Multi-hazard Loss Estimation Methodology
Earthquake Model
HAZUS-MH MR1

ADVANCED ENGINEERING BUILDING MODULE
TECHNICAL and USER'S MANUAL

Developed by: 
Department of Homeland Security
Emergency Preparedness and Response Directorate
FEMA
Mitigation Division
Washington, D.C. 

Under a contract with:
National Institute of Building Sciences
Washington, D.C.

Copyright 2003, Federal Emergency Management Agency 
(Secured by Assignment) 
HAZUS is a trademark of the Federal Emergency Management Agency

FOREWORD 
The research and development and studies that provided the basis for this 
publication were conducted pursuant to a contract with the Federal Emergency 
Management Agency (FEMA) by the National Institute of Building Sciences.

The National Institute of Building Sciences (NIBS), located in Washington, DC, is a 
nongovernmental, non-profit organization, authorized by Congress to encourage a more 
rational building regulatory environment, to accelerate the introduction of existing and 
new technology into the building process and to disseminate technical information. 

Copies of this report are available through the Federal Emergency Management Agency.
For information contact FEMA at http://www.fema.gov/hazus or:
FEMA Distribution Center 
P.O. Box 2012 
Jessup, Maryland 20794-2012 
Tel.: 1 800-480-2520 
Fax: 301-362-5335 

HAZUS is a trademark of the Federal Emergency Management Agency. 

ACKNOWLEDGMENTS

HAZUS-MH and HAZUS-MH MR1 

Earthquake Committee:
Chairman, William Holmes, Rutherford & Chekene, San Francisco, California 
Roger Borcherdt, U.S. Geological Survey, Menlo Park, California 
David Brookshire, University of New Mexico, Albuquerque, New Mexico 
Richard Eisner, California Office of Emergency Services, Oakland California 
Robert Olson, Robert Olson & Associates, Inc., Sacramento, California 
Michael O'Rourke, Rensselaer Polytechnic Institute, Troy, New York 
Henry Lagorio, University of California at Berkeley, Berkeley, California 
Robert Reitherman, Consortium of Universities for Research in Earthquake Engineering, 
Richmond, California 
Robert Whitman, Massachusetts Institute of Technology, Cambridge, Massachusetts, 
Chairman Emeritus 

Building Damage Subcommittee:
William Holmes, Rutherford & Chekene, San Francisco, California 
Robert Whitman, Massachusetts Institute of Technology, Cambridge, Massachusetts 

Shake Beta Subcommittee:
Chairman, William Holmes, Rutherford & Chekene, San Francisco, California 
Robert Whitman, Massachusetts Institute of Technology, Cambridge, Massachusetts 
Roger Borcherdt, U.S. Geological Survey, Menlo Park, California 
Richard Eisner, FAIA, California Office of Emergency Services, Oakland California 
Michael O'Rourke, Rennselaer Polytechnic Institute, Troy, New York 

Casualties Subcommittee:
Chairman, Robert Reitherman, Consortium of Universities for Research in Earthquake 
Engineering, Richmond, California 
Richard Eisner, California Office of Emergency Services, Oakland California 
William Holmes, Rutherford & Chekene, San Francisco, California 
Robert Olson, Robert Olson & Associates, Inc., Sacramento, California 
Henry Lagorio, University of California at Berkeley, Berkeley, California 

Earthquake Model Methodology Development:
PBS&J, Atlanta, Georgia 
Jawhar Bouabid, Program Manager; Scott Lawson 

Special thanks to the Environmental Protection Agency for its assistance in integrating 
ALOHA into the Earthquake Model.

Special thanks to the National Oceanic and Atmospheric Administration for making 
FloodWAV and FloodVIEW available and its assistance in integrating them into the 
Earthquake Model. 

Kircher & Associates, Palo Alto, California 
Charles Kircher 

San Jose State University Foundation, San Jose, California 
Thalia Anagnos 

Earthquake Model Validation 
Comartin-Reis, Stockton, California 
Craig Comartin, Evan Reis 

Software Committee:
Chairman, Dick Bilden, Consultant, Reston, Virginia 
Co-Chairman, Mike Haecker, Consultant, Austin, Texas 
Dan Cotter, Terrapoint, The Woodlands, Texas 
Gerry Key, Computer Sciences Corporation, San Diego, California 
Tracy Lenocker, Lenocker and Associates, Inc., Orange, California 
Ken Lewis, KVL and Associates, Inc., Scottsdale, Arizona 
Frank Opporto, DHS, EP&R Directorate (FEMA), Information Services Technology 
Division, Washington, D.C. 
Dirk Vandervoort, POWER Engineers, Inc., Boise Idaho 
Leslie Weiner-Leandro, DHS, EP&R Directorate (FEMA), Information Services 
Technology Division, Washington, D.C. 

Beta Test Subcommittee HAZUS-MH:
Darryl Davis, Corps of Engineers Hydrologic Engineering Center, Davis, California 
Neil Grigg, Colorado State University, Fort Collins, Colorado 
Charles Kircher, Kircher & Associates, Palo Alto, California 
Tracy Lenocker, Lenocker and Associates, Inc., Orange, California 
Kenneth Lewis, KVL and Associates, Inc., Scottsdale, Arizona 
Masoud Zadeh, Consultant, San Jose, California 

Beta Test Communities HAZUS-MH:
Division of Emergency Management, Tallahassee,Florida;
Washington State Emergency Management, Camp Murray, Washington;
Whatcom County Public Works, Bellingham, Washington;
Johnson County, Olathe, Kansas;
Mecklenburg County Stormwater Services, Charolotte, North Carolina;
Louisiana State University, Baton Rouge, Louisiana;
Charleson County Building Services, North Charleston, South Carolina 

Beta Test Subcommittee - HAZUS-MH MR1 
Douglas Bausch, Department of Homeland Security, Emergency Preparedness and 
Response Directorate (FEMA), Washington, D.C. 
Richard Eisner, Governor's Office of Emergency Services, Oakland, California 
John Knight, South Carolina Emergency Management Division, Columbia, South 
Carolina 
Kevin Mickey, The Polis Center, Indianapolis, Indiana 
Mark Neimeister, Delaware Geological Survey, Newark, Delaware 
Lynn Seirup, New York City Office of Emergency Management, New York, New York 

HAZUS-MH and HAZUS-MH MR1 Shell Development:
PBS&J, Atlanta, Georgia 
Mourad Bouhafs, Program Manager (HAZUS-MH);
Pushpendra Johari, Program Manager (HAZUSMH MR1);
Sandeep Mehndiratta 

Special thanks to ESRI for its assistance in coordinating ArcGIS with HAZUS-MH. 

Earthquake Model Software Development:
PBS&J, Atlanta, Georgia 
Pushpendra Johari, Program Manager;
Mourad Bouhafs,
Foued Bouhafs,
Sandeep Mehndiratta,
Eduardo Escalona,
Nabil Bouhafs 

Department of Homeland Security, Emergency Preparedness & Response Directorate 
(FEMA), Mitigation Division, Washington, D.C. 
Cliff Oliver, Chief, Risk Assessment Branch; Edward Laatsch, Chief, Building Science 
and Technology;
Claire Drury, Project Officer;
Paul Tertell,
Michael Mahoney,
Stuart Nishenko,
Scott McAfee,
Paul Bryant 

Technical Monitors 
Douglas Bausch, FEMA Region 8;
John Ingargiola,
Douglas Bellemo,
Allyson Lichtenfels, Divisional Coordination 

National Institute of Building Sciences, Washington, D.C. 
Philip Schneider, Director, Multihazard Loss Estimation Methodology Program;
Barbara Schauer, Senior Project Manager 

EXECUTIVE SUMMARY 
This manual describes procedures for developing building-specific damage and loss 
functions with the Advanced Engineering Building Module (AEBM). The AEBM 
procedures are an extension of the more general methods of the FEMA/NIBS earthquake 
loss estimation methodology (HAZUS) and provide damage and loss functions 
compatible with current HAZUSMH Software. Kircher & Associates working for the 
National Institute of Building Sciences (NIBS) has developed these procedures under 
agreements between NIBS and the Federal Emergency Management Agency (FEMA). 
The procedures have been pilot tested and reviewed by NIBS' Earthquake Committee and 
Building Damage Subcommittee. 

HAZUS damage and loss functions for generic model building types are considered to be 
reliable predictors of earthquake effects for large groups of buildings that include both 
above median and below median cases. They may not, however, be very good predictors 
for a specific building or a particular type of building that is known to have an inherent 
weakness or earthquake vulnerability (e.g., W1 buildings with weak cripple walls would 
be expected to perform much worse than typical wood- frame buildings). 

For mitigation purposes, it is desirable that users be able to create building-specific 
damage and loss functions that could be used to assess losses for an individual building 
(or group of similar buildings) both in their existing condition and after some amount of 
seismic rehabilitation. The term "building-specific" distinguishes the development of 
damage and loss functions, as described in this manual, from the "generic" building 
functions of HAZUS. Building-specific damage and loss functions are based on the 
properties of a particular building. The particular building of interest could be either an 
individual building or a typical building representing a group of buildings of an 
archetype. 

The procedures are of a highly technical nature, and users should be qualified 
seismic/structural engineers who, for example, might be advising a local jurisdiction 
regarding the merits of adopting an ordinance to require cripple-wall strengthening of 
older wood-frame residences. The accuracy of damage and loss estimates using building-
specific functions, and their improvement over predictions using generic building 
functions, will depend both on the quality and completeness of building-specific data and 
on ability of the user to transform this information into meaningful functions. The 
accuracy of damage and loss estimates for a group of buildings will also depend on the 
ability of the user to select a typical building that represents the archetype of interest. 

Users should have some background and experience in actual earthquake performance of 
buildings, be familiar with special seismic analysis (e.g., pushover) methods and be able 
to envision building damage patterns and failure modes. Even though the procedures are 
quite detailed, users will still need to apply judgement in the development of building-
specific damage and loss functions. 

To facilitate easier implementation of building-specific methods by users, an Advanced 
Engineering Building Module (AEBM) has been added to the HAZUS-SR2 Software. 
Some parameters and indeed some methods of loss calculation of the new AEBM are 
different than those of other modules of HAZUS. Revision 2 of this manual describes 
parameters and methods that are consistent with the new AEBM, even though some terms 
may not be fully documented in the HAZUS-MH Technical Manual. Revision 2 also 
includes an example application of the AEBM in Section 8 of the manual. 

The example application in Section 8 of this manual provides users with a step-by-step 
description of the calculation of building damage and loss using the AEBM. The example 
illustrates both the transformation of engineering data (e.g., pushover analysis results) 
into AEBM parameters (e.g., capacity and fragility curve parameters), and the 
implementation of these parameters using the AEBM of the HAZUS-MH Software. The 
example calculates damage and loss for a large, welded steel moment frame (WSMF) 
building in its current (original building) configuration and the calculation of damage and 
losses for the WSMF building with connections strengthened to avoid premature 
fracturing and failure. In both cases, damage and losses are calculated for the same level 
of ground shaking that is based on a magnitude M7.2 scenario earthquake on the Sierra 
Madre fault, the fault that dominates seismic hazard at the example building site. 

TABLE OF CONTENTS
Foreword

Acknowledgements 

Executive Summary 

Section 
1. Introduction  
1.1. Scope and Background  
1.2. Purpose and Approach  
1.3. Pilot Testing and Revision of Methods
1.4. Individual Buildings and Groups of Buildings of a Specific Type 
1.5. AEBM Overview  
1.6. Manual Organization  

2. Summary of HAZUS Earthquake Loss Estimation Methods  
2.1. Overview of Methodology 
2.2. Building Classification  
2.3. Seismic Design Levels and Construction Quality  
2.4. Structural and Nonstructural Systems and Contents  
2.5. Damage States  
2.6. Building Capacity Curves  
2.7. Building Response Calculation  
2.8. Building Fragility Curves  
2.9. Example Capacity and Fragility Data  
2.10. Building Loss Functions  

3. Summary of Building-Specific Data Provided by User  
3.1. Introduction  
3.2. Site/Source Seismic Hazard Data  
3.3. Inventory Data  
3.4. Performance Data  
3.4.1. Building Failure Modes  
3.4.2. Pushover Models and Modal Properties  
3.4.3. Element/Component Response Characteristics  
3.5. Loss Data  
3.5.1. Occupant Data  
3.5.2. Financial Data  

4. Summary of Damage and Loss Function Parameters 
4.1. Introduction  
4.2. Damage Functions  
4.2.1. Capacity Curve Parameters 
4.2.2. Response Parameters  
4.2.3. Fragility Curve Parameters  
4.3. Loss Functions  
4.3.1. Inventory Data  
4.3.2. Casualty Rates  
4.3.3. Repair Cost Rates - Loss Ratios  
4.3.4. Loss of Function and Recovery Time  

5. Development of Capacity Curves and Response Parameters  
5.1. Building Model and Pushover Criteria 
5.2. Development of Capacity Curve Control Points
5.2.1. Conversion of Pushover Curve to Capacity Curve
5.2.2. Yield and Ultimate Capacity Control Points 
5.3. Development of Response Parameters  
5.3.1. Response Calculation  
5.3.2. Elastic Damping Factors 
5.3.3. Degradation Factors 
5.3.4. Fraction of Nonstructural Components at Ground Level 

6. Development of Fragility Curves  
6.1. Building Response and Performance Criteria  
6.2. Development of Damage-State Medians  
6.2.1. Structural System  
6.2.2. Nonstructural Components  
6.3. Development of Damage-State Variability 

7. Development of Loss Functions  
7.1. Building Loss Criteria 
7.2. Direct Social Losses - Casualties  
7.3. Direct Economic Losses  
7.3.1. Repair Costs  
7.3.2. Loss of Function  

8. Example Estimation of Building Damage and Loss Using the AEBM  
8.1. Background  
8.2. Example Building Data  
8.2.1. LACDPW Headquarters Building  
8.2.2. Original Building (OB) Structure  
8.2.3. Connection-Only (CO) Retrofit Scheme  
8.2.4. Engineering Pushover Analyses  
8.2.5. Original Building (OB) Performance  
8.2.6. Connection-Only (CO) Retrofit Scheme Performance  
8.2.7. Ground Shaking Hazard  
8.3. HAZUS Software - Getting Started  
8.3.1. Defining a Study Region  
8.3.2. Defining Scenario Earthquake Ground Shaking  
8.3.3. Defining AEBM Inventory Data  
8.3.4. Defining Default AEBM Profile Data  
8.3.5. Running the AEBM  
8.3.6. Viewing and Printing AEBM Results  
8.4. Modifying Default AEBM Profile Data  
8.4.1. Building Characteristics  
8.4.2. Structural Fragility Curves 
8.4.3. Nonstructural Drift Fragility Curves  
8.4.4. Nonstructural Acceleration Fragility Curves  
8.4.5. Casualty Ratios (Per Occupant)  
8.4.6. Building Related Repair Cost Ratios  
8.4.7. Contents & Building Inventory Replacement Cost Ratios 
8.4.8. Loss of Function Parameters 
8.5. Example AEBM Results  
8.5.1. Interpretation 
8.5.2. Sensitivity Analysis  

9. References  

SECTION 1 
INTRODUCTION 
1.1. Scope and Background
This manual describes procedures for developing building-specific damage and loss 
functions with the Advanced Engineering Building Module (AEBM). The AEBM 
procedures are an extension of the more general methods of the FEMA/NIBS earthquake 
loss estimation methodology (HAZUS) and provide damage and loss functions 
compatible with current HAZUS-MH Software. Kircher & Associates working for the 
National Institute of Building Sciences (NIBS) has developed these procedures under 
agreements between NIBS and the Federal Emergency Management Agency (FEMA). 
The procedures have been pilot tested and reviewed by NIBS' Earthquake Committee and 
Building Damage Subcommittee. 

The FEMA/NIBS earthquake loss estimation methodology, commonly known as 
HAZUS, is a complex collection of components that work together to estimate casualties, 
loss of function and economic impacts on a region due to a scenario earthquake. The 
methodology is documented in the HAZUS-MH Technical Manual. One of the main 
components of the methodology estimates the probability of various states of structural 
and nonstructural damage to buildings. Damage state probabilities are used by other 
components of the methodology to estimate various types of building-related loss. 
Typically, buildings are grouped by model building type and evaluated on a census tract 
basis. 

Currently, HAZUS includes building damage functions for 36 model building types (and 
for various combinations of seismic design level and performance). Each model building 
type represents a "generic" group of buildings that share a common type of construction 
(e.g., W1 represents smaller wood-frame buildings) and a common seismic design level 
(e.g., Moderate- Code represents buildings of current Uniform Building Code Seismic 
Zone 2 design or older buildings of Seismic Zone 3 or 4 design). 

Damage and loss functions for generic building types are considered to be reliable 
predictors of earthquake effects for large groups of buildings that include both above 
median and below median cases. They may not, however, be very good predictors for a 
specific building or a particular type of building that is known to have a weakness or 
earthquake vulnerability (e.g., W1 buildings with weak cripple walls would be expected 
to perform much worse than typical wood-frame buildings). Although the theory is 
applicable to an individual building, building-specific damage and loss functions are not 
provided and would need to be developed by the user. The complexity of the methods 
and underlying seismological and engineering phenomena makes development of 
building-specific functions challenging unless the user is an engineer experienced in 
nonlinear seismic analysis (and seldom necessary for regional loss estimation studies). 

For mitigation purposes, it is desirable that users be able to create building-specific 
damage and loss functions that could be used to assess losses for an individual building 
(or group of similar buildings), both in their existing condition and after some amount of 
seismic rehabilitation.

"Users" in this context refer to seismic/structural engineers who, for example, might be 
advising a local jurisdiction regarding the merits of adopting an ordinance to require 
cripple-wall strengthening of older wood- frame residences. 

FEMA/NIBS projects in the area of earthquake hazard mitigation also include the 
Building Seismic Safety Council's (BSSC's) development of the NEHRP Guidelines for 
Seismic Rehabilitation of Buildings [FEMA, 1997], referred to simply as the NEHRP 
Guidelines. Like HAZUS, the NEHRP Guidelines represent a major, multi-year effort. 
Also like HAZUS, the NEHRP Guidelines use similar earth science theory and 
engineering techniques. For the first time, earthquake loss estimation and building 
seismic analysis are based on common concepts. For example, both the FEMA/NIBS 
methodology and the NEHRP Guidelines (1) use the same characterization of ground 
shaking (i.e., response spectra, as defined by the USGS maps/theory) and (2) use the 
same nonlinear (pushover) characterization of building response. The similarity of these 
fundamental concepts permits interfacing the methods of the NEHRP Guidelines with 
those of HAZUS for development of building-specific damage and loss models. 

1.2. Purpose and Approach
The primary purpose of the AEBM is to support mitigation efforts by providing building-
specific loss estimation tools for use by experienced seismic/structural engineers. To 
produce accurate results, the engineer must be capable of carrying out a relatively 
sophisticated pushover analysis as described below. While the expertise and required 
inputs may seem challenging, building-specific methods are intended for use by those 
experts who have the requisite skills and desire to go beyond the default methods and 
data of the more user-friendly "Level 1" or "Level 2" procedures of HAZUS. 

The underlying approach of AEBM procedures is a combination of the nonlinear static 
(pushover) analysis methods of the NEHRP Guidelines (and other sources, namely the 
ATC-40 document: Seismic Evaluation and Retrofit of Concrete Buildings, CSSC, 1996) 
with HAZUS loss estimation methods. Seismic/structural engineers having performed a 
detailed pushover analysis of a specific building are expected to have a much better 
understanding of the building's potential failure modes, overall response characteristics, 
structural and nonstructural system performance, and the cost and time required to repair 
damaged components. 

The NEHRP Guidelines provide a logical and appropriate starting point for seismic 
evaluation of existing buildings and provide state-of-the-art techniques, such as pushover 
analysis. The NEHRP Guidelines also provide limit state criteria for elements and 
components of buildings that are useful to engineers for determining building-specific 
damage states. Detailed investigation of a specific building should also provide other 
important loss-related information. For example, building owners would be expected to 
provide much more reliable estimates of total replacement cost (value) of the building, 
the extent and value of contents or inventory, and number of building occupants during 
different times of the day. All these are critical data required for reliable estimates of 
earthquake losses. 

1.3. Pilot Testing and Revision of the Manual
An initial draft of this manual (October 1999) was evaluated during the year 2000 by two 
separate pilot studies [Reis, 2000 and EQE, 2000]. Based on the findings of these studies, 
the Earthquake Committee of NIBS recommended certain improvements to building-
specific methods and the development of a new Advanced Engineering Building Module 
to facilitate easier implementation of building-specific methods in the HAZUS software.

Revision 1 of this manual (March 2001) incorporated improvements to building-specific 
methods recommended by the Earthquake Committee and updated descriptions of 
parameters and methods that are consistent with the "Beta" version of new AEBM 
(January 2001).

Revision 2 of this manual (January 2002) incorporates changes to the final version of the 
AEBM (and other updated modules) of the HAZUS-MH Software. Some parameters and 
indeed some methods of loss calculation of the new AEBM are different than those of 
other modules of the HAZUS. Revision 2 of this manual describes parameters and 
methods that are consistent with the new AEBM, even though some terms may not be 
fully documented in the HAZUS-MH Technical Manual. Revision 2 also includes an 
example application of the AEBM in Section 8 of this manual.

1.4 
Individual Buildings and Groups of Buildings of a Specific Type
The term "building-specific" distinguishes the development of damage and loss 
functions, as described in this manual, from the "generic" building functions of HAZUS. 
Building-specific damage and loss functions are based on the properties of a particular 
building. The particular building of interest could be either an individual building or a 
typical building representing a group of buildings of an archetype (e.g., wood frame 
residences with weak cripple walls). Throughout this manual, the term "the building" 
refers to a typical building of a group of buildings of an archetype, as well as to an 
individual building.

In the most complete sense, development of building-specific properties for a group of 
buildings would involve modeling and pushover analysis of a suite of structures that 
fairly represent the range of configurations and properties of the building group of 
interest. Results of the analyses could then be statistically evaluated to produce estimates 
of the distribution of the parameter of interest (e.g., estimates of median value and 
variability of building capacity). In general, this approach is neither practical nor 
warranted for most applications. The methods described in this manual assume that a 
typical building or theoretical archetype is selected by the user to represent the group of 
buildings of interest.

Results of the analysis of the typical building represent median properties of the group. 
Parameter variability is based on judgment considering the number and similarity of 
buildings in the group. Small groups of very similar buildings would have parameter 
variability commensurate with that of an individual building. Large or dissimilar-building 
groups would have parameter variability commensurate with that of the generic building 
types of HAZUS. Guidance is provided in Section 6 for development of damage-state 
variability considering the size and conformity of buildings in the group of buildings of 
interest. 

1.5. AEBM Overview
The Advanced Engineering Building Module (AEBM) implements building-specific 
methods in the HAZUS-MH Software through a variety of HAZUS software menus and 
dialog boxes that begin with defining a study region, include defining ground shaking 
hazard and AEBM inventory, running AEBM analyses and finally viewing or printing of 
AEBM results. Figure 1.1 illustrates the flow of HAZUS software elements related to the 
AEBM. 

Figure 1.1. HAZUS Software - Flowchart of AEBM Calculation of Damage and Loss
Run HAZUS
* Open/Create Study Region

Inventory Menu
* Define AEBM Inventory
* Define AEBM Profiles

Hazard Menu
* Open/Define Scenario Earthquake

Analysis Menu
* Run AEBM

Results Menu
* View Results
* Print Results

The software architecture of the AEBM has two main components (or databases), AEBM 
Inventory and AEBM Profiles. AEBM Inventory is structured to accept a "portfolio" of 
individual buildings each uniquely defined by (latitude/longitude) location, number of 
occupants, size, replacement cost and other building-specific financial data. The AEBM 
Profiles describe an extensive set building perfo rmance characteristics, including 
damage and loss function parameters. Each building in the AEBM Inventory must be 
linked to one of the AEBM Profiles to run the AEBM, but an AEBM Profile can be used 
for more than one building of the AEBM Inventory. Applications of the AEBM include 
evaluation of individual buildings or a group of buildings of a similar type, as described 
below.

* Evaluation of Individual Building(s) - In this case, the user creates an AEBM Inventory 
record and an AEBM Profiles record (linked to the AEBM Inventory record) for each 
individual building of interest. These sets of linked inventory and profile data define 
unique properties for each individual building of interest.

In Section 8 of this manual, the AEBM evaluates two "individual" buildings that 
represent the same building before and after seismic strengthening. In this example, the 
two records in the AEBM Inventory contain the same data (i.e., same building location, 
population and replacement value), but the two AEBM Profile records reflect differences 
in performance characteristics before and after seismic rehabilitation. Comparison of the 
AEBM results, before and after strengthening, provides a measure of the benefits of 
seismic mitigation. 

* Evaluation of a Group of Similar Buildings - In this case, the user creates an AEBM 
Inventory record for each building of the group, distributing them by (latitude/longitude) 
location throughout the study region, and a single AEBM Profile record (linked to each 
building of the group). These profile data define properties that represent the collective 
performance of the group (i.e., building type).

An example "group" application of the AEBM is the evaluation of a "new" building type, 
not well represented by an existing building type of HAZUS (e.g., URM buildings 
seismically-strengthened to meet certain performance criteria). The building-specific 
methods described in this manual may be used to create "customized" model building 
types, such as 
"strengthened URM" buildings, and the AEBM can be used to evaluate damage and loss 
to these buildings. For a regional study, the AEBM Inventory would locate representative 
inventory at the centroid of each census tract of the study region.

