successively 6.5.3 Comments on Procedures 
iterating displacement response. The initial 
displacement is estimated using the initial stiffness of From the above descriptions, it is clear that there are 
the structure and assuming elastic response for damping fundamental differences among the various NSPs. The 
equal to 5% of critical damping. The intersection of the displacement coefficient method primarily relies on the 
displacement estimate and the idealized force initial effective stiffness to determine a baseline spectral 
displacement curve determines a revised estimate of the displacement, and it considers strength to a lesser extent 
secant stiffness. Effective viscous damping is revised for short period structures. 
prescriptively, based on the displacement estimate. This 
calculation represents the increase in effective damping The secant and capacity spectrum methods are 
with increased hysteretic losses. The iterations continue insensitive to initial stiffness (for structures that yield) 
until satisfactory convergence is obtained. Figure 6 62, and displacement estimates depend primarily on yield 
illustrates the application of the method. strength and post yield stiffness. Effective damping 
varies with displacement amplitude in the capacity 
Spectral Pseudo 5% Damped Elastic Spectrum 
Acceleration 2 10, 15, and 20% Damped Spectra 
Pushover Curve 
Peak Displacement F Estimate 
Displacement or Spectral 
Displacement 
Figure 6 62 Schematic Depiction of Successive Iterations to Estimate Displacement Response Using the Capacity 
Spectrum Method 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
spectrum method, while it is invariant in the secant 
method. In the form presented in ATC 40, secant 
method displacement estimates are independent of 
hysteretic model. Through changes in coefficient C2, 
changes in the force displacement model may be 
incorporated in the displacement coefficient method. 
Differences in hysteresis model are accounted for in the 
capacity spectrum method adjusting effective damping 
for three structural behavior types." 
6.5.4 Application of Procedures to 
Undamaged and Damaged 
Oscillators 
Each procedure presumes that a smoothed, elastic 
design response spectrum is to be used in practice. To 
avoid uncertainties in interpretation of results, the actual 
pseudo acceleration spectra were used in place of a 
smoothed approximation in this study. For the capacity 
spectrum method, the actual pseudo acceleration 
spectra were computed for a range of damping levels, 
and the spectral reduction factors that are prescribed for 
use with smoothed design spectra were not employed. 
These modifications introduce some scatter in the 
resulting displacement estimates that would not occur if 
smoothed spectra had been used. Thus, some 
smoothing" of the data may be appropriate when 
interpreting the results. 
The NSPs were developed for use with undamaged 
structures. In this study, the NSPs were applied to the 
initially damaged structures using the assumptions 
described below, representing one of many approaches 
that can be taken. Recommended procedures for 
estimating displacements are described in Section 4.4 of 
FEMA 306. 
For the displacement coefficient method, the capacity 
curve was obtained by the procedure described in 
FEMA 273. For the uncracked oscillators, a bilinear 
curve was fit, crossing at 60% of the bilinear curve yield 
strength. For the damaged oscillators, the effective 
period of vibration was set at the initial period of the 
damaged oscillators. Displacements were amplified by 
the factor Cl without imposing the optional limit of 2 
specified in the provisions. 
The secant method was applied iteratively. For 
undamaged oscillators, the initial stiffness was the 
yield point secant stiffness. For damaged oscillators, it 
was set at the secant stiffness obtained at the 
displacement imposed by prior ductility demands. The 
initial stiffness of the damaged oscillators therefore 
reflected the previous damage. 
The capacity spectrum method was also applied 
iteratively, beginning with the same initial oscillator 
stiffness used in the secant method. Effective damping 
was determined by using the yield point of the 
undamaged oscillators. The capacity spectrum method 
was implemented for an intermediate building 
characteristic, identified as Type B. This type is 
considered to represent average existing buildings 
subjected to short duration motions and new buildings 
subjected to long duration motions. For this type, 
effective damping is limited to 29% of critical damping. 
For both the capacity spectrum and the secant stiffness 
methods, 10 iterations were performed for each 
structure. These iterations generally converged on a 
single result, and differences in successive 
approximations were typically less than 1%. On 
occasion, differences in successive approximations 
were large, suggesting a lack of convergence due to the 
jagged nature of the actual (not smoothed) spectra. 
Where these differences occurred, the displacement 
estimate at the tenth iteration was retained. 
6.6 Comparison of NSP and 
Dynamic Analysis Results 
6.6.1 Introduction 
In evaluating the utility of the NSPs, attention may be 
directed at two estimates. The first is peak displacement 
response; it could be expected that an acceptable 
procedure would estimate the peak displacement 
response, dd, of a nonlinear system within acceptable 
limits of accuracy. Second, it is possible that a 
procedure may be systematically biased, and hence may 
estimate displacement response poorly while providing 
reasonable estimates of displacement ratio; that is, the 
ratio of damaged structure displacement to undamaged 
structure displacement, d dldd. These response indices, 
dd and d d dd, are examined in detail in the following 
sections for Takeda oscillators designed for bilinear 
DDDs of 8. 
6.6.2 Displacement Estimation 
Peak displacement response of the undamaged Takeda 
oscillators was estimated for each earthquake record. 
The ratio of the peak displacement estimate from NSP 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
and the value computed for each Takeda5 oscillator, at 
each period and for each ground motion record, is 
plotted in Figure 6 63 for DDD = 8 and RSR = 1. The 
log scale plots the ratio of estimated and computed 
displacement, ddNsp dd. Plots are presented for each 
ground motion category and for each NSP. 
In Figure 6 63, it can be observed that the ratio of the 
estimated and computed displacements, ddNspldd, can 
vary significantly, ranging from less than 0.3 to more 
than 100. At any period ratio, the ratio ddNsp dd may 
approach or exceed an order of magnitude. Because the 
trends tend to be consistent for each ground motion 
record, the jaggedness of the actual spectra does not 
appear to be the source of most of the variability. 
Figure 6 64 plots mean values of ratios dd NSPldd 
determined for each NSP, for all ground motions and all 
DDD values. Results for short and long period 
Takeda5 oscillators are plotted separately. In 
Figure 6 64, it can be observed that the NSP procedures 
tend to overestimate, in a mean sense, the displacements 
computed for the short period Takeda5 oscillators for 
all DDD. Takeda oscillators having DDD = 1 often 
displaced less than their bilinear counterparts because 
the Takeda oscillators had initial stiffness equal to twice 
that of their bilinear counterparts. The difference in 
initial stiffness explains the tendency of the NSP 
methods to overestimate displacements for low DDD. 
This is particularly true for the secant method estimates 
of short period oscillators, for which mean ratios 
exceeded six for DDD greater than 1. The period ratio, 
Te Tg, marking the boundary of the elevated estimates 
tends to be less than one, possibly reflecting the 
effective increase in period of Takeda5 oscillators as 
their stiffness reduces (Figure 6 63) 
Figure 6 64 indicates that each NSP tends to 
overestimate the displacement response of short period 
oscillators and that the capacity spectrum method is 
most accurate for long period Takeda5 oscillators, in a 
mean sense. Nevertheless, Figure 6 63 indicates the 
substantial variability in displacement estimates and the 
potential to overestimate or underestimate 
displacements with all methods. A single estimate 
cannot capture the breadth of response variability that 
may occur at a given site. 
Based on Figures 6 63 and 6 64, the coefficient and 
capacity spectrum methods appear to be reasonably 
accurate and to have the least scatter. The secant method 
tended to overestimate displacement and exhibited more 
scatter in values of ddNSPdd 
6.6.3 Displacement Ratio Estimation 
The ratio of damaged oscillator displacement, d d, and 
the displacement of the corresponding Takeda oscillator 
having no initial damage, dd, was estimated using the 
NSP methods for each Takeda oscillator earthquake 
pair, as described in Section 6.5.4. This estimated 
displacement ratio is compared with the ratio computed 
from the dynamic analyses in Figures 6 65 through 
6 73. 
It can be observed that simple application of the 
displacement coefficient method using the initial 
stiffness of the undamaged oscillator to calculate dd and 
using the reduced stiffness of the damaged oscillator to 
calculate d d almost always overestimates the effects of 
damage for the cases considered. 
Application of the secant and capacity spectrum 
methods, using the initial and reduced stiffness values, 
typically led to nearly identical displacement estimates: 
estimates of d dldd were often approximately equal to 
one. Figures 6 68 through 6 73, which might appear to 
testify to the success of the methods, instead tend more 
to represent the inverse of the d dldd as computed for the 
Takeda models. Figures 6 38 through 6 40 indicate that 
computed values of ddld d should tend to be around one, 
decreasing slightly for small periods. 
The preceding plots examine the effectiveness of the 
methods, as implemented here, for estimating the 
consequences of prior ductility demand. It is also of 
interest to examine the effectiveness of the methods in 
accounting for strength loss. To do this, the ratio of the 
displacement obtained with RSR = 0.6 to that with 
RSR = 1.0 was evaluated for the nonlinear Takeda5 
oscillators having DDD = 8 and PDD = 1, in order to 
compare the NSP estimates of the displacement ratio 
with the displacement ratio computed for the nonlinear 
Takeda5 oscillators. The upper plots in Figures 6 74 
through 6 82 show the estimated displacement ratio for 
one of the three NSPs, and the lower plots of these 
figures normalize this displacement ratio by the 
displacement ratio computed for the Takeda5 
oscillators. It can be observed that the NSP methods 
tend to account correctly for the effect of strength 
reduction on displacement response, in a mean sense. 
(Text continued on page 177) 
Technical Resources 
Technical Resources
FEMA 307 n (0) 1 C. 
Short Duration Long Duration 
Forward Directive 
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Figure 6 64 Mean values of ddNspldd for all ground motions for each NSP method, for short and long period 
Takeda5 Models. See text in Section 6.6.2. 
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Figure 6 65 Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
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Figure 6 66 Coefficient Method Estimates of Ratio of Damaged and Undamaged Oscillator Displacement 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
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DDD = Design Displacement Ductility; PDD Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Records=LD; DDD=8; PDD=8; RSR=1; Model=Takeda5: 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMVA 307 Technical Resources 167 
Chapter 6: Analytical Studies 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 3 
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DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio FEMA 307 Technical Resources 169 
Chapter 6: Analytical Studies 
Records=FD; DDD=8; PDD=1; Model=Takeda5 4 
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having DDD= 8 and PDD= 1 DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Records=SD; DDD=8; PDD=1; Model=Takeda5 3 
Excludescases where prior damage (PDD) exceeds undamaged 
response 
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Figure 6 77 Secant Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having 
DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
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Figure 6 78 Secant Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having 
DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
172 Technical Resources FEMA 307 
Technical Resources FEMVA 307 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
O3 LN92LUCN.250 
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Figure 6 79 Secant Method Estimates of Displacement Ratio of RSR=0.6 and PSR=1.0 Takeda5 Oscillators having 
DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility o PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
FEMA 307 Technical Resources 173 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
3 WN87MWLN.090 
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5 Excludes cases where prior damage (PDD) exceeds undamaged response 
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Oscillators having DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strength Ratio 
17 174 Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
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3 Excludes cases where prior damage (PDD) exceeds undamaged response 
o CH85LLEO.010 
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i v response Excludes cases where prior damage (PDD) exceeds undamaged 
o CH85LLEO.010 A IV 40ELC N180 P I. 
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Chapter 6: Analytical Studies Records=FD; DDD=8; PDD=1; Model=Takeda5 
3 Excludes cases where prior damage (PDD) exceeds undamaged response o1LN92LUCN.250 Q A O IV79BRWY.315 CX0U. 
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Z5 Excludes cases where prior damage (PDD) exceeds undamaged response = LN92LUCN.250 O IV79BRWY.315 
A LP89SARA.360 V NR94NWHL.360
9 O. NR94SYLH.090 KO95TTRI.360 b 3 + Mean CapSpec 
a) r5 2 0 A 0l i 1 10) I CO I a 0 00.5 1 1.52 
Period, T (sec) [Figure 6 82 Capacity Spectrum Method Estimates of Displacement Ratio of RSR=0.6 and RSR=1.0 Takeda5 Oscillators having DDD= 8 and PDD= 1 
DDD = Design Displacement Ductility; PDD = Prior Ductility Demand; RSR = Reduced Strenqth Ratio Technical FEMA 307
4, 7 It (o Chapter 6: Analytical Studies 
6.7 Conclusions and Implications 
The analyses presented indicate that the displacement 
response characteristics of the ground motions generally 
conform to expectations based on previous studies. 
Forward directivity motions may have larger displacement 
response in the long period range than would be 
predicted by the equal displacement rule. The strength 
reduction factor, R, appropriate for forward directivity 
motions may need to be reduced somewhat relative to 
other classes of motion if ductility demands are to be 
held constant. 
The displacements of the Takeda oscillators were 
sometimes several fold greater or less than those of the 
bilinear oscillators. Although it is fundamentally 
important to consider displacements in seismic 
response, variability of the response estimates as 
affected by ground motions and hysteresis model must 
also be considered. 
Previous damage, modeled as prior ductility demand, 
did not generally cause large increases in displacement 
response when the Takeda models with positive post 
yield stiffness were exposed to performance level 
earthquakes associated with life safety or collapse prevention. 
Prior ductility demands were found to cause 
mean changes in displacement response ranging from 
3% to +10% for the Takeda5 and TakPinch oscillators 
having no strength degradation (Figures 6 55 and 6 56) 
PDDs of 8 often caused a slight decrease in the 
displacement response computed using the Takeda5 and 
TakPinch models; response infrequently was 20% to 
30% or more higher than that for the undamaged 
oscillator. 
For oscillators having cyclic strength degradation, 
represented by the TakPinch oscillators, the effect of 
strength degradation was generally to increase the mean 
displacement response, but only by a few percent. The 
mean increase was larger for the structures having lower 
DDD, reaching as much as 21% for oscillators having 
RSR = 0.6. This result merely indicates that strength 
degradation tends to cause displacement response to 
increase relative to undamaged or nondegrading systems. 
Further examination revealed that increasing PDD 
increases or decreases the mean response of TakPinch 
systems with strength degradation by only a few percent 
(Figure 6 56) The weaker oscillators, represented by 
larger DDD, are more likely to exhibit damage in a real 
earthquake, and to have smaller increases in 
displacement due to prior ductility demands. 
While prior damage causes relatively small changes in 
mean displacement response relative to undamaged 
structures, it also introduces some variability in 
displacement response. Variability in response is 
inherent in earthquake resistant design, and the 
variability introduced by prior damage should be 
considered in the context of variability arising from 
different ground motions, choice of hysteretic models, 
modeling assumptions, and other sources. For example, 
Figures 6 32 to 6 34 illustrate the degree to which 
different earthquakes can cause bilinear and Takeda 
oscillators of equal strength to have substantially 
different peak displacement response. Thus, the 
variability in response introduced by prior damage is 
not considered significant. 
Three NSPs for estimating peak displacement response 
were applied to the Takeda oscillators. Significant 
variability in the estimated displacements, when 
compared with the values calculated from nonlinear 
dynamic analysis, underscores the difficulty in 
accurately estimating response of a SDOF system to a 
known ground motion. The accuracy of the NSP 
estimates is compared in Figure 6 63. In Figure 6 64 it 
can be observed that the capacity spectrum and 
coefficient methods are more accurate, in a mean sense, 
than the secant method, and that all methods tend to 
overestimate the displacement response of short period 
Takeda5 oscillators. 
The NSPs were also used to estimate the change in 
displacement caused by a prior earthquake. Given the 
relatively small effect of damage on peak displacement 
response, it appears that damaged structures should be 
modeled similar to their undamaged counterparts, in 
order to obtain identical displacement estimates for 
performance events that are stronger than the damaging 
event. This results in damage having no effect on the 
displacement response, which closely approximates the 
analytical results. 
The accuracy with which an NSP accounts for strength 
reduction was explored. It was found that each NSP was 
reasonably able to capture the effect of strength 
reduction. 
The above findings pertain to systems characterized by 
ductile flexural response having degrading stiffness, 
with and without pinching. Systems with negative post 
yield stiffness were prone to collapse, even with DDD 
of 2. Such systems should remain nearly elastic if their 
collapse is to be avoided. 
FEMA 307 Technical Resources 
Chapter 6: Analytical Studies 
6.8 References 
Araki, H Shimazu, T and Ohta, Kazuhiko, 1990, On 
Residual Deformation of Structures after Earthquakes, 
Proceedings of the Eighth Japan Earthquake 
Engineering Symposium 1990, Tokyo, Vol. 
2, pp. 1581 1586. (In Japanese with English 
abstract.) 
ATC, 1996, Seismic Evaluation and Retrofit of Concrete 
Buildings, Applied Technology Council, ATC 40 
Report, Redwood City, California. 
ATC, 1997a, NEHRP Guidelines for the Seismic Rehabilitation 
of Buildings, prepared by the Applied 
Technology Council (ATC 33 project) for the 
Building Seismic Safety Council, published by the 
Federal Emergency Management Agency, Report 
No. FEMA 273, Washington, D.C. 
ATC, 1997b, NEHRP Commentary on the Guidelines 
for the Seismic Rehabilitation of Buildings, prepared 
by the Applied Technology Council (ATC 33 
project) for the Building Seismic Safety Council, 
published by the Federal Emergency Management 
Agency, Report No. FEMA 274, Washington, D.C. 
Boroschek, R.L 1991, PCNSPEC Manual, (Draft), 
Earthquake Engineering Research Center, University 
of California at Berkeley. 
Cecen, H 1979, Response of Ten Story Reinforced 
Concrete Model Frames to Simulated Earthquakes, 
Doctoral Thesis, Department of Civil Engineering, 
University of Illinois at Urbana. 
Fajfar, P. and Fischinger, M 1984, Parametric Study 
of Inelastic Response to Some Earthquakes 
Recorded in Southern Europe, Proceedings of the 
Eighth World Conference on Earthquake Engineering, 
Vol. 4, pp. 75 82. 
Humar, J 1980, Effect of Stiffness Degradation on 
Seismic Response of Concrete Frames, Proceedings 
of the Seventh World Conference on Earthquake 
Engineering, Vol. 5, pp. 505 512. 
Iwan, W.D 1973, A Model for the Dynamic Analysis 
of Deteriorating Structures, Proceedings of the 
Fifth World Conference on Earthquake Engineering, 
Vol. 2 pp. 1782 1791. 
Iwan, W.D 1977, The Response of Simple Stiffness 
Degrading Systems, Proceedings of the Sixth 
World Conference on Earthquake Engineering, Vol. 
2, pp. 1094 1099. 
Kawashima, K Macrae, G Hoshikuma, J and 
Nagaya, K 1994, Residual Displacement 
Response Spectrum and its Application, Journal of 
Structural Mechanics and Earthquake Engineering, 
Japan Society of Civil Engineers, No. 501, pp. 183192. 
(In Japanese with English abstract.) 
Lepage, A 1997, A Method for Drift Control in Earth 
quake Resistant Design of RC Building Structures, 
Doctoral Thesis, Department of Civil Engineering, 
University of Illinois at Urbana. 
Mahin, S.A 1980, Effects of Duration and Aftershocks 
on Inelastic Design Earthquakes, Proceedings 
of the Seventh World Conference on 
Earthquake Engineering, Vol. 5, pp. 677 679. 
Mahin, S.A and Lin, J 1983, Construction of Inelastic 
Response Spectra for Single Degree of Freedom 
Systems Computer Program and Applications, 
Earthquake Engineering Research Center, University 
of California at Berkeley, Report No. UCB 
EERC 83 17, Berkeley, California. 
Mahin, S.A and Boroschek, R 1991, Influence of 
Geometric Nonlinearities on the Seismic Response 
and Design of Bridge Structures, Background 
Report to California Department of Transportation, 
Sacramento, California. 
Minami, T and Osawa, Y 1988, Elastic Plastic 
Response Spectra for Different Hysteretic Rules, 
Earthquake Engineering and Structural Dynamics, 
Vol. 16, pp. 555 568. 
Miranda, E 1991, Seismic Evaluation and Upgrading 
of Existing Buildings, Doctoral Thesis, Department 
of Civil Engineering, University of California, Berkeley. 
Moehle, J.P Browning, J Li, Y.R and Lynn, A 1997, 
"Performance Assessment for a Reinforced Concrete 
Frame Building, (abstract) The Northridge 
Earthquake Research Conference, California Universities 
for Research in Earthquake Engineering, 
Richmond, California. 
Nakamura, T and Tanida, K 1988, Hysteresis Model 
of Restoring Force Characteristics of Reinforced 
Concrete Members, Proceedings of the Ninth 
World Conference on Earthquake Engineering, 
Paper 6 4 7, Vol. VI. 
Nasser, A.A and H. Krawinkler, H 1991, Seismic 
Demands for SDOF and MDOF Systems, John A. 
Blume Earthquake Engineering Center, Stanford 
University, Report No. 95, Stanford, California. 
FEMA 307 
Technical Resources
Technical Resources FEMA 307 
Chapter 6: Analytical Studies 
Newmark, N.M and Riddell, R 1979, A Statistical 
Study of Inelastic Response Spectra, Proceedings 
of the Second U.S. National Conference on Earthquake 
Engineering, pp. 495 504. 
Otani, S 1981, Hysteresis Models of Reinforced Concrete 
for Earthquake Response Analysis, Journal 
(B), Faculty of Engineering, University of Tokyo, 
Vol. XXXVI, No. 2, pp. 125 159. 
Palazzo, B and DeLuca, A 1984, Inelastic Spectra 
for Geometrical and Mechanical Deteriorating 
Oscillator, Proceedings of the Eighth World Conference 
on Earthquake Engineering, Volume IV, pp. 
91 98. 
Parducci, A and Mezzi, M 1984, Elasto Plastic 
Response Spectra of Italian Earthquakes Taking 
into Account the Structural Decay, Proceedings of 
the Eighth World Conference on Earthquake Engineering, 
Volume IV, pp. 115 122. 
Paulay, T, and Priestley, M.J.N 1992, Reinforced Concrete 
and Masonry Buildings: Design for Seismic 
Resistance, Wiley & Sons, New York. 
Qi, X and Moehle, J.P 1991, Displacement Design 
Approach for Reinforced Concrete Structures Subjected 
to Earthquakes, Earthquake Engineering 
Research Center, Report No. UCB EERC 91 02, 
University of California at Berkeley, Berkeley, California. 
Rahnama, M and Krawinkler, H 1995, Effects of P 
Delta and Strength Deterioration on SDOF Strength 
Demands", Proceedings of the 1 0 th European Conference 
on Earthquake Engineering, Vol. 2, pp. 
1265 1270. 
Riddell, R 1980, Effect of Damping and Type of 
Material Nonlinearity on Earthquake Response, 
Proceedings of the Seventh World Conference on 
Earthquake Engineering, Vol. 4, pp. 427 433. 
Saiidi, M 1980, Influence of Hysteresis Models on 
Calculated Seismic Response of R C Frames, Proceedings 
of the Seventh World Conference on 
Earthquake Engineering, Vol. 5, pp. 423 430. 
Sewell, R.T 1992, Effects of Duration on Structural 
Response Factors and on Ground Motion Damage 
ability, Proceedings of the SMIP92 Seminar on 
Seismological and Engineering Implications of 
Recent Strong Motion Data, pp. 7 1 to 7 15. 
Shimazaki, K and M.A. Sozen, M.A 1984, Seismic 
Drift of Reinforced Concrete Structures, Research 
Reports, Hasama Gumi Ltd Tokyo (in Japanese), 
and draft research report (in English) 
Somerville, P.G Smith, N.F Graves, R.W. and Abrahamson, 
N.A 1997, Modification of Empirical 
Strong Ground Motion Attenuation Relations to 
Include the Amplitude and Duration Effects of Rupture 
Directivity, Seismological Research Letters, 
Vol. 68, No. 1. 
Takeda, T Sozen, M.A and Nielsen, N.N 1970, 
"Reinforced Concrete Response to Simulated 
Earthquakes, Journal of the Structural Division, 
American Society of Civil Engineers, Vol. 96, No. 
ST12, pp. 2557 2573. 
Wolschlag, C 1993, Experimental Investigation of the 
Response of RIC Structural Walls Subjected to 
Static and Dynamic Loading, Doctoral Thesis, 
Department of Civil Engineering, University of Illinois 
at Urbana. 
Xie, L. L and Zhang, X 1988, Engineering Duration 
of Strong Motion and its Effects on Seismic Damage, 
Proceedings of the Ninth World Conference 
on Earthquake Engineering, Vol. 2, Paper 3 2 7. 
FEMA 307 Technical Resources 
Example Application
7. 7.1 Introduction 
This section gives an example of the use of FEMA 306 
recommendations to evaluate earthquake damage in a 
two story reinforced concrete building. The example is 
meant to be as realistic as possible and is based on an 
actual structure. 
7.1.1 Objectives 
The example is intended to help evaluating engineers 
understand such issues as: 
the overall process of a FEMA 306 evaluation. 
accounting for pre existing damage. 
how both observation and analysis are used in the 
evaluation procedures. 
determining and using the applicable FEMA 306 
Component Damage Classification Guides, 
including cases where an exactly applicable damage 
guide is not provided. 
foundation rocking of walls, which may be a 
prevalent behavior mode in many structures. 
some of the ways engineering judgment may need to 
be applied. 
how restoration measures can be determined based 
on either the direct method or the performance 
analysis method. 
aspects of using a nonlinear static procedure of 
analysis (pushover analysis) 
establishing displacement capacities and demands. 
Reading through the example could be the best introduction 
to an understanding of the FEMA 306 evaluation 
process. References to the applicable sections of 
FEMA 306 or 307 (or to other sources) are given in 
"bookmark" boxes adjacent to the text. Because the 
example is meant to be illustrative, it contains more 
description and explanation than would normally be 
contained in an engineer s evaluation report for an 
earthquake damaged building. 
It should be clear from this example that the FEMA 306 
recommendations for evaluating earthquake damage 
must be implemented under the direction of a knowledgeable 
structural engineer, particularly when a performance 
analysis is carried out. The responsible engineer 
should have a thorough understanding of the principles 
behind the FEMA 306 recommendations and should be 
familiar with the applicable earthquake research and 
post earthquake field observations. FEMA 307 provides 
tabular bibliographies and additional information 
on applicable research. 
A fundamental tenet of the component evaluation methods 
presented in FEMA 306 is that the severity of damage 
in a structural component may not be determined 
without understanding the governing behavior mode of 
the component, and that the governing behavior mode is 
a function not only of the component s properties, but 
of its relationship and interaction with surrounding 
components in a structural element. In the following 
sections, the evaluation of the example building emphasizes 
the importance of this principle. There may be a 
temptation among users of FEMA 306 to use the damage 
classification guides as simple graphical keys to 
damage, and to complete the analysis by simply matching 
the pictures in the guides to the observed damage. 
The example is intended to show that this is not the 
appropriate use of the guides. It is organized to emphasize 
the importance of the analytical and observation 
verification process that is an essential element of the 
evaluation procedure. 
7.1.2 Organization 
The example is organized as shown in the flow chart of 
Figure 7 1. This organization follows the overall evaluation 
procedure outlined in FEMA 306, beginning with 
a building description and observations of earthquake 
damage. 
The building has been subjected to a previous earthquake. 
The damage investigation establishes the preexisting 
conditions so that the loss from the recent 
earthquake can be evaluated. The preliminary classification 
of component types, behavior modes, and damage 
severity are made by observing the structure. It is 
shown, however, that classification of behavior modes, 
and hence damage severity, may be unclear when based 
on observation alone. Simple analytical tools provided 
in the material chapters of FEMA 306 are used to verify 
the expected component types and behavior modes, and 
damage severity is assigned accordingly. The steps 
required to estimate the loss by the direct method are 
FEMA 307 Technical Resources 
Chapter 7: Example Application 
00 Nl 04.l 4 Evaluation by 
Performance Analysis 
3vlainb h 4.1 4.2 Performance Objectives 
Nonlinear static analysis 
4.3 Pushover capacity curve 
4.4 Estimate of d9, the 
displacement caused by the 
damaging earthquake 
4.5 Displacement demand 
4.6 Analysis of the restored structure 
4.7 Performance restoration measures 
Figure 7 1 Flowchart for example 
FEMA 307 Resources FEMA 307
182Technical Technical Resources
182 Chapter 7: Example Application 
illustrated, and a relative performance analysis is carried 
out. It is emphasized that the direct method provides 
only loss estimation information, and that a 
relative performance analysis is required in order to 
make performance based design decisions. 
Damage records for all of the structural walls of the 
building are included. The damage records for two of 
the walls are discussed in detail. Damage records for the 
remaining walls are given at the end of the example. 
7.2 Investigation 
7.2.1 Building Description 
The example building is a two story concrete building 
located on a sloping site. The building is aT" shape in 
plan with the stem of the T on the downhill side, containing 
a partial lower story below the other two stories. 
The building was designed and constructed in the late 
1950s. The building is located about 3.6 miles from the 
epicenter of the damaging earthquake. 
The overall plan dimensions of the building are 362 feet 
in the North South direction by 299 feet in the East 
West direction. The floor slabs cantilever about 6 feet 
from the perimeter columns forming exterior sun 
screens balconies. The building facade along the perimeter 
is set back 8 feet from the edge of the slab. For the 
typical floor, the interior floor area is about 62, 600 
square feet, and the total slab area is about 70, 400 
square feet. The lower level encompasses about 20, 200 
square feet. Floor plans are shown in Figure 7 2 and an 
elevation is shown in Figure 7 3. The roof of the building 
supports mechanical equipment.
The floors and roof are constructed with waffle slabs 
comprised of a 4 % inch thick slab and 14 inch deep 
pans (18 2 inches total depth) Columns supporting the 
slabs are typically spaced at 26 feet in each direction. 
The interior columns are 18 inch square and the perimeter 
columns are 18 inch diameter. The columns are supported 
on spread footings. 
Reinforced concrete walls in both directions of the 
building resist lateral forces. The walls are 12 inches 
thick and are cast monolithically at each end with the 
gravity load carrying columns. The walls are typically 
located along corridors, and the corridor side of the wall 
has a 1 inch thick plaster coat. The typical solid wall 
configuration and reinforcement are shown in 
Figure 7 4. 
In the lower level there are several reinforced concrete 
masonry (CMU) walls that are framed between the 
ground and the first floor slab (basement level) in the 
three story section of the building. The CMU walls are 
attached to the first floor slab. However, these walls 
were not designed as shear resisting elements. Because 
the first floor slab is anchored to the foundation in the 
two story portion of the building, the contribution of the 
CMU walls to the lateral force resistance, particularly in 
the east west direction, is minimal. 
Several of the reinforced concrete walls have door 
openings, 7 feet 3 inches tall by 6 feet 6 inches wide, in 
the middle of the wall, creating a coupled wall. The typical 
coupled wall configuration and reinforcement are 
shown in Figure 7 5. In the three story section of the 
building (the stem of the T), the walls are discontinued 
at the lower level. This lower level contains a single 
reinforced concrete wall in the north south direction 
centered between the two walls above. 
7.2.2 Post earthquake Damage
Observations 
Following the damaging earthquake, Visual 
the engineers performed a post earth observation, 
quake evaluation of the building. The GuideNDE1, 
initial survey was conducted one Section 3.8 
month after the damaging earthquake. of FEMA306 
The structural drawings for the building were reviewed. 
The follow up investigations were conducted about 
three months following the earthquake. 
The post earthquake evaluations were conducted using 
visual observation techniques on exposed surfaces of 
the structural elements. The sections of wall above the 
ceiling were typically observed only where the suspended 
ceiling tiles had fallen during the earthquake. 
Crack widths were measured at selected locations using 
magnifying crack comparators for most of the significant 
cracks in each wall. 
7.2.2.1 Pre Earthquake Conditions 
The building had experienced some l 
cracking prior to the damaging earth vs. new 
quake. The pre existing damage is cracks, 
judged to have been caused by a previous Section 3.4 
earthquake. The heaviest damage of FEMA306 
appeared to have been in the coupling 
beams. The wall cracks above the ceiling line were 
observed to have been repaired by epoxy injection. 
183 Technical Resources 
FEMA 307 Technical Resources 183 
Chapter 7: Example Application 
T (yP) a) First and Second Floor Plan 
Reinforced 
Edge of 
Floor Slab 
b) Basement Floor Plan 
Figure 7 2 Floor Plans 
1 844 Technical Resources FEMA 307 
Chapter 7: Example Application 
I 11 I I I, 12nd I 
r E r r 1l T 1 list If 
Figure 7 3 Building Cross section 
13 f ars (13in. 
1 6 IL. H 1 8 in. S q Column 
41 I I II E second 
I t 11 @ First 1G 5" 
I l t v R rad1
lg X ff 4 8arq k Slab On 
P3 6 11 IIfI I I 90r (Type
I 1 1 1 Hook at Otto Footing
26 0" Figure 7 4 Example Solid Wall Detail (Condition at Line 7) 
FEMA 307 Technical Resources 18 
FEMA 307 Technical Resources 185 
as PRELIMINARY CLASSIFICATION 
BY OBSERVATION 
FINAL CLASSIFICATION 
BY ANALYSIS 
(Building Name: 
Element Component Damage Record 
Project ID: Prepared by: 
I COMPONENT TYPE 
0. Concrete Shear Wall Building 
Location Within Building: 
ATC 43 Example ATC 
Date Inspected: 
Floor 2nd Column: 2 24 Sep 97 
Sketch and Description of Component and Damage: 
Roof LJ C, 0 I | BEHAVIOR MODE I I BEHAVIOR MODE as 0 m 0 I I :a (p 0 0 i AS82, g , 1 Second B, C, H or M IM M (Overturning) x ITI 5. 01 L 1Ll 7L r Lr fi First I DAMAGE SEVERITY I Legend: 
Crack (Width< 0.030 inch) Spall 
Crack Width in Mils (0.00l Inch) Not Accessible 
Crack Previously Filled with Epoxy 
Crack at Pre existing Surface Patch Partition Moderate If H 
Insignificant If 
Key Plan B, C, or M 
A Tr L CD AIn 0 N. 
N PRELIMINARY CLASSIFICATION FINAL CLASSIFICATION 
BY OBSERVATION BY ANALYSIS 
0 COMPONENT TYPE I I COMPONENTTYPE I 
I I I I RC3 I 0 CD I IF. I II I I I CD RC3 lb RC3 RCI RCt RC1 RC1 I I1I II lil rn C) S I BEHAVIOR MODE II BEHAVIOR MODE I 4
CD CD m 5 i x rH CD
I ISor 1 C I11 I A 0 co w H N I H j S.
o 0 11 iII III li I DAMAGE SEVERITY I I DAMAGE SEVERITY I m I I m I
i Ea KLI U D.; 2 alI I a =I E I I
9 0S III IIrIII m 0 4

Chapter 7: Example Application 
observed to have horizontal cracks along the interface between the top of the wall and the floor slab above.
7.2.3 Preliminary Classification (by Observation) of Component Types, Behavior Modes, and Damage Severity 
The first critical step in interpreting o component damage records is to identify - types, the components within the structural - Table5-1 of element under investigation. In FEMA 306 this case, the example building is reinforced concrete, so the summary of relevant component types is found in Sections 2.4 and 5.2.1 of FEMA 306.
7.2.3.1 Component Types 
The first pass in the identification process is conducted by observation, keeping in mind that the definition of a component type is not a function of the geometry alone, but of the governing mechanism of lateral deformation for the entire element or structure. Thus the identification of structural components requires consideration of the wall element over multiple floor levels. Complete diagrams showing the crack pattern over multiple floor levels such as the ones shown in the attached damage records shown in Figures 7-6, 7-7 and Damage Records D1 through D19 (Appendix A) are essential.
For the typical coupled wall elements of the example building, shown in Component Figure 7-7, a survey of the element identification, geometry and the general pattern of FEMA 306 damage suggests that the beams over the openings may be classified as weaker coupling beams (RC3), and that the wall piers flanking the openings will behave as two-story cantilever components (RC 1). The thought process that leads to this conclusion includes the recognition that the beam elements are likely to be weaker than the walls on either side of the coupling beams, as well as a mental visualization of the lateral deformation of the walls and the attendant large deformation demands on the beams. As shown in Figure 7-6, the solid reinforced concrete wall component is type RCL.
7.2.3.2 Behavior Modes and Damage Severity 
Once the component types have been identified, an initial classification of the Behavior modes and damage severity modes, Table 5-2 of may be made by inspecting the visible FEMA 306 damage with reference to the component damage classification guides. Tables 5-1, 5-2, and 5-3 of FEMA 306 are also helpful in identifying behavior modes appropriate to the identified components.
For the typical coupled wall shown in Figure 7-7, the coupling beam component (RC3) on the second floor is observed to have light diagonal (shear) cracking, with little or no evidence of flexural cracking. As is typical of a building designed in the late 1950s, the coupling beam does not contain diagonal reinforcement, or even sufficient stirrup reinforcement, so mode A (ductile flexure) may be safely eliminated. The diagonal cracks then suggest that the behavior mode may be either mode B (flexure/diagonal tension) or mode H (preemptive diagonal tension). At the first floor coupling beams, the damage is more severe, but the behavior mode still appears to be either B or H.
In the first floor coupling beam, identification of the damage severity is relatively - Component straightforward: the observed Guides, Section 5.5 damage would be classified as Heavy of FEMA 306 regardless of the behavior mode. In many cases, however, the damage severity level may depend on the behavior mode. In the second floor coupling beam, for example, the damage would be classified as Insignificant if the behavior mode is identified as B (flexure followed by diagonal tension), but as Moderate if the behavior mode is identified as H (preemptive diagonal tension).
Similarly, the wall piers of the coupled walls (RC1) have light diagonal cracking, which may be indicative of early stages of mode B (flexure/diagonal tension), early stages of mode C (flexure/diagonal compression) or more advanced stages of mode H (preemptive diagonal tension). In the first two cases, damage would be classified as Insignificant, while in the last case, damage would be classified as Moderate.
It is often not possible to distinguish between the different behavior modes, and hence the damage severity, with- out some analysis. This is particularly important for lower levels of damage Verification Loop 1, 3 f EMA 306 where different modes may look very much alike, but which have different response at higher levels of damage.
Consider, for example, modes B and H. The flexural cracks that initiate mode B response may have closed and become nearly invisible. The light diagonal cracking that occurs at the outset of both modes B and H will then be indistinguishable from one another, and only analysis of the section will differentiate the two modes, and hence the severity of damage. In other cases, the differences between modes are of less importance - FEMA 307 Technical Resources Chapter 7: Example Application Modes B and C are physically different, but have a similar effect on the stiffness, strength, and deformation capacity of the component at all levels of damage severity.
7.2.4 Final Classification (by Analysis) of Component Type, Behavior Mode and Damage Severity 
In the previous section, component type, behavior mode, and damage severity were preliminarily defined based only on observation. In this section, those definitions are verified by calculation. In practice, iterations between observation and analysis may be needed to interpret correctly the seismic response and damage.
7.2.4.1 Expected Strength 
The expected pre-earthquake strengths for each of the components were calculated - Expected using the FEMA 306 strength, Section 3.6 Section 3.6 procedures. The design of FEMA 306 concrete strength was shown on the drawings to be 3000 psi. According to the discussion in FEMA 306, Section 5.3.2, expected concrete strengths ranging from 1.0 to 2.3 times the specified strength are not unrealistic. In the example building, concrete strength was suspect, so tests were conducted which revealed that expected strength was, in fact, near the specified strength. For the purposes of the following analysis an expected strength of 3000 psi was assumed.
Based on the drawing notes, reinforcing bars had a specified yield strength of 40 ksi. The expected strength of the reinforcing bars was assumed to be greater than the nominal yield strength by a factor of 1.25, so a value of 50 ksi was used for the yield strength in all calculations.
If, during the course of the analysis, it becomes difficult to reconcile analytically determined behavior modes with observed damage, assumed values for material strength may need to be re-evaluated or verified through tests.
There are two typical element types in the lateral-force- resisting system, solid walls and coupled walls. The following sections describe the details of the calculations and methodology used to classify the components of these elements.