1.6. Manual Organization 
The balance of this manual begins in Section 2 with a summary of HAZUS earthquake 
loss estimation methods for readers not familiar with HAZUS. This section includes 
material from 
the HAZUS-MH Technical Manual and from papers published in Earthquake Spectra that 
describe building damage and loss methods [Whitman et al., 1997, Kircher et al., 1997a, 
Kircher 
et al. 1997b]. 

Sections 3 and 4 summarize the type and format of data that are used in the AEBM to 
estimate building damage and loss. Section 3 describes building-specific data that must 
be provided by users, including site hazard information, performance properties and cost 
and occupant data. Section 4 describes the type and format of damage and loss 
parameters used by the Advanced Engineering Building Module (AEBM) of the 
HAZUS-MH Software.

Procedures for developing AEBM capacity curves (and related response parameters), 
AEBM fragility curves and AEBM loss functions from building-specific data are 
described in Sections 
5, 6 and 7, respectively. Section 5 methods provide guidance for the user's selection of 
capacity curve control points and other response parameters from the results of an 
existing nonlinear static (pushover) analysis of the building. Section 6 methods describe 
development of fragility curve properties (i.e., median va lue and variability of damage 
states). Median values of structural damage states are also based on the results of the 
building's pushover analysis, while damagestate variability is selected from pre-
calculated values that are tabulated as a function of key building characteristics. Section 7 
methods help users develop functions that relate social and economic losses to building 
damage.

Section 8 illustrates application of building-specific procedures with a step-by step 
example calculation of building damage and loss using the AEBM. The example 
illustrates both the 
transformation of engineering data (e.g., pushover analysis results) into AEBM 
parameters (e.g., capacity and fragility curve parameters), and the implementation of 
these parameters using the AEBM of the HAZUS-MH Software. The example calculates 
damage and loss for a large, welded steel moment frame (WSMF) building in its current 
(original building) configuration, 
and the calculation of damage and losses for the WSMF building with connections 
strengthened to avoid premature fracturing and failure. In both cases, damage and losses 
are calculated for the same level of ground shaking that is based on a magnitude M7.2 
scenario earthquake on the Sierra Madre fault, the fault that dominates seismic hazard at 
the example building site. 

SECTION 2 
SUMMARY OF HAZUS EARTHQUAKE LOSS ESTIMATION METHODS 
2.1. Overview of Methodology  
The FEMA/NIBS earthquake loss estimation methodology, commonly known as 
HAZUS, has many components, or modules, as described in the HAZUS-MH User's 
Manual and HAZUS-MH 
Technical Manual. Other sources of information on HAZUS include Earthquake Spectra 
papers: "Development of a National Earthquake Loss Estimation Methodology" 
[Whitman et al., 1997], 
"Development of Building Damage Functions for Earthquake Loss Estimation [Kircher et 
al., 1997a] and " Estimation of Earthquake Losses to Buildings" [Kircher et al., 1997b]. 
The user 
should have copies of the HAZUS-MH User's Manual and HAZUS-MH Technical 
Manual for reference and be familiar with HAZUS methods before attempting to develop 
building-specific 
damage and loss functions.

The flow of the HAZUS methodology between those modules related to building damage 
and loss is illustrated in Figure 2.1. Inputs to the estimation of building damage include 
ground 
shaking and ground failure, characterized by permanent ground deformation (PGD) due 
to settlement and lateral spreading. This manual describes building-specific methods for 
estimating damage and loss due to ground shaking, typically the dominant contributor to 
building-related losses. 

Figure 2.1. Building-Related Modules of the FEMA/NIBS Methodology 
Potential Earth Science Hazards 
* Ground Shaking 
 Response Spectra
 PGA 
*Ground Failure 
 PGD - Settlement 
 PGD - Lateral Spread 

Damage 
* Induced Damage 
 HazMat 
 Debris

*Buildings
(Essential Facilities)

*Lifelines 
 Transportation
 Utility 

Loss 
* Casualties 
 Fatalities 
 Injuries
* Economic 
 Capital 
 Income 
* Shelter 
 Households 
 Short-Term 
* Emergency 
 Loss of Function 
 Restoration Time 

Estimates of building damage are used as inputs to other damage modules, including 
hazardous materials facilities (HazMat) and debris generation, and as inputs to 
transportation and utility lifelines that have buildings as a part of the system (e.g., airport 
control tower). Most importantly, building damage is used as an input to a number of loss 
modules, including the 
estimation of casualties, direct economic losses, displaced households and short-term 
shelter needs, and loss of emergency facility function and the time required to restore 
functionality. 

HAZUS damage functions for ground shaking have two basic components: (1) capacity 
curves and (2) fragility curves. The capacity curves are based on engineering parameters 
(e.g., yield 
and ultimate strength) that characterize the nonlinear (pushover) behavior of 36 different 
model building types. For each of these building types, capacity parameters distinguish 
between 
different levels of seismic design and anticipated seismic performance. The fragility 
curves describe the probability of damage to the building's: (1) structural system, (2) 
nonstructural 
components sensitive to drift and (3) nonstructural components (and contents) sensitive 
to acceleration. For a given level of building response, fragility curves distribute damage 
between 
four physical damage states: Slight, Moderate, Extensive and Complete.

Earthquake loss due to building damage is based on the physical damage states that are 
deemed to be the most appropriate and significant contributors to that particular type of 
loss. For 
example, deaths are based primarily on the Complete state of structural damage, since 
partial or complete collapse of the building is assumed to dominate this type of loss. In 
contrast, direct economic loss (e.g., repair/replacement cost) is accumulated from all 
states of damage to both structural and nonstructural systems, since all are significant 
contributors to economic loss.

2.2. Building Classification 
Buildings are classified both in terms of their use, or occupancy class, and in terms of 
their structural system, or model building type. Damage is predicted based on model 
building type, 
since the structural system is considered the key factor in assessing overall building 
performance, loss of function and casualties. Occupancy class is important in determining 
economic loss, since building value is primarily a function of building use (e.g., hospitals 
are more valuable than most commercial buildings, primarily because of their expensive 
nonstructural systems and contents, not because of their structural systems).

Figure 2.2. Example Inventory Relationship of Model Building Type and Occupancy 
Class
Column Chart:
x axis = Occupancy Class (Residential , Commercial, Industrial, Other)
y axis = Model Building Type (Wood, Steel, Concrete, Masonry, Mobile Home)
z axis = Floor Area 

Table 2.1. Model Building Types of HAZUS
No.
Label No.
Description
(Height) Range: Name, Stories
(Height) Typical: Stories, Feet

1
W1
Wood, Light Frame ( 5,000 sq. ft.)
Range: na ,All
Typical: 1, 14

2
W2
Wood, Greater than 5,000 sq. ft.
Range: na , All
Typical: 2, 24

3
S1L
Steel Moment Frame
Range: Low-Rise, 1-3
Typical 2, 24

4
S1M
Steel Moment Frame
Range: Mid-Rise, 4-7
Typical: 5, 60

5
S1H 
Steel Moment Frame
Range: High-Rise, 8+
Typical: 13, 156

6
S2L 
Steel Braced Frame 
Range: Low-Rise, 1-3
Typical 2, 24

7
S2M 
Steel Braced Frame 
Range: Mid-Rise, 4-7
Typical: 5, 60

8
S2H
Steel Braced Frame
Range: High-Rise, 8+
Typical: 13, 156

9 
S3 
Steel Light Frame 
Range: na, All
Typical: 1, 15

10
S4L
Steel Frame with Cast-in-Place Concrete Shear Walls 
Range: Low-Rise, 1-3
Typical 2, 24

11 
S4M
Steel Frame with Cast-in-Place Concrete Shear Walls 
Range: Mid-Rise, 4-7
Typical: 5, 60

12
S4H
Steel Frame with Cast-in-Place Concrete Shear Walls 
Range: High-Rise, 8+
Typical: 13, 156

13
S5L
Steel Frame with Unreinforced Masonry Infill Walls 
Range: Low-Rise, 1-3
Typical 2, 24

14
S5M
Steel Frame with Unreinforced Masonry Infill Walls 
Range: Mid-Rise, 4-7
Typical: 5, 60

15
S5H
Steel Frame with Unreinforced Masonry Infill Walls 
Range: High-Rise, 8+
Typical: 13, 156

16
C1L
Concrete Moment Frame 
Range: Low-Rise, 1-3
Typical 2, 20

17
C1M
Concrete Moment Frame 
Range: Mid-Rise, 4-7
Typical: 5, 50

18
C1H
Concrete Moment Frame 
Range: High-Rise, 8+
Typical: 12, 120

19
C2L
Concrete Shear Walls 
Range: Low-Rise, 1-3
Typical 2, 20

20
C2M
Concrete Shear Walls 
Range: Mid-Rise, 4-7
Typical: 5, 50

21
C2H
Concrete Shear Walls 
Range: High-Rise, 8+
Typical: 12, 120

22
C3L
Concrete Frame with Unreinforced Masonry Infill Walls 
Range: Low-Rise, 1-3
Typical 2, 20

23
C3M
Concrete Frame with Unreinforced Masonry Infill Walls 
Range: Mid-Rise, 4-7
Typical: 5, 50

24
C3H
Concrete Frame with Unreinforced Masonry Infill Walls 
Range: High-Rise, 8+
Typical: 12, 120

25
PC1
Precast Concrete Tilt-Up Walls 
Range: na, All
Typical:  1,15

26 
PC2L 
Precast Concrete Frames with Concrete Shear Walls 
Range: Low-Rise, 1-3
Typical 2, 20

27
PC2M 
Precast Concrete Frames with Concrete Shear Walls 
Range: Mid-Rise, 4-7
Typical: 5, 50

28
PC2H 
Precast Concrete Frames with Concrete Shear Walls 
Range: High-Rise, 8+
Typical: 12, 120

29
RM1L 
Reinforced Masonry Bearing Walls with Wood or Metal Deck Diaphragms 
Range: Low-Rise, 1-3
Typical 2, 20

30
RM1M 
Reinforced Masonry Bearing Walls with Wood or Metal Deck Diaphragms 
Range: Mid-Rise, 4+
Typical: 5, 50

31
RM2L
Reinforced Masonry Bearing Walls with Precast Concrete Diaphragms
Range: Low-Rise, 1-3
Typical 2, 20

32 
RM2M
Reinforced Masonry Bearing Walls with Precast Concrete Diaphragms 
Range: Mid-Rise, 4-7
Typical: 5, 50

33 
RM2H
Reinforced Masonry Bearing Walls with Precast Concrete Diaphragms 
Range: High-Rise, 8+
Typical: 12, 120

34 
URML
Unreinforced Masonry Bearing Walls 
Range: Low-Rise, 1-2
Typical 1, 15

35 
URMM
Unreinforced Masonry Bearing Walls 
Range: Mid-Rise, 3+
Typical: 3, 39

36 
MH
Mobile Homes
Range: na, All
Typical: 1, 12

Thirty three occupancy classes are defined to distinguish among residential, commercial, 
industrial or other buildings; and 36 model building types are used to classify buildings 
within 
the overall categories of wood, steel, concrete, masonry or mobile homes. Building 
inventory data relate model building type and occupancy class on the basis of floor area, 
as illustrated in 
Figure 2.2, so that for a given geographical area the distribution of the total floor area of 
model building types is known for each occupancy class. For presentation purposes, 
Figure 2.2 shows only the four overall categories of occupancy and the five overall 
categories of construction, whereas FEMA/NIBS methodology calculations are based on 
all 28 occupancy classes and 36 model building types.

Model building types are derived from the same classification system that is used in the 
NEHRP Handbook for the Seismic Evaluation of Buildings - A Prestandard [FEMA, 
1998], but 
expanded to include mobile homes and to consider building height. Table 2.1 describes 
model building types and their heights. Typical building heights are used in the 
determination of 
generic-building capacity curve properties. 

2.3. Seismic Design Levels and Quality of Construction 
The building damage functions distinguish among buildings that are designed to different 
seismic standards, have different construction quality, or are otherwise expected to 
perform 
differently during an earthquake. These differenc es in expected building performance are 
determined primarily on the basis of seismic zone location, design vintage and use (i.e., 
special 
seismic design of essential facilities). 

The 1994 Uniform Building Code [ICBO, 1994] was used to establish differences in 
seismic design levels, since at the present time the 1994 UBC or earlier editions of this 
model code likely 
governed the design, if the building was designed for earthquake loads. For the purpose 
of loss estimation, buildings designed in accordance with the 1994 NEHRP Provisions 
[FEMA, 1995] 
are assumed to have the same damage functions to buildings designed to meet the 1994 
UBC (when NEHRP map area and UBC seismic zone criteria are similar). Damage 
functions are 
provided for three "Code" seismic design levels, labeled as High-Code, Moderate-Code 
and Low-Code, and an additional design level for Pre-Code buildings. The Pre-Code 
design level 
includes buildings built before seismic codes were required for building design (e.g., 
buildings built before 1941 in California and other areas of high seismicity). 

High-Code, Moderate-Code and Low-Code seismic design levels are based on 1994 UBC 
lateral force design requirements of Seismic Zones 4, 2B and 1, respectively. Damage 
functions for 
these design levels are directly applicable to modern code buildings of about 1975 or later 
design vintage. Pre-1975 buildings and buildings of other UBC seismic zones are 
associated with 
Moderate-Code, Low-Code or Pre-Code design levels, based either on the expertise of 
the user or on default relationships provided by the FEMA/NIBS methodology. For 
example, Moderate- 
Code (rather than High-Code) damage functions are used to estimate damage to UBC 
Seismic Zone 4 buildings built before 1975 (but after 1941). HAZUS guidelines for 
selection of damage 
functions for buildings are given in Table 2.2 based on the buildings age (design vintage) 
and the applicable seismic code (i.e., as defined by either the seismic zone of the 1994 
UBC or the map area of the 1994 NEHRP Provisions). 

The FEMA/NIBS methodology also includes "Special," above-Code, building damage 
functions for those essential facilities (e.g., post-1973 California hospitals) that are 
known to be of superior design and construction. Building damage functions for Special 
buildings are based on the same theory as that of Code buildings, except that the 
parameters of the capacity and fragility curves reflect greater seismic capacity and 
reliability of these buildings. 

Table 2.2. Recommended Seismic Design Level for Existing Buildings (w/o Retrofit) 
UBC Seismic Zone (NEHRP Map Area) 
Design Vintage: Post-1975, 1941-1975, Pre-1941

Zone 4 (MA 7)
High-Code, Moderate-Code, Pre-Code (*1)

Zone 3 (MA 6) 
Moderate-Code, Moderate-Code, Pre-Code (*1)

Zone 2B (MA 5)
Moderate-Code, Low-Code, Pre-Code (*2)

Zone 2A (MA 4) 
Low-Code, Low-Code, Pre-Code (*2)

Zone 1 (MA 2/3) 
Low-Code, Pre-Code (*2), Pre-Code (*2)

Zone 0 (MA 1) 
Pre-Code (*2), Pre-Code (*2), Pre-Code (*2)

(*1) Assume Moderate-Code design for residential wood-frame buildings (W1).
(*2) Assume Low-Code design for residential wood-frame buildings (W1).

Guidance given in Table 2.2 for selection of an appropriate seismic design level applies 
to generic building types of Ordinary construction quality. Conceptually, each type of 
generic 
building and level of seismic design also includes buildings of Inferior and Superior 
construction quality, although distinguishing between generic building type on the basis 
of construction quality is usually impossible (since only the design vintage is typically 
known). Nonetheless, the HAZUS provides users with opportunity of selecting from one 
of nine combinations of seismic design level (High, Moderate and Low) and construction 
quality (Superior, Moderate and Low). In terms of the amount damage predicted, 
buildings of Ordinary construction may be approximately related to other combinations 
of seismic design level and construction quality as shown in Table 2.3.

Table 2.3. Approximate Relationship of Seismic Design Level and Construction Quality 
Construction Quality
Seismic Design Level: High-Code , Moderate-Code, Low-Code, None

Superior 
Seismic Design Level: Special (*1), High-Code, Moderate-Code, Low-Code

Ordinary
Seismic Design Level: High Code, Moderate-Code, Low-Code, Pre-Code

Inferior
Seismic Design Level: Moderate-Code, Low-Code, Pre-Code, Pre-Code

(*1) Special High-Code includes essential facilities such as post-1973 California 
hospitals.

2.4. Pre-Code Structural and Nonstructural Systems and Contents
Buildings are composed of both structural (load carrying) and nonstructural systems (e.g., 
architectural and mechanical components). While damage to the structural system is the 
most 
important measure of building damage affecting casualties and catastrophic loss of 
function (due to unsafe conditions), damage to nonstructural systems and contents tends 
to dominate economic loss. Typically, the structural system represents about 25% of the 
building's worth.

To better estimate different types of loss, building damage functions separately predict 
damage to: (1) the structural system, (2) drift-sensitive nonstructural components, such as 
partition walls that are primarily affected by building displacement, and (3) acceleration-
sensitive nonstructural components, such as suspended ceilings, that are primarily 
affected by building shaking. Building contents are also considered to be acceleration 
sensitive. Distinguishing between drift- and acceleration-sensitive nonstructural 
components, and contents, permits more realistic estimates of damage considering 
building response. Table 2.4 lists typical drift-sensitive and acceleration-sensitive 
components and building components. 

Table 2.4. HAZUS Classification of Drift-Sensitive and Acceleration-Sensitive 
Nonstructural Components and Building Contents 
System Type
Component Description, Drift-Sensitive  or  Acceleration-Sensitive 

Architectural
* Nonbearing Walls/Partitions, Drift-Sensitive
* Cantilever Elements and Parapets, Acceleration-Sensitive
* Exterior Wall Panels, Drift-Sensitive 
* Veneer and Finishes, Drift-Sensitive
* Penthouses, Drift-Sensitive
* Racks and Cabinets, Acceleration-Sensitive
* Access Floors, Acceleration-Sensitive 
* Appendages and Ornaments, Acceleration-Sensitive 

Mechanical and Electrical 
* General Mechanical (boilers, etc.) , Acceleration-Sensitive
* Manufacturing and Process Machinery, Acceleration-Sensitive
* Piping Systems, Acceleration-Sensitive 
* Storage Tanks and Spheres, Acceleration-Sensitive 
* HVAC Systems (chillers, ductwork, etc.), Acceleration-Sensitive 
* Elevators, Acceleration-Sensitive 
* Trussed Towers, Acceleration-Sensitive 
* General Electrical (switchgear, ducts, etc.) , Acceleration-Sensitive
* Lighting Fixtures, Acceleration-Sensitive 

Contents 
* File Cabinets, Bookcases, etc., Acceleration-Sensitive 
* Office Equipment and Furnishings, Acceleration-Sensitive 
* Computer/Communication Equipment, Acceleration-Sensitive 
* Nonpermanent Manufacturing Equipment, Acceleration-Sensitive
* Manufacturing/Storage Inventory, Acceleration-Sensitive 
* Art and Other Valuable Objects, Acceleration-Sensitive

2.5. Damage States
Damage states are defined separately for structural and nonstructural systems of a 
building. Damage is described by one of four discrete damage states: Slight, Moderate, 
Extensive or 
Complete, and Collapse as subset of Complete structural damage. Of course, actual 
building damage varies as a continuous function of earthquake demand. Ranges of 
damage are used to 
describe building damage, since it is not practical to have a continuous scale, and damage 
states provide the user with an understanding of the building's physical condition. Loss 
functions relate the physical condition of the building to various loss parameters (i.e., 
direct economic loss, casualties, and loss of function). For example, direct economic loss 
due to Moderate damage is assumed to correspond to 10% replacement value of 
structural and nonstructural components, on the average.

The four damage states of the FEMA/NIBS methodology are similar to the damage states 
defined in Expected Seismic Performance of Buildings [EERI, 1994], except that damage 
descriptions vary for each model building type based on the type of structural system and 
material. Table 2.5 provides structural damage states for W1 buildings (light frame wood) 
typical of the conventional construction used for single-family homes. 

Table 2.5. Example Damage States - Light-Frame Wood Buildings (W1) 

Damage State - Description

Slight - Small plaster cracks at corners of door and window openings and wall-ceiling 
intersections; small cracks in masonry chimneys and masonry veneers. Small cracks are 
assumed to be visible with a maximum width of less than 1/8 inch (cracks wider than 1/8 
inch are referred to as "large" cracks). 

Moderate - Large plaster or gypsum-board cracks at corners of door and window 
openings; small diagonal cracks across shear wall panels exhibited by small cracks in 
stucco and gypsum wall panels; large cracks in brick chimneys; toppling of tall masonry 
chimneys.

Extensive - Large diagonal cracks across shear wall panels or large cracks at plywood 
joints; permanent lateral movement of floors and roof; toppling of most brick chimneys; 
cracks in foundations; splitting of wood sill plates and/or slippage of structure over 
foundations. 

Complete - Structure may have large permanent lateral displacement or be in imminent 
danger of collapse due to cripple wall failure or failure of the lateral load resisting 
system; some structures may slip and fall off the foundation; large foundation cracks. 
Three percent of the total area of buildings with Complete damage is expected to be 
collapsed, on average. 

2.6. Building Capacity Curves
A building capacity curve is a plot of a building's lateral load resistance as a function of a 
characteristic lateral displacement (i.e., a force-deflection plot). It is derived from a plot 
of static-equivalent base shear versus building displacement at the roof, known 
commonly as a pushover curve. In order to facilitate direct comparison with spectral 
demand, base shear is converted to spectral acceleration, and the roof displacement is 
converted to spectral displacement using modal properties that represent pushover 
response. Pushover curves and related-capacity curves, are derived from concepts similar 
to those of the NEHRP Guidelines for the Seismic Rehabilitation of Buildings [FEMA, 
1997], and in Seismic Evaluation and Retrofit of Concrete Buildings [SSC, 1996], known 
as ATC-40. 

Building capacity curves are constructed for each model building type and represent 
different levels of lateral force design and for a given loading condition, expected 
building performance. Each curve is defined by two control points: (1) the "yield" 
capacity, and (2) the "ultimate" capacity. The yield capacity represents the lateral strength 
of the building and accounts for design strength, redundancies in design, conservatism in 
code requirements and expected (rather than nominal) strength of materials. Design 
strengths of model building types are based on the requirements of current model seismic 
code provisions (e.g., 1994 UBC or NEHRP Provisions) or on an estimate of lateral 
strength for buildings not designed for earthquake loads. Certain buildings designed for 
wind, such as taller buildings located in zones of low or moderate seismicity, may have a 
lateral design strength considerably greater than those based on seismic code provisions.

The ultimate (plastic) capacity represents the maximum strength of the building when the 
global structural system has reached a full mechanism. Typically, a building is assumed 
capable of deforming beyond its ultimate point without loss of stability, but its structural 
system provides no additional resistance to lateral earthquake force. Up to yield, the 
building capacity curve is assumed to be linear with stiffness based on an estimate of the 
expected period of the building. From yield to the ultimate point, the capacity curve 
transitions in slope from an essentially elastic state to a fully plastic state. The capacity 
curve is assumed to remain plastic past the ultimate point. An example building capacity 
curve is shown in Figure 2.3. 

Figure 2.3. Example Building Capacity Curve and Control Points
Diagram displays Spectral Displacement (inches)   versus  Spectral Acceleration (g's)

The following parameters define the yield point and the ultimate point of capacity curves 
as shown in Figure 2.3: 
Cs = point of significant yielding of design strength coefficient (fraction of building's 
weight), 

Te = expected "elastic" fundamental- mode period of building (seconds), 

a1 = fraction of building weight effective in the pushover mode,

a2 = fraction of building height at the elevation where pushover-mode displacement is 
equal to spectral displacement (not shown in Figure 2.3), 

g = "overstrength" factor relating "true" yield strengt h to design strength, 

l = "overstrength" factor relating ultimate strength to yield strength, and 

m  = "ductility" ratio relating ultimate displacement to l times the yield displacement (i.e., 
assumed point of significant yielding of the structure). 

2.7. Building Response Calculation 
Building response is determined by the intersection of the demand spectrum and the 
building capacity curve. Intersections are illustrated in Figure 2.4 for three example 
demand spectra 
representing what can be considered as weak, medium and strong ground shaking, and 
two building capacity curves representing weaker and stronger construction, respectively. 
As shown in Figure 2.4, stronger and stiffer construction displaces less than weaker and 
more flexible construction for the same le vel of spectral demand, and less damage is 
expected to the structural system and nonstructural components sensitive to drift. In 
contrast, stronger (and stiffer) construction will shake at higher acceleration levels, and 
more damage is expected to 
nonstructural components and contents sensitive to acceleration.

The demand spectrum is based on the 5%-damped response spectrum at the building's 
site (or center of a study area containing a group of buildings), reduced for effective 
damping when 
effective damping exceeds the 5% damping level of the input spectrum. Background on 
the 5%-damped response spectrum of ground shaking is provided in Section 5. 

Figure 2.4. Example Intersection of Demand Spectra and Building Capacity Curves
Diagram displays Spectral Displacement (inches)   versus  Spectral Acceleration (g's)

2.8. Building Fragility Curves
Building fragility curves are lognormal functions that describe the probability of 
reaching, or exceeding, structural and nonstructural damage states, given median 
estimates of spectral 
response, for example spectral displacement. These curves take into account the 
variability and uncertainty associated with capacity curve properties, damage states and 
ground shaking. 