7.2.4.2 Example 1 -Solid Wall (28-2C) 
Once a preliminary damage classification has been made by visual observation, it will generally be necessary to perform some analysis to distinguish between behavior modes that are different but visually similar.
As a first example, consider the damage record for the wall shown in Figure 7-6. The wall is 12 inches thick with 18-inch square boundary elements at each end.
The wall length from center to center of the boundary elements is 26 feet, and the story height is 13 feet-6 inches. Note that the wall is L-shaped in plan and has a 26-foot return along line B.
Component Type. 
The definition of this wall as a single RC 1 component (isolated wall or stronger wall pier) is easily and intuitively verified by sketching the inelastic deformation mechanism for the wall and its surrounding structure. The slabs framing into the wall clearly do not have the stiffness or strength to force a "weaker wall" type of behavior. The wall is therefore a single component with a height of 27 feet.
Behavior Mode. 
The preliminary classification identified four possible Component behavior modes for this component guides, that were consistent with the component - and RC2H, type and the observed damage: Section 5.5 mode B (flexure/diagonal tension), of FEMA 306 mode C (flexure/diagonal compression), mode H (preemptive diagonal tension), and mode M (foundation rocking). For each of these behavior modes, Component Guides provide, in addition to the visual description of the different behavior modes, guidance in the analytical steps required to verify a particular behavior mode. See for example the Component Damage Classification Guide RClB under "How to distinguish behavior mode by analysis". Based on the recommendations of the guide, the shear associated with the development of the maximum strength in flexure, diagonal tension, web crushing, and foundation rocking were calculated. Calculation results are summarized in Table 7-1. Selected details of the calculations are provided in the box on page 192.
The relationship between capacities of the different potential behavior modes defines the governing component behavior mode. Initially, consider the first five modes listed in Table 7-1, temporarily neglecting the overturning (foundation rocking) response. Because the wall is flanged, its response depends op the direction of seismic force, and the flexural capacity must be calculated for each direction. It is possible that a different behavior mode will govern in each of the two different loading directions. In this example, the diagonal tension strength at low ductility is less than the flexural strength Technical Resources FEMA 307 Chapter 7: Example Application Table7-1 Capacity of Potential Behavior Modes for Typical Solid Wall (2B-2C) Behavior Mode Shear FEMA 306 Comments Capacity Reference (kips) Flexure (modes A & B) -flange 1570 Sect. 5.3.5 All distributed reinforcement is included in compression in the calculation of flexural strength, as is the contribution of the flange reinforcement - Me = 31, 300 k-ft.
Flexure (A & B) -flange in tension 2230 Sect. 5.3.5 Me =44, 600 k-ft Diagonal Tension (B & H) -at 1350 Sect. 5.3.6b Low ductility implies yu< 2 and high ductility low flexural ductility implies y 2 5, but for this example the exact displacement ductility is not Diagonal Tension (B) -at high Sect. 5.3.6b important. Capacity at high ductility does flexural ductility not govern, since flexural yielding does not occur.
Web crushing (C) 2560 Sect. 5.3.6c Overturning (M) -flange in compression - 343 Sect. 5.2.6 When the flange is in tension, the vertical Me = 6, 860 k-ft load includes dead load contribution of flange.
Overturning (M) -flange in tension -923 Sect. 5.2.6 Me= 18, 000 k-ft Shear associated with development of the moment strength in either loading direction, so mode H (preemptive restoring force. However, the overturning value calculated diagonal tension) appears to be the governing the is sufficiently less than the other behavior modes behavior mode. In either direction, web crushing can be to suggest that damage will be limited by rocking on the eliminated as a potential behavior mode since its capacity -foundation. Mode M is therefore the behavior mode for is greater than that of all of the other modes. In the wall.
absence of overturning, mode H would therefore be selected as the behavior mode for this component. Damage Severity L. The identification of the rocking behavior mode is important, because the damage severity - Additional calculations indicate, however, that foundation - is different for mode M than for mode H. While rocking (overturning of the wall and its foundation) there is no explicit Component Damage Classification will occur before the other failure modes can develop. Guide provided for the rocking mode-the component This is indicated in the last two rows of Table 7-1, may be considered as roughly analogous to the portion where overturning capacity with the flange in compression -of a flexural wall (mode A) above the plastic hinge is shown to be less than other behavior modes. As region-there is a ductile fuse in the structure below the shown in the example calculations (see sidebar), the component in question that will prevent the development - foundation rocking capacity is based on the static over- of the brittle, force-controlled behavior mode H turning force associated with all tributary gravity loads. by limiting the development of additional seismic force.
In reality, there are a number of factors that would Using this analogy, and Component Guide RC1A, the increase the force required to overturn the wall, so the damage severity is classified as Insignificant. Without calculated value may be a lower bound. For example, as the rocking mechanism, the behavior mode would be the foundation lifts, it will pick up an increasing tribu-classified as H, and the damage severity would be Moderate tary area of the surrounding slabs, thus increasing the rather than Insignificant. It is important to note FEMA 307 Technical Resources 
Chapter 7: Example Application 
EXAMPLE CALCULATIONS FOR DIFFERENT BEHAVIOR MODES EXAMPLE CALCULATIONS FOR DIFFERENT BEHAVIORMODES EXAMPLE 1 -SOLID WALL 
Flexure: The boundary elements at each end of the wall have 4-#10 and 7-#1 1 bars. The vertical wall reinforcement is #4 bars at 13" on center in each face. An approximation of the flexural capacity with the flange in compression may be made, assuming that all the steel in the tension boundary and all the wall vertical steel is yielding, as follows: Boundary Wall Verts. Dead Load Me (comp.) = Agfye 'wal + Asvfye, wall/2 + PDL (wall}) Ia.l /2 = (15.3) 50 (26) + (9.2) 50 (13) + (419) 13 = 31, 300k-ft With the flange in tension the capacity increases because of the yielding of the wall vertical reinforcing in the effective flange width assumed to be one half the effective wall height (M/V) plus the wall thickness, or about ten feet. The capacity also increases because of the additional dead load resistance of the flange. An approximation of the flexural capacity with the flange in tension is then: Flange Verts. Flange Dead Load Me (ten.) = Me (comp.) + Asvfye I wall + PDL flange) I wall = 31, 317 + (3.8) 50 (26) + (320) 26 = 44, 600 k-ft These approximations for moment capacities were checked using strain compatibility calculations and found to be acceptable. Using an M/V ratio of 20 ft the shear forces associated with the moment capacities are 1570 k (flange in compression) and 2230 k (flange in tension).
Diagonal Tension (Shear Strength) : In order to include the effect of axial load on shear strength, and the potential degradation of the shear in plastic hinge zones, the equations recommended in Section 5.3.6b of FEMA 306 were used to calculate the diagonal tension strength.
V =V+V+V p it C An M/V ratio of 20 feet was used (approximately 0.75 times the component height) based on the analysis results for shear and moment.
As=41.2 in2 A = 4176in 2 Ps = 0.0098 Thus Equations 5-3 and 5-4 of FEMA 306 yield a= 1.5 krc = 3.5 (low ductility) P= 0.7 krc= 0.6 (high ductility) and the concrete contribution (Equation 5-2) becomes ge Vc = kc/krfc b. (0. 81 ) Vc= 605 kips at low ductility demand Vc = 104 kips at high ductility demand - The steel contribution is given by Equation 5-5: S= pnfyef b h where Pn=.00256, fye = 50 ksi, bw = 12", and hd is limited by the component height of 27'-0". Thus V, =498kips The axial load contribution is given by Equation 5-6. Considering only the structure dead load tributary to the wall (419 kips) VP becomes (I -c) N = (iM I) V = 264 kips (flange in compression) = 249 kips (flange in tension) NOTE: c = 16.8 in. (flange in compression), c = 33 in.
 (flange in tension) Therefore, Equation 5-1 for the diagonal tension strength gives a value of 1352 kips at low ductility demand, and 851 kips at high ductility demand, both with the flange in tension.
Diagonal Compression (Web Crushing) : The web crushing strength is given by Equation 5-7. This equation requires an estimate of the drift ratio to which the component is subjected, with increasing drift corresponding to a decrease in capacity. An upper bound estimate of 1 percent drift is assumed, to get a lower bound on the web crushing strength: 1.8f'b (0.81, ) 2560 kips 1+ (600 -2000 A) 4 Asf' Foundation Rocking (Overturning) : The static overturning calculation includes not only the dead weight of the wall and tributary slabs at the 2nd floor and roof, but also a tributary area of the slab on grade (496 kips total) and the foundation weight (16 kips per footing).
When the wall flange is in tension, the weight of the flange and additional DL are included.
1 I V, = Mo, =- (496k (26' 1 2) + 16k (26') ) (M/V) 20 = 343 kips (flange in compression) 1 (M /V) 1 =- (496k (26' / 2) + 446k (26') +16k (26') ) 20 923 kips (flange in tension) Technical Resources FEMA 307 Chapter 7: Example Application that the damage severity is not a function of the observed crack pattern alone -the governing behavior mode must be known before a judgement of the damage severity can be made.
7.2.4.3 Example 2 -Coupled Wall (7L-7M) 
As an example of the second typical wall element type, consider the damage record for the coupled wall shown in Figure 7-7. Like the solid wall example, the wall is 12 inches wide with 18-inch-square boundary elements at each end. However, there is a 6'-6" wide by 7-3" tall opening in the center of the wall at each floor. The wall length from center to center of the boundary elements is 26 feet, and the story height is 13'-6". The coupled wall has an L-shaped plan with a 26-foot flange along line M. The coupling beam and wall are similar to the example shown in Figure 7-5, except that this particular coupled wall is discontinuous below the first floor and is supported on 24-inch-square reinforced-concrete columns at the basement.
Component Type. 
Visual observation leads to the division of this structural element into two RC1 wall piers and two RC3 coupling beams. Analysis will verify that the beams are weaker than the walls, and thus that the initial classification is valid.
Behavior Mode. 
In the preliminary classification, the coupling beams were designated by observation as mode B (flexure / diagonal tension) or mode H (preemptive diagonal tension), and the wall piers were designated as mode B (flexure / diagonal tension), mode C (flexure / diagonal compression), mode H (preemptive diagonal tension), or mode N (individual pier rocking).
As in the first example, the shears associated with the development of the maximum strength in flexure, diagonal tension, and web crushing were calculated, with results summarized in Tables 7-2 and 7-3. Selected details of the calculations are provided for reference on pages 196 through 198.
Looking first at the RC3 coupling beam component, the calculation results shown in Table 7-2 indicate that the shear strength will be reached before the development of the moment strength, even at low ductility levels, so the behavior mode H (preemptive diagonal tension) governs.
For the RC1 wall pier components, the calculations and discussions that follow show that behavior mode N, individual pier rocking, governs the seismic response.
For the piers of the coupled wall, which discontinue below the first floor and are supported on basement columns, this behavior mode involves the yielding in flexure of the basement columns and the coupling beams reaching their capacity in shear. The wall pier rotates about the supporting column in a manner similar to Table 7-2 Capacity of Potential Behavior Modes for Typical Coupling Beam Coupling Beams RC3 Behavior Mode Limiting Component Shear (kips) FEMA 306 Reference Comments Flexure (mode A) Me=1210 k-ft 373 Sect. 5.3.5 Note that slab reinforcement was ignored in the calculation of the beam flexure capacity. Since preemptive shear governs (242 < 373), this is irrelevant.
A more accurate calculation would be warranted if the capacities in the different modes were similar.
Diagonal Tension (B and H) -242 Sect. 5.3.6b Governing capacity at low flexural ductility Diagonal Tension (B) -at high flexural ductility 137 Sect. 5.3.6b This capacity does not govern since flexural yielding does not occur.
Sliding Shear (D) 150 Sect. 5.3.6c This mode is unlikely since it typically occurs after flexural yielding. Such yielding is not expected since preemptive diagonal tension governs over flexural response.
 Component shear in beam associated with development of the component moment strength Technical Resources FEMA 307 Technical Resources Chapter 7: Example Application Table7-3 Shear Capacities for Potential Behavior Modes of Wall Pier (RC1) Components in Coupled Wall Potential Behavior Mode Limiting FEMA 306 Notes Component Reference Shear (kips) Flexure (mode A) See notes Sect. 5.3.5 In example calculations, moment capacities are compared to moment demands corresponding to mode N. Flexure is shown not to govern.
Diagonal Tension (mode B and H) at Low Flexural Ductility Sect. 5.3.6b Limiting shears are compared to those for RC1 @7L-load to east 690 behavior mode N. To consider redistribution - RCl @7L-load to west 311 of lateral forces, the sum of shears RCI @7M-load to east 328 for the two wall piers is considered.
RC1@7M-load to west 692 Diagonal Tension (mode B) at High Flexural Ductility Sect. 5.3.6b These capacities do not govern, since RC 1 @ 7L-load to east 470 flexural yielding does not occur.
RC1 @7L-load to west 163 RCI @7M-load to east 166 RCI @7M-load to west 472 Web Crushing (mode C) Sect. 5.3.6c Web crushing not applicable for low axial RC1 @7L-load to east 1710 load or tension.
RC1 @7M-load to west 1810 Rotation about Column Shear in piers is limited by capacity of (mode N) coupling beam (RC3) components.
RC1 @7L-load to east 330 RC1 @7L-load to west 300 RC1 @7M-load to east 300 RC1 @7M-load to west 330 foundation rocking. Free body diagrams corresponding The limiting component shears associated with possible to this mechanism and behavior mode are shown in the behavior modes for the wall piers are summarized in example calculations that follow. Table 7-3. The table verifies that the web crushing (diagonal compression) can be eliminated as a possible Comparison of the moment demands corresponding to behavior mode because the capacity is much higher the behavior mode N to moment capacities of the wall than that corresponding to other behavior modes.
pier sections is shown in the example calculations. The Behavior mode H, preemptive diagonal tension, is moment demands are well below the moment capacity investigated by comparing the limiting shears to those ties, indicating that flexural yielding will not occur. This of mode N eliminates modes B (flexure/diagonal tension) and C (flexure/diagonal compression) as possible behavior Diagonal tension capacities at high ductility are only modes. relevant for the combined flexure/diagonal tension behavior mode, which will not occur since flexural 194 Technical Resources FEMA 307 Chapter 7: Example Application yielding and the consequent degradation of the V, component of shear strength does not occur. The relevant diagonal tension capacities are those at low ductility.
The diagonal tension capacities of 31 1k (RCl @7L-load to west) to 328k (RC 1@7M-load to east) for the wall piers subject to axial tension are similar to the shear demands in the pier rotation mode after failure of the coupling beams; however, there is significant capacity of 690k (RC1 @7L-load to east) to 692k (RC1 @7M load to west) in diagonal tension on the corresponding compression sides of the wall. A diagonal tension failure cannot fully develop on one side of the coupled wall without transferring lateral forces to the other side of the wall. Considering that shear can be transferred as axial forces in the coupling beam and slab according to the stiffness and strength of each wall pier, the sum of wall pier component strengths on each side of the coupled wall can be used to determine the governing behavior mode. For the individual pier rotation behavior, the associated total shear demand is 630k on the coupled wall element. For a diagonal tension behavior mode occurring in both wall piers, the associated shear capacity is 1003k to 1018k. Diagonal tension failure will not govern, since the pier rotation behavior mode occurs at a lower total lateral load. Thus, the results of the analytical calculations indicate the pier rotation (N) is the governing behavior mode for the RC1 components.
This analytical conclusion agrees with field observation.
The degree of diagonal cracking observed in the wall pier RC1 components is consistent with substantial shear stress, but less than that which might be expected for diagonal tension failure.
Damage Severity. 
For the RC3 components behaving in mode H, the damage classification guides indicate that the observed damage is moderate in the second story and heavy in the first story coupling beam. In the wall piers, the protection of the element by a ductile mode (similar to mode N, Foundation Rocking) in surrounding components places them in an insignificant damage category.
7.2.5 Other Damage Observations 
Several of the walls were observed to have horizontal cracks just below the roof slab and/or the second-floor slab. In addition to new cracks of this type, a few walls had pre-existing horizontal cracks below the slabs, which had been repaired by epoxy injection. The widest of these horizontal cracks occurred under the roof slab of the wall on column lines 7C-7D, as shown in the Component Damage Record D3. The engineer in the field indicated that joint movement occurred at this crack and suspected that sliding shear behavior may have occurred.
Subsequent thinking by the evaluating engineers about this observation, however, weighed against the conclusion of sliding shear behavior. The crack was not observed to extend into the boundary columns of the wall, and there was no evidence of lateral offset at the boundary columns. While the crack is located near a likely construction joint where poor construction practice can exacerbate sliding shear behavior, the crack is not located in the maximum moment region of the wall.
As is indicated in FEMA 306, sliding shear behavior is most likely to occur after flexural yielding has occurred.
For this wall, flexural yielding would initiate at the base of the wall where moments are at a maximum, not at the top. In any case, foundation rocking preempts flexural yielding for the typical solid wall, as indicated previously in this example. A quick calculation of sliding shear strength shows that the behavior mode is not expected to govern the wall's response.
Given this information, the damage observations are reconsidered, and it is judged that sliding movements did not occur at the horizontal crack. Therefore, the most likely explanation is that these horizontal cracks are caused by earthquake displacements in the out-of- plane direction of the wall. It is judged that the horizontal cracks, whose widths are less than 0.03 inches, do not significantly affect seismic response.
7.2.6 Summary of Component Classifications 
7.2.6.1 Solid Walls 
All wall components of the building are evaluated in a similar manner, as described in the preceding sections.
In total, the building has six coupled walls plus five solid walls acting in the North-South direction, and two coupled walls plus six solid walls acting in the East- West direction. The damage records for these walls can be found in Component Damage Records D1-D19 (Appendix A).
Each solid wall is a single structural component (RC 1), while each coupled wall has four components: two coupling beams (RC3) and two wall piers (RC1). Thus there are a total of 43 structural wall components in the building, as indicated in Tables 7-4 and 7-5. For each of these, the component type, behavior mode and damage severity is established as described below and shown in the tables.
195 Technical Resources FEMA 307 Technical Resources 195 Chapter 7: Example Application EXAMPLE CALCULATIONS FOR DIFFERENT BEHAVIOR MODES EXAMPLE 2 -COUPLED WALL (7L-7M) COUPLING BEAMS The total diagonal tension strength is then 242 kips at low ductility, and 137 kips at high ductility.
RC3 Flexure: RC3 Sliding (Sliding Shear) : The moment strength of the coupling beams is calculated as discussed in FEMA 306, Section 5.3.5 using expected values -FEMA 306 Section 5.3.6d gives the sliding shear strength for material properties (f'ce = 3 000 psi, fye = 50 ksi). The for coupling beams at moderate ductility levels as beams are 6'-3" deep, with 3 -#9 bars at top and bottom and #4 bars @ 13" on center at each face. The calculated moment capacity is 1210 k-ft. This capacity is determined using strain compatibility calculations that demonstrate that sliding = 3h) Vfebwd = 150 kips all longitudinal bars yield. The MN ratio for the coupling beam is 3-3", so the shear associated with development of This failure mode is generally associated with beams that the moment capacity at each end of the beam is 373 kips. are well reinforced for diagonal tension, and that undergo Note that slab reinforcement is ignored in the calculation of multiple cycles at a moderate ductility level. Since the pre- the beam flexure capacity. It will be shown below that pre-emptive shear failure mode governs, the sliding shear mode emptive shear clearly governs, so this is irrelevant. How-is not a potential failure mode.
ever, a more accurate calculation would be warranted if the capacities in the different modes were similar. WALL PIERS RC3 Diagonal Tension (Shear Strength) : RC1 Flexure: The equations for diagonal tension strength in The figures below show the free body diagrams of the wall Section 5.3.6b of FEMA 306 may be used for coupling for lateral forces toward the east and toward the west. In beams. For beams, the axial load is not significant, thus both cases it is assumed that the coupling beams and first Vp = 0 and Equation 5-1 becomes: floor slab have reached their capacities. It is also assumed that the columns beneath the first floor are yielding in flexure.