Figure 2.5 provides an example of fragility curves for the four damage states used in the 
FEMA/NIBS methodology and illustrates differences in damage-state probabilities for 
three 
levels of spectral response corresponding to weak, medium, and strong earthquake 
ground shaking, respectively. The terms "weak," "medium," and "strong" are used here 
for simplicity; 
in the actual methodology, only quantitative values of spectral response are used. 

Figure 2.5. Example Fragility Curves for Slight, Moderate, Extensive and Complete 
Damage 
Diagram displays Spectral Response (Weak Shaking, Medium Shaking, Strong Shaking)   
versus   Probability (0.0, 0.5, 1.0 )

The fragility curves distribute damage among Slight, Moderate, Extensive and Complete 
damage states. For any given value of spectral response, discrete damage-state 
probabilities are 
calculated as the difference of the cumulative probabilities of reaching, or exceeding, 
successive damage states. The probabilities of a building reaching or exceeding the 
various damage levels at a given response level sum to 100%. Discrete damage-state 
probabilities are used as inputs to the calculation of various types of building-related loss. 
Figure 2.6 provides an example of discrete damage state probabilities for the three levels 
of earthquake ground shaking. 

Each fragility curve is defined by a median value of the demand parameter (e.g., spectral 
displacement) that corresponds to the threshold of that damage state and by the variability 
associated with that damage state. For example, the spectral displacement, Sd, that 
defines the threshold of a particular damage state (ds) is given by Equation (2-1): 

Sd =  the median value of spectral displacement of damage state (ds)  multiplied by  
lognormal random variable with a unit median value and a logarithmic standard deviation 
(bds)

Figure 2.6. Example Damage-State Probabilities for Weak, Medium and Strong Shaking 
Levels 
Column chart 
x axis = Shaking Level (Weak, Medium, Strong)
y axis = Damage State (None, Slight, Moderate, Extensive, Complete)
z axis = Probability (0, 0.2, 0.4, 0.6) 

In a more general formulation of fragility curves, the lognormal standard deviation, b, has 
been expressed in terms of the randomness and uncertainty components of variability, bR 
and bU, respectively [Kennedy, et. al., 1980]. In this formulation, uncertainty represents 
the component of the variability that could theoretically be reduced with improved 
knowledge; whereas, 
randomness represents the inherent variability (in response) that cannot be eliminated, 
even with perfect knowledge. Since it is not considered practical to separate uncertainty 
from randomness, the combined variability, b, is used to develop a composite "best-
estimate" fragility curve.

The conditional probability of being in, or exceeding, a particular damage state, ds, given 
the spectral displacement, Sd, (or other seismic demand parameter) is defined by 
Equation (2-2): 
Product of threshold of damage state divided by median value of spectral displacment = 
the standard normal cumulative distribution function times the sum of 1 over the standard 
deviation of the natural logarithm of spectral displacement for damage state (ds), 
multiplied by the 1n {the median value of spectral displacement over the median value of 
spectral displacement at which the building reaches the threshold of damage state (ds).

2.9. Example Capacity and Fragility Data
Figures 2.7 through 2.11 are plots of capacity curves and damage-state medians for light-
frame wood, low-rise URM bearing wall, and low-rise, mid-rise and high-rise concrete 
moment frame buildings, respectively. Below each figure, Tables 2.6 through 2.10 
summarize elastic period data and drift ratios corresponding to capacity curve control 
points and damage-state medians. Each figure (and table) includes capacity and fragility 
data for different seismic design levels.

Comparison of Figure 2.7 and Table 2.6 data for light-wood frame buildings with Figure 
2.8 and Table 2.7 data for low-rise URM bearing wall buildings illustrates capacity curve 
and fragility 
properties ranging from the strongest, most "ductile" to the weakest, least "ductile" 
generic building types. Comparison of data shown in Figures 2.9, 2.10 and 2.11 (and 
corresponding 
tables) illustrates the reduction in stiffness and strength of capacity curves (and related 
changes to damage-state medians) with increase in building height. 

2.10 Building Loss Functions
Building loss functions of HAZUS may be thought of as the second part of an integral 
two-step process in which estimates of building damage (i.e., probability of damage state) 
are transformed into estimates of various types of loss. 

The building loss functions are numerous and often complex, and a proper description of 
the background and theory would be too extensive to include in this manual. Users are 
directed to the HAZUS-MH Technical Manual for complete description of building loss 
functions. The Earthquake Spectra paper "Estimation of Earthquake Losses to Buildings" 
[Kircher, 1997b] also 
describes building loss functions used to calculate direct economic loss and compares 
calculated values with dollar losses of the 1994 Northridge earthquake. 

Figure 2.7. Generic Building Type W1 (Light Frame Wood < 5,000 sq. ft.)1 - Capacity 
Curves and Structural Damage-State Thresholds (Fragility Medians) for Five Seismic 
Design Levels (Special High, High, Moderate, Low and Pre -Code) 
Line Chart displays Spectral Displacement (inches = 0, 5, 10, 15, 20, 25, 30)   versus   
Spectral Acceleration (0.0, 0.5, 1.0, 1.5, 2.0)
Points: Capacity - Yield Point, Capacity - (Fully) Plastic Point, Slight Damage, Moderate 
Damage Threshold, Extensive Damage Threshold, Complete Damage Threshold

Table 2.6. Generic Building Type W1 (Light Frame Wood < 5,000 sq. ft.)(*1) - Elastic 
Period Values and Average Inter-Story Drift Ratios of Capacity Curve Control Points and 
Structural Damage State Thresholds (Fragility Medians)

Seismic Design Level:
Elastic Period (sec.): 
(Average Inter-Story Drift Ratio) Capacity Curve Control Points: Yield, Plastic
(Average Inter-Story Drift Ratio) Structural Damage State Thresholds (Fragility 
Medians): Slight, Moderate, Extensive, Complete

Seismic Design Level: Special High-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0057, 0.1371 
Structural Damage State Thresholds (Fragility Medians): 0.0050, 0.0150, 0.0500, 0.1250

Seismic Design Level: High-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0038, 0.0913
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0120, 0.0400, 0.1000

Seismic Design Level: Moderate-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0029, 0.0514
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0099, 0.0306, 0.0750

Seismic Design Level: Low-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0019, 0.0343
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0099, 0.0306, 0.0750

Seismic Design Level: Pre-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0019, 0.0343
Structural Damage State Thresholds (Fragility Medians): 0.0032, 0.0079, 0.0245, 0.0600

(*1) A typical W1 building is 1-story (i.e., 14 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.75W multiplied 
by spectral acceleration. 

Figure 2.8. Generic Building Type URML (Low-Rise Unreinforced Masonry Bearing 
Walls)(*1) - Capacity Curves and Structural Damage-State Thresholds (Fragility 
Medians) for the Pre -Code Seismic Design Level
Line Chart displays Spectral Displacement (inches = 0, 5, 10, 15, 20, 25, 30)   versus   
Spectral Acceleration (0.0, 0.5, 1.0, 1.5, 2.0)
Points: Capacity - Yield Point, Capacity - (Fully) Plastic Point, Slight Damage, Moderate 
Damage Threshold, Extensive Damage Threshold, Complete Damage Threshold
(*1) A typical URML building is 1-story (i.e., 15 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.50W multiplied 
by spectral acceleration.

Table 2.7. Generic Building Type URML (Mid-Rise URM Bearing Walls)(*1) - Elastic 
Period Values and Average Inter-Story Drift Ratios of Capacity Curve Control Points and 
Structural Damage State Thresholds (Fragility Medians)

Seismic Design Level:
Elastic Period (sec.): 
(Average Inter-Story Drift Ratio) Capacity Curve Control Points: Yield, Plastic
(Average Inter-Story Drift Ratio) Structural Damage State Thresholds (Fragility 
Medians): Slight, Moderate, Extensive, Complete

Seismic Design Level: Special High-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0057, 0.1371 
Structural Damage State Thresholds (Fragility Medians): 0.0050, 0.0150, 0.0500, 0.1250

Seismic Design Level: High-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0038, 0.0913
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0120, 0.0400, 0.1000

Seismic Design Level: Moderate-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0029, 0.0514
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0099, 0.0306, 0.0750

Seismic Design Level: Low-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0019, 0.0343
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0099, 0.0306, 0.0750

Seismic Design Level: Pre-Code
Elastic Period (sec.): 0.35
Capacity Curve Control Points: 0.0019, 0.0343
Structural Damage State Thresholds (Fragility Medians): 0.0032, 0.0079, 0.0245, 0.0600

(*1) A typical URML building is 1-story (i.e., 15 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.50W multiplied 
by spectral acceleration. 

Figure 2.9. Generic Building Type C1L (Low-Rise Concrete Moment Frame)(*1) - 
Capacity Curves and Structural Damage-State Thresholds (Fragility Medians) for Five 
Seismic Design Levels (Special High, High, Moderate, Low and Pre-Code)
Line Chart displays Spectral Displacement (inches = 0, 5, 10, 15, 20, 25, 30)   versus   
Spectral Acceleration (0.0, 0.5, 1.0, 1.5, 2.0)
Points: Capacity - Yield Point, Capacity - (Fully) Plastic Point, Slight Damage, Moderate 
Damage Threshold, Extensive Damage Threshold, Complete Damage Threshold
(*1) A typical C1L building is 2-stories (i.e., 20 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.80W multiplied 
by spectral acceleration.

Table 2.8. Generic Building Type C1L (Low-Rise Concrete Moment Frame)(*1) - Elastic 
Period Values and Average Inter-Story Drift Ratios of Capacity Curve Control Points and 
Structural Damage State Thresholds (Fragility Medians)

Seismic Design Level:
Elastic Period (sec.): 
(Average Inter-Story Drift Ratio) Capacity Curve Control Points: Yield, Plastic
(Average Inter-Story Drift Ratio) Structural Damage State Thresholds (Fragility 
Medians): Slight, Moderate, Extensive, Complete

Seismic Design Level: Special High-Code
Elastic Period (sec.): 0.40
Capacity Curve Control Points: 0.0033, 0.0782 
Structural Damage State Thresholds (Fragility Medians): 0.0063, 0.0125, 0.0375, 0.1000

Seismic Design Level: High-Code
Elastic Period (sec.): 0.40
Capacity Curve Control Points: 0.0022, 0.0522
Structural Damage State Thresholds (Fragility Medians): 0.0050, 0.0100, 0.0300, 0.0800

Seismic Design Level: Moderate-Code
Elastic Period (sec.): 0.40
Capacity Curve Control Points: 0.0011, 0.0196
Structural Damage State Thresholds (Fragility Medians): 0.0050, 0.0087, 0.0233, 0.0600

Seismic Design Level: Low-Code
Elastic Period (sec.): 0.41
Capacity Curve Control Points: 0.0006, 0.0082
Structural Damage State Thresholds (Fragility Medians): 0.0050, 0.0080, 0.0200, 0.0500

Seismic Design Level: Pre-Code
Elastic Period (sec.): 0.41
Capacity Curve Control Points: 0.0006, 0.0098
Structural Damage State Thresholds (Fragility Medians): 0.0040, 0.0064, 0.0160, 0.0400

(*1) A typical C1L building is 2-stories (i.e., 20 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.80W multiplied 
by spectral acceleration.

Figure 2.10. Generic Building Type C1M (Mid-Rise Concrete Moment Frame)(*1) - 
Capacity Curves and Structural Damage-State Thresholds (Fragility Medians) for Five 
Seismic Design Levels (Special High, High, Moderate, Low and Pre-Code)
Line Chart displays Spectral Displacement (inches = 0, 5, 10, 15, 20, 25, 30)   versus   
Spectral Acceleration (0.0, 0.5, 1.0, 1.5, 2.0)
Points: Capacity - Yield Point, Capacity - (Fully) Plastic Point, Slight Damage, Moderate 
Damage Threshold, Extensive Damage Threshold, Complete Damage Threshold
(*1) A typical C1M building is 5-stories (i.e., 50 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.80W multiplied 
by spectral acceleration.

Table 2.9. Generic Building Type C1M (Mid-Rise Concrete Moment Frame)(*1) - 
Elastic Period Values and Average Inter-Story Drift Ratios of Capacity Curve Control 
Points and Structural Damage State Thresholds (Fragility Medians)

Seismic Design Level:
Elastic Period (sec.): 
(Average Inter-Story Drift Ratio) Capacity Curve Control Points: Yield, Plastic
(Average Inter-Story Drift Ratio) Structural Damage State Thresholds (Fragility 
Medians): Slight, Moderate, Extensive, Complete

Seismic Design Level: Special High-Code
Elastic Period (sec.): 0.75
Capacity Curve Control Points: 0.0038, 0.0614 
Structural Damage State Thresholds (Fragility Medians): 0.0042, 0.0083, 0.0250, 0.0667

Seismic Design Level: High-Code
Elastic Period (sec.): 0.75
Capacity Curve Control Points: 0.0026, 0.0410
Structural Damage State Thresholds (Fragility Medians): 0.0033, 0.067, 0.0200, 0.0533

Seismic Design Level: Moderate-Code
Elastic Period (sec.): 0.76
Capacity Curve Control Points: 0.0013, 0.0154
Structural Damage State Thresholds (Fragility Medians): 0.0033, 0.0058, 0.0156, 0.0400

Seismic Design Level: Low-Code
Elastic Period (sec.): 0.76
Capacity Curve Control Points: 0.0006, 0.0064
Structural Damage State Thresholds (Fragility Medians): 0.0033, 0.0053, 0.0133, 0.0333

Seismic Design Level: Pre-Code
Elastic Period (sec.): 0.76
Capacity Curve Control Points: 0.0006, 0.0077
Structural Damage State Thresholds (Fragility Medians): 0.0027, 0.0043, 0.0107, 0.0267

(*1) A typical C1M building is 5-stories (i.e., 50 feet) in height. Spectral displacement is 
equal to 0.75 multiplied by roof displacement and base shear is equal to 0.80W multiplied 
by spectral acceleration.

Figure 2.11. Generic Building Type C1H (High-Rise Concrete Moment Frame)(*1) - 
Capacity Curves and Structural Damage-State Thresholds (Fragility Medians) for Five 
Seismic Design Levels (Special High, High, Moderate, Low and Pre-Code)
Line Chart displays Spectral Displacement (inches = 0, 10, 20, 30, 40, 50, 60)   versus   
Spectral Acceleration (0.0, 0.25, 0.5, 0.75, 1.00)
Points: Capacity - Yield Point, Capacity - (Fully) Plastic Point, Slight Damage, Moderate 
Damage Threshold, Extensive Damage Threshold, Complete Damage Threshold
(*1) A typical C1H building is 12-stories (i.e., 120 feet) in height. Spectral displacement 
is equal to 0.60 multiplied by roof displacement and base shear is equal to 0.75W 
multiplied by spectral acceleration.

Table 2.10. Generic Building Type C1H (High-Rise Concrete Moment Frame)(*1) - 
Elastic Period Values and Average Inter-Story Drift Ratios of Capacity Curve Control 
Points and Structural Damage State Thresholds (Fragility Medians)

Seismic Design Level:
Elastic Period (sec.): 
(Average Inter-Story Drift Ratio) Capacity Curve Control Points: Yield, Plastic
(Average Inter-Story Drift Ratio) Structural Damage State Thresholds (Fragility 
Medians): Slight, Moderate, Extensive, Complete

Seismic Design Level: Special High-Code
Elastic Period (sec.): 1.45
Capacity Curve Control Points: 0.0035, 0.0419 
Structural Damage State Thresholds (Fragility Medians): 0.0031, 0.0063, 0.0188, 0.0500

Seismic Design Level: High-Code
Elastic Period (sec.): 1.45
Capacity Curve Control Points: 0.0023, 0.0279
Structural Damage State Thresholds (Fragility Medians): 0.0025, 0.050, 0.0150, 0.0400

Seismic Design Level: Moderate-Code
Elastic Period (sec.): 1.45
Capacity Curve Control Points: 0.0012, 0.0105
Structural Damage State Thresholds (Fragility Medians): 0.0025, 0.0043, 0.0117, 0.0300

Seismic Design Level: Low-Code
Elastic Period (sec.): 1.46
Capacity Curve Control Points: 0.0006, 0.0044
Structural Damage State Thresholds (Fragility Medians): 0.0025, 0.0040, 0.0100, 0.0250

Seismic Design Level: Pre-Code
Elastic Period (sec.): 1.46
Capacity Curve Control Points: 0.0006, 0.0052
Structural Damage State Thresholds (Fragility Medians): 0.0020, 0.0032, 0.0080, 0.0200

(*1) A typical C1H building is 12-stories (i.e., 120 feet) in height. Spectral displacement 
is equal to 0.60 multiplied by roof displacement and base shear is equal to 0.75W 
multiplied by spectral acceleration.

SECTION 3 
SUMMARY OF BUILDING-SPECIFIC DATA PROVIDED BY USER 
3.1. Introduction 
The accuracy of building-specific loss estimates depends primarily on the extent and 
quality of the information provided by the user (e.g., the seismic/structural engineer). 
While default data is provided as a starting point and may be used if considered 
appropriate, the more effort the user puts into the determination of building-specific data, 
the more reliable the results will be. 
Conversely, not all input data have the same level of importance in terms of the reliability 
of the results. This section describes required input data to be provided by the user and 
indicates, 
qualitatively, the likely relative importance of the data to loss estimates. 

3.2 . Site/Source Seismic Hazard Data
Seismic hazard data are not required for development of building damage and loss 
functions, but are arguably the most important data that will be input by the user for loss 
estimation. HAZUS permits users to select the scenario earthquake magnitude, source 
type and location, and other factors affecting seismic hazard at the building site. 

For building-specific loss estimation, it would generally be expected that the user has 
carefully researched and determined an appropriate scenario earthquake. Typically, this 
would include 
identifying source type, magnitude and geographical location of the fault rupture plane 
for Western United States (WUS) events, or the epicenter for Central and Eastern United 
States 
(CEUS) events. It would also be expected that the user has obtained certain geotechnical 
data including site class (soil type), the susceptibility of the site to either liquefaction or 
landslide, and a determination that surface fault rupture is not a credible hazard at the 
site.

Site data on soil type (and ground failure) cannot be input directly to the AEBM, but can 
be input to the HAZUS software as soil or ground failure data maps or by modifying 
default data on a 
census tract-by-census basis. If the user provides no information, the AEBM will 
calculate damage and loss based on ground shaking corresponding to the default soil type 
(i.e., Soil Class 
D) and will ignore the effects of ground failure. Section 9.2.7 of the HAZUS-MH User's 
Manual describes how users may include site conditions (other than Soil Class D) and 
effects of ground 
failure in HAZUS analyses. Users would need to make changes to default soil type (and 
ground failure data) prior to running the AEBM. 

3.3 . Inventory Data 
It is expected that the user will have basic (inventory) data on each AEBM building (or 
group of buildings) of interest, including building location, size, occupancy, replacement 
value and other 
financial data. In general, these data are known by building owners or are otherwise 
available to users performing detailed building-specific analyses. For individual 
buildings, inventory data 
include the following:
* Building Location - What is the geographical location of the building (e.g., address and 
latitude/longitudinal coordinates of site)? 
* Building Occupants - How many people use the building during the day and at night? 
What percentage of the building is owner occupied? 
* Building Size - What is the gross square footage, the number of floors and height of the 
building?
* Replacement Value - What is the replacement value of the building, contents (and/or 
business inventory)? 
* Loss of Function Cost - What are the financial data and costs associated with loss of 
building function, including business income, wages paid, and relocation costs due to 
disruption of 
operation and rental of temporary space?

Users must provide inventory data to run the AEBM. In contrast, performance data that 
define building response properties, capacity curves and fragility (damage) functions, and 
loss data 
described in the following sections may be based entirely on default values of HAZUS 
parameters.

The AEBM develops an initial "profile" of building response, damage and loss 
parameters based on default values of HAZUS corresponding to the (1) occupancy class, 
(2) building type, (3) 
seismic design level and (4) building quality of the building (or group of buildings) of 
interest. As a minimum, users must provide these four building characteristics to run the 
AEBM. These 
characteristics can be very important to AEBM estimates of damage and loss, if default 
values are not modified to incorporate building-specific data. 

3.4. Performance Data
Data describing the expected performance of the structural system and nonstructural 
components are required to develop improved building-specific damage functions. These 
data include an improved understanding of the structure's response properties and damage 
to components and elements as a function of the amplitude of response. These data are 
best determined from a pushover analysis of the building using procedures of the FEMA 
Guidelines or the Seismic Evaluation and Retrofit of Concrete Buildings (ATC-40). It is 
expected that users are familiar 
with these documents and will perform a pushover analysis to determine input data. 

3.4.1. Building Failure Modes 
The single most important benefit of pushover analysis is an improved understanding of 
the failure mode(s) of the building due to ground shaking. The user is expected to be 
familiar with 
the building type (i.e., structural system), knowledgeable regarding the type of damage 
that has occurred to similar structures in past earthquakes, and capable of developing and 
analyzing 
representative models. While pushover analysis will produce detailed information on the 
performance of elements and components, the results are valid only if elements and 
components 
are modeled in a realistic and appropriate manner. Models need not be overly complex, 
but must capture the important characteristics of plausible modes of failure.

Pushover analyses typically assume the building is free to displace laterally. Adjacent 
buildings or other structures are often close and would prevent free movement. In such 
cases, the pushover analysis would not capture "pounding" effects (unless the pushover 
model was developed with gap elements, etc.).

On a more general basis, pushover analysis is limited to evaluating peak building 
response due to ground shaking. In general, ground shaking controls damage and loss 
estimates. However, at sites with high or very high susceptibility to liquefaction or 
landslide, ground failure can dominate the calculation of loss. In such cases, developing 
detailed pushover models would not 
significantly improve the accuracy of damage and loss estimates. Likewise, pushover 
analysis does not address other non-shaking failure modes, such as those due to 
inundation, fire, and 
hazardous materials release.

Pushover analysis necessarily focuses on structural failure modes. Nonstructural 
components and contents can play a dominant role in building losses. For example, does 
the building have 
particularly vulnerable or hazardous nonstructural systems or components (e.g., hollow 
clay tile partition walls) or particularly vulnerable or hazardous contents (e.g., large 
quantity of hazardous of flammable material)? Building surveys and evaluations of 
nonstructural components and contents may be used to identify hazardous nonstructural 
components and contents. 

3.4.2. Pushover Models and Modal Properties
HAZUS methods estimate building damage based on inter-story drift and floor 
acceleration. It is important that pushover models incorporate a sufficient number of 
elements/components to 
accurately capture inter-story drift and floor acceleration. Foundation and/or diaphragm 
flexibility should also be modeled, if such behavior would significantly influenced 
performance 
of elements and components.

For buildings with complex configurations or which are susceptible to torsion, pushover 
models would need to be 3-dimensional (with push force applied on principle axes), or 
otherwise need to account for building rotation. Pushover curves should be developed for 
each direction of response (with unique response properties) of each structural segment 
(if the building has more 
than one segment) of the building. Each pushover curve should incorporate the flexibility 
of all elements and components that contribute significantly to building response. 

Pushover curves (as used in the NEHRP Guidelines and ATC-40) represent roof 
displacement vs. base shear. Typically, these curves are calculated up to the 
"performance point" which is based on some specified level of seismic demand. HAZUS 
methods estimate response (damage and loss) for an arbitrary level of shaking and 
therefore require building capacity information at all possible displacements. Pushover 
curves should be calculated at displacements up to complete failure of the structural 
system. HAZUS methods estimate spectral response using the capacity spectrum method. 
Capacity curves are derived from pushover curves using the shape of pushover mode, and 
the distribution of mass throughout the building. Pushover mode shape (and mass 
distribution throughout the building) data should be calculated for each pushover curve.

3.4.3. Element/Component Response Characteristics 
HAZUS methods estimate building damage based on threshold values of inter-story drift 
(and floor acceleration) that initiate different states of damage (e.g., Slight, Moderate, 
Extensive and 
Complete). These threshold values of damage states represent generic building types and 
are not necessarily appropriate for a specific building. In particular, buildings with certain 
types of 
irregularities or vulnerable configurations could have significantly lower damage-state 
thresholds. Values of inter-story drift defining structural damage states should be selected 
considering irregularities (e.g., soft story), brittle failure of elements an components and 
other factors that influence the performance of the structural system.

The results of pushover analysis of a specific building provide a much better 
understanding of the behavior (performance) of elements/components. It is expected that 
users will perform 
pushover analysis in accordance with the nonlinear static analysis procedures of the 
NEHRP Guidelines (or ATC-40) and relate the performance of elements/components to 
various levels of 
earthquake response (e.g., building drift). This manual guides users in the determination 
of appropriate threshold values of damage states (and loss functions) based on this 
information. 
This is both the most important and most subjective aspect of incorporating pushover 
analysis results into HAZUS loss estimation. 

3.5. Loss Data 
Data on occupants, the financial value of the building and its operation (including costs 
of repairs) and the time required to make repairs are required to develop improved 
building-specific 
loss functions. HAZUS loss functions are typically based on the specific or general 
occupancy (use) of the building, and building occupancy is mapped to model building 
type on a census-tract basis in regional loss studies. On an individual building basis, loss 
functions can be greatly improved by the use of building-specific data. 

Loss data may be divided into two groups: occupant data related to the calculation of 
injuries and deaths, and financial and loss of function data related to calculation of direct 
economic losses. A possible third data group, related to direct social losses resulting from 
displaced households and short-term shelter needs, is not included in the methods since 
building-specific data could not be used to improve the estimates of these types of losses.