These assumptions define a potential inelastic lateral V =V +1V mechanism for the wall. If the assumed lateral mechanism for the coupled wall is correct, the flexural capacity of the Using an M/V ratio of 3-3" (half the clear span of the coupling - RC 1 components must be sufficient to generate the diagonal beams) Equations 5-3 and 5-4 of FEMA 306 yield tension failure in the RC3 coupling beams. The moment a= 1.5 Pg= 0.0 0 5 9 demand diagrams for the RC 1 pier components are also Krc 3.5, 0.6 shown below.
, B=0.61 F = 55 psi The boundary elements in the wall piers at lines L and M each contain 8-#1 1 vertical bars. The vertical wall reinforcing comprises #4 bars at 13" on center in each face. Using and the concrete contribution Equation 5-2 becomes strain compatibility calculations, the moment capacities at the top and bottom of the piers (between the first floor and ba/3krc.
the top of the door opening) corresponding to the appropriate - Vc= bW (0.81w) axial loads are calculated.
V4 = 127 kips at low ductility The moment capacity and demand for the RC1 components must be determined with respect to the same axis. For RC1 @L the elastic centroid is selected. For RC1 @M the V, = 22 kips at high ductility elastic centroid of the component neglecting the return wall is used as the axis. When the return wall is in compression it The steel contribution is given by Equation 5-5 contributes little to the flexural strength of the wall pier.
However, when in tension, the reinforcement in the return V = Pnfyebwh d increases moment strength. Therefore, in the capacity calculations, the vertical reinforcement in approximately 10 ft.
where pn =.00256 is based on the vertical (stirrup) reinforcement - of return is included. This distance is estimated in accordance with FEMA 306 Section 5.3.5b as 50% to 100% of, he = 50 ksi is the expected steel yield strength, the MIV for the entire wall.
bw = 12", and hd = 75" is the horizontal length over which vertical stirrup reinforcement contributes to shear strength, The flexural demand and capacity of the RC 1 components in this case the length of the coupling beam. Thus are summarized in the following table: V, = 115 kips - 196 Technical Resources FEMA 307 Chapter 7: Example Application CALCULATIONS FOR EXAMPLE 2-COUPLED WALL (continued) Component Load Direction Location on Pier Axial Load (k, comp.+) Moment Capacity (k-ft) Moment Demand (k-ft) Top 773 6470 1650 East Bottom 773 6470 3960 RCWLs Top -265 2190 428 Bottom -265 2190 1660 East Top -215 2400 618 East @M Bottom -215 7120 1480 RC1@M Top 823 6660 1850 West Bottom 823 6660 4160 I9 26' Return wall on Return wall on Line M 3k Line M (Coupling bm. DL) 220 k 201 k 201 k 1 /220i -g-= I 106k 11 13.5' 106k 113.5' (Column DL) 119k. (Column DQ 119k 110k 99Zk 99 k 9110k 13.5' 106k 13.5' 106 k 143k 143 k 330 k 300 k 3< I -I K5 K5 ' 33 K 443ft-k 280 ft-k (Col. moment capacity 248ft-k 431 ft-k (Col. moment capacity axial load) @associated t at associated axial load) 773 kf AxialforcesinRC1 215k Axial forces in RC1 823k 265 4; components I (comp.) (comp.) components T (ten.) (ten.) Free Body Diagram for Seismic For to East : West Roof i Roof i 244 i Second i Second 21 i i M/V=1F2.6' i \v 1 First i3960 t1482 Moment Diagram (@ centroid of i i Moment Diagram (Q centroid of piers) for Load to East Moment Diagram (d centroid of piers) for Load to West (plotted on tension side ink-ft) (plotted on tension side in k-ft) j FEMA 307 Technical Resources Chapter 7: Example Application CALCULATIONS FOR EXAMPLE 2 -COUPLED WALL (continued) 26' 12" 18" :01 'z im wall 126" I flange) Plan Distance to the elastic centroid from gridline: / [126 (12) +2 (18) 3] X= ([1 26 (12) 126/2+2 (18) 3 (9) ] 1-9 = 50.2" or 4.2' Comp. Load Axial Load Reduce Net Tot. Duct.
Direct. (k) vc for Ten. VC VS VP V (k) (k) (k) (k) East 773 265 1.0 265 133 292 690 low RC1 @L (comp.) 45 45 470 high West -265 265 0.67 178 133 0 311 low (ten.) 45 30 163 high East -215 265 0.74 195 133 0 328 low RC1@M (ten.) 45 33 166 high West 823 265 1.0 265 133 294 692 low (comp.) 45 45 472 high RC1 Diagonal Tension (Shear Strength) : V, = 133 kips The equations in Section 5.3.6 of FEMA 306 were again The compressive axial load contribution is given by used to calculate the diagonal tension strength. Equation 5-6.
V.= v, + +v,, v, = ( (I, -c) NM Using the component M/V values from the moment diagrams - (2 -M), Equations 5-3 and 5-4 yield V ax= 1.5 fl=0.76 p = 0.0013 Considering all of the above contributions the diagonal tension - g strengths of the RC 1 components are summarized in the and the concrete contribution from Equation 5-2 becomes table above: Vc =-ocskrc+/ f'bw (0 8hw) RC1 Diagonal Compression (Web Crushing) : V, Iaflk,.Vrf, beW The web crushing strength is given by Equation 5-7. This = 265 kips at low ductility equation requires an estimate of the drift ratio to which the component is subjected, with increasing drift decreasing the V, = 45 kips at high ductility capacity. An upper bound estimate of 1% is assumed to get a lower bound on the web crushing strength: When the component experiences net axial tension ACI 318-95, eqn. 11-8 specifies the the concrete contribution to 18fbW (08lw) shear strength, Vc, be reduced by the factor 1-[N, / (500 V. N. 1710psfbRCI 7L load to East Ag) ]. 1+ 600-2000 A Lj The steel contribution is given by Equation 5-5 = 1807 kips foRC RO 7Mload to West V, = pnfyewihd Web crushing is not typically an issue for low axial loads or where pn =. 0 0 2 56 'fye = 50 ksi, bw = 12", and hd is limited net tension.
by the height of the door 7'-3". Thus Technical Resources FEMA 307 Chapter 7: Example Application The typical solid walls were calculated to behave in a foundation rocking (or overturning) mode (type M).
There are no damage guides for this behavior mode.
However, component behavior description in FEMA 306 considers this mode to have moderate to high ductility.
The damage associated with this behavior mode may not be apparent based on the observations of the walls. Damage to other structural and nonstructural elements, such as damage to the floor slab at the base or to the beams framing into the ends of the walls, should be used to assess the severity of the mode. Since there was no significant damage to the adjacent structural and nonstructural elements, the damage severity is judged to be Insignificant.
7.2.6.2 Coupling Beams 
Based on calculations, the behavior mode of the coupling beams is Preemptive Diagonal Tension (Type H).
Based on the damage observations and the component guides, the damage for the coupling beams with spalling, bar-buckling, and/or significant cracking was classified as Heavy. For the coupling beams with shear cracking, but no bar-buckling or significant spalling, the damage is Moderate.
7.2.6.3 Wall Piers 
The walls adjacent to the coupling beams are expected to behave in a mode of individual pier rocking (type N).
There are no Component Guides for this behavior mode.
However, the component behavior description for this mode of behavior considers this mode to have moderate to high ductility. Similar to the solid shear walls, the lack of damage to the adjacent structural and nonstructural elements was used to classify the damage as Insignificant.
7.3 Evaluation by the Direct Method The effects of damage are quantified by the costs associated with potential Hypothetical repairs (component restoration measures -repairs for), which if implemented, would method, restore the components to their pre- Section 4.6 event condition. In the direct method, of FEMA 306 restoration measures are considered on a component-by-component basis without an analysis of global performance. It is intended to be a simple and approximate approach. The Component Damage Classification Guides in FEMA 306 are used to determine the appropriate potential repairs to restore each component.
The potential repairs required to restore the structural performance and nonstructural functionality of the building include both structural and nonstructural (e.g., cosmetic) measures for each damaged component.
7.3.1 Structural Restoration Measures 7.3.1.1 Coupling Beams As shown in Tables 7-4 and 7-5, three of the coupling beams were classified Damage as component type RC3, behavior guide for mode H, having Heavy damage. As Table 5-2 of recommended for this component FEMA306 type, behavior mode, and damage severity, the component restoration measure chosen is to replace these components. The proposed repair would be to remove the concrete at the coupling beam and a portion of the floor slab, install new reinforcing bars, and cast new concrete for the wall. The new reinforcing steel in the coupling beams would be detailed in accordance with the current provisions of the governing building code for coupled shear walls, as shown in Figure 7-8.
The coupling beams with Moderate damage could be repaired by epoxy injection of all diagonal shear cracks greater than 10 mils wide, since epoxy injection is recommended for structural restoration using the damage guide for RC3H. Although it is possible to inject smaller cracks, the additional cost does not justify the marginal benefit. Since cracks as large as 12 mils can be tolerated in normal concrete structures (ACI, 1994), the unrepaired cracks should not be detrimental. The length of the cracks to be injected is estimated as 100 feet.
7.3.1.2 Solid Walls The remaining wall components are type N or M. There are no Component Guides for these modes to indicate the appropriate repairs directly. As discussed earlier, these modes have moderate to high ductility capacity.
Conservatively, the damage guide for Type B, flexure / diagonal tension, is used since this is a moderate ductility mode, analogous to the actual behavior mode. The Component Guides for the type RC1B components indicate that if cracks are less than 1/16 inch, the damage can be classified as Insignificant, and therefore structural repairs are not necessary. Two of the shear wall components had cracks that exceeded 1/16 inch.
This amount of cracking would be classified as Moder- FEMA 307 Technical Resources Chapter 7: Example Application Table 7-4 Summary of Component Type, Behavior Mode, and Damage Severity for Wall Components (North-South Direction) Column Floor Wall Type Component Type and Damage Severity Line Behavior Mode B / 2-3 First-Second Coupled RC1N Insignificant Coupled First t 0 First-Second Coupled RC1N Insignificant B I 5-7 First-Second Coupled RC1N Insignificant First Coupled RC3H Moderate First-Second Coupled RC1N Insignificant B /10-12 First-Second Coupled RClN Insignificant First Coupled RC3H Moderate First-Second Coupled RClN Insignificant Second> Coupled" j CH" Moderate B /14-15 First-Second Coupled RC1N Insignificant E /2-3 First- Second Coupled RC 1N Insignificant E / 2-3 First-Second Coupled RC1N Insignificant irt Second Coupled RC3H Insignificant E 1-5 Second Coupled RC3H Insignificant First-Second Coupled RC1N Insignificant G I 7-8 First-Second Solid RC1M Insignificant G / 9-10 First-Second Solid RC1M Insignificant M / 7-8 First-Second Solid RC1M Insignificant M / 9-10 First-Second Solid RC1M Insignificant M / 8-9 Ground Solid RC1B Insignificant 200 Technical Resources FEMA 307 200 Technical Resources FEMA 307 Chapter 7: Example Application Table 7-5 Summary of Component Type, Behavior Mode, and Damage Severity for Wall Components (East-West Direction) Column Floor Wall Type Component Type and Damage Severity Line Behavior Mode 7 /L-M First-Second Coupled RC1N Insignificant First-Second Coupled RC1N Insignificant 10/ L-M First-Second Coupled RC1N Insignificant First-Second Coupled RC1N Insignificant 2/ B-C First-Second Solid RC1M Insignificant 2/ D-E First-Second Solid RC1M Insignificant 7/ C-D First-Second Solid RC1M Insignificant 10/ C-D First-Second Solid RC1M Insignificant 15 /B-C First-Second Solid RC1M Insignificant 15 / D-E First-Second Solid RC1M Insignificant ate for type B behavior. Epoxy injection is recommended -In addition, many of the suspended ceiling tiles became in the Component Damage Classification dislodged and fell during the earthquake. The nonstructural - Guides for these cracks. Thus, for performance restoration - repairs would include replacing the ceiling tiles.
by the direct method, these walls would have all of the cracks exceeding 1/16 inch repaired by injection 7.3.3 Restoration Summary and Cost with epoxy. The total length of crack to be injected is Table 7-6 summarizes the performance restoration measured estimated at 22 feet. Tbe 76 performance restoration estimated at 22 feet and estimated costs. Additional costs related to Spalls (other than at the coupling beams that are being inspection, evaluation, design, management and indirect placed) could be repaired by application of a concrete costs may also be involved repair mortar to restore the visual appearance. The total volume of concrete spalls is estimated to be 3 cubic 7.4 Evaluation by Performance feet.
Analysis 7.3.2 Nonstructural Restoration 
The use of the direct method is limited to an estimate of Measures the loss associated with the damaging earthquake. It wall components with visible cracks could be cannot be used to evaluate actual performance. For repaired by patching the cracks with plaster, and then these purposes, relative performance analysis as painting the entire wall. This repair is only intended to described in FEMA 306 is used. The basic procedure restore the visual appearance of the wall. Restoration of comprises a comparison of the anticipated performance other nonstructural characteristics, such as water tight-of the building in future earthquakes in its pre-event, ness and fire protection, are not necessary in this damaged, and repaired conditions. This comparison instance. may be made for one or more performance objectives.
FEMA 307 Technical Resources 201 Chapter 7: Example Application Remove & Replace Existing Concrete Coupling Beam #4 Hoops @ 2 1/2 inches Diagonal Bars in a Existing 3-#9 Bars 6 inch x 8 inch Cage to Remain Epoxy Dowel 38 inches into Existing Wall #4 Bars @ 12 inches Elevation #4 Stirrups @ Floor Slab Joists Section Figure 7-8 Detail of Coupling Beam Replacement Table 7-6 Restoration Cost Estimate by the Direct Method Item Unit Cost Quantity Cost (1997 dollars) (1997 dollars) Epoxy Injection $25.00 ft 122 ft $ 3, 050.
Coupling Beam Removal and Replacement $74.00 /cu ft 122 cu ft $ 9, 028.
Patch and paint walls $0.60 /sq ft 10, 175 sq ft $ 6, 105.
Replace ceiling tiles $2.00 /sq ft 15, 000 sq ft $30, 000.
General Conditions, Fees, Overhead & Profit (@ 30%) $14, 455.
Total $62, 638.
7.4.1 Performance Objectives return period (10 percent probability of exceedance in Two performance objectives are 50 years) for this site. The response spectrum for this considered in this example. The first is Performance earthquake is shown in Figure 7-9. The soil at the site objectives, was determined to be type S,. Using the available the life safety performance level, as Section 4.2 seismic data, the spectral response at short periods (T = defined in FEMA 273, for an of FEMA306 0.2 sec) for this site is 1.0 g and the spectral response at earthquake associated with a 475-year 1 second is 0.56 g.
202 Technical Resources FEIVA 307 Chapter 7: Example Application 1.2 0.
0 0 0.6 0 0 1 -E 0.4 I.
4'0.2 CO) 0 I 0 0.5 1 1.5 2 2.5 3 Period (Sec) Figure 7-9 Response Spectra for Selected Performance Levels The building was also checked for immediate occupancy performance level using an earthquake with a 50 percent probability of exceedance in 50 years. For this earthquake, the spectral response at short periods at this site is 0.68 g and the spectral response at 1 second is 0.35 g. The response spectra for the immediate occupancy performance level is also shown in Figure 7-9.
It should be noted that these performance objectives do not necessarily correspond to the original criteria used for design of the building.
7.4.2 Nonlinear Static Analysis 
7.4.2.1 Computer Model 
The building is analyzed in its pre-event, post-event and repaired conditions using a three-dimensional computer model. Modeling of the building is done using the recommendations of FEMA 273 and FEMA 306. The model is subjected to a nonlinear static (pushover) analysis to assess its force/displacement response. For this example, the analysis is run only in the East-West direction, which is the direction that experienced the most significant damage.
The computer analysis program SAP2000 (CSI, 1997) is used to model the structure. The reinforced concrete walls and coupling beams are modeled using beam elements. The beam elements are located at the center of gravity of each wall section, and are given properties that represent the wall section stiffness. Rigid end offsets are used to model the joint regions in the coupled walls as shown in Figure 7-10. Small models of individual walls are used to verify that the beam elements used to model the walls have approximately the same stiffness and shear distribution as a model using shell elements for the walls. A three dimensional view of the global model is shown in Figure 7-11. The horizontal floor and roof diaphragms are modeled using beam elements, as shown in Figure 7-11, with lumped masses at the nodes.
The pushover analysis is conducted by applying static loads at the locations of the lumped masses in a vertical distribution pattern as described in the second option of Section 3.3.3.2 C, of FEMA 273. Sixty percent of the total lateral force is applied to the roof, thirty percent is applied at the second floor, and ten percent is applied at the first floor. The nodal loads are increased proportionally in progressive iterations. When elements reach their strength limit, their stiffness is iteratively reduced to an appropriate secant stiffness and the model is rerun at the same load level until no elements resist loads in excess of their calculated capacities. (Secant stiffness method, see side bar.) The pushover analysis is continued to cover the displacement range of interest, which is based on a preliminary estimate of the maximum displacement demand.
A global pushover curve is then produced.
FEMA 307 Technical Resources Chapter 7: Example Application I I I I I I I I I I I I Figure 7-10 Mathematical Model of Coupled Shear Wall 7.4.2.2 Component Force-Displacement Behavior Component force-displacement curves are developed for each of the typical wall components using the generalized force-displacement curves from Figure 6-1 of FEMA 273.
The acceptance limits for the coupling beam components are based on Table 6-17 of FEMA 273 for the case of Component force- displacement relations, FEMA 273 and Sections 4.3 and 4.4 of FEMA 306 "nonconforming", transverse reinforcement, and shear exceeding 6twAwr-. The pre-event shear-strength-to- I I L L.
I I chord-rotation relationship is shown in Figure 7-12 (a).
Also shown in this figure are the points representing the displacement limits for immediate occupancy and life safety performance.
The initial slope of the component force/deformation curves is based on modeling for the initial elastic stiffness of the com-pre-event. The pre-event structure is condition, modeled using the effective initial Section 4.4.3.1 of stiffness values recommended in Table 6-4 of FEMA 273. Walls and coupling FEMA 306 COEFFICIENT Either of two methods are recommended for establishing displacement demands for a nonlinear static analysis: the coefficient method and the capacity spectrum method. A description of these methods is included in ATC 40. The coefficient method is also described in FEMA 273, and the coefficient and capacity spectrum methods are described in FEMA 274. Although either method may be used, it is essential for a valid comparison that the same method be used to assess the performance of the pre-earthquake, post-earth- quake, and repaired structure, as outlined in FEMA 306.
In this example, the coefficient method is used. In this method, a target displacement, dt is calculated and compared to the displacement of a control node, generally located at the roof. The target displacement is determined by multiply- AND CAPACITY SPECTRUM METHODS ing a set of coefficients times a function of the effective building period and the spectral acceleration.
T2 =CoCiC 2C3Sa 4 2 g t 4, r To use the coefficient method, the nonlinear static analysis must be conducted in order to construct the pushover curve.
The pushover curve can be presented as spectral acceleration versus spectral displacement or as base shear versus roof displacement. Once the pushover curve is constructed, an equivalent bilinear curve is fitted to approximate the actual curve. The equivalent bilinear curve is then used to obtain the effective stiffness of the building and the yield base shear needed for calculating the target displacement.
Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application Beam Elements Representing Solid Wall Figure 7-11 Mathematical Model of Full Building beams are given a flexural rigidity of 0.5Ecg. The basement columns of the structure, which support the discontinuous walls, are given a flexural rigidity of 0.7Eclg. As recommended in FEMA 273, the shear rigidities of all components are set equal to gross section values.
The post-event structure is modeled with stiffness values multiplied by the Ak factors recommended in FEMA 306. Heavily damaged coupling beams have their stiffness reduced to 20 percent (ok = 0.2) of the pre-event value. Moderately damaged coupling beams have their stiffness reduced to 50 percent (o'k = 0.5) of the pre- event value. For the solid shear walls, where damage is classified between Insignificant and None, stiffness is reduced to between 80 percent to 100 percent of the pre- event stiffness depending on the amount of cracking.
The horizontal plateau of the component force/deformation curves is based on the strength of the governing behavior mode. For the pre-event structure, the strength Beam Elements Representing Floor Slab Nodes Where Lateral Loads are Applied is based on calculations as illustrated in Section 7.2.4 of this example. For the post-event structure, the pre-event strength is multiplied by the IQ factors recommended in FEMA 306. Heavily damaged coupling beams have their strength reduced to 30 percent of the pre-event value. Moderately damaged coupling beams have their strength reduced to 80 percent of the pre-event value.
For components where damage is classified either Insignificant or None, the strength is not reduced.
Figure 7-12 (b) shows the force-deformation curves for the moderately and heavily damaged coupling beams.
7.4.2.3 Foundation Rocking 
Since the governing behavior mode of the solid concrete walls is identified to be foundation rocking, this behavior is incorporated into the pushover analysis. To model the rocking, the stiffness of the lower story wall elements is reduced when the shear force in those elements reaches the shear force that causes rocking. Once the wall element in the model had started to overturn in the analysis, the stiffness is adjusted so that the wall FEMA 307 Technical Resources Chapter 7: Example Application NONLINEAR ANALYSIS USING LINEAR ANALYSIS COMPUTER PROGRAMS 
Currently, there are few commercially available computer programs for direct implementation of the nonlinear analysis required for a pushover analysis. Many of the nonlinear pro- grams available are sophisticated but can be expensive and difficult to use. For many buildings, a linear elastic analysis program can be used to assess iteratively the nonlinear behavior of the building.
There are two ways to implement a nonlinear static analysis using a linear computer program. Both methods are based on adjusting the stiffness of an element once the analysis indicates that the element has reached its yield level. One method uses the tangential stiffness of the element at the dis placement level above yield; the other uses a secant stiff- ness. The figures below depict the difference between the two methods.
Model #4 Models Model #2, a) C.
L o ILL fo el #1 / Sum of models gives final forces and displacements Displacement Figure i -Tangential Stiffness Method The tangential stiffness method is described in detail in ATC 40 (ATC, 1996). Lateral forces are applied to the building and proportionally increased until an element reaches its yield level. A new model is then created in which the yielding component has its stiffness reduced to zero or a small post-yield value. An incremental load is applied to the new would resist about 10 to 20 percent more shear force than that calculated to cause overturning. This adjustment is made to account for the additional dead weight of the structure that the wall would pick up once it started to uplift. The amount of additional overturning resistance in the wall is based on the shear and moment capacity of the beams framing into the wall.
Model #3 M Model #2 Mo/e/ / Model #1 ILL Model #4 gives forces and displacements Displacement A Xs #lk-A i ls.-%-.M-Jlt4X 16t model until another component reaches its yield level. The process continues until a complete mechanism has formed or until the maximum displacement level of interest has been reached. The sum of forces and deformations of each of the incremental models then represent the global behavior of the structure.
In the secant stiffness method, lateral forces are applied to the building and proportionally increased until a component reaches its yield level. A new model is then created in which the yielding element has its stiffness reduced by a value chosen to produce the correct post-yield force in the component.
The new model is then rerun at the same force level, and components are checked to verify that the force in the component has not exceeded, or reduced significantly below, its yield level. If necessary, the stiffness of the yielding element may need to be adjusted so that the force in that element is approximately equal to the post-yield force level. Other elements need also be checked since they may be resisting additional load no longer resisted by the yielding element.
After iterating until all elements are at approximately the correct force level, a new model is created at a larger lateral force level. The process is repeated at each force level. The behavior of the structure and each element at a given force level is represented directly by the behavior of the appropriate model, rather than combining the results of several models.
7.4.3 Force-Displacement Capacity (Pushover Analysis) Results 7.4.3.1 Pre-Event Structure The results of the pushover analysis indicate the progression of displacement events to be as follows for East-West loading (See Figure 7-2 for wall locations) : o Initially the two solid walls on lines 7 and 10 between lines C and D reach their rocking capacity.
FEMA 307 Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application 250.-.2 200150 1 -l1 & I1 '.1l I -I 1S-I I I.1 (n 100 50 0 ltI -Ir L I-I1z; II IT t I 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 300 Rotation (Radians) a) Pre-event 300 1 1I I I 250 1- co 'W1W -+Moderate CL 200 W =11 -Heavy " 150 I s1 100 Cl) 50 0 -U = I 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Rotation (Radians) b) Post-event In I c 300 250 4-co.2 200 -150 a4 100 50 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Rotation (Radians) I c) Replacement Coupling Beam with Diagonal Reinforcement Figure 7-12 Component Force-Displacement Curves for Coupling Beams FEMA 307 Technical Resources 207 Chapter 7: Example Application Comparison of Pre-event and Post-event Pushover Curves 9, 000 8, 000 - 7, 000 - -6, 000- 0.
X 5, 000 t) 4, 000- o 1 m 3, 000 -Post-event 2, 000 - 1, 000 0 4 0 0.5 1 1.5 2 2.5 Roof Displacement (Inches) Figure 7-13 Comparison of Pre-event and Post-event Pushover Curves When the solid walls between lines C and D are As shown in Figure 7-13, the pushover analysis softened, the solid walls on lines 2 and 15 between indicates that global nonlinearity begins at a base shear lines B and C, and between D and E at the first floor of approximately 5000 k. As lateral displacements pick up additional force and reach their rocking increase, the base shear climbs to about 8000 k. Since capacity. 10% of the total is applied at the first floor and is transmitted directly into the foundation, the force As the solid walls are softened, the coupled walls on resisted by the structure above the first floor prior to lines 7 and 10 between lines L and M resist more global nonlinearity is about 4500 k. Allowing for some force. The first floor coupling beam picks up more increase in capacity to reflect rocking behavior more force than the second floor coupling beam and accurately (see Section 7.4.2.3), this agrees well with reaches its shear capacity first. the hand-calculated capacities of the walls summarized in Tables 7-1 and 7-3. The applied load in excess of the Additional coupling beams reach their capacity and capacity of the walls is resisted by the columns. The solid walls continue to rock as the displacement magnitude of the increased load is compatible with the of the structure is increased. capacity of the columns. In the analysis, the first story coupling beams are the first element to reach the The approximate target roof displacement is reached immediate occupancy and life safety acceptability after the coupling beams have exceeded their limits. The component deformation limit for immediate collapse prevention acceptability limit, requiring a occupancy occurs when the roof displacement reaches reduction in their capacity. about 0.65 inches and that for life safety is reached at FEMA307 Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application about 0.88 inch. These displacements are taken as the displacement capacity d^, as defined in FEMA 306.
The progression of damage shown in the analysis is consistent with the observed damage.
7.4.3.2 Post-Event Condition 
For the post-event structure, the progression of displacement events is modeling of essentially the same as that outlined condition, for the pre-event structure. The results Section 4.4.3.2 of the post-event pushover analysis of FEMA306 are shown in Figure 7-13. In this analysis, the first story coupling beams reach the immediate occupancy acceptability limit at a roof displacement of 0.47 inches; the beams reach the life safety limit at a roof displacement of 0.66 inches. These values are used for d'.
7.4.3.3 Comparison of Force-Displacement Capacity Curves (Pushover Curves) The performance of the post-event building was slightly different than the pre-event performance; the overall building is softer since more deflection is obtained for the same magnitude of applied load. The reduced stiffness of the damaged components causes the global reduction of stiffness of the post-event structure. The Moderate and Heavy damage to some of the components corresponds to a reduction in their strength. At 1.2 = co.0 I0.8 o 0.6 a XO.4 u.
0.2 (0 0.0 0 0.5 1 larger displacements (greater than about 1.5 inches) the response of the pre-event and post-event structures are essentially the same.
7.4.4 Estimation of Displacement, de, Caused by Damaging Earthquake The accuracy of the structural model of the building can be verified by estimating the maximum displacement, de, that was caused by the damaging event. This is done in two ways. If the data were available, actual ground motion records could be used to predict displacement analytically. Secondly, the pushover curve in conjunction with component capacity data could be used to estimate displacements from the observed damage.
In this case, a spectrum from recorded ground motion at a site approximately 1.5 mi. from the building was available (see Figure 7-14). FEMA 273 (equation 3-11) uses the displacement coefficient method to estimate maximum displacement from spectral acceleration as follows: 2 de= CoCiC2C3Sa g (7-1) In this expression the coefficients C0 to C3 modify the basic relationship between spectral acceleration and 1.5 2 2.5 3 Period (Sec.) Figure7-14 Response Spectra from Damaging Earthquake FEMA 307 Technical Resources Chapter 7: Example Application placement for an elastic system as a function of the effective period of the structure, The effective period for the pre-event structure is approximately 0.3 sec. The spectral acceleration for this period from Figure 7-14 would be approximately 0.5 to 0.6 g producing an elastic spectral displacement between 0.4 and 0.5 in.
The coefficient C0 converts spectral displacement to roof displacement and has an approximate value of 1.25 for two- and three-story buildings.
For short-period buildings, the maximum inelastic displacement often is greater than the elastic. FEMA 273 provides the following expression Cl to adjust conservatively from elastic to inelastic: 01.0+ (R -1.0) To Cl = R e where R = Sa 1 (7-2) W In these expressions, the effective base shear at yield as a portion of the building weight, or about 0.28 in this case. This would result in an R-factor of approximately 1.4 to 1.7. The point where the spectral acceleration transitions from the acceleration to velocity controlled zone occurs at a period of around 0.5 to 0.6 sec. These values would combine to result in a coefficient Cl of around 1.2 to 1.4.
The coefficient C2 accounts for the shape of the hysteresis curve and is equal to 1.0 in this case. The coefficient C3 accounts for dynamic P-A effects and is also equal to 1.0 for this case.
Combining all of the coefficients and the elastic spectral displacement results in an estimate for the maximum displacement at the roof, de, of between 0.6 to 0.9 in.
From the damage observations, one of the first-floor coupling beams in the east-west direction appeared to reach its capacity, since a severe crack had developed and a transverse bar had buckled. Shear cracking had also developed in the wall piers adjacent to the coupling beams.
From the pushover analysis, at displacement demands between 0.3 inches and 0.5 inches, the coupling beams reach their capacity. The pushover analysis also indicates that the first floor coupling beam would be the first to reach its capacity, which is verified by the observations.
Since only the first floor beams were heavily damaged, the displacement demand of the damaging event should not have been much greater than 0.5 in.
The difference between the analytical estimate of and the estimate from the model and observed damage is not large. The difference is acceptable because the building is farther away from the epicenter than the site where the motion was recorded, and actual recorded building response is usually less than that which is predicted analytically.
Based on the comparison there is no need to adjust the structural model.
7.4.5 Displacement Demand 7.4.5.1 Estimate of Target Displacement Estimating the target displacement can be an interactive process. The nonlinear static analysis produces a force- displacement pushover curve covering the displacement range of interest. Based on the procedures of FEMA 273, an equivalent bilinear curve is fitted to the pushover curve and a yield point is estimated.
Using this yield point and the associated effective period, the target displacement is calculated using the coefficient method. Given the calculated target displacement, the equivalent bilinear curve can be refitted, adjusting the yield point, and giving a new target displacement.
The revised target displacement is close to the original estimate so further iteration is not needed.
EXAMPLE CALCULATIONS FOR PRE-EVENT AND POST-EVENT DISPLACEMENT DEMANDS Section 5.4 of FEMA 306 describes the procedures for calculating the displacement demand for both the pre-event and the post-event structures. The pre-event and post-event pushover curves for this example are shown in Figure 7-13.
For this example, the coefficient method is used to calculate the target displacements and FEMA 306 procedures are used to determine the corresponding displacement demands.
Pre-Event Target Displacement, dd An idealized bi-linear capacity curve for the pre-event structure is developed to approximate the actual pushover curve. Based on this idealized curve, the yield level base shear V. is 6000 kips and the yield level displacement Dy is 0.31 inches. The effective stiffness Ke then becomes 19, 400 kips/inch.
Technical Resources FEMA 307 Chapter 7: Example Application EXAMPLE CALCULATIONS FOR PRE-EVENT AND POST-EVENT DISPLACEMENT DEMANDS (continued) aU, 0.
10, 000 : 8, 000 M 6, 000 Pushover curve U) 4, 000 idealized curve U) CD 2, 000 m 0 0 0.5 1 1.5 2 Roof Displacement (Inches) Comparison of idealized bilinear curve to pushover the pre-event effective stiffness and the post-yield stiffness curve for the post-event curve to calculate a target displacement.
In this example, the slopes of the post-yield curves for the The initial period 0.25 seconds taken from the initial pre-event and post-event conditions are similar. Therefore, structural model. The effective period is calculated to be the target displacements will be essentially the same. The 0.30 seconds using the ratio of the initial to the effective value for d'd1 will be taken as the pre-event demand displacement - stiffness., which is 1.68 inches.
K. 27900 T  A = 0.25 = 0.30 Post-Event Target Displacement, d'd2 K 19400 Considering the post-event pushover curve, the effective stiffness Ke, with V. = 5600 and D. = 0.32 is 17, 500. The spectral acceleration Sa, based on the life safety earth- initial and effective periods are 0.25 seconds and 0.31 seconds - quake response spectra at the effective period is 1.0 g..
The coefficients are: The damping coefficient 13 for the post-event structure is calculated = 1.25 for a 2-to-3-story building to be 0.06 based on Equation 5-3 of FEMA 306, due to the change in the post-event effective stiffness. The Cl = 1.58 using the equation for T, in the constant damping adjustments for the response spectrum (B, and BI), acceleration region of the spectrum interpolating from Table 2-15 in FEMA 273, are 1.06 and 1.04 respectively. This changes the spectral acceleration for C2 = 1.0 the post-event structure to 0.97.
C3= 1.0 The value for Cl becomes 1.55, and the other coefficients Thus the target displacement from Equation 3-11 of FEMA are the same as for the pre-event condition. Using these val273 is: the new target displacement is calculated as: dt = 1.25 (1.58) (l.Og) (386 in/sec2g) (0.30) 2/4it2 dt= 1.71inches = 1.68 inches This value is assigned as dd, the maximum displacement in This value is assigned as d'd2.
its pre-event condition. The displacement demand from the damaging earthquake de was estimated to be 0.6 inches. Since d'dl is greater than de, Post-Event Target Displacement, d'dl the displacement demand for the post-event structure d'dis There are two values for the post-event displacement equal to d'dl, which is 1.68 inches.
demand that need to be calculated. The first value, d'd, uses 211 Technical Resources FEMA 307 Technical Resources 211 Chapter 7: Example Application The target displacement dd for the d pre-event structure for life safety performance -demand, against the 475-year-Section 4.4.4 return-period earthquake, based on of FEMA306 the coefficient method calculations, is 1.68 inches. The displacement demand for immediate occupancy after the 100-year earthquake is 0.97 inches.
Calculations (see sidebar on previous page) indicate that displacement demand for the post-event structure is essentially the same as for the pre-event structure.
7.4.5.2 Effects of Damage on Performance 
The changes in displacement capacity and displacement demand caused by the effects of damage are summarized in Table 7-7. The Performance Indices, P and PF in Table 7-7 are the ratios of the displacement capacity, d, or dc', to displacement demand, dd or id, as defined in FEMA 308. The displacement capacities calculated in Section 7.4.3 are based on the assumption that the coupling beams are primary components. FEMA 273 allows coupling beams to be treated as secondary members.
Since the global capacity is controlled by the acceptability of the coupling beams, the displacement capacities are determined again assuming that the coupling beams are secondary components and the results are included in Table 7-7. The global displacement capacity, although higher for Life Safety, is still controlled by the coupling beams. The relative change in Performance Index is similar in both cases, indicating that the effects of damage are the same.
The Performance Indices for both the pre-event and post-event structures are less than one for both performance objectives, indicating that the objectives are not met. The effects of damage can be quantified by identifying restoration measures to return the Performance Index to its pre-event value, as outlined in the following sections. The actual course of action to accept, restore, or upgrade the damaged building is a separate consideration for the owner and the local building authority.
7.4.6 Analysis of Restored Structure 7.4.6.1 Proposed Performance Restoration Measures The primary difference between the pushover models of the pre-event building and the post-event building is the performance of the coupling beams. In their post-earth- quake condition, the coupling beams were considered to have less stiffness and strength than in their pre-event condition. The displacement limits were also reduced by the A'D factor of 0.7. This resulted in the overall reduced stiffness, strength, and displacement capacity of the structure.
To restore the overall performance of the building, various schemes could be investigated, for example, the addition of new concrete walls without repairing damaged components. In this case however, the most straightforward repair appears to be the same component-by-component restoration considered in the direct method. This principally involves the repair of the damaged coupling beams. The coupling beams would be repaired as suggested by the Component Guides in FEMA 306 for the RC3H components. The moderately Table7-7 Performance Indices for Pre-event and Post-event Structures Displacement Capacity (inches) Displacement Demand (Inches) Life Immediate Safety Occupancy; dd =1.68 dd =0.97 dd'= 1.68d, '= 0.47 dd'= 0.97 0. s Gondar comj0 & d, = 0.65 dd =1.68 dd =0.97 d' = 0.47 dd' = 1.68 dd' = 0.97 Performance Index (Capacity/Demand) Life Immediate Safety Occupancy P =0.52 P =0.67 P'= 0.39 P'= 0.48 P =0.60 P =0.67 P' = 0.45 P' = 0.48 Life Safety b g..
treated Coupling beams treated Pre-event d, =0.88 Post-event dj= 0.66 Coupling be ins treated Pre-event d, =1.00 Post-event d' = 0.76 Immediate Occupancy 0 S primary, = 0.65 FEMA 307 Technical Resources Technical Resources FEMA 307 Chapter 7: Example Application damaged coupling beams are repaired by injecting the cracks with epoxy. The heavily damaged coupling beams are repaired by removing the damaged coupling beams and replacing them with new coupling beams.
Each new coupling beam will be designed using the provisions of the current building code, which requires diagonal reinforcing bars be installed as the primary shear resistance. A detail of the potential repair is shown in Figure 7-8.
7.4.6.2 Analysis Results The moderately damaged coupling beams are "repaired" in the model by revising their stiffness and strength based on the Component Damage Classification Guides. The heavily damaged coupling beams that were replaced are given stiffness values for initial, undamaged elements and displacement capacities as in FEMA 273 for flexure-governed beams with diagonal reinforcement, as shown in Figure 7-12 (c). The stiffness of the moderately damaged coupling beams is restored to 80 percent of the pre-event stiffness. The strength and displacement limits are restored to the pre-event values.
The strength and stiffness of the other components in 9, 000 - 8, 000 - -7, 000- = 6, 000-, 5, 000- #-4, 000 - 1) 3, 000 M 2, 000 co 1, 000 0- 0.5 the model are unchanged from their post-event condition.
The pushover analysis is then conducted using the same procedures and load patterns.
The progression of displacement events for the repaired structure is similar to that for the pre-event structure except that the replaced coupling beam does not reach its collapse prevention displacement limit. Figure 7-15 shows the pushover curve for the repaired structure.
Also shown on this curve is the pre-event pushover curve. The overall behavior of the repaired structure closely matches that of the pre-earthquake structure, as it was designed to do. The ratio of displacement capacity to demand, d2 I dd, is 0.53 for the life safety performance level and 0.66 for immediate occupancy, which are the same as those for the pre-event performance.
The displacement capacity for the repaired structure is governed by the component deformation limits of the coupling beams that were not replaced. Note that an effective upgrade measure might be to replace all coupling beams, as this would greatly increase global displacement capacity.
1 1.5 2 Roof Displacement (Inches) Figure 7-15 Comparison of Pre-event and Repaired Pushover Curves FEMA 307 Technical Resources Chapter 7: Example Application 7.4.7 Performance Restoration 7.5 Discussion of Results Measures 7.5.1 Discussion of Building 7.4.7.1 Structural Restoration Measures Performance Based on the relative performance analysis, replacing the three heavily Hypothetical repairs for damaged coupling beams and injecting relative the cracks in the moderately dam-performance aged coupling beams restores the method, Section 4.5 of performance of the structure. The volume of reinforced concrete coupling FEMA 306 beams to be removed is estimated to be about 41 cubic feet per coupling beam. The length of shear cracks to be injected in the moderately damaged coupling beams is estimated to be 100 feet.