3.5.1. Occupant Data 
HAZUS methods provide estimates of casualties at 2:00 a.m. (nighttime building 
population), 2:00 p.m. (daytime building population) and 5:00 p.m. (large commuting 
population). The latter 
is not included in building-specific methods. Daytime (or nighttime) building population 
is based on basic building use (e.g., residential, commercial or industrial) and building 
inventory 
and census data that distributes the population of the study region among the three basic 
building use groups (and the fraction assumed to be commuting). HAZUS does not 
distribute daytime or nighttime populations (of a study region) to individual buildings.

The user will need to provide the number of daytime and nighttime occupants of 
individual buildings of the AEBM. The user should also determine if the distribution of 
the building 
population is significantly correlated with building failure (e.g., collapse). For example, 
suppose only a specific portion of a building is determined to be susceptible to collapse. 
Is this portion of the building densely populated, have an average building population, or 
perhaps have a very low population (e.g., storage area)? 

3.5.2. Financial Data 
HAZUS estimates direct economic loss to buildings based on separate damage and loss 
estimates for the structural system, drift-sensitive nonstructural components, acceleration-
sensitive 
nonstructural components, and contents (and business inventory). The repair or 
replacement cost of each damage state is expressed as a fraction of total replacement cost 
of the system of interest (i.e., loss ratio). Total building replacement value, including 
regional adjustment, is distributed between structural, nonstructural drift-sensitive and 
nonstructural acceleration-sensitive systems. The value of contents is crudely based on a 
fraction (e.g., 50%) of the building's replacement cost. 

The user will need to provide the replacement cost of individual buildings of the AEBM, 
their contents and business inventories (if applicable). The replacement costs of the last 
two items can 
be of particular importance for buildings or businesses that have special (expensive) 
contents or inventory items (e.g., laboratory or special process equipment). The user 
should also confirm (or revise accordingly) default values of HAZUS that distribute 
replacement cost of the building between structural, nonstructural drift-sensitive 
components and nonstructural accelerationsensitive components, respectively.

HAZUS relates each damage state to an amount of financial loss as a fraction of 
replacement value. Users should confirm (or revise accordingly) the default values of 
HAZUS parameters 
that relate damage states to financial loss, considering element/component damage as a 
function of building drift (e.g., spectral displacement). Users may choose to develop 
building-specific 
loss ratios for each damage state that better reflect construction costs associated with 
inspection, demolition, phasing, unavoidable impact of repair on undamaged systems, 
etc. Ideally, users 
would identify damage from pushover analysis, describe the type and extent of repairs 
required to correct damage, and develop associated repair costs for each damage state. 

In addition to repair and replacement costs, direct economic losses also include the 
financial effects of loss of building function on busine ss income, wage income, 
relocation and temporary 
space rental. Users should confirm (or revise accordingly) default values of HAZUS of 
the time required for clean-up and repair (construction time), considering the extent of 
damage determined from pushover analysis and evaluation of damage to building 
components.

SECTION 4 
SUMMARY OF DAMAGE AND LOSS FUNCTION PARAMETERS 
4.1. Introduction
This section summarizes the names, definitions and formats (units) of parameters that are 
used by Advanced Engineering Building Module (AEBM) of the HAZUS-MH Software 
to define 
damage and loss functions for buildings. Parameter names and definitions generally 
follow those used in the HAZUS-MH Technical Manual. Tables and sections of the 
HAZUS-MH Technical Manual that provide default values of parameters for generic 
building types are identified for reference by users. 

The AEBM has an "Inventory" database and a "Building Characteristics" database. The 
AEBM Building Characteristics database contains a large number of terms that define 
damage functions (i.e., response, capacity and fragility parameters) and loss functions 
(i.e., casualty, direct economic and loss of function parameters). In most cases, these 
terms are identical with the terms and formulas used by the HAZUS-MH Technical 
Manual to estimate various types of loss.

While consistent with the underlying methods of HAZUS, certain terms of AEBM 
databases are used in formulas to calculate losses that are not fully documented in the 
HAZUS-MH Technical Manual. In such cases, his section describes the formulas used by 
the AEBM to calculate losses.

4.2 . Damage Functions 
Damage function data are contained in the AEBM Building Characteristics database (i.e., 
Cells 6 - 38 of AEBMBP.DBF) and include capacity curve parameters and response 
parameters. 

4.2.1. Capacity Curve Parameters 
Each building has one capacity curve that is defined by two control points, the yield 
control point and the ultimate control point:
* Yield Capacity Control Point: spectral displacement, Dy, in inches, and spectral 
acceleration, Ay, in units of acceleration (g).
* Ultimate Capacity (Plastic) Control Point: spectral displacement, Du, in inches, and 
spectral acceleration, Au, in units of acceleration (g).

Default values of the yield and ultimate capacity control points for each of the 36 
(generic) model building types are given in Tables 5.7a through 5.7d of the HAZUS-MH 
Technical Manual for High-Code, Moderate-Code, Low-Code and Pre-Code seismic 
design levels, respectively.

4.2.2. Response Parameters
Peak displacement building response is defined by the intersection of demand spectrum 
(of the scenario earthquake of interest) and the capacity curve. The demand spectrum is 
the 5%-damped spectrum of ground shaking at the building site reduced for effective 
damping above 5% of critical. Two parameters, the elastic pre-yield damping and the 
degradation of post-yield hysteretic response, influence the amount of damping 
reduction:
* Elastic Damping, BE, expressed as a percentage of critical damping.
* Degradation (Kappa) Factors, kS, kM, kL, expressed as a fraction of non-degraded 
hysteretic behavior for Short, Medium and Long shaking duration.

Values of elastic damping range from 5% of critical for most steel structures to 15% of 
critical for wood structures (with nailed joints) and generally follow the 
recommendations of Table 3 of 
Earthquake Spectra and Design [Newmark & Hall, 1982] for materials at or just below 
yield. Values of the degradation (Kappa) factor are given in Table 5.18 of the HAZUS-
MH Technical Manual for each of the 36 (generic) model building types, as a function of 
the building's seismic design level and the duration of post-yield shaking (i.e., Short, 
Moderate or Long duration).

Acceleration-sensitive nonstructural components and building contents at upper- floors 
are influenced by the peak acceleration response of the structure (e.g., capacity curve 
plateau), 
while components and contents at lower- floors are influenced more by ground shaking 
(i.e., peak ground acceleration). Acceleration demand on nonstructural (acceleration-
sensitive) components and contents is based on a weighted combination of the fraction of 
components/contents at the base of the building with those components/contents located 
at upper- floors. 

Nonstructural Fraction (FNS) of acceleration-sensitive nonstructural components (and 
contents) at lower-floors varies as a function of building height and is assumed to be 0.5 
for low-rise buildings, 0.33 for mid-rise buildings and 0.2 for high- rise buildings.

4.2.3. Fragility Curve Parameters 
A total of twelve fragility curves describe the probabilities of reaching or exceeding the 
four discrete damage states (i.e., Minor, Moderate, Extensive and Complete) of the 
structural, nonstructural drift-sensitive and nonstructural acceleration-sensitive systems, 
respectively, given a particular level of building response. There are two parameters, the 
median value of the probability function (assumed to be log-normally distributed) and the 
lognormal standard deviation value of the distribution, that define each fragility curve:
* Damage-State Median spectral displacement, Sd,ds, in inches, of each structural and 
nonstructural drift-sensitive damage state, or median spectral acceleration, Sd,ds, in units 
of 
acceleration (g), of each nonstructural acceleration-sensitive damage state.
* Damage-State (Beta) Lognormal Standard Deviation, Bds, of each structural, 
nonstructural drift-sensitive and nonstructural acceleration-sensitive damage state. 

Median and Beta values defining structural damage states of each of the 36 (generic) 
model building types are given in Tables 5.9a through 5.9d of the HAZUS-MH Technical 
Manual for 
High-Code, Moderate-Code, Low-Code and Pre-Code seismic design levels, respectively. 
Median and Beta values defining nonstructural drift-sensitive damage states of each of 
the 36 (generic) model building types are given in Tables 5.11a through 5.11d of the 
HAZUS-MH Technical Manual for High-Code, Moderate-Code, Low-Code and Pre-
Code (No) seismic design levels, respectively. Median and Beta values defining 
nonstructural acceleration-sensitive damage states of each of the 36 (generic) model 
building types are given in Tables 5.13a through 5.13d of the HAZUS-MH Technical 
Manual for High-Code, Moderate-Code, Low-Code and Pre-Code seismic design levels, 
respectively.

4.3. Loss Functions 
Loss function data are contained in the AEBM Building Characteristics database (i.e., 
cells 39 - 93 of AEBMBP.DBF) and in the AEBM Inventory database (i.e., cells 10 - 20 
of AEBM.DBF). Loss function data include casualty rates, direct economic loss 
parameters related to damage repair and loss of function factors. The Inventory database 
defines certain basic building data that are used with other factors to estimate losses, as 
described below. 

4.3.1. Inventory Data 
Number of Daytime Occupants, NDO, and Nighttime Occupants, NNO, are used in the 
calculation of the number of expected casualties following the logic described in Section 
13.2.1 of the HAZUS-MH Technical Manual (for each Casualty Severity Level). Table 
13.2 of the HAZUS-MH Technical Manual provides guidance for estimating the fraction 
of all occupants likely to be in the building during the day and during the night.

The logic of Section 13.2.1 involves numerous combinations of struc tural damage and 
casualty severity levels. However, serious injuries and fatalities tend to be dominated by 
only a few combinations of Complete structural damage for which the building has also 
sustained some degree of collapse. The following equations illustrate the calculation of 
daytime casualties due to full building collapse:

SL_ENDOi = NDO * P[Si|COL] * P[COL|PSTR5] * PSTR5 

where: 
SL_ENDOi = Expected number of daytime casualties of Severity Level i
P[Si|COL] = Probability of Severity Level i given full building collapse 
P[COL|STR5] = Probability of full building collapse given Complete structural damage 
(STR5) 
PSTR5 = Probability of Complete structural damage
NDO = Number of daytime occupants of the building.

Total Floor Area, FA, (in square feet) is not used directly in the AEBM but provides a 
basis to relate building-specific estimates of economic loss to the corresponding methods 
of the HAZUS-MH 
Technical Manual for generic building types.

Replacement Value (in dollars) of the building, RVB, is used in calculations of direct 
economic loss due to the repair (or replacement) of the structural system, nonstructural 
drift-sensitive 
components and nonstructural acceleration-sensitive components, respectively:

EL_STR = FVSTR * RVB * 5 over sigma with damage state=2 (PSTRds * STRDds)

where: 
EL_STR = Loss due to repair of the structural system (dollars) 
EL_NSD = Loss due to repair of nonstructural drift-sensitive components (dollars) 
EL_NSA = Loss due to repair of nonstructural acceleration-sensitive components 
(dollars) 
PSTRds = Probability of building being in structural damage state, ds 
PNSDds = Probability of building being in nonstructural drift-sensitive damage state, ds 
PNSAds = Probability of building being in nonstructural acceleration-sensitive damage 
state, ds 
STRDds = Structural system repair cost of damage state, ds, expressed as a fraction of the 
total cost of the structural system 
NSDDds = Nonstructural repair cost of damage state, ds, expressed as a fraction of the 
total cost of nonstructural drift-sensitive components 
NSADds = Nonstructural repair cost of damage state, ds, expressed as a fraction of the 
total cost of nonstructural acceleration-sensitive components 
FVSTR = Fraction of total building replacement value, RVB, associated with the 
structural system 
FVNSD = Fraction of the fraction of total building replacement value, RVB, associated 
with nonstructural drift-sensitive components 
RVB = Replacement value of building (dollars). 

The Replacement Value of the building, RVB, may be estimated as the product of the 
Total Floor Area, FA, and the total cost per square foot of structural and nonstructural 
systems. 

Appendices 15A and 15C of the HAZUS-MH Technical Manual provide background on 
the derivation of regional per square foot costs for various occupancies using Means data. 

Replacement Value (in dollars) of contents, RVC, and business inventory, RVINC, are 
used in calculations of direct economic loss due to the replacement of these contents or 
inventory: 

EL_CCD = RVC * 5 over sigma with damage state=2 (PNSAds * CDds)
EL_INV = RVINV * 5 over sigma with damage state=2 (PNSAds * INVDds)

where:
EL_CCD = Loss due to replacement of damaged contents (dollars) 
EL_INV = Loss due to replacement of business inventory (dollars) 
PNSAds = Probability of building being in nonstructural acceleration-sensitive damage 
state, ds
CDds = Contents replacement cost of damage state, ds, expressed as a fraction of the total 
cost of contents 
INVDds = Business inventory replacement cost of damage state, ds, expressed as a 
fraction of the total cost of nonstructural drift-sensitive components 
RVC = Replacement value of building contents (dollars)
RVINV = Replacement value of business inventory (dollars).

Default replacement values of contents, CV, expressed as a fraction of the Replacement 
Value of the building, RVB, are provided in Table 15.5 of the HAZUS-MH Technical 
Manual for 
various building occupancies. Default replacement values of business inventory are based 
on the size of the building, the level of annual gross sales and the type of business, as 
described in 
Section 15.2.3 of the HAZUS-MH Technical Manual. 

Business Income, BINC, by building occupants (dollars per day) is used by the AEBM in 
the calculation of loss of business income:

EL_INC = (1 - RFBI) * BINC * 5 over sigma with damage state=1 (PSTRds * LOFds)

where:
EL_INC = Loss of business income (dollars) 
PSTRds = Probability of building being in structural damage state, ds 
LOFds = Loss of function for damage state ds (days) 
BINC = Business income for building occupants (dollars/day) 
RFBI = Recapture factor for loss of business income.

Wages Paid, WAGE, by building occupants (dollars per day) is used by the AEBM in the 
calculation of loss of wages: 

EL_WAGE = (1 - RFW) * WAGE *  5 over sigma with damage state=1 (PSTRds * 
LOFds)

where: 
EL_WAGE = Loss of wages (dollars)
PSTRds = Probability of building being in structural damage state, ds
LOFds = Loss of function for damage state ds (days) 
WAGE = Wages paid by building occupants (dollars/day) 
RFW = Recapture factor for loss of wages. 

Section 15.2.6.1 of the HAZUS-MH Technical Manual provides default values of wage 
and business income recapture factors based on building occupancy type. 

Disruption Cost, DISC, (dollars), Rental Cost, RENT, (dollars per day) and percentage of 
the building that is Owner Occupied, OO, are used by the AEBM in the calculation of 
losses due 
business relocation and rental income:

EL_REL = DISC * 5 over sigma with damage state=3 PSTRds + OO * RENT * 5 over 
sigma with damage state=3 (PSTRds * RTds)
EL_RENT = (1 - OO) * RENT * 5 over sigma with damage state=3 (PSTRds * RTds)

where:
EL_REL = Loss due to business relocation expenses (dollars) 
EL_RENT = Loss due to rental of temporary space (dollars) 
PSTRds = Probability of building being in structural damage state, ds 
RTds = Recovery time for damage state ds (days) 
RENT = Rental costs for replacement space (dollars/day) 
DISC = Disruption "lump sum" relocation cost (dollars) 
OO = Percentage of building occupied by the owner. 

Table 15.13. of the HAZUS-MH Technical Manual provides defa ult values of rental and 
disruption costs (per square foot) as a function based on building occupancy type.

4.3.2. Casualty Rates 
Sixteen Casualty Rates specify Severity 1, Severity 2, Severity 3 or Severity 4 casualties 
as a fraction of building occupants for each state of structural damage, assuming that the 
building has not collapsed. In general, these rates do not govern the estimates of serious 
injuries and fatalities, which are primarily a function of building collapse. Users are 
encouraged to use (without modification) the casualty rates given in Tables 13.3 through 
13.6 of the HAZUS-MH Technical Manual for the generic building type that is the most 
similar to the specific building 
of interest.

Collapse Casualty Rates, P[Si|COL] specify the fractions of building occupants expected 
to be Severity 1, Severity 2, Severity 3 or Severity 4 casualties, respectively, given that 
Complete 
structural damage and Collapse has occurred.

The Collapse Factor, P[COL|STR5], specifies the probability of full building collapse 
given Complete structural damage has occurred, or weighted combination of the 
probabilities of multiple modes of collapse for which the weighting factor is proportional 
to the fraction of the building population exposed to collapse. The probability of collapse 
(given Complete structural damage) may also be thought of as the effective fraction (or 
ratio) of the building that has collapsed such that when multiplied by total building 
population the result is expected number of building occupants exposed to life-
threatening collapse.

Default values of collapse casualty rates are specified in Table 13.7 of the HAZUS-MH 
Technical Manual for each casualty severity level as a function of model building type. 
Default values of the collapse factor are specified in Table 13.8 of the HAZUS-MH 
Technical Manual as a function of model building type.

Chapter 13 of the HAZUS-MH Technical Manual distinguishes between "indoor" and 
"outdoor" casualties, the later referring to deaths and injuries to pedestrians (or people in 
cars, etc.) that are near the building at the time of the earthquake. Tables 13.5 through 
13.7 of the HAZUS-MH Technical Manual specify "indoor" casualty rates that are used 
by the AEBM to estimate building-specific casualties. The AEBM does not calculate 
"outdoor" casualties.

4.3.3. Repair Cost Rates - Loss Ratios 
Twelve Loss Ratios specify the fractions of the total cost of the structural system, 
STRDds, the fractions of the total cost of nonstructural drift-sensitive components, 
NSDDds, and the fractions of the total cost of nonstructural acceleration-sensitive 
components, NSADds, respectively, associated with repair of each damage state, ds.

Repair costs (in dollars per square foot) are the multiplication of loss ratios times the total 
cost per square foot of the system of interest. Default values of structural repair costs are 
given in 
Tables 15.2a through 15.2d of the HAZUS-MH Technical Manual for each damage state, 
respectively, as a function of building occupancy and model building type. Default values 
of nonstructural acceleration-sensitive and nonstructural drift-sensitive repair costs are 
given in Tables 15.3 and 15.4, respectively, of the HAZUS-MH Technical Manual for 
each damage state as a function of building occupancy type. Default repair costs include 
regional cost modifiers that adjust repair costs based on the building's geographical 
location.

The Fractional Value, FVSTR, is the fraction of the total replacement value of the 
building, RVB, associated with the value of the structural system. The Fractional Value, 
FVNSD, is the fraction of the total replacement value of the building, RVB, associated 
with the value of nonstructural systems sensitive to drift. The balance of the total 
replacement value of the building, RVB, is associated with the value of nonstructural 
systems sensitive to acceleration.

Four Loss Ratios specify fractions of the total cost of contents, CDds, associated with 
each damage state, ds. Default values of content loss ratios, CD, are given in Table 15.6 
of the HAZUS-MH Technical Manual for each damage state as a function of building 
occupancy type.

Four Loss Ratios specify fractions of the total cost of business inventory, INVds, 
associated with each damage state, ds. Default values of business inventory loss ratio, 
INV, are given in 
Table 15.6 of the HAZUS-MH Technical Manual for each damage state as a function of 
building occupancy type. 

4.3.4. Loss of Function and Recovery Time 
Building repair time is the time in days required for clean up and construction to repair or 
replace damage to structural and nonstructural systems. Default values of building repair 
time, BRT are given in Table 15.10 of the HAZUS-MH Technical Manual for each 
damage state as a function of building occupancy type. 

Building Recovery Time, BCTds, (in days) is the time required to make repairs of each 
structural damage state, ds, including additional time due to delays in decision-making, 
financing, inspection, etc. Default values of Building Recovery Time are given in Table 
15.11 of the HAZUS-MH Technical Manual for each damage state as a function of 
building occupancy type.

Loss of Function, LOFds, (in days) is the time that the facility is not capable of 
conducting business and is typically less than repair time due to temporary solutions such 
as the use of alternative space, etc. Building and service interruption time multipliers may 
be used to assess Loss of Function as a fraction of Building Recovery Time . Service 
interruption multipliers, MOD, are given in Table 15.12 of the HAZUS-MH Technical 
Manual for each damage state as a function of building occupancy type.

Recapture Factors for business income, RFBI, and wages, RFW, account for a portion of 
business income and wage losses (due to loss of function) that are recouped by working 
overtime, etc. Default values of Recapture Factors are given in Section 15.2.6.1 HAZUS-
MH Technical Manual as a function of building occupancy type.

SECTION 5 
DEVELOPMENT OF CAPACITY CURVES AND RESPONSE PARAMETERS 
5.1. Building Model and Pushover Criteria 
This section guides users in the development capacity curves and related parameters that 
are used by Advanced Engineering Building Module (AEBM) to calculate building 
response as a function of ground shaking at the building site. It is assumed that the user 
has already performed nonlinear static (pushover) analysis of the building that conforms 
essentially to the methods of NEHRP Guidelines (or ATC-40) and to certain other criteria 
as set forth in this section.

The pushover analysis must appropriately represent the force-deflection and response 
characteristics of the building of interest. For use in developing fragility functions, the 
pushover analysis must also appropriately capture the damage patterns of elements and 
components of the building (as described in the next section). In general, the latter 
requires more detailed and 
complex analysis than that required simply for evaluation of building response.

The NEHRP Guidelines (and ATC-40) provide users with a fairly complete description 
of the nonlinear static (pushover) method of analysis, including guidance on modeling 
and evaluation post-yield behavior of elements and components. Additional guidance is 
provided in this section for performing pushover analysis and using the results in loss 
estimation studies. Since the NEHRP Guidelines (and ATC-40) are design documents, 
the user should be aware that they intentionally (or unintentionally) include some 
conservatism that is not appropriate for loss estimation. For loss estimation, as compared 
to design procedures and building code rules, pushover analysis methods and models 
should fairly represent building (building group) without conservative bias. Building 
geometry, material strengths and response limits, etc. should all represent typical building 
conditions and likely response behavior, rather than being based on conservative or 
"worst-case" assumptions.

Users must determine how many different pushover models are required for loss 
estimation. For complex buildings, a model could be developed for each horizontal 
direction of response (if 
response is different in different directions) and for separate structural segments of the 
building. It is common for large buildings (in plan) to be composed of more than one 
structure, separated by construction joints. Each structure can have different capacity and 
response properties (and fragility and loss functions). For simple symmetrical buildings, a 
single pushover model would likely be sufficient to represent building behavior. If a 
single pushover model is used to evaluate a complex and/or irregular building, then the 
model would need to represent those modes of response and failure that are most likely to 
occur and cause damage and loss.

Consider, for example, a large tilt-up building, composed of three structural segments in a 
line (three by one rectangle in plan). Such buildings are commonly used for industrial 
manufacturing and warehousing facilities. The segments at each end are similar and have 
tilt- up panels of three sides. The segment in the middle is structurally different and has 
panels on only two opposing sides of the building. All three segments are strong in the 
plane of the tilt- up panels near the building's perimeter, but generally weak in the 
direction perpendicular to the panels away from building corners. All three segments 
have flexible diaphragms. Possible building response and failure modes include the 
following (there may be others):
* Local, out-of-plane failure of some tilt-up planes (due to failure of panel-to-roof 
connections) accentuated by diaphragm flexibility - most likely to occur at mid-span 
locations (away from 
building corners) 
* Full collapse of center section in weak direction (perpendicular to tilt- up panels)
* Partial collapse of end sections in the weak direction (near joints with center section) 
accentuated by torsion response.

The user would likely develop multiple pushover models to evaluate the different modes 
of response and failure of the building, described above. Multiple pushover analyses 
could be converted into multiple building damage and loss models (one model per 
building segment) or folded into a single building damage and loss model. If multiple 
models of different building segments are developed, then damage and loss would be 
calculated separately for each and aggregated for the building as a whole.

Developing a single building damage and loss model (e.g., a single capacity curve) for a 
complex building requires users to judge the mode of failure, direction of response, etc., 
that best represents the most likely source of earthquake damage and loss. Sections 5.2 
and 5.3 assume that the user has resolved building complexity and describe methods for 
converting a single pushover curve into capacity and response parameters that are 
compatible with the AEBM.

Users must determine how many and to what degree elements and components are 
required to be explicitly modeled in pushover analyses used for loss estimation. Fragility 
concerns (next section) usually control this issue, although modeling of building elements 
and components is also important to building capacity. For determining capacity curve 
properties, it is necessary that the pushover mode shape include all elements and 
components whose individual stiffness (flexibility) significantly affects global building 
response. From a dynamics standpoint, this requirement may also be thought of as 
including all "degrees of freedom" that significantly influence dynamic response of the 
1st-mode of the building in the direction of interest.

Flexibility of the foundation, floor diaphragms, etc., should be explicitly modeled in the 
pushover analysis if the addition of the flexibility of these element/components to the 
pushover model would significantly change pushover mode shape and response. 
Similarly, no structural elements or components should be excluded from the pushover 
model simply because they are considered to be of secondary, rather than primary, 
importance to the structural system. Likewise, architectural elements and components 
that add significant stiffness to the building (e.g., hollow-clay tile used as in- fill 
partitions) should be modeled in the pushover analysis (and effectively removed from the 
model as they fail during pushover analysis).

5.2. Development of Capacity Curve Control Points 
5.2.1 Conversion of Pushover Curve to Capacity Curve
The first step in developing capacity curve control points is to convert pushover 
coordinates of base shear force and control point (e.g., roof) displacement to spectral 
acceleration and displacement, respectively. The coordinate conversion is described 
somewhat vaguely as Method 2 in the commentary of the NEHRP Guidelines and more 
completely in ATC-40, the latter being consistent with HAZUS format and terminology.

The conversion of pushover to capacity is illustrated in Figure 5.1. An example pushover 
curve (normalized by the building's weight, W) is converted to capacity using pushover 
mode factors, a1 and a2. Each point on the normalized pushover curve (Dp, Ap) is 
factored by the pushover mode factors to create a corresponding point on the capacity 
curve (Dc, Ac). Provided the pushover curve was developed using a push force pattern 
based on the 1st-mode shape of the building, then the initial (pre-yield) slope of the 
capacity curve is directly related to the building's elastic (pre- yield) period (Te) as 
described by Equation (5-5). Axes are labeled in terms of Spectral Acceleration and 
Spectral Displacement in Figure 5.1, recognizing that while pushover and capacity curves 
can have the same units, they are in different coordinate systems.

Figure 5.1. Example Conversion of Pushover Curve to Capacity Curve Using Pushover 
Mode Factors
Diagram displays Spectral Displacement (inches)   versus  Spectral Acceleration (g's)
DC = DPa2 
AC = AP/a1

HAZUS defines the two pushover mode factors: 
a1  = fraction of building weight effective in pushover mode 
a2 = fraction of building height at the elevation where pushover- mode displacement is 
equal to spectral displacement. 

Consistent with ATC-40 methods (and terms), a1 is defined by the distribution of 
building mass and pushover mode shape: 

Equation 5-1:
a1 = product of [N over sigma with i=1 (WiQip)/g] squared |
[N over sigma with i=1 (Wi)/g] [N over sigma with i=1 (WiQ2ip)/g]

where:
Wi/g = mass assigned to the ith degree of freedom
Qip = amplitude of pushover mode at ith degree of freedom. 

Typically, the shape of the pushover mode is based on the 1st-mode of the building in the 
direction of interest. In general, the pushover mode shape is amplitude dependent, after 
elements and components begin to yield. While the most appropriate pushover shape 
would be the amplitude-dependent shape at the amplitude of interest, the pre-yield (1st-
mode) shape may be used to calculate a1 without significant loss of accuracy. This 
statement does not apply to element/component demands that are directly related to the 
post-yield changes to pus hover mode shape. The term "degree of freedom" is used 
herein, rather than the term "level" of ATC-40, to indicate that there may be more than 
one node (degree of freedom) per floor (e.g., buildings with flexible diaphragms would 
need several nodes to represent diaphragm response).

Consistent with ATC-40 (and discussion of the C0 factor in the commentary of the 
NEHRP Guidelines), the modal factor, a2, is defined by amplitude of the normalized 
pushover mode shape at the control point and the pushover mode participation factor:

Equation 5-2:
a2 = 1 | PFpf cp,p 
= product of N over sigma with i=1 (WiQ2ip)/g |
[N over sigma with i=1 (WiQip)/g] f cp,p

where:
Wi/g = mass assigned to the ith degree of freedom 
Qip = amplitude of pushover mode at ith degree of freedom
Qcp,p = amplitude of pushover mode at control point.

Typically, the roof is used as the location of the control point. The shape of the pushover 
mode is typically based on the 1st-mode of the building in the direction of interest and is, 
in general, amplitude dependent after elements and components begin to yield. As for the 
a1 term, the most appropriate pushover shape would be the amplitude-dependent shape at 
the amplitude of interest, but the pre-yield (1st-mode) shape may be used to calculate a2 
in most cases without significant loss of accuracy. 

The pushover mode factors are used directly to calculate the capacity curve from the 
pushover curve where each point on the capacity curve is defined by a spectral 
displacement, SD, and a spectral acceleration, SA:

Equation 5-3:
SD = a 2? cp
Equation 5-4:
SA = V/ W | a 1

where:
Dcp = Pushover control point (e.g., roof) displacement
V = Pushover base shear force (kips)
W = Building weight (kips). 

Certain structural analysis software programs (e.g., SAP2000 Nonlinear) automatically 
convert pushover curves to capacity curves using these formulas. 

5.2.2. Yield and Ultimate Capacity Control Points
Capacity curve control points are determined from the capacity curve using both 
judgment and the following rules: 
* Yield capacity control point (Dy, Ay) is selected as the point where significant yielding 
is just beginning to occur (slope of capacity curve is essentially constant up to the yield 
point).
* The expected period, Te, of the building, at or just below yield, should be the true 
"elastic" fundamental- mode period of the building:

Equation 5-5:
Te = approximately 0.32 by the square root of Dy | Ay

* Ultimate capacity control-point acceleration, Au, is selected as the point of maximum 
spectral acceleration (maximum building strength), not to exceed the value of spectral 
acceleration at which the structure has just reached its full plastic capacity (i.e., ignore 
additional straining at the point at which the structure becomes a mechanism).
* Ultimate capacity control-point displacement, Du, is selected as the greater of either the 
spectral displacement at the point of maximum spectral acceleration or the spectral 
displacement corresponding to Equation (5-6): 

Equation 5-6:
Du = 2 * Dy Au | Ay

The HAZUS definition of the elastic period, Te, is the same as the initial period, Ti, of 
the NEHRP Guidelines and should not be confused with the definition of the effective 
period, Te, of the NEHRP Guidelines. The effective period, Te, of the NEHRP 
Guidelines is based on stiffness at 60% of the ultimate strength of the building and should 
not be used with HAZUS methods since it could significantly overestimate pre-yield 
displacement of the building.

Three sets of pushover and capacity curves and the Control Points selected for each using 
the rules described above are shown in Figures 5.2, 5.3 and 5.4, respectively. As shown 
in these figures, capacity curves typically extend beyond "ultimate" control-point 
displacement, Du, which defines the displacement at which the system is assumed to be 
fully plastic, but has not necessarily failed. The median values of fragility curves, 
described in the next section, define various states of damage along the HAZUS-
compatible capacity curve.

Figure 5.2. Example Development of the Capacity Curve for a Structure with "Saw- 
Tooth" Force-Deflection Behavior
Diagram displays Spectral Displacement (inches) versus Spectral Acceleration (g's), 
along with HAZUS-Compatible Capacity Curve, Ultimate Capacity Control Point, Yield 
Capacity Control Point, and Capacity Curve from Pushover Analysis.

In Figure 5.2, the first set of curves is for a structure that sustains shear failure and load 
reduction in a number of components at different levels of spectral displacement. The 
sequential shear failure of components creates a "saw-tooth" effect that is enveloped by 
the HAZUS capacity curve. In Figure 5.3, the second set of curves represents "brittle" 
force-deflection behavior and catastrophic failure of the structure. The Ultimate Capacity 
Control Point is actually selected to be past the point of failure. This is not inappropriate, 
since the ultimate point does not define the fragility of the building, only the plateau of 
the capacity curve.

Figure 5.3. Example Development of the Capacity Curve for a Structure with "Brittle" 
Force-Deflection Behavior
Diagram displays Spectral Displacement (inches) versus Spectral Acceleration (g's), 
along with HAZUS-Compatible Capacity Curve, Ultimate Capacity Control Point, Yield 
Capacity Control Point, and Capacity Curve from Pushover Analysis.

The third set of curves shown in Figure 5.4 illustrate force-deflection behavior of a 
"ductile" building up to the formation of a complete mechanism (fully plastic state). The 
pushover curve indicates some additional strength beyond the fully plastic state due to 
strain hardening assumptions.

Figure 5.4. Example Development of the Capacity Curve for a Structure with "Ductile" 
Force-Deflection Behavior 
Diagram displays Spectral Displacement (inches) versus Spectral Acceleration (g's), 
along with HAZUS-Compatible Capacity Curve, Ultimate Capacity Control Point (at 
fully plastic state), Yield Capacity Control Point, and Capacity Curve from Pushover 
Analysis.

Both the initial stiffness (i.e., elastic period, Te) and ultimate strength of the capacity 
curve will, in general, degrade with repeated cycles of post-yield earthquake demand. 
The effects of degradation of stiffness and strength on capacity and response of the 
building are accounted for by degradation factors. Development of degradation factors is 
described in the next subsection.

5.3. Development of Response Parameters 
Response parameters include Elastic Damping and degradation (Kappa) factors that 
reduce hysteretic damping and affect the intersection capacity and demand, and the 
fraction of 
nonstructural components at lower- floors (FNS) which affects the calculation of demand 
on nonstructural-acceleration sensitive components. Background on the use of the elastic 
damping and degradation factors in the calculation of response is given in the following 
subsection.

5.3.1. Response Calculation 
HAZUS characterizes ground shaking using a standard response spectrum shape, 
consistent with the format and parameters of the 1997 NEHRP Provisions and the 
NEHRP Guidelines. The standard shape consists of two primary parts: (1) a region of 
constant spectral acceleration at short periods and (2) a region of constant spectral 
velocity at long periods. Short-period spectral acceleration, SS, is defined by 5%-damped 
spectral acceleration at a period of 0.3 seconds. The constant spectral velocity region has 
spectral acceleration proportional to 1/T and is anchored to the 1-second, 5%-damped 
spectral acceleration, S1. A region of constant spectral displacement exists at very long 
periods, although this region does not usually affect calculation of building damage. 
Amplification of ground shaking to account for local site conditions is based on the short-
period (FA) and velocity-domain (FV) soil factors of the 1997 NEHRP Provisions.

HAZUS modifies elastic system properties to simulate inelastic response by use of 
"effective" stiffness and damping properties of the building. Effective stiffness properties 
are based on secant stiffness, and effective damping is based on combined viscous and 
hysteretic measures of dissipated energy. Effective damping greater than 5% of critical is 
used to reduce spectral demand in a manner similar to the capacity-spectrum method of 
ATC-40.

Figure 5.4 illustrates the process of developing an inelastic response (demand) spectrum 
from the 5%-damped elastic response (input) spectrum. The demand spectrum is based 
on elastic response divided by amplitude-dependent damping reduction factors (i.e., RA 
at periods of constant acceleration and RV at periods of constant velocity). The demand 
spectrum intersects the building's capacity curve at the point of peak response 
displacement, D, and acceleration, A. The amount of spectrum reduction typically 
increases for buildings that have reached yield and dissipate hysteretic energy during 
cyclic response.

Figure 5.4. Example Demand Spectrum Construction and Calculation of Peak Response 
Point (D, A)

Spectrum reduction factors are a function of the effective damping of the building, beff, 
as defined by Equations (5-8) and (5-9):

Equation 5-8:
RA = 2.12/(3.12 - 0.68ln(B eff))
Equation 5-9:
RV = 1.65/(2.31 - 0.41ln(B eff))

These equations are based on the formulas given in Table 2 of Earthquake Spectra and 
Design [Newmark and Hall, 1982] for construction of elastic response spectra at different 
damping levels (expressed as a percentage of critical damping). The factors of Newmark 
and Hall represent all site classes (soil profile types), but distinguish between domains of 
constant acceleration and constant velocity. For either domain, the reduction factor is the 
ratio of 5%-damped response to response of the system with beff damping. Equations (5-
8) and (5-9) yield reduction values of RA = 1.0 and RV = 1.0, respectively, for a value of 
B eff = 5% of critical.

Effective damping, beff, is defined as the total energy dissipated by the building during 
peak earthquake response and is the sum of an elastic damping term, BE, and a hysteretic 
damping term, BH, associated with post-yield, inelastic response:

Equation 5-10:
B eff = BE + BH

The elastic damping term, BE, is assumed to be a constant (i.e., amplitude independent) 
and follows the recommendations of Table 3 of Earthquake Spectra and Design for 
materials at or just below their yield points. The hysteretic damping term, bH, is 
dependent on the amplitude of post-yield response and is based on the area enclosed by 
the hysteresis loop at peak response displacement, D, and acceleration, A, as shown in 
Figure 5.5. Hysteretic damping, BH, is defined in Equation (5-11): 

Equation 5-11:
BH = k (Area | 2 pi D A)

where:
Area = is the area enclosed by the hysteresis loop, as defined by a symmetrical push-pull 
of the building capacity curve up to peak positive and negative displacements,  D, 
assuming no degradation of components,
D = is the peak displacement response of the capacity curve,
A = is the peak acceleration response at peak displacement, D
k = is a degradation factor that defines the fraction of the Area used to determine 
hysteretic damping.

For a value of k = 1.0, Equation (5-11) may be recognized as the definition of equivalent 
viscous damping, found in modern vibration textbooks [e.g., Chopra, 1995] and traceable 
to the early work of Jacobsen [1930] and others. The k (Kappa) factor in Equation (5-11) 
reduces the amount of hysteretic damping as a function of model building type, seismic 
design level and shaking duration to simulate degradation (e.g., pinching) of the 
hysteresis loop during cyclic response. Shaking duration is described qualitatively as 
either short, moderate or long, and is assumed to be primarily a function of earthquake 
magnitude, although proximity to fault rupture can also influence the duration of the level 
of shaking that is most crucial to building damage.

Figure 5.6 shows a typical capacity curve and three example demand spectra for damping 
levels corresponding to short (kS = 0.8), moderate (kM = 0.5) and long (kL= 0.3) 
duration ground shaking, respectively. In this example, building displacement due to 
long-duration ground shaking is more than twice that due to short-duration ground 
shaking (although building acceleration does not increase). Damage to the structural 
system and nonstructural, drift-sensitive components and related losses increase 
significantly with increase in the duration of ground shaking for buildings that have 
reached yield.

Figure 5.6. Example Demand Spectra - Post-Yield Response due to Strong Ground 
Shaking of Either Short, Moderate or Long-Duration

5.3.2 Elastic Damping Factors 
As described in the preceding subsection, Elastic Damping factors estimate the damping 
of the building at or just below yield of the structural system. These values should be 
selected on the basis of the building type, reflecting the inherent differences in the 
damping behavior of different materials. In general, the Elastic Damping factors included 
in HAZUS for general building stock should be used without modification for building-
specific applications. Table 5.1 summarizes the Elastic Damping values of HAZUS for 
different building types.

Table 5.1. Suggested Elastic Damping Values
Building Type by Material:  Mobile Home	
Damping (% of Critical):  5%

Building Type by Material:  Steel Buildings
Damping (% of Critical):  5% - 7%

Building Type by Material:  Reinforced-Concrete and Pre-cast Concrete Buildings
Damping (% of Critical):  7%

Building Type by Material: Reinforced-Masonry Buildings
Damping (% of Critical):  7% - 10%

Building Type by Material: Unreinforced-Masonry Bearing-Wall and In-Fill Buildings
Damping (% of Critical): 10%

Building Type by Material: Wood Buildings
Damping (% of Critical):  10% - 15%

5.3.3 Degradation Factors 
Degradation (Kappa) factors are a function of the expected amplitude and duration 
(number of cycles) of post-yield building response. These parameters depend on the level 
of ground shaking, which is different for each building site and scenario earthquake. The 
default values of the Kappa factor developed for generic-building analysis assume that 
the building would have ground shaking strong enough to effect significant post-yield 
response of the structure, and degradation is based on the magnitude of the scenario 
event. The larger the magnitude of the event, the longer the assumed duration of ground 
shaking. In this sense, earthquake magnitude became a surrogate indicator of the duration 
of post- yield response, assuming shaking was strong enough to push the structure 
beyond the yield point. It should be recognized that if the ground shaking were not strong 
enough to yield the building, there would be little or no degradation, regardless of the 
magnitude of the scenario earthquake (or the type of structural system). 

Kappa factors should be selected considering the extent to which brittle failure of the 
elements and components reduces the strength of the structural system. The capacity 
curve developed by pushover analysis provides some guidance on the selection of 
appropriate Kappa factors. If the capacity curve indicates a loss of strength at the ultimate 
capacity control point, then the Kappa factor should indicate a somewhat proportional 
reduction in hysteretic loop area. For example, in Figure 5.1 the capacity curve indicates 
about a 50% reduction in full strength, and a commensurate amount of degradation would 
be appropriate (e.g., kM = 0.50 for a moderate duration of post- yield response). In Figure 
5.2, the capacity curve indicates nearly complete (brittle) failure (at the ultimate capacity 
control point) and a very low value of the degradation factor would be appropriate (e.g., 
kM = 0.10 for a moderate duration of post-yield response). In Figure 5.3, the capacity 
curve indicates nearly fully ductile behavior, and a relatively high value of the 
degradation factor would be appropriate (e.g., kM = 0.90 for a moderate duration of 
ground shaking).

Table 5.2 provides some general guidance on the selection of the degradation (Kappa) 
factor. The Kappa factors are shown as a function of the level of response (i.e., one- half 
yield, yield and post-yield levels of peak response) and for post-yield response as a 
function of post-yield shaking duration (i.e., short, moderate and long). The table also 
relates suggested values of Kappa factors to the seismic design level and quality of 
construction used to characterize generic building types of HAZUS. 

Table 5.2. Suggested Values of the Degradation (Kappa) Factor
Design Level and Construction Quality: Seismic Design Level *1 (SHC, HC, MC, LC, 
PC)
QC *2: S, O, I
Degradation (Kappa) Factor: At Half Yield, At Yield, Post-Yield Shaking Duration 
(Short, Moderate, Long)

QC: SHC, HC = S
Degradation (Kappa) Factor:  At Half Yield = 1.0
Degradation (Kappa) Factor:  At Yield = 1.0
Degradation (Kappa) Factor:  Post-Yield Shaking Duration (Short = 1.0, Moderate = 0.9, 
Long = 0.7)

QC: HC = O, MC = S
Degradation (Kappa) Factor:  At Half Yield = 1.0
Degradation (Kappa) Factor:  At Yield = 1.0
Degradation (Kappa) Factor:  Post-Yield Shaking Duration (Short = 0.9, Moderate = 0.7, 
Long = 0.5)

QC: HC = I, MC = O, LC = S
Degradation (Kappa) Factor:  At Half Yield = 1.0
Degradation (Kappa) Factor:  At Yield = 0.9
Degradation (Kappa) Factor:  Post-Yield Shaking Duration (Short = 0.7, Moderate = 0.5, 
Long = 0.3)

QC: MC = I, LC = O, PC = S
Degradation (Kappa) Factor:  At Half Yield = 1.0
Degradation (Kappa) Factor:  At Yield = 0.7
Degradation (Kappa) Factor:  Post-Yield Shaking Duration (Short = 0.5, Moderate = 0.3, 
Long = 0.1)

QC: LC = I, PC = O
Degradation (Kappa) Factor:  At Half Yield = 1.0
Degradation (Kappa) Factor:  At Yield = 0.5
Degradation (Kappa) Factor:  Post-Yield Shaking Duration (Short = 0.3, Moderate = 0.1, 
Long = 0.0)

(*1) Seismic Design Level Designation - Special High-Code (SHC), High-Code (HC), 
Moderate-Code (MC), Low-Code (LC) and Pre-Code (PC) 
(*2) Construction Quality (QC) Designation - Superior (S), Ordinary (O) and Inferior (I) 

The suggested values of the Kappa factor given in Table 5-2 do not apply to seismically 
rehabilitated buildings. If the user is developing damage functions for a building that 
been 
strengthened, or otherwise seismically improved, then the selection of Kappa's should be 
based on a seismic design level and quality of construction that reflects these 
improvements. For example, substantial seismic rehabilitation of a Pre-Code building of 
Ordinary construction (i.e., older building constructed before seismic codes were 
adopted) might now be considered to be equivalent to a building of Moderate Code 
seismic design level of Superior construction quality. Of course, the amount by which the 
seismic design level and/or construction quality should be increased depends on the type 
and extent of the seismic improvements made to the structural system. 

5.3.4. Fraction of Nonstructural Components at Ground Level
The fraction of nonstructural components at the ground level (FNS) is used in the 
methodology to determine the portion of nonstructural acceleration-sensitive components 
(and contents) at lower floors. At this level, peak ground acceleration, rather than spectral 
acceleration is used for evaluation of nonstructural components (and contents). In 
determining the nonstructural fraction, the user should base the fraction on the value of 
nonstructural acceleration-sensitive components and contents. If most of the value of 
such components happens to be at lower floors (e.g., very expensive equipment is located 
in the basement), then direct economic losses should be based on ground shaking defined 
by peak ground acceleration. In contrast, if all of the valuable mechanical equipment is 
located in a roof penthouse, then peak floor acceleration (based on spectral acceleration) 
should be used to estimate direct economic loss.

SECTION 6 
DEVELOPMENT OF FRAGILITY CURVES 
6.1. Building Response and Performance Criteria 
This section guides users in the development of fragility curves parameters that are used 
by Advanced Engineering Building Module (AEBM) to calculate damage as a function of 
building response. It is assumed (and essential) that the user has already performed a 
detailed nonlinear static (pushover) analysis of the building that conforms essentially to 
the methods of the NEHRP Guidelines (or ATC-40) and to certain other criteria as set 
forth in this section (and Section 5). 

The pushover analysis must appropriately capture the damage patterns of elements and 
components of the building and evaluate modes of building failure (i.e., partial or full 
collapse of the structure). As previously discussed in Section 5.1, users must carefully 
consider modes of building failure and develop appropriate and representative models of 
structural response and element/component behavior. More than one pushover model 
could be used to evaluate different modes of response and failure (e.g., of different 
building segments). Section 6.2 and 6.3 assume that the user has resolved building 
complexity and describe methods for developing fragility parameters from a single 
pushover analysis.

There are certain key aspects to the damage functions of which users must be aware when 
developing fragility parameters. First, the damage functions should predict damage 
without bias such as that inherent to the conservatism of seismic design codes and 
guidelines. In general, limit states of the NEHRP Guidelines (or ATC-40) will under-
predict the capability of the structure, particularly for the more critical performance 
objectives, such as Collapse Prevention (CP). The NEHRP Guidelines' criteria for 
judging CP certainly do not intend that 50 out of 100 buildings that just meet CP limits 
would collapse. Most engineers would likely consider an acceptable fraction of CP 
failures (given that buildings just meet CP criteria) to be between 1 and 10 in every 100 
buildings. In contrast, the median drift value of the Complete structural damage state of 
HAZUS is the amount of building displacement that would cause, on the average, 50 out 
of 100 buildings of the building type of interest to have Complete damage (e.g., full 
financial loss). In general, users should not derive median values of HAZUS damage 
states directly from the performance limits of the NEHRP Guidelines (and ATC-40).

Fragility parameters of the more extreme damage states are particularly difficult to 
estimate since these levels of damage are rarely observed even in the strongest ground 
shaking. In the 1995 Kobe earthquake, the worst earthquake disaster to occur in a modern 
urban region, only about 10 in every 100 mid-rise commercial buildings located close to 
fault rupture had severe damage or collapse. Typically, the fraction of modern buildings 
with such damage (e.g., Complete structural damage) is much less than 10 in 100. In 
selecting median values of damage states, users should be mindful that median values 
represent the 50 percentile (e.g., 50 in every 100 buildings have reached the state of 
damage of interest). Median values of spectral displacement (or spectral acceleration) for 
the more extensive states of damage may appear large relative to seismic code or 
guideline design criteria. 

Calculation of damage-state probability is a step in the sequential process of estimating 
earthquake losses. Some leeway is available to users in determining building-specific 
fragility curves, since the building-specific loss functions will also be developed based on 
the fragility assumptions. What is essential is that the amount and type of damage 
associated with each damage state be consistent with the amount and type of damage 
assumed in the development of loss functions. For example, the user may have a choice 
of 4 inches, 5 inches or 6 inches of spectral displacement to represent Moderate structural 
damage to the building. In this example, these spectral displacements represent a range of 
plausible estimates resulting in "moderate" damage to elements and components, but with 
distinct differences in the cost of repair. That is, 6 inches of spectral displacement would 
cause more damage and cost more to repair than 4 inches of spectral displacement. The 
user may choose either 4 inches, 5 inches or 6 inches of spectral displacement to 
represent Moderate structural damage, provided the loss functions for Moderate damage 
are developed for the same amount of spectral displacement.

Fragility curves define boundaries between damage states. That is, the median value of 
the Damage State of interest defines the threshold of damage, and this state of damage is 
assumed to exist up to next state of damage. This description is illustrated in Figures 6.1, 
which includes example fragility curves for Slight, Moderate, Extensive and Complete 
structural damage. In this illustration, a shaded region illustrates the probability-response 
space associated with Moderate damage. The boundary on the left of the shaded region is 
defined by the fragility curve for Moderate (or greater) structural damage, and the 
boundary on the right of the shaded region is defined by the fragility curve for Extensive 
(or greater) damage. The probability of Moderate damage at a given level of spectral 
demand is calculated as the difference of the probability of Moderate (or greater) damage 
less the probability of Extensive (or greater) damage - a probability of 0.40 at 6 inches of 
spectral displacement in the example shown in Figure 6.1.

Figure 6.1. Example Fragility Curves - Calculation of Damage-State Probability
Diagram displays Spectral Displacement (inches = 0, 5, 10, 15, 20, 25) versus Probability 
- P[ds|Sd] (0.0, 0.5, 1.0)
Points: Slight Damage Curve, Moderate Damage Curve, Extensive Damage Curve, 
Complete Damage Curve, Moderate Damage Median, Extensive Damage Median, and 
P[Moderate|Sd = 6 inches]

The slope of the fragility curve is controlled by the lognormal standard deviation value 
(Beta). The smaller the value of Beta, the less variable the damage state, and the steeper 
the fragility curve. The larger the value of Beta, the more variable the damage state, and 
the flatter the fragility curve. Figure 6.2 illustrates this trend for fragility curves that share 
a common median (i.e., spectral displacement of 5 inches), but have Beta values ranging 
from 0.4 to 1.2. This range of Beta values approximately covers the range of Beta values 
that could be used for buildingspecific fragility curves.