7.4.7.2 Nonstructural Restoration Measures The Component Guides for the type RC1B components indicate that if cracks are less than 1/8 inch, the damage can be classified as Insignificant, and therefore structural repairs are not necessary. Two of the wall components had cracks that exceeded 1/16 inch. These wall components will have all of the cracks exceeding 1/16 inch repaired by injection with epoxy. The total length of these cracks is estimated to be about 22 feet.
The wall components with visible cracks will be repaired by patching the cracks with plaster and painting the entire wall. This repair is only intended to restore the visual appearance of the wall. Restoration of other nonstructural characteristics, such as water tightness and fire protection, is not necessary.
7.4.7.3 Summary of Restoration Measures and Costs Table 7-8 summarizes the repairs and estimated costs.
Additional costs related to inspection, evaluation, management, and indirect costs may also be involved.
The example building contains some typical features found in older concrete wall buildings, such as lightly reinforced concrete elements and discontinuous wall elements. Although the building was designed adequately according to the building code at the time, the design would not be appropriate by current building codes. Because of the improvement in seismic design provisions over the years, it is expected that the building, in its pre-event condition, would not meet the life safety performance level of FEMA 273.
The weak link in the building, as determined by analysis and confirmed with the field observations, is the shear capacity of the coupling beams. Although the analysis indicates that foundation rocking of the solid walls is probably the initial nonlinearity in the building, the rocking of the walls is not detrimental to the global behavior under the anticipated seismic demands.
In the section of the building in which the coupling beams were damaged, the coupled shear walls are discontinuous and are supported by columns at the ends of the walls. Normally, columns supporting discontinuous walls are susceptible to high compressive stresses, and consequently reduced ductility capacity, as the wall overturns. During the pushover analysis, the forces in the columns supporting the coupled walls remained within their capacity. The reason the columns were not overstressed is that the coupling beams acted as fuses for the coupled wall element. The overturning force in the columns could not be greater than the shear capacity of the coupling beams. If the strength of the replaced coupling beams is too large, the overturning force generated could cause failure of the columns below the Table7-8 Restoration Cost Estimate by the Relative Performance Method Item Unit Cost (1997 Dollars) Epoxy Injection $25.00 /lin ft Coupling Beam Removal and Replacement $74.00 / cu ft Patch and paint walls $0.60 /sq ft Replace ceiling tiles $2.00 /sq ft General Conditions, Fees, Overhead & Profit (@ 30%) Total Quantity 122 ft 122 ft3 10, 175 ft2 15, 000 ft2 Cost (1997 Dollars) $3, 050.
$9, 028.
$6, 105.
$ 30, 000.
$ 14, 455.
$ 62, 638.
FEMA 307 Technical Resources 
FEMA 307 Technical Resources Chapter 7: Example Application wall, resulting in a partial collapse of the building. For this reason, the capacity of the repaired coupling beam was designed to be similar to that of the previous coupling beam.
One of the advantages of the relative performance analysis is the ability to assess the behavior of structure and the influence of the behavior of the individual components on the overall behavior. Strengthening a single component may not produce a significant improvement in the overall performance if the progression of failure shifts to a less desirable mode. The pushover analysis of the repaired structure needs to consider the change in overall behavior caused by the repairs.
Because of the improved performance of the first story coupling beams that were replaced, these beams no longer control the global displacement limit of the structure. The force/displacement capacity of the second story coupling beams in their repaired condition is the same as in the pre-event condition. The displacement demand at which the second story coupling beams reach their acceptability limit is very close to the limit at which the first story coupling beams in the pre-event condition reached their limit. Therefore, the overall performance of the building is not improved substantially.
The information gained from these analyses can be used to assess whether an upgrade of the building to improve its performance may be cost effective.
7.5.2 Discussion of Methodology and Repair Costs This example has illustrated some of the important aspects in the FEMA 306 approach to assessing the earthquake damage to concrete and masonry wall buildings.
The example building represents an actual building that experienced a damaging earthquake.
FEMA 306 presents two methods for calculating the loss associated with earthquake damage, the direct method and the relative performance method. These methods are used to determine the loss, which is measured as the cost associated with returning the building to its pre-event performance. In this example, the cost of restoring the performance using the two methods produce the same result, principally because the repairs chosen in the relative performance method match those suggested by the direct method. In other buildings, there can be differences between the results obtained by the two methods.
The Nonlinear Static Procedure described in FEMA 273 is used in the relative performance method to assess the performance of the building in the pre-event, post-event and repaired conditions. This analysis method is relatively new and is still subject to further refinements.
This procedure can be time-consuming to implement properly. As the method and the analytical tools become further developed, this method should be easier to implement.
7.6 References ACI Committee 201, 1994, "Guide for Making a Condition Survey of Concrete in Service," Manual of Concrete Practice, American Concrete Institute, Detroit, Michigan.
CSI, 1997, SAP2000: Integrated Structural Design & Analysis Software, Computers and Structures Inc, Berkeley, California ATC, 1996, The Seismic Evaluation and Retrofit of Concrete Buildings, Applied Technology Council, ATC-40 Report, Redwood City, California.
Technical Resources FEMA 307 Technical Resources Appendix A. Component Damage Records for Building Evaluated in Example Application FEMA 307 Technical Resources Component Damage Records for Building Evaluated in Example Application Component Damage Record DI Building Name: Project ID: Prepared by: Concrete Shear Wall Building ATC 43 Example ATC Location Within Building: Date: Floor: 1st/ 2nd Column Line: 2 Component Type: 24-Sep-97 Sketch and Description of Damage: Legend: Crack Spall Z Crack Width in Mils (0.001 Inch) LNA 2 Crack Previously Filled with Epoxy ( Not Accessible Crack at Pre-existing Surface Patch Partition FEMA 307 Technical Resources Technical Resources FEMA 307 Component Damage Records for Building Evaluated in Example Application Component Damage Record D2 Building Name: Project ID: Prepared by: Concrete Shear Wall Building ATC43 Example ATC Location Within Building: Date: Floor: 1st/ 2nd Column Line: 2 Component Type: 24-Sep-97 Sketch and Description of Damage: X Legend: Crack Spall 0 Crack Width in Mils (0.001 Inch) [NA.
x<; Crack Previously Filled with Epoxy o Not Accessible Crack at Pre-existing Surface Patch WA/ Partition FEMA 307 Technical Resources 219 

Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D3 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building IATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: 7 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack zD Spall
-Z Crack Width in Mils (0.001Inch) LNA | 
X, Crack Previously Filled with Epoxy / Not Accessible 
Crack at Pre-existing Surface Patch 
k},AI Partition 
FEMA 307 
Technical Resources 
220 Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D4 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: 7 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001 Inch) LNA 4 
Crack Previously Filled with Epoxy ' Not Accessible 
Crack at Pre-existing Surface Patch 
I/I Partition 
FEMA 307 Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage RecordD5 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: 10 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
I-Crack Width in Mils (0.001Inch) KNA 1 
X X Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
I/i Partition 
FEMA 307 Technical Resources
Technical Resources FEMRA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D6 LL 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC43 Example ATC 
Location Within Building Date: 
Floor: 1st/ 2nd Column Line: 10 Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001Inch) LNAJ 
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch P 
J of Partition 223 
Technical Resources 
FEMA 307 Technical Resources 223 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D7 
Building Name: | Project ID: Prepared by: 
Concrete Shear Wall Building I ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/ 2nd Column Line: 15 Component Type: 24-Sep-97 
Sketch and Description of Damage: C Legend: -Crack Spall 0 Crack Width in Mils (0.001 Inch) LNA. 
y y Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch Partition 
Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage RecordD8 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/2nd Column Line: 15 Component Type: 24-Sep-97 
Sketch and Description to Damage: 
Legend: 
Crack A Spall 
Crack Width in Mils (0.001Inch) [LNA. 
X; Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch Partition I 
FEMA 307 Technical Resources 225 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D9 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/2nd Column Line: B Component Type: 24-Sep-97 I
Sketch and Description of Damage: 
Legend: -Crack M Spall 
Crack Width in Mils (0.001 Inch) LNA | 
X.X Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
Technical Resources FEMIA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D10 
Building Name: 
Concrete Shear Wall Building 
Location Within Building: 
Floor: 1st 2nd Column Line: B 
Sketch and Description of Damage:
Legend: -Crack Project ID: ATC 43 Example 
Component Type: 
4M Spall Prepared by: 
ATC. Date: 24-Sep-97 
3P Crack Width in Mils (0.001 Inch) 
LNA.E X, Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
307 Technical Resources 227 Partition
FEMA 307 Technical Resources 227 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record Dll 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building': Date: 
Floor: lst/2nd Column Line: B Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Legend: Crack Spall 
Crack Width in Mils (0.001 Inch) LSNA N 
Crack Previously Filled with Epoxy Not Accessible 
X Crack at Pre-existing Surface Patch 
Partition 
228 FEMA 307
Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D12 
Building Name:, Project ID: Prepared by 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2nd Column Line: B Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Legend: Crack Spall
2 i.O Crack Width in Mils (0.001 Inch) LNA | 
Crack Previously Filled with Epoxy Not Accessible 
X; Crack at Pre-existing Surface Patch 
Partition 
FEMA 307 Technical Resources 229 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D13 
Building Name: Project ID: Prepared by-
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building* Date: 
Floor: 1st/2nd Column Line: E Component: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001 Inch) [NA 
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D14 
Building Name: Project ID: prepared by: 
Concrete Shear Wall Building I ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/ 2nd Column Line: E Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
;0. Crack Width in Mils (0.001 Inch) [ NA| 
Crack Previously Filled with Epoxy Not Accessible 
)( X Crack at Pre-existing Surface Patch 
Partition 
FEMA 307 Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D15 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: 1st/2nd Column Line: G Component Type: 24-Sep-97 
Sketch and Description of Damage: j 
Legend: 
Crack A Spall 
30 Crack Width in Mils (0.001 Inch) [NA| 
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
Technical Resources FEMA 307 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D16 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2 nd Column Line: G Component Type: 24-Sep-97 
5ketch and 
Legend: 
Crack Spall 
30 Crack Width in Mils (0.001 Inch)
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch l: Partition 
FEMA 307 Technical Resources 233; 
Component Damage Records for Building Evaluated in Example Application 
FEMA 307
Technical Resources FEMA 307
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D18 
Building Name:- Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2nd Column Line: M Component Type: 24-Sep-97 
Sketch and Description of Damage: 
Legend: 
Crack Spall 
Crack Width in Mils (0.001 Inch) 
Crack Previously Filled with Epoxy Not Accessible 
A X Crack at Pre-existing Surface Patch 
l5/ Partition 
FEMA 307 Technical Resources 
Component Damage Records for Building Evaluated in Example Application 
Component Damage Record D19 
Building Name: Project ID: Prepared by: 
Concrete Shear Wall Building ATC 43 Example ATC 
Location Within Building: Date: 
Floor: lst/2nd Column Line: M Component Type: 24-Sep-97 
Sketch and Description of Damage: 
First 
I XI 
Ground 
Legend: 
Crack 
Crack Width in Mils (0.001 Inch) 
Spall
Crack Previously Filled with Epoxy Not Accessible 
Crack at Pre-existing Surface Patch 
Partition 
236 
Technical Resources 
Technical Resources FEMA 307 
ATC-43Project Participants 
ATC MANAGEMENT 
Mr. Christopher Rojahn, 
Principal Investigator 
Applied Technology Council 
555 Twin Dolphin Drive, Suite 550 
Redwood City, CA 94065 
Technical Management Committee 
Prof. Dan Abrams 
University of Illinois 
1245 Newmark Civil Eng'g. Lab., MC 250 
205 North Mathews Avenue 
Urbana, IL 61801-2397 
Mr. James Hill 
James A. Hill & Associates, Inc. 
1349 East 28th Street 
Signal Hill, CA 90806 
FEMA/PARR Representatives 
Mr. Timothy McCormick 
PaRR Task Manager 
Dewberry & Davis 
8401 Arlington Boulevard 
Fairfax, VA 22031-4666 
Mr. Mark Doroudian 
PaRR Representative 
42 Silkwood 
I Aliso Viejo, CA 92656 
Mr. Craig Comartin, 
Co-PI and Project Director 
7683 Andrea Avenue 
Stockton, CA 95207 
Mr. Andrew T. Merovich 
A.T. Merovich & Associates, Inc. 
1163 Francisco Blvd., Second Floor 
San Rafael, CA 94901 
Prof. Jack Moehle 
Earthquake Engineering Research Center 
University of California at Berkeley 
1301 South 46th Street 
Richmond, CA 94804 
Prof. Robert Hanson 
FEMA Technical Monitor 
74 North Pasadena Avenue, CA-1009-DR 
Parsons Bldg., West Annex, Room 308 
Pasadena, CA 91103 
FEMA 307 Technical Resources 
Materials Working Group 
Dr. Joe Maffei, Group Leader 
Consulting Structural Engineer 
148 Hermosa Avenue 
Oakland California 
Mr. Brian Kehoe, Lead Consultant 
Wiss, Janney, Elstner Associates, Inc. 
2200 Powell Street, Suite 925 
Emeryville, CA 94608 
Dr. Greg Kingsley 
KL&A of Colorado 
805 14th Street 
Golden, CO 80401 
Analysis Working Group 
Prof. Mark Aschheim, Group Leader 
University of Illinois at Urbana 
2118 Newmark CE Lab 
205 North Mathews, MC 250 
Urbana, IL 61801 
Project Review Panel 
Mr. Gregg J. Borchelt 
Brick Institute of America 
11490 Commerce Park Drive, #300 
Reston, VA 20191 
Dr. Gene Corley 
Construction Technology Labs 
5420 Old Orchard Road 
Skokie, IL 60077-1030 
Mr. Edwin Huston 
Smith & Huston 
Plaza 600 Building, 6th & Stewart, #620 
Seattle, WA 98101 
Prof. Richard E. Klingner 
University of Texas 
Civil Engineering Department 
Cockbell Building, Room 4-2 
Austin, TX 78705 
ATC-43 Project Participants 
Mr. Bret Lizundia 
Rutherford & Chekene 
303 Second Street, Suite 800 North 
San Francisco, CA 94107 
Prof. John Mander 
SUNY at Buffalo 
Department of Civil Engineering 
212 Ketter Hall 
Buffalo, NY 14260 
Prof. Mete Sozen, Senior Consultant 
Purdue University, School of Engineering 
1284 Civil Engineering Building 
West Lafayette, IN 47907-1284 
Mr. Vilas Mujumdar 
Office of Regulation Services 
Division of State Architect 
General Services 
1300 I Street, Suite 800 
Sacramento, CA 95814 
Dr. Hassan A. Sassi 
Governors Office of Emergency Services 
74 North Pasadena Avenue 
Pasadena, CA 91103 
Mr. Carl Schulze 
Libby Engineers 
4452 Glacier Avenue 
San Diego, CA 92120 
Mr. Daniel Shapiro 
SOH & Associates 
550 Kearny Street, Suite 200 
San Francisco, CA 94108 
Technical Resources 
Technical Resources FEMA 307 
ATC-43 Project Participants 
Prof. James K. Wight Mr. Eugene Zeller 
University of Michigan Long Beach Department of Building & Safety 
Department of Civil Engineering 333 W. Ocean Boulevard, Fourth Floor 
2368 G Brown Long Beach, CA 90802
Ann Arbor, MI 48109-2125
Technical Resources 
FEMA 307 Technical Resources 
Applied Technology Council Projects And Report 
Information 
One of the primary purposes of Applied Technology 
Council is to develop resource documents that translate 
and summarize useful information to practicing engineers. 
This includes the development of guidelines and 
manuals, as well as the development of research recommendations 
for specific areas determined by the profession. 
ATC is not a code development organization, 
although several of the ATC project reports serve as 
resource documents for the development of codes, standards 
and specifications. 
Applied Technology Council conducts projects that 
meet the following criteria: 
1. The primary audience or benefactor is the design 
practitioner in structural engineering. 
2. A cross section or consensus of engineering opinion 
is required to be obtained and presented by a neutral 
source. 
3. The project fosters the advancement of structural 
engineering practice. 
A brief description of several major completed projects 
and reports is given in the following section. Funding 
for projects is obtained from government agencies and 
tax-deductible contributions from the private sector. 
ATC-1: This project resulted in five papers that were 
Published as part of Building Practices for Disaster 
Mitigation, Building Science Series 46, proceedings of a 
workshop sponsored by the National Science Foundation 
(NSF) and the National Bureau of Standards 
(NBS). Available through the National Technical Information 
Service (NTIS), 5285 Port Royal Road, Springfield, 
VA 22151, as NTIS report No. COM-73-50188. 
ATC-2: The report, An Evaluation of a Response Spectrum 
Approach to Seismic Design of Buildings, was 
funded by NSF and NBS and was conducted as part of 
the Cooperative Federal Program in Building Practices 
for Disaster Mitigation. Available through the ATC 
office. (Published 1974, 270 Pages) 
ABSTRACT: This study evaluated the applicability 
and cost of the response spectrum approach to seismic 
analysis and design that was proposed by various 
segments of the engineering profession. 
Specific building designs, design procedures and 
parameter values were evaluated for future application. 
Eleven existing buildings of varying dimensions 
were redesigned according to the procedures. 
ATC-3: The report, Tentative Provisions for the Development 
of Seismic Regulations for Buildings (ATC-3-
06), was funded by NSF and NBS. The second printing 
of this report, which includes proposed amendments, is 
available through the ATC office. (Published 1978, 
amended 1982, 505 pages plus proposed amendments) 
ABSTRACT: The tentative provisions in this document 
represent the results of a concerted effort by a 
multi-disciplinary team of 85 nationally recognized 
experts in earthquake engineering. The provisions 
serve as the basis for the seismic provisions of the 
1988 Uniform Building Code and the 1988 and subsequent 
issues of the NEHRP Recommended Provisions for 
the Development of Seismic Regulation for 
New Buildings. The second printing of this document 
contains proposed amendments prepared by a 
joint committee of the Building Seismic Safety 
Council (BSSC) and the NBS. 
ATC-3-2: The project, Comparative Test Designs of 
Buildings Using ATC-3-06 Tentative Provisions, was 
funded by NSF. The project consisted of a study to 
develop and plan a program for making comparative 
test designs of the ATC-3-06 Tentative Provisions. The 
project report was written to be used by the Building 
Seismic Safety Council in its refinement of the ATC-3-
06 Tentative Provisions. 
ATC-3-4: The report, Redesign of Three Multistory 
Buildings: A Comparison Using ATC-3-06 and 1982 
Uniform Building Code Design Provisions, was published 
under a grant from NSF. Available through the 
ATC office. (Published 1984, 112 pages) 
ABSTRACT: This report evaluates the cost and technical 
impact of using the 1978 ATC-3-06 report, 
Tentative Provisions for the Development of Seismic 
Regulations for Buildings, as amended by a joint 
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committee of the Building Seismic Safety Council 
and the National Bureau of Standards in 1982. The 
evaluations are based on studies of three existing 
California buildings redesigned in accordance with 
the ATC-3-06 Tentative Provisions and the 1982 
Uniform Building Code. Included in the report are 
recommendations to code implementing bodies. 
ATC-3-5: This project, Assistance for First Phase of 
ATC-3-06 Trial Design Program Being Conducted by 
the Building Seismic Safety Council, was funded by the 
Building Seismic Safety Council to provide the services 
of the ATC Senior Consultant and other ATC personnel 
to assist the BSSC in the conduct of the first phase of its 
Trial Design Program. The first phase provided for trial 
designs conducted for buildings in Los Angeles, Seattle, 
Phoenix, and Memphis. 
ATC-3-6: This project, Assistance for Second Phase of 
ATC-3-06 Trial Design Program Being Conducted by 
the Building Seismic Safety Council, was funded by the 
Building Seismic Safety Council to provide the services 
of the ATC Senior Consultant and other ATC personnel 
to assist the BSSC in the conduct of the second phase of 
its Trial Design Program. The second phase provided 
for trial designs conducted for buildings in New York, 
Chicago, St. Louis, Charleston, and Fort Worth. 