Figure 6.2. Example Lognormal Fragility Curves (Beta = 0.4, 0.6, 0.8, 1.0 and 1.2) and 
Calculation of  1s Spectral Displacement
Diagram displays Spectral Displacement (inches = 0, 5, 10, 15, 20) versus Probability - 
P[ds|Sd] (0.00, 0.16, 0.50, 0.84, 1.00)

Figure 6.2 illustrates the calculation of spectral displacement at  1 standard deviation ( 
1s) probability levels for a typical Beta value of 0.8. In this example, the +1s level of 
spectral displacement is more than twice the median value (and the -1s level of spectral 
displacement is less than one-half the median value) for a Beta value of 0.8 which 
illustrates the large amount of variability typical of HAZUS fragility curves.

6.2. Development of Damage-State Medians 
Development of Damage-State Medians involves three basic steps: 
* Develop a detailed understanding of damage to elements and components as a 
continuous function of building response (e.g., average inter-story drift or floor 
acceleration) 
* Select specific values of building response that best represent the threshold of each 
discrete damage state
* Convert damage-state threshold values (e.g., average inter-story drift) to spectral 
response coordinates (i.e., same coordinates as those of the capacity curve). 

In general, the implementation of the three steps will be significantly different for 
structural and nonstructural systems. It is expected that detailed pushover analysis of the 
building will be the primary source of information regarding structural damage and 
selection of appropriate damagestate threshold values. In most cases, generic-building 
fragility values of HAZUS would not be used for the structural system (but could provide 
a "sanity check" of building-specific results). In contrast, pushover analysis typically 
provides only minimal information of nonstructural system performance, and users will 
rely primarily on the generic-building fragility values of HAZUS to determine threshold 
values of nonstructural damage states.

6.2.1. Structural System
Selection of Damage-State Medians should be consistent with the broad descriptions of 
structural damage given in Section 5.3.1 of the HAZUS-MH Technical Manual for 
different 
model building types. Descriptions of damage in HAZUS are sufficiently vague to permit 
user selection of values that best fit the damage patterns of dominant elements and 
components of the structural system. In addition, general guidance is provided below in 
Table 6.1 regarding the selection of appropriate Damage-State Medians for the structural 
system.

Table 6.1. General Guidance for Selection of Structural Damage-State Medians 
Damage State: (Slight, Moderate, Extensive, Complete)
Likely Amount of Damage, Direct Economic Loss, or Building Condition (Range of 
Possible Loss Ratios, Probability of Long-Term Building Closure, Probability of Partial 
or Full Collapse, Immediate Post-Earthquake Inspection)

Damage State: Slight
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Range of 
Possible Loss Ratios = 0% - 5%
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Long-Term Building Closure = P = 0
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Partial or Full Collapse = P = 0
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Immediate 
Post-Earthquake Inspection = Green Tag

Damage State: Moderate
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Range of 
Possible Loss Ratios = 5% - 25%
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Long-Term Building Closure = P = 0
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Partial or Full Collapse = P = 0
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Immediate 
Post-Earthquake Inspection = Green Tag

Damage State: Extensive
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Range of 
Possible Loss Ratios = 25% - 100%
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Long-Term Building Closure = P = approx. 0.5
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Partial or Full Collapse = P = approx. 0 (*1)
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Immediate 
Post-Earthquake Inspection = Yellow Tag

Damage State: Complete
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Range of 
Possible Loss Ratios = 100%
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Long-Term Building Closure = P = approx. 1.0
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Probability of 
Partial or Full Collapse = P greater than 0
Likely Amount of Damage, Direct Economic Loss, or Building Condition:  Immediate 
Post-Earthquake Inspection = Red Tag

(*1) Extensive damage may include local collapse (e.g., out-of-plane failure of URM 
infill walls).

Pushover analysis results typically express performance in terms of component ductility 
demand, rather than in terms of physical damage. The structural criteria of Table 2-4 
(Vertical Elements) and Table 2-5 (Horizontal Elements) of the NEHRP Guidelines 
provide some description of damage expected at various performance levels (e.g., 
component ductility) and may be used to relate element and component performance to 
physical description of damage. It is expected that the results of the pushover analysis, 
whether expressed in terms of physical damage (e.g., crack size) or in terms of 
component ductility demand, will be sufficient for users to tabulate the type and sequence 
of damage (and failure) of elements and components. 

Damage to elements and components of the structural system should be tabulated as a 
function of the lateral displacement of the building, quantified by the average inter-story 
drift ratio (i.e., roof displacement divided by building height). Of course, individual 
stories of multi-story building would not all be expected to have the same drift, nor would 
inter-story drift be the same at all locations on a given floor if there was diaphragm 
flexibility or a rotational component to the pushover mode shape. However, average 
inter-story drift provides a convenient measure of building response that may be 
compared against default values of average inter-story drift that define damage states for 
generic building types of HAZUS. 

The NEHRP Guidelines provide acceptance criteria that define deformation limits for 
large number of structural components and elements of different material types. These 
acceptance criteria imply various degrees of component or element damage and thus may 
be used to determine appropriate values of the average inter-story drift ration for each 
damage state of the structural system. However, in using the acceptance criteria of the 
NEHRP Guidelines users must be aware and account for each of the following four 
issues:
* Conservative Deformation Limits - The deformation limits of the NEHRP Guidelines 
are, in general, conservative estimates of true component or element capacity. In concept, 
the 
deformation limits are based on "backbone" curves that represent average multi- linear 
behavior of the subassembly of interest (e.g., as determined by cyclic- load testing). 
However, control points of idealized backbone curves necessarily incorporate some 
conservatism (that could be removed if the component or element were tested). Further, 
the 
Collapse Prevention deformation limits of primary components or elements are defined 
as 75% of that permitted for secondary elements, reflecting added conservatism for 
design of primary components or elements. The NEHRP Guidelines (like other seismic 
"codes") include inherent conservatism in limit states. While appropriate for design, 
conservatism 
should be removed from deformation limits used to estimate actual damage and loss.
* Deformation Limits vs. Damage States - The NEHRP Guidelines provide limits on 
component or element deformation rather than explicitly defining damage in terms of 
degree of concrete cracking, nail pull-out, etc., or whether component of element damage 
is likely to repairable (or not). For estimating direct economic loss it is important to 
understand the type of damage, not just the degree of yielding, to establish if repair would 
be required and what the nature (and cost) of such repairs would be.
* Global vs. Local Damage - Local damage (as inferred from the deformation limits of 
the NEHRP Guidelines) of individual components and elements must be accumulated 
over the 
entire structure to represent a global damage state. In general, any number of different 
combinations of local damage to components and elements could result in the same 
amount of global damage. Moderate damage could result due to a modest amount of 
damage to many components of elements, but would most likely be caused by significant 
damage to a limited number of components or elements that would cost 5% to 25% of the 
value of the structural system to repair (or replace).
* Collapse Failure - In general, collapse failures of the structural system require 
consideration of the interaction of components and elements and evaluation of possible 
global instability. The NEHRP Guidelines define "Collapse Prevention" deformation 
limits for components that are intended (with some degree of conservatism) to avoid local 
structural failure of components and elements. Reaching the "Collapse Prevention" 
deformation limit of components or elements does not necessarily imply structural 
collapse. Typically, structural systems can deform significantly beyond "Collapse 
Prevention" deformation limits before actually sustaining a local or global instability. It 
should be noted that while only a few buildings have actually collapsed during a major 
earthquake, case studies of the NEHRP Guidelines found that "Collapse Prevention" 
deformation limits were typically exceeded for strong ground shaking [FEMA, 1999]. 

Table 6.2 provides general guidance to users wishing to relate deformation (or 
deformation ratio) limits of the NEHRP Guidelines to average inter-story drift ratios of 
structural damage states. Table 6.2 provides two sets of criteria for each structural 
damage state. The first set of criteria establish damage states in terms of the fraction (by 
replacement value) of structural components reaching the control point "C" (or control 
point "E") on the idealized load versus deformation (backbone) curve. The second set of 
criteria establish an upper-bound on the average inter-story drift ratio of damage states by 
factors applied to the displacement at which 50% of structural components have reached 
their individual yield points (i.e., control point "B"). Figure 6.3 (taken from Figure 2-5 of 
the NEHRP Guidelines, illustrates points B, C and E on the idealized load versus 
deformation (backbone) curve.

Table 6.2. General Guidance for Relating Component (or Element) Deformation to the 
Average Inter-Story Drift Ratios of Structural Damage-State Medians
Damage State: (Slight, Moderate, Extensive, Complete)
Component (Criteria Set No. 1) (*1) (Fraction(*2), Limit(*3), Factor(*4))
Component (Criteria Set No. 2) (*1) (Fraction(*2), Limit(*3), Factor(*4))

Damage State: Slight
Component (Criteria Set No. 1) (*1) (Fraction(*2) = less than 0%, Limit(*3) = C, 
Factor(*4) = 1.0)
Component (Criteria Set No. 2) (*1) (Fraction(*2) = 50%, Limit(*3) = B, Factor(*4) = 
1.0)

Damage State: Moderate
Component (Criteria Set No. 1) (*1) (Fraction(*2) = less than or equal to 5%, Limit(*3) = 
C, Factor(*4) = 1.0)
Component (Criteria Set No. 2) (*1) (Fraction(*2) = 50%, Limit(*3) = B, Factor(*4) = 
1.5)

Damage State: Extensive
Component (Criteria Set No. 1) (*1) (Fraction(*2) = less than or equal to 25%, Limit(*3) 
= C, Factor(*4) = 1.0)
Component (Criteria Set No. 2) (*1) (Fraction(*2) = 50%, Limit(*3) = B, Factor(*4) = 
4.5)

Damage State: Complete
Component (Criteria Set No. 1) (*1) (Fraction(*2) = less than or equal to 50%, Limit(*3) 
= E, Factor(*4) = 1.0-1.5(*5))
Component (Criteria Set No. 2) (*1) (Fraction(*2) = 50%, Limit(*3) = B, Factor(*4) = 
12)

(*1) The average inter-story drift ratio of structural damage state is lessor of the two drift 
ratios defined by Criteria Sets No. 1 and No.2, respectively. 
(*2) Fraction defined as the repair or replacement cost of components at limit divided by 
the total replacement value of the structural system. 
(*3) Limit defined by the control points of Figure 6-2 and the acceptance criteria of 
NEHRP Guidelines.
(*4) Factor applied to average inter-story drift of structure at deformation (or deformation 
ratio) limit to calculate average inter-story drift ratio of structural damage-state median. 
(*5) Complete factor is largest value in range for which the structural system is stable.

As an example of the use of the 1st set of criteria of Table 6-2 (i.e., limits of 2nd criteria 
set are assumed not to govern), consider the development of damage-state medians for 
the "pushover" curve shown in Figure 6-4. This pushover curve corresponds to the "saw-
tooth" capacity curve shown previously in Section 5, except that curve is now shown in 
terms of base shear versus average inter-story drift ratio (i.e., roof displacement 
normalized by building height. This pushover curve is assumed to have been developed 
by nonlinear static analysis of the structure using the modeling and acceptance theory of 
the NEHRP Guidelines.

Figure 6.3. Idealized Component Load versus Deformation Curve (from Figure 2-5 of the 
NEHRP Guidelines)
Diagram displays Deformation or Deformation Ratio versus Normalized Force, with 
points B, C, and E

Figure 6.4. Example Damage-State Medians of "Saw-Tooth" Pushover Curve 
Diagram displays Average Inter-Story Drift Ratio versus Base Shear, with HAZUS-
Compatible Capacity Curve, Capacity Curve from Pushover Analyis, showing Slight, 
Moderate, Extensive, and Complete points

Following the guidance of Table 6-2, the median of Slight damage is defined by the first 
structural component to reach control point C on its load deformation curve (i.e., point 
where component capacity of component drops, as illustrated in Figure 6.3). On a global 
basis, this point may be recognized as the first "tooth" of the capacity curve (i.e., point 
where structure capacity drops abruptly, as illustrated in Figure 6.4).

Moderate damage is defined by a median value for which a sufficient number of 
components have each reached control point C (on their respective load deformation 
curves) such that it will cost at least 5% of the replacement value of the structural system 
to repair (or replace) these components. Moderate damage is likely to be localized, since 
only a limited number of components can be repaired (or replaced) for 5% of the 
replacement value of the structural system. In Figure 6.4, an oval indicates that this extent 
damage might occur at the second or third "tooth" of the capacity curve, depending on 
type of repair, accessibility of damaged components and other factors that influence 
repair cost.

Extensive damage is defined by a median value similar to Moderate damage, except that 
damage repair now costs at least 25% of the value of the structural system. Extensive 
damage is likely to affect a number of components distributed throughout the building or 
affect all components at the most vulnerable story. Again, an oval indicates the sensitivity 
of the median to repair cost factors. The Extensive damage oval extends up to the point 
on the pushover curve for which there is a large drop in load capacity without significant 
recovery indicating (in this example) that a large number of elements would require 
repair or replacement at this level of response.

Complete damage is defined by a median value for which at least 50% (in terms of 
repair/replacement cost) of structural components have each lost full lateral capacity, as 
defined by control point E on their respective load deformation curves. Table 6.2 
acknowledges the inherent conservatism in the values of control point E (as defined by 
the NEHRP Guidelines) and suggests that the median of the Complete damage state 
should be as much as 1.5 times greater than control point E, provided that the structure is 
not likely to collapse.

In Figure 6.4, a large oval indicates the range of possible median values for the Complete 
damage state. This range extends from 1.0 to 1.5 times the point of the last large drop in 
the load-carrying capacity of the pushover curve, indicating that most elements have 
reached their limit. The Complete damage state and related collapse failure modes are the 
most difficult to rationalize using engineering methods, even when evaluated using the 
sophisticated nonlinear methods of the NEHRP Guidelines. Correlation of predicted and 
observed damage and losses indicate that very liberal interpretations of engineering 
acceptance criteria are required to accurately predict Complete damage and the number of 
collapses that have actually occurred.

The average inter-story drift ratios of structural damage states of generic building types 
may be found in Table 6.4a and Tables 5.9a through 5.9d of the HAZUS-MH Technical 
Manual. These tables provide drift ratios of each model building type for Special High-
Code, High-Code, Moderate-Code, Low-Code and Pre-Code seismic design levels, 
respectively. These drift ratios are also summarized below in Table 6.3. The HAZUS drift 
ratios for generic buildings may be used as a "sanity check" of building-specific values, 
recognizing that generic-building damage-state median values represent a typical 
building of the group and could be a factor of 2 or more greater (or less than) the medians 
of a specific building. 

It should also be noted that Table 6.3 incorporates the effects of diaphragm flexibility 
(and other contributors to the overall flexibility of the structural system) in the values of 
average inter-story drift ratio that define the damage-state medians of generic buildings. 
In contrast, the control points and acceptance criteria of the NEHRP Provisions apply 
strictly to the component of interest. For structural systems with very stiff components 
(e.g., URM buildings), average inter-story drift ratios developed from pushover analysis 
using the modeling and acceptance criteria of the NEHRP Guidelines should also 
incorporate diaphragm (and other sources of) flexibility before comparison with the 
default values summarized in Table 6.3 for generic building types.

 Table 6.3. HAZUS Average Inter-Story Drift Ratio (Dds) of Structural Damage States 

Model Building Type:
Structual Damage States (Slight, Moderate, Extensive, Complete):

Low-Rise Buildings - High-Code Design Level:
Model Building Type: W1, W2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.012
Structual Damage States: Extensive = 0.040
Structual Damage States: Complete = 0.100
Model Building Type: S1
Structual Damage States: Slight = 0.006
Structual Damage States: Moderate = 0.012
Structual Damage States: Extensive = 0.030
Structual Damage States: Complete = 0.080
Model Building Type: C1, S2
Structual Damage States: Slight = 0.005
Structual Damage States: Moderate = 0.010
Structual Damage States: Extensive = 0.030
Structual Damage States: Complete = 0.080
Model Building Type: C2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.010
Structual Damage States: Extensive = 0.030
Structual Damage States: Complete = 0.080
Model Building Type: S3, S4, PC1, PC2, RM1, RM2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.008
Structual Damage States: Extensive = 0.024
Structual Damage States: Complete = 0.070

Low-Rise Buildings - Moderate-Code Design Level:
Model Building Type: W1, W2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.010
Structual Damage States: Extensive = 0.031
Structual Damage States: Complete = 0.075
Model Building Type: S1
Structual Damage States: Slight = 0.006
Structual Damage States: Moderate = 0.010
Structual Damage States: Extensive = 0.024
Structual Damage States: Complete = 0.060
Model Building Type: C1, S2
Structual Damage States: Slight = 0.005
Structual Damage States: Moderate = 0.009
Structual Damage States: Extensive = 0.023
Structual Damage States: Complete = 0.060
Model Building Type: C2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.008
Structual Damage States: Extensive = 0.023
Structual Damage States: Complete = 0.060
Model Building Type: S3, S4, PC1, PC2, RM1, RM2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.007
Structual Damage States: Extensive = 0.019
Structual Damage States: Complete = 0.053

Low-Rise (LR) Buildings - Low-Code Design Level:
Model Building Type: W1, W2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.010
Structual Damage States: Extensive = 0.031
Structual Damage States: Complete = 0.075
Model Building Type: S1
Structual Damage States: Slight = 0.006
Structual Damage States: Moderate = 0.010
Structual Damage States: Extensive = 0.020
Structual Damage States: Complete = 0.050
Model Building Type: C1, S2
Structual Damage States: Slight = 0.005
Structual Damage States: Moderate = 0.008
Structual Damage States: Extensive = 0.020
Structual Damage States: Complete = 0.050
Model Building Type: C2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.008
Structual Damage States: Extensive = 0.020
Structual Damage States: Complete = 0.050
Model Building Type: S3, S4, PC1, PC2, RM1, RM2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.006
Structual Damage States: Extensive = 0.016
Structual Damage States: Complete = 0.044
Model Building Type: S5, C3, URM
Structual Damage States: Slight = 0.003
Structual Damage States: Moderate = 0.006
Structual Damage States: Extensive = 0.015
Structual Damage States: Complete = 0.035

Low-Rise (LR) Buildings - Pre-Code Design Level:
Model Building Type: W1, W2
Structual Damage States: Slight = 0.003
Structual Damage States: Moderate = 0.008
Structual Damage States: Extensive = 0.025
Structual Damage States: Complete = 0.060
Model Building Type: S1
Structual Damage States: Slight = 0.005
Structual Damage States: Moderate = 0.008
Structual Damage States: Extensive = 0.016
Structual Damage States: Complete = 0.040
Model Building Type: C1, S2
Structual Damage States: Slight = 0.004
Structual Damage States: Moderate = 0.006
Structual Damage States: Extensive = 0.016
Structual Damage States: Complete = 0.040
Model Building Type: C2
Structual Damage States: Slight = 0.003
Structual Damage States: Moderate = 0.006
Structual Damage States: Extensive = 0.016
Structual Damage States: Complete = 0.040
Model Building Type: S3, S4, PC1, PC2, RM1, RM2
Structual Damage States: Slight = 0.003
Structual Damage States: Moderate = 0.005
Structual Damage States: Extensive = 0.013
Structual Damage States: Complete = 0.035
Model Building Type: S5, C3, URM
Structual Damage States: Slight = 0.002
Structual Damage States: Moderate = 0.005
Structual Damage States: Extensive = 0.012
Structual Damage States: Complete = 0.028

Mid-Rise Buildings(*1):
Model Building Type: All, Mid-Rise Building Types
Structual Damage States: Slight = 2/3 * LR
Structual Damage States: Moderate = 2/3 * LR
Structual Damage States: Extensive = 2/3 * LR
Structual Damage States: Complete = 2/3 * LR

High-Rise Buildings(*1):
Model Building Type: All, High-Rise Building Types
Structual Damage States: Slight = 1/2 * LR
Structual Damage States: Moderate = 1/2 * LR
Structual Damage States: Extensive = 1/2 * LR
Structual Damage States: Complete = 1/2 * LR

(*1) Mid-rise and high-rise buildings have damage-state drift values based on low-rise 
(LR) drift criteria reduced by factors of 2/3 and 1/2, respectively, to account for higher-
mode effects and differences between average inter-story drift and individual inter-story 
drift.

As the final step in the development of Damage-State Medians for the structural system, 
average inter-story drift values for each damage state are converted to the corresponding 
amount of spectral displacement using the modal factor, a2, and other terms:

Equation 6-1:
Sd,ds = ? ds * HR * a2

where:
Sd,ds = Median spectral displacement value of damage state, ds (inches) 
Dds = Average inter-story drift ratio at the threshold of damage state, ds, determined by 
user (consistent with generic values of Table 6.2) 
HR = Height of building at the roof level (inches) 
a2 = Pushover modal factor from Equation (5-2). 
  
6.2.2. Nonstructural Components 
In most applications, Damage-State Medians for nonstructural components may be based 
directly on the default values of HAZUS. Exceptions include buildings with nonstructural 
components or contents that are either significantly more rugged or significantly more 
vulnerable than the normal make-up of components of nonstructural systems in a typical 
commercial building. Examples of buildings with particularly vulnerable systems include 
certain manufacturing facilities (e.g., buildings with clean rooms), laboratories, computer 
facilities, historical buildings (architectural components), art museums and other 
buildings with special contents. Examples of buildings with particularly rugged systems 
include certain military, industrial or emergency facilities whose nonstructural systems 
and contents have been specially anchored or braced to resist earthquake shaking. 

HAZUS default values for the drift ratio of the threshold of each damage state are 
summarized in Table 6.3 for drift-sensitive nonstructural components. These damage-
state drift ratios are assumed to be the same for all building types and seismic design 
levels. The same values of drift ratio are also assumed to be appropriate for special 
buildings, such as emergency facilities, since drift-sensitive components (partitions) 
typically do not receive special design or detailing to accommodate building 
displacement.

Table 6.4. HAZUS Damage-State Criteria for Nonstructural Systems and Contents
Design Level:
Nonstuctural Damage States - All Building Types (Slight, Moderate, Extensive, 
Complete):

Inter-Story Drift Ration (Dds) - Drift-Sensitive Components
Design Level:  All
Nonstructual Damage States: Slight = 0.004
Nonstructual Damage States: Moderate = 0.008
Nonstructual Damage States: Extensive = 0.025
Nonstructual Damage States: Complete = 0.050

Peak Floor Acceleration (Amax,ds) - Acceleration-Sensitive Components/Contents (g's)
Design Level: Special High-Code
Nonstructual Damage States: Slight = 0.45
Nonstructual Damage States: Moderate = 0.9
Nonstructual Damage States: Extensive = 1.8
Nonstructual Damage States: Complete = 3.6
Design Level: High-Code
Nonstructual Damage States: Slight = 0.30
Nonstructual Damage States: Moderate = 0.6
Nonstructual Damage States: Extensive = 1.2
Nonstructual Damage States: Complete = 2.4
Design Level: Moderate-Code
Nonstructual Damage States: Slight = 0.25
Nonstructual Damage States: Moderate = 0.5
Nonstructual Damage States: Extensive = 1.0
Nonstructual Damage States: Complete = 2.0
Design Level: Low-Code
Nonstructual Damage States: Slight = 0.20
Nonstructual Damage States: Moderate = 0.4
Nonstructual Damage States: Extensive = 0.8
Nonstructual Damage States: Complete = 1.6
Design Level: Pre-Code
Nonstructual Damage States: Slight = 0.20
Nonstructual Damage States: Moderate = 0.4
Nonstructual Damage States: Extensive = 0.8
Nonstructual Damage States: Complete = 1.6

HAZUS default values of peak floor acceleration defining the threshold of each damage 
state are summarized in Table 6.3 for acceleration-sensitive nonstructural components 
(and contents). These damage-state accelerations are assumed to be the same for all 
building types, but to vary by seismic design level. Similarly, emergency or other 
facilities that have special anchorage and bracing requirements for nonstructural 
components and equipment (Special High-Code design level) have damage-state 
accelerations increased by a factor of 1.5.

Considering the importance to the estimates of certain types of loss, in particular 
estimates of direct economic loss, it would seem desirable to develop building-specific 
damage-state parameters for nonstructural components and contents, rather than rely on 
generic building data. However, rigorous development of nonstructural parameters would 
require detailed evaluation of component capacity, similar to that used to evaluate the 
structural system, only much more difficult to perform due to the complexity and variety 
of different nonstructural systems and components. Nonstructural systems and contents 
would need to be thoroughly inspected (detailed field survey). Capacity of anc horage 
and bracing would need to be evaluated (possibly requiring dynamic analysis of complex 
systems such as piping runs). Fragility values would then need to be developed based on 
the results of the analysis, available test data (e.g., of similar equipment), and/or 
experience data. This process is not practical for most applications and would likely be 
limited to a "walk-down" of nonstructural systems and building contents.

If the user has access to the building and is concerned that nonstructural components 
and/or contents are not "typical," then it is recommended that a building "walk-down" be 
performed using checklists and other guidance provided by FEMA 74 [FEMA, 1994] or 
FEMA 310 [FEMA, 1998]. These documents do not estimate damage or loss but are 
useful in spotting potential deficiencies in typical nonstructural systems. The user need 
not perform calculations, but may rely on judgement to estimate the approximate drift 
ratio (for drift-sensitive components) or peak floor acceleration (for acceleration-sensitive 
components) at which different nonstructural components would begin to fail and require 
repair or replacement.

Damage-State Medians for drift-sensitive nonstructural components must be converted 
from drift ratio to spectral displacement in a manner similar to that used for the structural 
system. Inter-story drift ratios for each damage state are converted to the corresponding 
amount of spectral displacement using the modal factor, a2, and other terms:

Equation 6-2:
Sd,ds = FQP,ds * ? ds *HR * a2

where:
Sd,ds = Median spectral displacement value of damage state, ds (inches)
FQp,ds = Factor relating average inter-story drift to the drift ratio of the component at 
damage state, ds, as defined by Equation (6-3)
Dds = Component drift ratio corresponding to threshold of damage state, ds, determined 
by user (consistent with the generic values of Table 6.3)
HR = Height of building at the roof level (inches)
a2 = Pushover modal factor from Equation (5-2). 

The factor, FfP,ds, is used to relate average inter-story drift to maximum inter-story drift 
to account for the effects of an uneven distribution of drift over the height of the building. 
Uneven distribution of drift causes damage to occur at certain stories sooner than at other 
stories. The factor, FfP,ds, is based on both the shape of the pushover mode and damage-
state loss ratio:

Equation 6-3:
FfP,ds = product of fR,P (1-NSDds) | HR * ?max,P
- NSDds

where:
QR,P = Roof displacement of the pushover mode for damage state, ds (inches) 
NSDds = Nonstructural drift-sensitive component loss ratio of damage state, ds 
(expressed as a fraction)
HR = Height of building at the roof level (inches)
Dmax,P = Maximum inter-story drift ratio (considering torsion) over the height of the 
building corresponding to the roof displacement, QR,P.

The factor, FfP,ds, makes use of the results of the pushover analysis to better predict 
localized damage and loss for buildings that have a structural irregularity (e.g., soft 
story). When drift is uniformly distributed over building height, the value of the factor is 
equal 1.0. When drift is not uniformly distributed over building height, the factor reduces 
median values to reflect the lower thresholds of damage associated with accentuated drift 
of critical stories. The factor varies with the loss ratio of the damage state, effectively 
reducing the influence of localized damage on the more extensive states of damage (i.e., 
factor is 1.0 for Complete Damage).

Damage-State Medians for nonstructural acceleration-sensitive components (and 
contents) are developed in terms of peak floor acceleration. In general, medians 
expressed in terms of spectral acceleration are taken as equal to peak floor acceleration 
values since spectral acceleration (obtained by the intersection of pushover curve and 
spectral demand) is assumed to represent peak floor acceleration of a typical upper floor 
of the building. Demand on components (and contents) at ground level is based directly 
on peak ground acceleration and is also assumed to represent peak (ground) floor 
acceleration. The trivial equation summarizing conversion peak floor acceleration of each 
damage state to the corresponding amount of spectral acceleration is:

Equation 6-4:
Sa,ds = Amax,ds

where:
Sa,ds = Median spectral acceleration value of damage state, ds (units of g)
Amax,ds = Peak floor acceleration of the threshold of damage state, ds (units of g) 
determined by user or based on generic values of Table 6.3.

The assumption that peak floor acceleration is the same as spectral acceleration demand 
ignores higher-mode shaking effects (not included in the pushover analysis) and the 
uneven distribution of floor acceleration over building height. Higher-mode effects can 
significantly increase upperfloor accelerations, although they may not cause failure of 
systems that have some ductility. Users concerned about higher-mode response could 
reduce median values by a factor inversely proportional to the increase in (damaging) 
floor acceleration associated with higher-mode response.

Peak floor acceleration will vary over the height of the building, typically with the largest 
accelerations at the roof. The intersection of the pushover and demand spectrum 
corresponds to building response at a floor elevation of about a2 x HR. Users concerned 
that this location is not representative of a typical upper floor of nonstructural 
acceleration-sensitive components (e.g., all the equipment is on the roof) could modify 
median values based on the location of the components and the shape of the pushover 
mode. Such modification would have little effect on the prediction of damage for most 
buildings with well distributed nonstructural systems.

6.3. Development of Damage-State Variability 
Lognormal standard deviation (Beta) values describe the total variability of fragility-
curve damage states. Three primary sources contribute to the total variability of any given 
state, 
namely, the variability associated with the capacity curve, bC, the variability associated 
with the demand spectrum, bD, and the variability associated with the discrete threshold 
of each damage state, bT,ds, as described in Equation (6-5):

Equation 6-5:
ds = square root of (CONV[C,D])squared + (T,ds)squared

where:
,ds = is the lognormal standard deviation parameter that describes the total variability of 
damage state, ds,  
C = is the lognormal standard deviation parameter that describes the variability of the 
capacity curve, 
D = is the lognormal standard deviation parameter that describes the variability of the 
demand spectrum (values of bD = 0.45 at short periods and bD = 0.50 at long periods 
were used to develop Tables 6.5 - 6.7),
T,ds = is the lognormal standard deviation parameter that describes the variability of the 
threshold of damage state, ds.

Since the demand spectrum is dependent on building capacity, a convolution process is 
required to combine their respective contributions to total variability. This is referred to 
as "CONV" in Equation (6-5). The third contributor to total variability, bT,ds, is assumed 
mutually independent of the first two variables and is combined with the results of the 
CONV process using the square-root-sum-of-the squares (SRSS) method. Additional 
background on the calculation of Damage-State Beta's is provided in the HAZUS-MH 
Technical Manual and the Earthquake Spectra paper "Development of Building Damage 
Functions for Earthquake loss Estimation" [Kircher et al., 1997a].

The variability of the demand spectrum (i.e., variability of ground shaking) is a key 
parameter in the calculation of damage-state variability. The values of demand 
variability, bD = 0.45 at short periods and bD = 0.50 at long periods, are the same as 
those used to calculate the default fragility curves of the HAZUS-MH Technical Manual. 
These value s are consistent with the variability (e.g., dispersion factor) of ground 
shaking attenuation functions used by HAZUS to predict response spectra for large-
magnitude events in the Western United States (WUS). It may be noted that if there were 
no variability of demand (response spectrum is known exactly), then Equation (6-5) 
would become:

Equation 6-6:
,ds = the sqaure root of (C)squared + (T,ds)squared

This equation provides a lower-bound on the damage-state variability appropriate for use 
in probabilistic calculations of damage and loss that are based on the integration of the 
fragility with hazard functions that have already incorporated ground shaking variability 
in the hazard calculations. Similarly, Equation (6-6) also provides a lower-bound on 
damage-state variability for calculation of damage and loss using a response spectrum 
that is reasonably well known (i.e., response spectrum of recorded ground shaking). 
Arguably, there would always be some amount variability (uncertainty) in ground 
shaking demand, D, but such can be ignored in the calculation of total damage-state 
variability, ds, when substantially less than both capacity curve variability, C, and 
damage-state threshold variability, T,ds.

The convolution process involves a complex numerical calculation that would be very 
difficult for most users to perform. To avoid this difficulty, sets of pre-calculated values 
of Damage-State Beta's have been compiled in Tables 6.5 through 6.7 from which users 
may select appropriate values of variability for the structural system, nonstructural drift-
sensitive components and nonstructural acceleration-sensitive components. The Beta 
values of these tables are a function of the following building characteristics and criteria:
* Building Height Group - Low-Rise Buildings (Table 6.5), Mid-Rise Buildings (Table 
6.6)
* Post-Yield Degradation of the Structural System - Minor, Major and Extreme 
Degradation
* Damage-State Threshold Variability - Small, Moderate or Large Variability 
* Capacity Curve Variability - Very Small, Small, Moderate or Large Variability.

The Beta values of the tables are applicable to all model building types. For example, a 
low-rise concrete-frame building (C1L) would have the same set of Beta's as a low-rise 
braced steel frame building (S2L), provided the two buildings have the same amount of 
capacity curve and damage-state threshold variability, and the same amount of post-yield 
degradation of the structural system.

Post-yield degradation of the structural system is defined by a Kappa factor, which is an 
direct measure of the effects of seismic design level and construction quality on the 
variability of response. Buildings that are seismically designed and/or have superior 
construction are less likely to degrade during post-yield earthquake shaking, and 
therefore have more predictable response, than buildings that are not seismically designed 
and/or have inferior construction.

To select a set of building-specific Damage-State Beta's (i.e., a structural Beta, a 
nonstructural drift-sensitive Beta and a nonstructural acceleration-sensitive Beta), users 
must first determine the building height group that best represents the specific building of 
interest. The height groups are defined by the same criteria as those used by HAZUS to 
define generic building types. For example, a 5-story, reinforced concrete building would 
be classified as a mid-rise building as per the height criteria of Table 2-1.

Tables 6-5 through 6-7 (referred to as the Beta tables) provide recommended sets of 
Damage-State Beta's for each of the three building height groups, respectively. In each of 
these tables, the Beta's are based on 36 possible combinations of capacity curve 
variability, damage threshold variability and the amount of post-yield degradation 
expected for the structural system.

Estimation of structural system degradation (minimum or maximum) is made on the basis 
of Kappa factors suggested by Table 5.2 (Section 5.3.3) and the degree of post-yield 
response expected for the damage state of interest. Kappa factors decrease with increase 
in response level (and damage). Slight damage corresponds to response between 1/2 yield 
and full yield; Moderate damage to response at or just beyond yield; and Extensive and 
Complete damage correspond to post-yield response for the duration of scenario 
earthquake shaking. Beta values are given in Tables 6-5 through 6-7 for k greater than or 
equal to 0.9 (minor degradation), k = 0.5 (major degradation) and k greater than or equal 
to 0.1 (extreme degradation) of the structural system; and linear interpolation may used to 
establish 
Beta's for other values of the Kappa factor.

Estimation of the variability of the capacity curve (C) and the variability of the threshold 
of the damage state (T,ds) must be made by users on a judgmental basis (with some 
guidance provided herein). To assist the user, the Beta tables express capacity curve and 
damage threshold variability qualitatively (e.g., Small Variability) and in term of the 
numerical value used to develop the Beta's in the CONV process. Numerical values of 
variability (C and T,ds) are lognormal standard deviation parameters and may be used, 
as illustrated in Figure 6.2, to construct the distribution of capacity or damage threshold 
that they represent.

The variability of capacity curves and the damage-state thresholds are influenced by: 
* Uncertainty in capacity curve properties and the thresholds of damage states, and 
* Building population (i.e., individual building or group of buildings).

Relatively low variability of damage states would be expected for an individual building 
with well known properties (e.g., complete set of as-built drawings, material test data, 
etc.) and whose performance and failure modes are known with confidence. The taller the 
building the greater the variability in damage state due to uncertainty in the prediction of 
response and damage using pushover analysis. Relatively high variability of damage 
states would be expected for a group of buildings whose properties are not well known 
and for which the user has low confidence in the results (of pushover analysis) that 
represent performance and failure modes of all buildings of the group. The latter case 
essentially describes the original development of damage-state fragility curves for generic 
model building that were based on capacity variability, C = 0.3, and damage-state 
threshold variability, T,ds = 0.3 (Structure), T,ds = 0.5 (NSD) and T,ds = 0.6 (NSA). 
The generic model building types represent large populations of buildings for which 
properties are 
not well known.

Table 6.5. Low-Rise Building Fragility Beta's
Building System (*2)
Post-Yield Degradation of Structural System (*3)
Minor Degradation (k greater than equal to 0.9), Major Degradation (k=0.5), Extreme 
Degradation (k less than equal to 0.1)
Damage Variability (*4) (T,ds) = Small (0.2), Medium (0.4) or Large (0.6)

(*2) Building Systems include the Structure, Nonstructural Drift-Sensitive Components 
(NSD) and Nonstructural Acceleration-Sensitive (NSA) components.

Structural Systems with Very Small Capacity Curve Variability (*5) (C = 0.1) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.80
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Small Capacity Curve Variability (*5) (C = 0.2) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.80
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Moderate Capacity Curve Variability (*5) (C = 0.3) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.80
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.95
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.95
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.80
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.95
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Large Capacity Curve Variability (*5) (C = 0.4) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.80
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.85
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.95
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 1.00
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.10
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.10
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.20
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.85
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.95
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 1.00
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.10
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Table 6.6. Mid-Rise Building Fragility Beta's
Building System (*2)
Post-Yield Degradation of Structural System (*3)
Minor Degradation (k greater than equal to 0.9), Major Degradation (k=0.5), Extreme 
Degradation (k less than equal to 0.1)
Damage Variability (*4) (T,ds) = Small (0.2), Medium (0.4) or Large (0.6)

(*2) Building Systems include the Structure, Nonstructural Drift-Sensitive Components 
(NSD) and Nonstructural Acceleration-Sensitive (NSA) components.

Structural Systems with Very Small Capacity Curve Variability (*5) (C = 0.1) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.70
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.70
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.85
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.05
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.70
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Small Capacity Curve Variability (*5) (C = 0.2) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.75
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Moderate Capacity Curve Variability (*5) (C = 0.3) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Large Capacity Curve Variability (*5) (C = 0.4) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.75
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Table 6.7. High-Rise Building Fragility Beta's
Building System (*2)
Post-Yield Degradation of Structural System (*3)
Minor Degradation (k greater than equal to 0.9), Major Degradation (k=0.5), Extreme 
Degradation (k less than equal to 0.1)
Damage Variability (*4) (T,ds) = Small (0.2), Medium (0.4) or Large (0.6)

(*2) Building Systems include the Structure, Nonstructural Drift-Sensitive Components 
(NSD) and Nonstructural Acceleration-Sensitive (NSA) components.

Structural Systems with Very Small Capacity Curve Variability (*5) (C = 0.1) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.55
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.75
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.85
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.80
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.00
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.55
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.75
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.05
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Small Capacity Curve Variability (*5) (C = 0.2) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.65
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.70
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.05
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.75
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Moderate Capacity Curve Variability (*5) (C = 0.3) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.70
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.90
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

Structural Systems with Large Capacity Curve Variability (*5) (C = 0.4) 
Building System: Stucture
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.75
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.95
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.10
Building System: NSD
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.60
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.70
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.85
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.80
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.90
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 1.00
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 1.05
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 1.15
Building System: NSA
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Minor Degradation (k greater than equal to 0.9), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Small (0.2) = 0.35
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Medium (0.4) = 0.50
Major Degradation (k=0.5), Damage Variability (*4) (T,ds): Large (0.2) = 0.65
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Small 
(0.2) = 0.35
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): 
Medium (0.4) = 0.50
Extreme Degradation (k less than equal to 0.1), Damage Variability (*4) (T,ds): Large 
(0.2) = 0.65

SECTION 7 
DEVELOPMENT OF LOSS FUNCTIONS 
7.1. Building Loss Criteria 
This section guides users in the development of loss functions that are used by Advanced 
Engineering Building Module (AEBM) to calculate building losses as a function of 
damage-state probability (i.e., building fragility). It is essential that this section be 
coordinated with the development of fragility parameters in Section 6 for those 
parameters that share common assumptions (e.g., repair/replacement cost assumed for 
damage states).

Building loss data may be thought of as falling into either one or the other of two basic 
groups: 
* Non-Damage-Related - Loss data related to building occupancy or economic value 
including the number of building occupants and the replacement cost of the building and 
contents
* Damage-Related - Loss data derived from and related to the damage states such as the 
cost of earthquake repair and time required for clean up and repair.

HAZUS default inventory data assume a certain size, square footage, replacement value 
and number of occupants for each building occupancy and type that may be very different 
from that of the specific building of interest. HAZUS default inventory data should not be 
used for building-specific applications without verification. Typically, owners would be 
able to provide and/or verify non-damage-related data for specific buildings.

Development of damage-related loss data require users to either calculate or estimate 
different types of loss for the specific states of damage described by the pushover 
analysis. For development of casualty rates, users should consider how collapse failure 
could occur (e.g., local collapse, single-story collapse or "pancake " collapse of the whole 
building) and injure or kill building occupants. For development of direct economic loss 
rates, users should consider the process (scope of work and time required) to repair each 
state of damage (i.e., Slight, Moderate, Extensive and Complete) to the structural system, 
nonstructural components and contents of the building. Users may choose to use the 
default values of HAZUS loss functions, but should always verify that the default values 
appear reasonable for the specific building of interest.

7.2 . Direct Social Losses - Casualties
HAZUS methods distinguish between "indoor" and "outdoor" casualties, the later 
referring to deaths and injuries to pedestrians (or people in cars, etc.) that are near the 
building at the time of the earthquake. The AEBM estimates deaths and injuries using 
"indoor" casualty rates and does not calculate "outdoor" casualties.

HAZUS methods base "indoor" casualty rates solely on structural damage states and base 
collapse-related deaths solely on Complete structural damage. Some buildings may have 
Collapse failure of elements or components (e.g., out-of-plane failure of in- fill wall) 
prior to the building reaching a Complete state of damage. Some buildings may also have 
nonstructural components and equipment whose failure could cause injury and death of 
occupants. Additionally, casualties due to fire, release of hazardous materials, 
electrocution or other indirect effects of structural or nonstructural damage, are not 
included in HAZUS casualty rates. For most buildings, these effects do not dominate 
earthquake casualties. Structural damage tends to dominate deaths and serious injuries, 
particularly when there is a significant probability of Complete structural damage.

The default rates of HAZUS seem to produce reasonable estimates of casualties for large 
study regions composed of many buildings, but may significantly under-predict (or over-
predict) casualties, in particular deaths, for an individual building. To better estimate 
deaths, users may choose to develop building-specific casualty rates for the Complete 
structural damage. The validity of building-specific rates is dependent on accurate 
prediction of collapse failure modes by pushover analysis, and the user's subjective 
evaluation of the relative likelihood of Collapse failure given the building is in the 
Complete state of damage. As described in Subsection 4.3.2, Collapse Casualty Rates, 
P[Si|COL], are conditional on the Collapse Factor, P[COL|STR5], where "STR5" is the 
state of Complete structural damage. Definitions of casualty severity are given in Table 
7.1. 

Table 7.1. HAZUS Casualty Classification Scale
Casualty Level:
Casualty Description:

Casualty Level: Severity 1
Casualty Description:  Injuries requiring basic medical aid, but without hospitalization 
(treat and release) 

Casualty Level: Severity 2
Casualty Description:  Injuries requiring medical attention and hospitalization, but not 
considered to be life-threatening 

Casualty Level: Severity 3
Casualty Description:  Casualties that include entrapment and require expeditious rescue 
and medical treatment to avoid death

Casualty Level: Severity 4
Casualty Description:  Immediate deaths

Casualty rates given collapse, P[Si|COL], apply only to occupants in the portion of the 
building that has actually collapsed. For most building types, the default values of 
HAZUS assume that only 10 in every 100 occupants in the collapsed portion of the 
building would be killed immediately (Severity 4) and another 5 in every 100 occupants 
would be trapped and not survive without expeditious rescue and treatment (Severity 3). 
These values are based on a variety of generic building configurations and the 
assumption that even with collapse the vast majority of exposed occupants can crawl out 
of the structure. These values may be low by as much as a factor of 5 for evaluation of 
specific buildings that are expected to have "pancake" types of failure or could otherwise 
bury occupants under heavy building debris. Such failures would trap and kill a much 
larger fraction of occupants in the collapsed portion of the building, although most 
exposed occupants would still be expected to survive.

In cases where collapse failure is expected to crush or bury building occupants under 
heavy building debris (e.g., concrete or masonry material), users should modify the 
casualty rates, P[Si|COL]. In such cases, casualty rates for Severity 3 and 4 should be 
increased by a factor ranging from 2 (for local collapse involving heavy debris) to 5 (for 
full pancake collapse of stories). The casualty rate for Severity 1 should also be adjusted 
downward as required for the sum of the casualty rates (and the implicit probability of no 
injury or death) to equal 1.0.

The Collapse Factor, P[COL|STR5], is a probability that effectively defines the fraction 
of building occupants expected to be exposed to some type of collapse given that the 
building has reached the Complete state of damage. Default values of HAZUS collapse 
rates range from a probability of 3% to 15% as summarized in Table 7.2.

Table 7.2. HAZUS Collapse Rates for Generic-Building Types
Model Building Type:  
Collapse Rate:  

Model Building Type:  W1, W2, S1H, S2H, S3, S4H, S5H and MH
Collapse Rate:  3%  

Model Building Type:  S1M, S2M, S4M, S5M, C1H, C2H and RM2H
Collapse Rate:  5%  

Model Building Type:  S1L, S2L, S4L and S5L
Collapse Rate:  8%  

Model Building Type:  C1M, C2M, C3H, PC2H, RM1M and RM2M
Collapse Rate:  10%  

Model Building Type:  C1L, C2L, C3M, PC2M, RM1L and RM2L
Collapse Rate:  13%  

Model Building Type:  C3L, PC1, PC2L, URML and URMM
Collapse Rate:  15%  

The expected fraction of occupants exposed to Collapse may be thought of the 
"weighted" sum of the individual fractions associated with each different collapse failure 
mode. The fraction of occupants exposed to a given Collapse failure mode is calculated 
by multiplying the likelihood of that mode of Collapse failure times the number of 
occupants that would be exposed to such failure. Following this logic, the Collapse 
Factor, P[COL|STR5], is expressed by Equation (7-1):

Equation 7-1:
P[COL|STR5] = sigma over i P[C1] * FBO,i

where:
P[C1] = Probability of Collapse failure mode i 
FBO,i = Fraction of building occupants exposed to Collapse failure mode i. 

While there could be many types of Collapse failure modes (given Complete structural 
damage has occurred), the user may wish to consider the following four general types:
* C0 No Collapse - Building is a complete loss, but does not threaten life safety
* CL Local Collapse - Localized collapse of building elements or components (e.g., out-
ofplane collapse of infill walls)
* CS Story Collapse - Collapse of an individual story or portion thereof (e.g., soft-story)
* CG Global Collapse - Collapse over multiple stories (e.g., "pancake" collapse).

For each of these four possible types of Collapse failure, the user would estimate both the 
probability of the failure mode, P[Ci] , and the fraction of exposed occupants, FBO,i. For 
example, the probability of various failure modes and fraction of exposed occupants of a 
mid-rise unreinforced masonry building (URMM) might be estimated as follows:
* P[C0] = 0  FBO,i = 0.0:  Building is assumed to have sustained some amount of 
collapse, (P[CO] = 0), since at least some local (e.g. wall) failure will have occurred if the 
building has reached the Complete state of damage
* P[CL] = 0.5  FBO,i = 0.1: Building is assumed to have a 50% probability of localized 
failure of walls; but localized failure would only expose about 10% of building occupants 
to collapse
* P[CS] = 0.5  FBO,i = 0.25:  Building is assumed to have a 50% probability of single-
story collapse; a single-story failure would expose about 20% of building occupants to 
collapse (i.e., for a 5-story building)
* P[CG] = 0.0 FBO,i = 1.0 Building is assumed to have no significant probability of total 
building collapse that would expose all building occupants to collapse.

The calculation of the Collapse Factor, P[COL|STR5], for this exa mple is shown in 
Equation (7-2):

Equation 7-2:
P [COL|STR5] = 0.0 x 0.0 + 0.5 x 0.1 + 0.5 x 0.2 + 0.0 x 1.0 = 15%
 
In this case, the calculated value of the Collapse Factor, 15%, is found to be the same as 
the HAZUS default value for a generic URMM building given in Table 7.2. This 
probability value is based on two equally likely failure modes, involving either local 
collapse of a wall or collapse of a single story, without significant likelihood of total 
building collapse. The Collapse Factor would be substantially greater than 15% if the 
building was deemed to have a significant probability of total collapse.

7.3. Direct Economic Losses 
Direct economic losses include costs of building repair (or replacement) of structural and 
nonstructural systems, contents and business inventory. Direct economic losses also 
include costs due to loss of building function. Users may choose to use the default values 
of HAZUS loss functions, but should always verify that the default values appear 
reasonable for damage states of the specific building of interest. When developing 
building-specific values, or simply verifying the appropriateness of default values, users 
should carefully think through the process, work and time that would be required to 
repair Slight, Moderate, Extensive and Complete damage to elements and components as 
described by pushover analysis.

Some consideration should be given to prevailing codes and ordinances that would 
govern the repair work.. Do prevailing regulations require strengthening as well as 
repair? Is the building of historical significance, or otherwise have special conditions that 
could influence repair? 

Earthquake repair and strengthening of historical buildings can be extremely expensive 
(due to preservation of historical features), even though the damage triggering suc h 
repair may be relatively modest. For example, the historical San Francisco City Hall 
sustained only Moderate damage due to the 1989 Loma Prieta earthquake, but the cost of 
repair and strengthening the building was many times the cost of a new building of 
comparable size. The default loss ratio of 10% for Moderate damage would not be 
appropriate in this case and would not produce an accurate estimate of the direct 
economic loss that actually occurred. However, if only Slight damage had occurred (e.g., 
due to a lower level of ground shaking), then damage would likely have not triggered 
seismic retrofit and post-earthquake clean- up efforts would have cost only a small 
fraction of total building value (more like the 2% default loss ratio for Slight damage).