ATC-4: The report, A Methodology for Seismic Design 
and Construction of Single-Family Dwellings, was published 
under a contract with the Department of Housing 
and Urban Development (HUD). Available through the 
ATC office. (Published 1976, 576 pages) 
ABSTRACT:
This report presents the results of an 
in-depth effort to develop design and construction 
details for single-family residences that minimize 
the potential economic loss and life-loss risk associated 
with earthquakes. The report: (1) discusses 
the ways structures behave when subjected to seismic 
forces, (2) sets forth suggested design criteria 
for conventional layouts of dwellings constructed 
with conventional materials, (3) presents construction 
details that do not require the designer to perform 
analytical calculations, (4) suggests 
procedures for efficient plan-checking, and (5) presents 
recommendations including details and schedules 
for use in the field by construction personnel 
and building inspectors. 
ATC-4-1: The report, The Home Builders Guide for 
Earthquake Design, was published under a contract 
with HUD. Available through the ATC office. (Published 
1980, 57 pages) 
ABSTRACT: This report is an abridged version of 
the ATC-4 report. The concise, easily understood 
text of the Guide is supplemented with illustrations 
and 46 construction details. The details are provided 
to ensure that houses contain structural features 
that are properly positioned, dimensioned and 
constructed to resist earthquake forces. A brief 
description is included on how earthquake forces 
impact on houses and some precautionary constraints 
are given with respect to site selection and 
architectural designs. 
ATC-5: The report, Guidelines for Seismic Design and 
Construction of Single-Story Masonry Dwellings in 
Seismic Zone 2, was developed under a contract with 
HUD. Available through the ATC office. (Published 
1986, 38 pages) 
ABSTRACT: The report offers a concise methodology 
for the earthquake design and construction of 
single-story masonry dwellings in Seismic Zone 2 
of the United States, as defined by the 1973 Uniform 
Building Code. The Guidelines are based in 
part on shaking table tests of masonry construction 
conducted at the University of California at Berkeley 
Earthquake Engineering Research Center. The 
report is written in simple language and includes 
basic house plans, wall evaluations, detail drawings, 
and material specifications. 
ATC-6: The report, Seismic Design Guidelines for 
Highway Bridges, was published under a contract with 
the Federal Highway Administration (FHWA). Available 
through the ATC office. (Published 1981, 210 
pages) 
ABSTRACT: The Guidelines are the recommendations 
of a team of sixteen nationally recognized 
experts that included consulting engineers, academics, 
state and federal agency representatives from 
throughout the United States. The Guidelines 
embody several new concepts that were significant 
departures from then existing design provisions. 
Included in the Guidelines are an extensive commentary, 
an example demonstrating the use of the 
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Guidelines, and summary reports on 21 bridges 
redesigned in accordance with the Guidelines. 
The guidelines have been adopted by the American 
Association of Highway and Transportation 
Officials as a guide specification. 
ATC-6-1: The report, Proceedings of a Workshop 
on Earthquake Resistance of Highway Bridges, was 
published under a grant from NSF Available 
through the ATC office. (Published 1979, 625 pages) 
ABSTRACT: The report includes 23 state-of-the-
art and state-of-practice papers on earthquake 
resistance of highway bridges. Seven of the 
twenty-three papers were authored by participants 
from Japan, New Zealand and Portugal. 
The Proceedings also contain recommendations 
for future research that were developed by the 45 
workshop participants. 
ATC-6-2: The report, Seismic Retrofitting Guidelines 
for Highway Bridges, was published under a 
contract with FHWA. Available through the ATC 
office. (Published 1983, 220 pages) 
ABSTRACT: The Guidelines are the recommendations 
of a team of thirteen nationally recognized 
experts that included consulting engineers, 
academics, state highway engineers, and federal 
agency representatives. The Guidelines, applicable 
for use in all parts of the United States, 
include a preliminary screening procedure, 
methods for evaluating an existing bridge in 
detail, and potential retrofitting measures for the 
most common seismic deficiencies. Also 
included are special design requirements for various 
retrofitting measures. 
ATC-7: The report, Guidelines for the Design of 
Horizontal Wood Diaphragms, was published under 
a grant from NSF. Available through the ATC 
office. (Published 1981, 190 pages) 
ABSTRACT: Guidelines are presented for designing 
roof and floor systems so these can function 
as horizontal diaphragms in a lateral force resisting 
system. Analytical procedures, connection 
details and design examples are included in the 
Guidelines. 
ATC-7-1: The report, Proceedings of a Workshop 
of Design of Horizontal Wood Diaphragms, was 
published under a grant from NSF. Available 
through the ATC office. (Published 1980, 302 pages) 
ABSTRACT: The report includes seven papers on 
state-of-the-practice and two papers on recent 
research. Also included are recommendations 
for future research that were developed by the 35 
workshop participants. 
ATC-8: This report, Proceedings of a Workshop on 
the Design of Prefabricated Concrete Buildings for 
Earthquake Loads, was funded by NSF. Available 
through the ATC office. (Published 1981, 400 pages) 
ABSTRACT: The report includes eighteen state-
of-the-art papers and six summary papers. Also 
included are recommendations for future 
research that were developed by the 43 workshop 
participants. 
ATC-9: The report, An Evaluation of the Imperial 
County Services Building Earthquake Response and 
Associated Damage, was published under a grant 
from NSF. Available through the ATC office. (Published 
1984, 231 pages) 
ABSTRACT: The report presents the results of an 
in-depth evaluation of the Imperial County Services 
Building, a 6-story reinforced concrete 
frame and shear wall building severely damaged 
by the October 15, 1979 Imperial Valley, California, 
earthquake. The report contains a review 
and evaluation of earthquake damage to the 
building; a review and evaluation of the seismic 
design; a comparison of the requirements of various 
building codes as they relate to the building; 
and conclusions and recommendations pertaining 
to future building code provisions and future 
research needs. 
ATC-10: This report, An Investigation of the Correlation 
Between Earthquake Ground Motion and 
Building Performance, was funded by the U.S. Geological 
Survey (USGS). Available through the ATC 
office. (Published 1982, 114 pages) 
ABSTRACT: The report contains an in-depth analytical 
evaluation of the ultimate or limit capacity 
of selected representative building framing 
types, a discussion of the factors affecting the 
seismic performance of buildings, and a sum-
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summary and comparison of seismic design and seismic 
risk parameters currently in widespread use. 
ATC-10-1: This report, Critical Aspects of Earthquake 
Ground Motion and Building Damage Potential, was 
co-funded by the USGS and the NSF. Available 
through the ATC office. (Published 1984, 259 pages) 
ABSTRACT: This document contains 19 state-of-
the-art papers on ground motion, structural 
response, and structural design issues presented by 
prominent engineers and earth scientists in an ATC 
seminar. The main theme of the papers is to identify 
the critical aspects of ground motion and building 
performance that currently are not being 
considered in building design. The report also contains 
conclusions and recommendations of working 
groups convened after the Seminar. 
ATC-11: The report, Seismic Resistance of Reinforced 
Concrete Shear Walls and Frame Joints: Implications 
of Recent Research for Design Engineers, was published 
under a grant from NSF. Available through the 
ATC office. (Published 1983, 184 pages) 
ABSTRACT: This document presents the results of 
an in-depth review and synthesis of research reports 
pertaining to cyclic loading of reinforced concrete 
shear walls and cyclic loading of joint reinforced 
concrete frames. More than 125 research reports 
published since 1971 are reviewed and evaluated in 
this report. The preparation of the report included a 
consensus process involving numerous experienced 
design professionals from throughout the United 
States. The report contains reviews of current and 
past design practices, summaries of research developments, 
and in-depth discussions of design implications 
of recent research results. 
ATC-12: This report, Comparison of United States and 
New Zealand Seismic Design Practices for Highway 
Bridges, was published under a grant from NSF. Available 
through the ATC office. (Published 1982, 270 
pages) 
ABSTRACT: The report contains summaries of all 
aspects and innovative design procedures used in 
New Zealand as well as comparison of United 
States and New Zealand design practice. Also 
included are research recommendations developed 
at a 3-day workshop in New Zealand attended by 16 
U.S. and 35 New Zealand bridge design engineers 
and researchers. 
ATC-12-1: This report, Proceedings of Second Joint 
U.S.-New Zealand Workshop on Seismic Resistance of 
Highway Bridges, was published under a grant from 
NSF. Available through the ATC office. (Published 
1986, 272 pages) 
ABSTRACT: This report contains written versions of 
the papers presented at this 1985 Workshop as well 
as a list and prioritization of workshop recommendations. 
Included are summaries of research 
projects being conducted in both countries as well 
as state-of-the-practice papers on various aspects of 
design practice. Topics discussed include bridge 
design philosophy and loadings; design of columns, 
footings, piles, abutments and retaining structures; 
geotechnical aspects of foundation design; seismic 
analysis techniques; seismic retrofitting; case studies 
using base isolation; strong-motion data acquisition 
and interpretation; and testing of bridge 
components and bridge systems. 
ATC-13: The report, Earthquake Damage Evaluation 
Data for California, was developed under a contract 
with the Federal Emergency Management Agency 
(FEMA). Available through the ATC office. (Published 
1985, 492 pages) 
ABSTRACT: This report presents expert-opinion 
earthquake damage and loss estimates for industrial, 
commercial, residential, utility and transportation 
facilities in California. Included are damage 
probability matrices for 78 classes of structures and 
estimates of time required to restore damaged facilities 
to pre-earthquake usability. The report also 
describes the inventory information essential for 
estimating economic losses and the methodology 
used to develop loss estimates on a regional basis. 
ATC-14: The report, Evaluating the Seismic Resistance 
of Existing Buildings, was developed under a grant from 
the NSF. Available through the ATC office. (Published 
1987, 370 pages) 
ABSTRACT: This report, written for practicing 
structural engineers, describes a methodology for 
performing preliminary and detailed building seismic 
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evaluations. The report contains a state-of-
practice review; seismic loading criteria; data collection 
procedures; a detailed description of the 
building classification system; preliminary and 
detailed analysis procedures; and example case 
studies, including nonstructural considerations. 
ATC-15: The report, Comparison of Seismic Design 
Practices in the United States and Japan, was published 
under a grant from NSF. Available through the ATC 
office. (Published 1984, 317 pages) 
ABSTRACT: The report contains detailed technical 
papers describing design practices in the United 
States and Japan as well as recommendations emanating 
from a joint U.S.-Japan workshop held in 
Hawaii in March, 1984. Included are detailed 
descriptions of new seismic design methods for 
buildings in Japan and case studies of the design of 
specific buildings (in both countries). The report 
also contains an overview of the history and objectives 
of the Japan Structural Consultants Association. 
ATC-15-1: The report, Proceedings of Second U.S.-
Japan Workshop on Improvement of Building Seismic 
Design and Construction Practices, was published 
under a grant from NSF. Available through the ATC 
office. (Published 1987, 412 pages) 
ABSTRACT: This report contains 23 technical 
papers presented at this San Francisco workshop in 
August, 1986, by practitioners and researchers from 
the U.S. and Japan. Included are state-of-the-practice papers and case studies of actual building 
designs and information on regulatory, contractual, 
and licensing issues. 
ATC-15-2: The report, Proceedings of Third U.S.-
Japan Workshop on Improvement of Building Structural 
Design and Construction Practices, was published 
jointly by ATC and the Japan Structural Consultants 
Association. Available through the ATC office. (Published 
1989, 358 pages) 
ABSTRACT: This report contains 21 technical 
papers presented at this Tokyo, Japan, workshop in 
July, 1988, by practitioners and researchers from 
the U.S., Japan, China, and New Zealand. Included 
are state-of-the-practice papers on various topics, 
including braced steel frame buildings, beam-column joints in reinforced concrete buildings, summaries 
of comparative U. S. and Japanese design, 
and base isolation and passive energy dissipation 
devices. 
ATC-15-3: The report, Proceedings of Fourth U.S.-
Japan Workshop on Improvement of Building Structural 
Design and Construction Practices, was published 
jointly by ATC and the Japan Structural Consultants 
Association. Available through the ATC office. (Published 
1992, 484 pages) 
ABSTRACT: This report contains 22 technical 
papers presented at this Kailua-Kona, Hawaii, 
workshop in August, 1990, by practitioners and 
researchers from the United States, Japan, and Peru. 
Included are papers on postearthquake building 
damage assessment; acceptable earth-quake damage; 
repair and retrofit of earthquake damaged 
buildings; base-isolated buildings, including Architectural 
Institute of Japan recommendations for 
design; active damping systems; wind-resistant 
design; and summaries of working group conclusions 
and recommendations. 
ATC-15-4: The report, Proceedings of Fifth U.S. Japan 
Workshop on Improvement of Building Structural 
Design and Construction Practices, was published 
jointly by ATC and the Japan Structural Consultants 
Association. Available through the ATC office. (Published 
1994, 360 pages) 
ABSTRACT: This report contains 20 technical 
papers presented at this San Diego, California 
workshop in September, 1992. Included are papers 
on performance goals/acceptable damage in seismic 
design; seismic design procedures and case studies; 
construction influences on design; seismic isolation 
and passive energy dissipation; design of irregular 
structures; seismic evaluation, repair and upgrading; 
quality control for design and construction; and 
summaries of working group discussions and recommendations. 
ATC-16: This project, Development of a 5-Year Plan 
for Reducing the Earthquake Hazards Posed by Existing 
Nonfederal Buildings, was funded by FEMA and was 
conducted by a joint venture of ATC, the Building Seismic 
Safety Council and the Earthquake Engineering 
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Research Institute. The project involved a workshop in 
Phoenix, Arizona, where approximately 50 earthquake 
specialists met to identify the major tasks and goals for 
reducing the earthquake hazards posed by existing non-
federal buildings nationwide. The plan was developed 
on the basis of nine issue papers presented at the workshop 
and workshop working group discussions. The 
Workshop Proceedings and Five-Year Plan are available 
through the Federal Emergency Management Agency, 
500 "C" Street, S.W., Washington, DC 20472. 
ATC-17: This report Proceedings of a Seminar and 
Workshop on Base Isolation and Passive Energy Dissipation, 
was published under a grant from NSF. Available 
through the ATC office. (Published 1986, 478 
pages) 
ABSTRACT:
The report contains 42 papers describing 
the state-of-the-art and state-of-the-practice in 
base-isolation and passive energy-dissipation technology. 
Included are papers describing case studies 
in the United States, applications and developments 
worldwide, recent innovations in technology development, 
and structural and ground motion issues. 
Also included is a proposed 5-year research agenda 
that addresses the following specific issues: (1) 
strong ground motion; (2) design criteria; (3) materials, 
quality control, and long-term reliability; (4) 
life cycle cost methodology; and (5) system 
response. 
ATC-17-1: This report, Proceedings of a Seminar on 
Seismic Isolation, Passive Energy Dissipation and 
Active Control, was published under a grant from NSF. 
Available through the ATC office. (Published 1993, 841 
pages) 
The 2-volume report documents 70
ABSTRACT: 
technical papers presented during a two-day seminar 
in San Francisco in early 1993. Included are 
invited theme papers and competitively selected 
papers on issues related to seismic isolation systems, 
passive energy dissipation systems, active 
control systems and hybrid systems. 
ATC-18: The report, Seismic Design Criteria for 
Bridges and Other Highway Structures: Current and 
Future, was published under a contract from the Multidisciplinary 
Center for Earthquake Engineering 
Research (formerly NCEER), with funding from the 
Federal Highway Administration. Available through the 
ATC office. (Published 1997, 152 pages) 
ABSTRACT: This report documents the findings of a 
4-year project to review and assess current seismic 
design criteria for new highway construction. The 
report addresses performance criteria, importance 
classification, definitions of seismic hazard for 
areas where damaging earthquakes have longer 
return periods, design ground motion, duration 
effects, site effects, structural response modification 
factors, ductility demand, design procedures, foundation 
and abutment modeling, soil-structure interaction, 
seat widths, joint details and detailing 
reinforced concrete for limited ductility in areas 
with low-to-moderate seismic activity. The report 
also provides lengthy discussion on future directions 
for code development and recommended 
research and development topics. 
ATC-19: The report, Structural Response Modification 
Factors was funded by NSF and NCEER. Available 
through the ATC office. (Published 1995, 70 pages) 
ABSTRACT: This report addresses structural 
response modification factors (R factors), which are 
used to reduce the seismic forces associated with 
elastic response to obtain design forces. The report 
documents the basis for current R values, how R 
factors are used for seismic design in other countries, 
a rational means for decomposing R into key 
components, a framework (and methods) for evaluating 
the key components of R, and the research 
necessary to improve the reliability of engineered 
construction designed using R factors. 
ATC-20: The report, Procedures for Postearthquake 
Safety Evaluation of Buildings, was developed under a 
contract from the California Office of Emergency Services 
(OES), California Office of Statewide Health 
Planning and Development (OSHPD) and FEMA. 
Available through the ATC office (Published 1989, 152 
pages) 
ABSTRACT: This report provides procedures and 
guidelines for making on-the-spot evaluations and 
decisions regarding continued use and occupancy 
of earthquake damaged buildings. Written specifically 
for volunteer structural engineers and building 
inspectors, the report includes rapid and detailed 
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evaluation procedures for inspecting buildings and 
posting them as "inspected" (apparently safe), "limited 
entry" or "unsafe". Also included are special 
procedures for evaluation of essential buildings 
(e.g., hospitals), and evaluation procedures for non-
structural elements, and geotechnical hazards. 
ATC-20-1: The report, Field Manual: Postearthquake 
Safety Evaluation of Buildings, was developed under a 
contract from OES and OSHPD. Available through the 
ATC office (Published 1989, 114 pages) 
ABSTRACT:
This report, a companion Field Manual 
for the ATC-20 report, summarizes the 
postearthquake safety evaluation procedures in 
brief concise format designed for ease of use in the 
field. 
ATC-20-2: The report, Addendum to the ATC-20 
Postearthquake Building Safety Procedures was published 
under a grant from the NSF and funded by the 
USGS. Available through the ATC office. (Published 
1995, 94 pages) 
ABSTRACT:
This report provides updated assessment 
forms, placards, and procedures that are based 
on an in-depth review and evaluation of the widespread 
application of the ATC-20 procedures following 
five earthquakes occurring since the initial 
release of the ATC-20 report in 1989. 
ATC-20-3: The report, Case Studies in Rapid 
Postearthquake Safety Evaluation of Buildings, was 
funded by ATC and R. P. Gallagher Associates. Available 
through the ATC office. (Published 1996, 295 
pages) 
ABSTRACT: This report contains 53 case studies 
using the ATC-20 Rapid Evaluation procedure. 
Each case study is illustrated with photos and 
describes how a building was inspected and evaluated 
for life safety, and includes a completed safety 
assessment form and placard. The report is intended 
to be used as a training and reference manual for 
building officials, building inspectors, civil and 
structural engineers, architects, disaster workers, 
and others who may be asked to perform safety 
evaluations after an earthquake. 
ATC-20-T: The report, Postearthquake Safety Evaluation 
of Buildings Training Manual was developed under 
a contract with FEMA. Available through the ATC 
office. (Published 1993, 177 pages; 160 slides) 
ABSTRACT: This training manual is intended to 
facilitate the presentation of the contents of the 
ATC-20 and ATC-20-1. The training materials consist 
of 160 slides of photographs, schematic drawings 
and textual information and a companion 
training presentation narrative coordinated with the 
slides. Topics covered include: posting system; 
evaluation procedures; structural basics; wood 
frame, masonry, concrete, and steel frame structures; 
nonstructural elements; geotechnical hazards; 
hazardous materials; and field safety. 
ATC-21: The report, Rapid Visual Screening of Buildings for 
Potential Seismic Hazards: A Handbook, was 
developed under a contract from FEMA. Available 
through the ATC office. (Published 1988, 185 pages) 
ABSTRACT: This report describes a rapid visual 
screening procedure for identifying those buildings 
that might pose serious risk of loss of life and 
injury, or of severe curtailment of community services, 
in case of a damaging earthquake. The 
screening procedure utilizes a methodology based 
on a "sidewalk survey" approach that involves identification 
of the primary structural load resisting 
system and building materials, and assignment of a 
basic structural hazards score and performance 
modification factors based on observed building 
characteristics. Application of the methodology 
identifies those buildings that are potentially hazardous 
and should be analyzed in more detail by a 
professional engineer experienced in seismic 
design. 
ATC-21-1: The report, Rapid Visual Screening of 
Buildings for Potential Seismic Hazards: Supporting 
Documentation, was developed under a contract from 
FEMA. Available through the ATC office. (Published 
1988, 137 pages) 
ABSTRACT: Included in this report are (1) a review 
and evaluation of existing procedures; (2) a listing 
of attributes considered ideal for a rapid visual 
screening procedure; and (3) a technical discussion 
of the recommended rapid visual screening procedure 
that is documented in the ATC-21 report. 
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ATC-21-2: The report, Earthquake Damaged Buildings: 
An Overview of Heavy Debris and Victim Extrication, 
was developed under a contract from FEMA. 
(Published 1988, 95 pages) 
ABSTRACT: Included in this report, a companion 
volume to the ATC-21 and ATC-21-1 reports, is 
state-of-the-art information on (1) the identification 
of those buildings that might collapse and trap victims 
in debris or generate debris of such a size that 
its handling would require special or heavy lifting 
equipment; (2) guidance in identifying these types 
of buildings, on the basis of their major exterior features, 
and (3) the types and life capacities of equipment 
required to remove the heavy portion of the 
debris that might result from the collapse of such 
buildings. 
ATC-21-T: The report, Rapid Visual Screening of 
Buildings for Potential Seismic Hazards Training Manual 
was developed under a contract with FEMA. Available 
through the ATC office. (Published 1996, 135 
pages; 120 slides) 
ABSTRACT: This training manual is intended to 
facilitate the presentation of the contents of the 
ATC-21report. The training materials consist of 
120 slides and a companion training presentation 
narrative coordinated with the slides. Topics covered 
include: description of procedure, building 
behavior, building types, building scores, occupancy 
and falling hazards, and implementation. 
ATC-22: The report, A Handbook for Seismic Evaluation 
of Existing Buildings (Preliminary), was developed 
under a contract from FEMA. Available through the 
ATC office. (Originally published in 1989; revised by 
BSSC and published as the NEHRP Handbook for Seismic 
Evaluation of Existing Buildings in 1992, 211 
pages) 
ABSTRACT: This handbook provides a methodology 
for seismic evaluation of existing buildings of 
different types and occupancies in areas of different 
seismicity throughout the United States. The methodology, 
which has been field tested in several programs 
nationwide, utilizes the information and 
procedures developed for and documented in the 
ATC-14report. The handbook includes checklists, 
diagrams, and sketches designed to assist the user. 
ATC-22-1: The report, Seismic Evaluation of Existing 
Buildings: Supporting Documentation, was developed 
under a contract from FEMA. (Published 1989, 160 
pages) 
ABSTRACT: Included in this report, a companion 
volume to the ATC-22 report, are (1) a review and 
evaluation of existing buildings seismic evaluation 
methodologies; (2) results from field tests of the 
ATC-14 methodology; and (3) summaries of evaluations 
of ATC-14 conducted by the National Center 
for Earthquake Engineering Research (State University 
of New York at Buffalo) and the City of San 
Francisco. 
ATC-23A: The report, General Acute Care Hospital 
Earthquake Survivability Inventory for California, Part 
A: Survey Description, Summary of Results, Data Analysis 
and Interpretation, was developed under a contract 
from the Office of Statewide Health Planning and 
Development (OSHPD), State of California. Available 
through the ATC office. (Published 1991, 58 pages) 
ABSTRACT: This report summarizes results from a 
seismic survey of 490 California acute care hospitals. 
Included are a description of the survey procedures 
and data collected, a summary of the data, 
and an illustrative discussion of data analysis and 
interpretation that has been provided to demonstrate 
potential applications of the ATC-23 database. 
ATC-23B: The report, General Acute Care Hospital 
Earthquake Survivability Inventory for California, Part 
B: Raw Data, is a companion document to the ATC23A 
Report and was developed under the above-mentioned contract from OSHPD. Available through the 
ATC office. (Published 1991, 377 pages) 
ABSTRACT: Included in this report are tabulations 
of raw general site and building data for 490 acute 
care hospitals in California. 
ATC-24: The report, Guidelines for Seismic Testing of 
Components of Steel Structures, was jointly funded by 
the American Iron and Steel Institute (AISI), American 
Institute of Steel Construction (AISC), National Center 
for Earthquake Engineering Research (NCEER), and 
NSF. Available through the ATC office. (Published 
1992, 57 pages) 
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ABSTRACT: This report provides guidance for most 
cyclic experiments on components of steel structures 
for the purpose of consistency in experimental 
procedures. The report contains recommendations 
and companion commentary pertaining to loading 
histories, presentation of test results, and other 
aspects of experimentation. The recommendations 
are written specifically for experiments with slow 
cyclic load application. 
ATC-25: The report, Seismic Vulnerability and Impact 
of Disruption of Lifelines in the Conterminous United 
States, was developed under a contract from FEMA. 
Available through the ATC office. (Published 1991, 440 
pages) 
ABSTRACT:
Documented in this report is a national 
overview of lifeline seismic vulnerability and 
impact of disruption. Lifelines considered include 
electric systems, water systems, transportation systems, 
gas and liquid fuel supply systems, and emergency 
service facilities (hospitals, fire and police 
stations). Vulnerability estimates and impacts 
developed are presented in terms of estimated first 
approximation direct damage losses and indirect 
economic losses. 
ATC-25-1: The report, A Model Methodology for 
Assessment of Seismic Vulnerability and Impact of Disruption 
of Water Supply Systems, was developed under 
a contract from FEMA. Available through the ATC 
office. (Published 1992, 147 pages) 
ABSTRACT:
This report contains a practical methodology 
for the detailed assessment of seismic vulnerability 
and impact of disruption of water supply 
systems. The methodology has been designed for 
use by water system operators. Application of the 
methodology enables the user to develop estimates 
of direct damage to system components and the 
time required to restore damaged facilities to pre-
earthquake usability. Suggested measures for mitigation 
of seismic hazards are also provided. 
ATC-28: The report, Development of Recommended 
Guidelines for Seismic Strengthening of Existing Buildings, 
Phase I: Issues Identification and Resolution, was 
developed under a contract with FEMA. Available 
through the ATC office. (Published 1992, 150 pages) 
ABSTRACT:
This report identifies and provides resolutions 
for issues that will affect the development of 
guidelines for the seismic strengthening of existing 
buildings. Issues addressed include: implementation 
and format, coordination with other efforts, 
legal and political, social, economic, historic buildings, 
research and technology, seismicity and mapping, 
engineering philosophy and goals, issues 
related to the development of specific provisions, 
and nonstructural element issues. 
ATC-29: The report Proceedings of a Seminar and 
Workshop on Seismic Design and Performance of 
Equipment and Nonstructural Elements in Buildings 
and Industrial Structures, was developed under a grant 
from NCEER and NSF. Available through the ATC 
office. (Published 1992, 470 pages) 
ABSTRACT:
These Proceedings contain 35 papers 
describing state-of-the-art technical information 
pertaining to the seismic design and performance of 
equipment and nonstructural elements in buildings 
and industrial structures. The papers were presented 
at a seminar in Irvine, California in 1990. Included 
are papers describing current practice, codes and 
regulations; earthquake performance; analytical and 
experimental investigations; development of new 
seismic qualification methods; and research, practice, 
and code development needs for specific elements 
and systems. The report also includes a 
summary of a proposed 5-year research agenda for 
NCEER. 
ATC-29-1: The report, Proceedings Of Seminar On 
Seismic Design, Retrofit, And Performance Of Non-
structural Components, was developed under a grant 
from NCEER and NSF. Available through the ATC 
office. (Published 1998, 518 pages) 
ABSTRACT:
These Proceedings contain 38 papers 
presenting current research, practice, and informed 
thinking pertinent to seismic design, retrofit, and 
performance of nonstructural components. The 
papers were presented at a seminar in San Francisco, 
California, in 1998. Included are papers 
describing observed performance in recent earthquakes; 
seismic design codes, standards, and procedures 
for commercial and institutional buildings; 
seismic design issues relating to industrial and hazardous 
material facilities; design, analysis, and testing 
FEMA 307 Technical Resources 
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and seismic evaluation and rehabilitation of 
conventional and essential facilities, including hospitals. 
ATC-30: The report, Proceedings of Workshop for Utilization 
of Research on Engineering and Socioeconomic 
Aspects of 1985 Chile and Mexico Earthquakes, was 
developed under a grant from the NSF. Available 
through the ATC office. (Published 1991, 113 pages) 
ABSTRACT: This report documents the findings of a 
1990 technology transfer workshop in San Diego, 
California, co-sponsored by ATC and the Earthquake 
Engineering Research Institute. Included in 
the report are invited papers and working group recommendations 
on geotechnical issues, structural 
response issues, architectural and urban design considerations, 
emergency response planning, search 
and rescue, and reconstruction policy issues. 
ATC-31: The report, Evaluation of the Performance of 
Seismically Retrofitted Buildings, was developed under 
a contract from the National Institute of Standards and 
Technology (NIST, formerly NBS) and funded by the 
USGS. Available through the ATC office. (Published 
1992, 75 pages) 
ABSTRACT: This report summarizes the results from 
an investigation of the effectiveness of 229 seismically 
retrofitted buildings, primarily unreinforced 
masonry and concrete tilt-up buildings. All buildings 
were located in the areas affected by the 1987 
Whittier Narrows, California, and 1989 Loma Prieta, 
California, earthquakes. 
ATC-32: The report, Improved Seismic Design Criteria 
for California Bridges: Provisional Recommendations, 
was funded by the California Department of Transportation 
(Caltrans). Available through the ATC office. 
(Published 1996, 215 Pages) 
ABSTRACT: This report provides recommended 
revisions to the current Caltrans Bridge Design 
Specifications (BDS) pertaining to seismic loading, 
structural response analysis, and component design. 
Special attention is given to design issues related to 
reinforced concrete components, steel components, 
foundations, and conventional bearings. The recommendations 
are based on recent research in the 
field of bridge seismic design and the performance 
of Caltrans-designed bridges in the 1989 Loma Prieta 
and other recent California earthquakes. 
ATC-34: The report, A Critical Review of Current 
Approaches to Earthquake Resistant Design, was developed 
under a grant from NCEER and NSF. Available 
through the ATC office. (Published, 1995, 94 pages) 
This report documents the history of U.
ABSTRACT. 
S. codes and standards of practice, focusing primarily 
on the strengths and deficiencies of current 
code approaches. Issues addressed include: seismic 
hazard analysis, earthquake collateral hazards, performance 
objectives, redundancy and configuration, 
response modification factors (R factors), 
simplified analysis procedures, modeling of structural 
components, foundation design, nonstructural 
component design, and risk and reliability. The 
report also identifies goals that a new seismic code 
should achieve. 
ATC-35: This report, Enhancing the Transfer of U.S. 
Geological Survey Research Results into Engineering 
Practice was developed under a contract with the 
USGS. Available through the ATC office. (Published 
1996, 120 pages) 
ABSTRACT: The report provides a program of recommended 
"technology transfer" activities for the 
USGS; included are recommendations pertaining to 
management actions, communications with practicing 
engineers, and research activities to enhance 
development and transfer of information that is 
vital to engineering practice. 
ATC-35-1: The report, Proceedings of Seminar on New 
Developments in Earthquake Ground Motion Estimation 
And Implications for Engineering Design Practice, 
was developed under a cooperative agreement with 
USGS. Available through the ATC office. (Published 
1994, 478 pages) 
ABSTRACT: These Proceedings contain 22 technical 
papers describing state-of-the-art information on 
regional earthquake risk (focused on five specific 
regions California, Pacific Northwest, Central 
United States, and northeastern North America); 
new techniques for estimating strong ground 
motions as a function of earthquake source, travel 
path, and site parameters; and new developments 
Technical Resources 
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specifically applicable to geotechnical engineering 
and the seismic design of buildings and 
bridges. 
ATC-37: The report, Review of Seismic Research 
Results on Existing Buildings, was developed in conjunction 
with the Structural Engineers Association of 
California and California Universities for Research 
in Earthquake Engineering under a contract from the 
California Seismic Safety Commission (SSC). Available 
through the Seismic Safety Commission as 
Report SSC 94-03. (Published, 1994, 492 pages) 
ABSTRACT. This report describes the state of 
knowledge of the earthquake performance of 
nonductile concrete frame, shear wall, and 
infilled buildings. Included are summaries of 90 
recent research efforts with key results and conclusions 
in a simple, easy-to-access format written 
for practicing design professionals. 
ATC-40: The report, Seismic Evaluation and Retrofit 
of Concrete Buildings, was developed under a contract 
from the California Seismic Safety 
Commission. Available through the ATC office. 
(Published, 1996, 612 pages) 
ABSTRACT. This 2-volume report provides a 
state-of-the-art methodology for the seismic 
evaluation and retrofit of concrete buildings. 
Specific guidance is provided on the following 
topics: performance objectives; seismic hazard; 
determination of deficiencies; retrofit strategies; 
quality assurance procedures; nonlinear static 
analysis procedures; modeling rules; foundation 
effects; response limits; and nonstructural components. 
In 1997 this report received the Western 
States Seismic Policy Council "Overall 
Excellence and New Technology Award." 
ATC-44: The report, Hurricane Fran, South Carolina, 
September 5, 1996: Reconnaissance Report, is 
available through the ATC office. (Published 1997, 
36 pages.) 
ABSTRACT: This report represents ATC's 
expanded mandate into structural engineering 
problems arising from wind storms and coastal 
flooding. It contains information on the causative 
hurricane; coastal impacts, including storm 
surge, waves, structural forces and erosion; 
building codes; observations and interpretations 
of damage; and lifeline performance. Conclusions 
address man-made beach nourishment, the 
effects of missile-like debris, breaches in the 
sandy barrier islands, and the timing and duration 
of such investigations. 
ATC-R-1: The report, Cyclic Testing of Narrow Plywood 
Shear Walls, was developed with funding from 
the Henry J. Degenkolb Memorial Endowment Fund 
of the Applied Technology Council. Available 
through the ATC office (Published 1995, 64 pages) 
ABSTRACT: This report documents ATC's first 
self-directed research program: a series of static 
and dynamic tests of narrow plywood wall panels 
having the standard 3.5-to-1 height-to-width 
ratio and anchored to the sill plate using typical 
bolted, 9-inch, 5000-lb. capacity hold-down 
devices. The report provides a description of the 
testing program and a summary of results, 
including comparisons of drift ratios found during 
testing with those specified in the seismic 
provisions of the 1991 Uniform Building Code. 
251 
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FEIVA 
ATC BOARD OF DIRECTORS (1973-Present) 
Milton A. Abel (1979-85) : John F. Meehan* (1973-78) 
James C. Anderson (1978-81) Andrew T. Merovich (1996-99) 
Thomas G. Atkinson* (1988-94) David L. Messinger (1980-83) 
Albert J. Blaylock (1976-77) Stephen McReavy (1973) 
Robert K. Burkett (1984-88) Bijan Mohraz (1991-97) 
James R. Cagley (1998-2001) William W. Moore* (1973-76) 
H. Patrick Campbell (1989-90) Gary Morrison (1973) 
Arthur N. L. Chiu (1996-99) Robert Morrison (1981-84) 
Anil Chopra (1973-74) Ronald F. Nelson (1994-95) 
Richard Christopherson* (1976-80) Joseph P. Nicoletti* (1975-79) 
Lee H. Cliff (1973) Bruce C. Olsen* (1978-82) 
John M. Coil* (1986-87, 1991-97) Gerard Pardoen (1987-91) 
Eugene E. Cole (1985-86) Stephen H. Pelham (1998-2001) 
Edwin T. Dean (1996-99) Norman D. Perkins (1973-76) 
Robert G. Dean (1996-2001) Richard J. Phillips (1997-2000) 
Edward F. Diekmann (1978-81) Maryann T. Phipps (1995-96) 
Burke A. Draheim (1973-74) Sherrill Pitkin (1984-87) 
John E. Droeger (1973) Edward V. Podlack (1973) 
Nicholas F. Forell* (1989-96) Chris D. Poland (1984-87) 
Douglas A. Foutch (1993-97) Egor P. Popov (1976-79) 
Paul Fratessa (1991-92) Robert F. Preece* (1987-93) 
Sigmund A. Freeman (1986-89) Lawrence D. Reaveley* (1985-91) 
Barry J. Goodno (1986-89) Philip J. Richter* (1986-89) 
Mark R. Gorman (1984-87) John M. Roberts (1973) 
Gerald H. Haines (1981-82, 1984-85) Charles W. Roeder (1997-2000) 
William J. Hall (1985-86) ArthurE. Ross* (1985-91, 1993-94) 
Gary C. Hart (i975-78) C. Mark Saunders* (1993-2000) 
Lyman Henry (1973) Walter D. Saunders* (1975-79) 
James A. Hill (1992-95) Lawrence G. Selna (1981-84) 
Ernest C. Hillman, Jr. (1973-74) Wilbur C. Schoeller (1990-91) 
Ephraim G. Hirsch (1983-84) Samuel Schultz* (1980-84) 
William T. Holmes* (1983-87) Daniel Shapiro* (1977-81) 
Warner Howe (1977-80) Jonathan G. Shipp (1996-99) 
Edwin T. Huston* (1990-97) Howard Simpson* (1980-84) 
Paul C. Jennings (1973-75) Mete Sozen (1990-93) 
Carl B. Johnson (1974-76) Donald R. Strand (1982-83) 
Edwin H. Johnson (1988-89, 1998-2001) James L. Stratta (1975-79) 
Stephen E. Johnston* (1973-75, 1979-80) Scott Stedman (1996-97) 
Joseph Kallaby* (1973-75) Edward J. Teal (1976-79) 
Donald R. Kay (1989-92) W. Martin Tellegen (1973) 
T. Robert Kealey* (1984-88) John C. Theiss* (1991-98) 
H. S. (Pete) Kellam (1975-76) Charles H. Thornton* (1992-99) 
Helmut Krawinkler (1979-82) James L. Tipton (1973) 
James S. Lai (1982-85) Ivan Viest (1975-77) 
Gerald D. Lehmer (1973-74) Ajit S. Virdee* (1977-80, 1981-85) 
James R. Libby (1992-98) J. John Walsh (1987-90) 
Charles Lindbergh (1989-92) Robert S. White (1990-91) 
R. Bruce Lindermann (1983-86) James A. Willis* (1980-81, 1982-86) 
L. W. Lu (1987-90) Thomas D. Wosser (1974-77) 
Walter B. Lum (1975-78) Loring A. Wyllie (1987-88) 
Kenneth A. Luttrell (1991-98) Edwin G. Zacher (1981-84) 
Newland J. Malmquist (1997-2000) Theodore C. Zsutty (1982-85) 
Melvyn H. Mark (1979-82) 
John A. Martin (1978-82) * President 
ATC EXECUTIVE DIRECTORS (1973-Present) 
Ronald Mayes (1979-81) Roland L. Sharpe (1973-79) 
Christopher Rojahn (1981-present) 
Technical Resources FEMA 307 
Applied Technology Council 
Sponsors, Supporters, and Contributors 
Sponsors 
Structural Engineers Association of California 
James R. & Sharon K. Cagley 
John M. Coil 
Burkett & Wong 
Supporters 
Charles H. Thornton 
Degenkolb Engineers 
Japan Structural Consultants Association 
Contributors 
Lawrence D. Reaveley 
Omar Dario Cardona Arboleda 
Edwin T. Huston 
John C. Theiss 
Reaveley Engineers 
Rutherford & Chekene 
E. W. Blanch Co. 
Technical Resources 253 
FEMA 307 Technical Resources 253