The extraordinary cost of repair of the San Francisco City Hall after the 1989 Loma 
Prieta earthquake (over $100 million) would be difficult to estimate using HAZUS 
methods, unless 
replacement value also included additional value due to the historical significance and 
importance of the building (and the large amount of available relief funding). As 
discussed in the HAZUS-MH Technical Manual, replacement value is the preferred 
measure of economic loss, although other measures could be used, such as loss of market 
value. Market value would, in general, produce entirely different loss estimates. For 
example, an older building of no special importance or historical significance is to be 
vacated and completely renovated, but instead an earthquake occurs and destroys the 
structure. Should economic loss be based on the replacement value (e.g., cost of a new 
building of comparable size and function), the near zero value of the existing building, or 
on the market value of the building (which would also include value of the land)? These 
types of question are crucial to the estimation of economic loss, but are beyond the scope 
of this manual. It is assumed that building-specific economic loss functions will be based 
on repair and replacement value of the building and contents, consistent with HAZUS 
methods for generic building types.

7.3.1. Repair Costs 
Repair cost rates define expected dollar costs (e.g., as fraction of building value) that 
would be required to repair or replace building damage. Repair and replacement costs are 
required for each state of damage of the structural system, nonstructural drift-sensitive 
components, nonstructural acceleration-sensitive components and building contents and 
business inventory. HAZUS default values of repair and replacement costs are different 
for each occupancy, and estimation of structural costs is also different for each model 
building type.

Development of building-specific cost factors involves two basic components: 
* Determining the total replacement cost of building systems, contents and business 
inventory 
* Determining the appropriate fractions (loss ratios) of the total replacement cost 
corresponding to each damage state.

It is expected that the user (e.g., with owner assistance) would be able to develop an 
estimate of the total replacement cost of building systems (and contents and business 
inventory) and would not need to rely on the default vales of HAZUS. The total 
replacement cost of the building should be divided into the cost of the structural system, 
the cost of nonstructural drift-sensitive components and the cost of nonstructural 
acceleration-sensitive components. For reference, Table 2.4 lists typical drift-sensitive 
and acceleration-sensitive components of nonstructural systems. Table 7.3 summarizes 
the fractional costs of buildings systems assumed by HAZUS for some common 
combinations of occupancy and building type. Also shown in Table 7.3 are the 
percentages of total nonstructural cost associated with drift-sensitive and acceleration-
sensitive components, respectively.

Table 7.3. Fractional Cost of Structural and Nonstructural Systems of HAZUS Generic 
Building Types and Occupancies
Common Combinations of Occupancy and Building Type (Occupancy Group)
Fraction of Total Building Cost:  Structural System and Nonstructural System (Percent of 
Total Nonstructural Cost):

Single-Family Residences - RES1/W1 (All Single-Family Residences)
Fraction of Total Building Cost: Structural System = 0.25
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Drift-Sensitive = 0.49 (65%)
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Acceleration-Sensitive = 0.26 (35%)

Multi-Family Residences - RES3(A-F)/W1 (All Non-Single-Family Residences) 
Fraction of Total Building Cost: Structural System = 0.18
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Drift-Sensitive = 0.41 (50%)
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Acceleration-Sensitive = 0.41 (50%)

Retail Commercial - COM1/S1M (All Commercial Buildings) 
Fraction of Total Building Cost: Structural System = 0.38
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Drift-Sensitive = 0.25 (40%)
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Acceleration-Sensitive = 0.37 (60%)

Light Industrial - IND2/PC1 (All Industrial Buildings)
Fraction of Total Building Cost: Structural System = 0.27
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Drift-Sensitive = 0.11 (15%)
Fraction of Total Building Cost: Nonstructural System (Percent of Total Nonstructural 
Cost): Acceleration-Sensitive = 0.62 (85%)

HAZUS default values of direct economic loss for structural and nonstructural systems 
are based on the following assumptions of the loss ratio corresponding to each state of 
damage:
* Slight damage would be a loss of 2% of building's replacement cost
* Moderate damage would be a loss 10% of the building's replacement cost
* Extensive damage would be a loss of 50% of the building's replacement cost
* Complete damage would be a loss of 100% of the building's replacement cost.

As discussed previously, the default values of loss ratio should not be used to develop 
building-specific loss functions, unless the user has used the same values to guide the 
development of damage-state medians (Section 6.2).

HAZUS assumes contents loss ratios to be one- half of the default loss ratios of the 
building on the basis that one-half of building contents are not vulnerable to ground 
shaking and could be salvaged even if the building were severely damaged. Building-
specific contents damage (loss ratios), CDds, should be based on an appropriate fraction 
(e.g., one-half) of the loss ratios of acceleration-sensitive nonstructural components.

7.3.2. Loss of Function
Repair time, recovery time and service interruption multipliers do not affect the 
calculation of capital stock losses (e.g., repair/replacement costs), but significantly 
influence income-related losses, such as relocation, wages and rental income losses. 
Users should develop building-specific values for repair time based on the scope of 
repair/replacement work estimated for each damage state. Proportiona l changes to 
recovery time should also be made, if building-specific repair times are used in lieu of 
HAZUS default values. In general, users would be expected to use the default values of 
service interruption multipliers to determine "loss of function" time for most building-
specific applications.

SECTION 8 
EXAMPLE ESTIMATION OF BUILDING DAMAGE AND LOSS USING THE 
AEBM 
8.1. Background 
This section demonstrates building-specific methods by developing damage and loss 
parameters for an individual building (before and after seismic upgrade), and by 
implementing these parameters in the AEBM of the HAZUS-MH Software to estimate 
losses for a scenario earthquake. In this example, the AEBM illustrates the calculation of 
earthquake losses that could be used by engineers and building owners to evaluate the 
benefits of seismic rehabilitation.

The example building is the Headquarters of Los Angeles County Department of Public 
Works (LACDPW) located in Alhambra, California. The Los Angeles office of Black & 
Veatch has investigated seismic hazard mitigation for this building [Chen et al., 2001]. 
Their study included a site-specific hazard evaluation [Geomatrix, 1999], field 
investigations and laboratory testing of girder-column connections at the University of 
California at San Diego [Chi and Uang, 2000], development of several different schemes 
for seismic retrofit of the structural system and estimation of the costs of each scheme. 
Performance of the structural system was evaluated by detailed nonlinear pushover 
analyses of the original building and each retrofit scheme.

The Black & Veatch study provides the requisite engineering and ground shaking data for 
AEBM evaluation of damage and loss. A scenario earthquake is selected based on the 
findings of Geomatrix' evaluation of ground shaking hazard at the site. Performance of 
the structural system is based on the results of pushover analyses of the original building 
and for one of the retrofit alternatives (i.e., scheme to strengthen girder-column 
connections). Damage and losses due to the scenario earthquake are calculated using the 
pushover results and other data specific to the LACDPW Headquarters building.

Section 8.2 describes pertinent building data, including engineering (pushover) analysis 
results of the Black & Veatch study and site-specific hazard data of the Geomatrix study. 
Subsequent sections show how these data are used to develop input to the AEBM of the 
HAZUS-MH Software, including entry (or editing) of building-specific data in AEBM 
databases. Similar to the HAZUS-MH User's Manual, screen shots of AEBM windows 
and pull-down menus are included in the example to illustrate manipulation of the AEBM 
software. The HAZUS-MH User's Manual should be referred to for manipulation of other 
HAZUS software modules (e.g., defining scenario earthquake hazard). 

8.2. Example Building Data

8.2.1. LACDPW Headquarters Building
The LACDPW Headquarters building has twelve above-grade levels, a mezzanine 
between the ground and second floor, a mechanical penthouse, and a basement level. The 
facility was originally constructed in 1971 for Sears Company in accordance with the 
1967 Uniform Building Code [ICBO, 1967). 

The plan of the building for the above grade level is square in shape (167 ft. x 167 ft.). 
The floor to floor height is 14 ft.- 0 in., except that the 2nd floor is 27 ft.-5 in. above the 
ground floor. A photo of the DPW Building is included as Figure 8.1.

Figure 8.1. Photo of the DPW Building

8.2.2. Original Building (OB) Structure
The structural system of LACDPW Headquarters building features a perimeter welded 
steel moment frame (WSMF) with a bay width of 15 ft. and a story height of 14 ft. Figure 
8.2 shows a typical floor framing plan and Figure 8.3 shows an elevation view of 
perimeter framing. A typical perimeter girder-column connection is shown in Figure 8.4. 
Welded moment connections also exist at sixteen interior gravity connections to increase 
the stiffness in east-west direction. The period of the OB is approximately 2.2 seconds. 
According to the as-built drawings, the building was designed for a lateral seismic force 
equal to 3.24% of the dead weight of the structure.

An inspection of the moment connections and a seismic evaluation of the building were 
conducted after the 1994 Northridge earthquake. The inspection did not reveal any 
damage due to the earthquake (i.e., ground shaking at the building site in Alhambra was 
relatively low). However, the inspection identified widespread poor-quality welds. As a 
result, the County (with funding provided in part by FEMA) has decided to seismically 
upgrade the building.

Figure 8.2. Typical Floor Framing of the DPW Building [Che n et al., 2001]

Figure 8.3. Elevation View at Perimeter of the DPW Building [Chen et al., 2001] 

Figure 8.4. Typical Girder-Column Connection - Original Building [Chen et al., 2000] 

8.2.3. Connection-Only (CO) Retrofit Scheme 
The Connection-Only (CO) retrofit scheme consists of strengthening all the existing 
moment frame connections so that the plastic capacity of the girders can be developed, as 
envisioned in the original design. Many methods of connection repair were considered. 
The most costeffective method was one that would not require removal of the concrete 
floor slab and modification to the top flange of the girder, or strengthening of the column 
to meet strong column-weak beam provisions.

The chosen repair was a haunch scheme, in which a diagonal plate is added to the bottom 
of the girder at the connection. Figure 8.5 shows a typical girder-column connection of 
the CO retrofit scheme, strengthened with haunches. This scheme proved to be the most 
cost effective, and was successfully tested at UCSD. The addition of haunches increases 
both the stiffness and strength of the structural system. The period of the CO retrofit 
scheme is approximately 1.8 seconds.

In addition to the connection repair, other strengthening measures are required to enable 
the frame to develop the plastic capacity of the girders. These include repairing all partial 
penetration welded column splices, adding side plates to the end column to increase its 
axial load carrying capacity, and strengthening the concrete base to carry the loads from 
the steel frame to the ground.

Figure 8.5. Typical Girder-Column Strengthening Detail [Chen et al., 2001]

8.2.4. Engineering Pushover Analyses 
Seismic performance of the original building (OB) and the connection-only (CO) retrofit 
scheme were evaluated using the nonlinear static (pushover) analysis method of FEMA 
273 [FEMA, 1997]. Due to the symmetry and regularity of the building's lateral force 
resisting system, the behavior of the steel frame and connections was analyzed using a 
two dimensional model of the west exterior frame.

The program used for analysis was SAP 2000 Nonlinear [CSI, 2000]. All steel girders 
and columns in the frame were modeled with the base of the columns considered as fixed 
at the top of the concrete wall below the second floor girder. Dead and live loads were 
applied to all members, and the effects of P-Delta were included by a dummy column 
with lumped masses at floor levels slaved to each floor. The pushover analysis was 
performed per the requirements of FEMA 273 using a code shaped distribution of lateral 
forces.

The girder-column connection was modeled to include the effects of shear deformation 
and shear yielding in the panel zone per the recommendations of FEMA 273. Test 
analyses were performed on the connection model to compare its behavior with the data 
from the full scale testing, and good conformance was observed.

8.2.5. Original Building (OB) Performance
Three different models of OB connections were created for the girder to column 
connection. The first two models were analyzed to establish upper-bound and lower-
bound pushover response of the structure. The final model was compared to the bounding 
curves as a check of the results. In the upper-bound model, all connections were assumed 
to be fully ductile, with all connections behaving as elastic and plastic with no 
degradation in strength. For the lower-bound model, the bottom flanges of the girders in 
tension were assumed to crack at a stress of 33 ksi, and bottom flanges in compression 
and all top flanges were assumed to not crack. Once cracked, the girder end was modeled 
as a T-shaped section with the ability to perform in an inelastic manner. In the third 
analysis, the connections were modeled to match the strength and stiffness in both the 
elastic and inelastic regions as recorded in the UCSD testing. The pushover curves for the 
upper-bound and lower-bound models, as well as the model that using the backbone 
curve that match UCSD testing, are shown in Figure 8.6.

Figure 8.6. Pushover Curves and Connection Damage - Original Building
Diagram displays Roof Replacement (feet: 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 
5.0) versus Normalized Base Shear (V/W: 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 
0.40, 0.45, 0.50) versus Bottom Flange Fracture (%: 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 
100) with Upper-Bound Pushover Response, Lower-Bound Pushover Response, 
Pushover based on UCSD Tests, and Bottom Floange Fracture Percentage points

Using the data from the UCSD testing, the average plastic rotation at fracture for bottom 
flanges was computed as 0.0033 radians. Cracking of the girder bottom flange, defined as 
exceeding 0.0033 radians of plastic rotation, was first observed at a roof displacement of 
approximately 10 inches, with additional cracks occurring with additional displacement. 
The pushover curve indicates that the maximum strength of the building is developed at a 
roof displacement of 15.6 inches, with significant fractures developing at displacements 
of 12 to 22 inches. Based on a mean plastic rotation capacity of 0.0033 radians, the 
number of fractured (bottom flange) connections was calculated as a function of pushover 
displacement. The percentage of connections with bottom flange fractures is shown in 
Figure 8.6.

8.2.6. Connection-Only (CO) Retrofit Scheme Performance
Pushover analysis of the Connection-Only (CO) retrofit scheme was performed using the 
same SAP 2000 Nonlinear (frame) model as the OB with stiffer and stronger connections 
(see Figure 8.5). Strengthened connections were modeled to match UCSD test results, 
using a "backbone" curve similar to Figure 2-6 of FEMA 273. Strengthened connections 
do not fracture prematurely and inelastic behavior is due to primarily to yielding of 
girders (and columns). The pushover curve for the CO retrofit scheme is shown in Figure 
8.7.

Figure 8.7. Pushover Curve - Connection-Only Retrofit Scheme
Diagram displays Roof Replacement (ft: 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0) 
versus Normalized Base Shear (V/W: 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 
0.45, 0.50)

The pushover curve for the CO retrofit scheme indicates fully elastic behavior up to about 
a foot of roof displacement, after which girders (and columns) begin to yield. At about 
2.5 feet of roof displacement, yielded girders begin loose strength (consistent with the 
shape of the "backbone" curve). Strength loss becomes significant at about 3.5 feet and 
full loss of strength occurs at about 5 feet of roof displacement. 

8.2.7. Ground Shaking Hazard 
Earthquake ground-shaking hazard at the LACDPW Headquarters building is dominated 
by faults in close proximity to the site. Most notably, these faults are: (1) the Raymond 
fault zone, which has a scarp mapped at the surface approximately 33/4 km (2.4 mile) 
north of the site and dips steeply to the north (away from the site); (2) the Verdugo-Eagle 
Rock fault zone, which is mapped as having a concealed surface trace approximately 4 
km (21/2 mile) north- northeast of the site and dips to the northeast (also away from the 
site); (3) the Sierra Madre fault zone, which is mapped as close as approximately 12 km 
(71/2 mile) north- northeast of the site and dips to the north-northeast (away from the site, 
as well); and (4) the Hollywood-Santa Monica-Malibu Coast fault zone, situated about 12 
km (71/2 mile) to the west. As shown by the hazard curves in Figure 8.8, the Sierra 
Madre fault is the dominant contributor to short-period (PGA) and 1-second spectral 
response at the LACDPW Headquarters site.

Figure 8.8. DPW Building Site Hazard Curves [Geomatrix, 1999] 

Geomatrix developed site-specific spectra of Basic Safety Earthquake 1 (BSE-1) and 
Basic Safety Earthquake 2 (BSE-2) ground shaking, as defined by FEMA 273. The BSE-
1 is the level 
of ground shaking that has a 10% probability of being exceeded in a 50-year period. The 
BSE-2 is the level of ground shaking that has a 2% probability of being exceeded in a 50- 
year period, but need not exceed 1.5 times the median deterministic level of ground 
shaking for maximum magnitude events on active faults near the site. Due to its very 
close proximity, Verdugo fault has potential to produce the strongest ground shaking at 
the site with a maximum magnitude M6.9 event (even though the Sierra Madre fault can 
produce a maximum magnitude M7.2 event). Site-specific response spectra of the BSE-1, 
the BSE-2 (probabilistic definition) and maximum magnitude events on the Verdugo and 
Sierra Madre faults are shown in Figure 8.9.

Figure 8.9. Site-Specific Response Spectra - DPW Building
Diagram displays Period (seconds: 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4) versus Spectral 
Acceleration (g), with Sierra Madre Fault - M7.2, Verdugo - M6.9, BSE-1 (10% in 50 
Years), BSE-2 (2% in 50 Years)

8.3. HAZUS Software - Getting Started
Before the AEBM can be used to evaluate building-specific dama ge and loss, the 
HAZUS software must be installed and users should have some experience with the 
software. Chapter 2 of HAZUS-MH User's Manual should be referred to for help with 
installing and starting HAZUS. Chapters 3 and 9 of the HAZUS-MH User's Manual 
should be referred to for running HAZUS (with either default data or user-supplied data).

The AEBM is implemented through a variety of HAZUS software menus and dialog 
boxes that begin with defining a study region, include defining ground shaking hazard 
and AEBM 
inventory, running AEBM analyses and finally viewing or printing of AEBM results. 
Figure 8.10 illustrates the flow of HAZUS software elements related to the AEBM.

Figure 8.10. HAZUS Software  - Flowchart of AEBM Calculation of Damage and Loss
Run HAZUS
* Open/Create Study Region

then,

Inventory Menu
* Define AEBM Inventory
* Define AEBM Profiles

and/or

Hazard Menu
* Open/Define Scenario Earthquake

then

Analysis Menu
* Run AEBM

then

Results Menu
* View Results
*Print Results

8.3.1 Defining a Study Region 
As the first step, the user must define a study region that includes the location (i.e., 
latitude/longitude) of all buildings to be evaluated. The study region may be as small as a 
single census tract or as large as that used for regional loss studies. A large region 
provides a better picture of the spatial distribution of ground shaking (and damage and 
loss), but requires a greater time for HAZUS software to aggregate inventory data that are 
not required for AEBM calculations. Users are cautioned that very large study regions 
can take hours to aggregate and run. HAZUS requires users to define a new (or open an 
existing) study region when the program is initially turned on. Section 3.1 of the 
HAZUS-MH User's Manual describes the specific steps and options for creating a study 
region.

Los Angeles County was selected for the AEBM example to provide basis for comparing 
individual building losses with those for the region. Default data were used for 
aggregation of 
inventory in the study region covers over 4,000 square miles and includes a total 
population of 8,863,164 inhabitants (based on 1990 census data). There are about 1.96 
million buildings in the region estimated to have a replacement value of about $465 
billion, exclud ing contents (based on 1994 dollar value). Figure 8.11 shows a screen shot 
of Los Angeles County census tracts. 

Figure 8.11. Map of Los Angeles County and Scenario Earthquake Ground Shaking
(screen capture)

8.3.2.  Defining Scenario Earthquake Ground Shaking 
Users must define a scenario earthquake for calculation of ground shaking. The scenario 
earthquake may be a deterministic event, a probabilistic analysis of seismic hazard or by 
a usersupplied map of ground motion. The deterministic option will likely be the most 
useful and convenient method of defining AEBM ground shaking. Deterministic events 
may be defined based on maps of historical epicenter data, maps of seismic sources or 
arbitrarily defined by the user. Section 9.2 of the HAZUS-MH User's Manual describes 
these options for creating scenario earthquake ground shaking.

A magnitude M7.2 event on the Sierra Madre fault is defined as the scenario earthquake 
for the AEBM example. The Sierra Madre fault represents the most likely source of a 
major earthquake to affect the building site and an magnitude M7.2 event is the 
"maximum" magnitude for this fault system, as determined by a site-specific hazard 
study [Geomatrix, 1999]. Clearly, geotechnical expertise is crucial in determining which 
faults most affect ground shaking hazard at the site and what magnitude of event is 
possible for each fault system.

Additionally, geotechnical expertise is also essential in determining local site conditions 
(i.e., soil type). Based on mapped geology, available soil boring information and shear 
wave velocity measurements, the Geomatrix study characterized the LACDPW 
Headquarters building site as Site Class C (very stiff soil). Rather than importing a soil 
data into HAZUS, the default soil type, Site Class D, was used for this example. The ratio 
of Site Class D amplification to Site Class C amplification is only about 1.2 (i.e., 1.8/1.5 
for 1-second spectral acceleration of 0.3g on rock). In this case, the use of the default soil 
type is a reasonable approximation and slightly conservative with respect to actual site 
conditions.

The HAZUS software was used to generate scenario earthquake ground shaking for the 
Los Angeles study region, as shown in Figure 8.11 for 1-second spectral acceleration. 
Maps of 
scenario earthquake ground shaking are useful for AEBM calculation since it provides 
users with hazard data that can be compared with the results of site-specific studies. The 
location of the LACDPW Headquarters building is shown in Figure 8.11 (by a star) and 
1-second spectral acceleration at this site is about 0.43 g. This value of spectral 
acceleration is about 15% less than the 0.5 g value of 1-second spectral acceleration 
calculated by the site-specific hazard study for a magnitude M7.2 event of the Sierra 
Madre fault, as shown in Figure 8.9. The difference in ground shaking calculated by 
HAZUS and the site-specific study is due to different methods used for (1) soil 
type/amplification, (2) attenuation and (3) fault geometry/distance to site.

8.3.3. Defining AEBM Inventory Data 
Users must input (or modify) a large number of "inventory" data that describe properties 
of individual buildings. These data are input through the AEBM Inventory and AEBM 
Profiles options under the Inventory pull-down menu. Clicking on the AEBM Inventory 
option returns a blank table with 22 data fields to be filled by the user. A right click on 
the mouse will display an editing menu with various options including Add record for 
manual entry of data or an import database.. for automated entry of data. Figure 8.12 
shows a portion of the Inventory table (and editing menu box) after addition of two 
records of the AEBM example.

Figure 8.12. AEBM Example Inventory Table
(screen capture)

Table 8.1 lists the 22 parameters (fields) of the Inventory table and summarizes data used 
for the AEBM example. In this example, there are two buildings (hence two inventory 
records) representing the Original Building and the CO Retrofit Scheme. Inventory data 
are the same for these two buildings, since the size, value, etc., of the building would not 
be changed as a result of the CO Retrofit Scheme. Arguably, the LACDPW Headquarters 
building would be of greater value after seismic retrofit, but this increase in value is not 
included in the AEBM example.

The source of many of the inventory data used in the AEBM example are either obvious 
(e.g., name and address) or are arbitrary (e.g., ID No. and Profile Name). Users must 
provide Latitude and Longitude data (since HAZUS software does not automatically use 
address information to geo-code building location). Latitude and Longitude data may be 
estimated from detailed maps, GPS measurements taken at the building site or from geo-
coding software contained in MapInfo or available at map-related web sites on the 
Internet. The latter was used to obtain the Latitude and Longitude data for the AEBM 
example. As shown in Figure 8.12, there is a Map button at the bottom of the Inventory 
table that may be used to show the of AEBM buildings within the study region. Mapping 
is a useful tool for overlaying the location of AEBM buildings with hazard contours (as 
shown in Figure 8.11) and also provides a "sanity check" of building location.

Building occupants, size, replacement value and operational cost data are based on or 
derived from information compiled by Black & Veatch during their seismic mitigation 
study (or in certain cases are based on generic building rates of the HAZUS-MH 
Technical Manual). These data are approximate, and in many cases just "best estimates" 
of actual building parameters (e.g., value of building contents). Data are rounded to one 
or two significant decimal places to indicate this lack of precision.

Table 8.1. Example AEBM Inventory Data
Parameter Field Name:  
Record No. 1:  
Record No. 2:  

Parameter Field Name:  ID No.
Record No. 1:  OB
Record No. 2:  CO

Parameter Field Name:  Name
Record No. 1:  LACDPW Headquarters Building
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Profile Name
Record No. 1:  Original Building
Record No. 2:  CO Retrofit Scheme

Parameter Field Name:  Address
Record No. 1:  900 South Fremont
Record No. 2:  Same as Record No. 1

Parameter Field Name:  City
Record No. 1:  Alhambra
Record No. 2:  Same as Record No. 1

Parameter Field Name:  State
Record No. 1:  CA
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Zip Code
Record No. 1:  91803-1331
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Latitude
Record No. 1:  34.085
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Longitude
Record No. 1:  -118.15197
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Daytime Occupants
Record No. 1:  1,600
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Nighttime Occupants
Record No. 1:  80
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Building Area (sq. ft.)
Record No. 1:  400,000
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Building Value ($)
Record No. 1:  60,000,000
Record No. 2:  Same as Record No. 1
 
Parameter Field Name:  Contents Value ($)
Record No. 1:  15,000,000
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Business Inventory ($)
Record No. 1:  0
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Business Income ($/day)
Record No. 1:  32,000
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Wages Paid ($/day)
Record No. 1:  130,000
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Relocation Disruption Costs ($)
Record No. 1:  280,000
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Rental Costs ($/day)
Record No. 1:  13,000
Record No. 2:  Same as Record No. 1

Parameter Field Name:  Ratio of Building Owner Occupied
Record No. 1:  100
Record No. 2:  Same as Record No. 1

Parameter Field Name:  County FIPS
Record No. 1:  06037
Record No. 2:  Same as Record No. 1

The number of daytime occupants (1,600) assumes a fully occupied and functional 
building of about 1,500 employees and 100 visitors. Nighttime occupants are assumed to 
be 5% of the daytime building population, since the building is not in use after hours. 

The building is approximately 400,000 square feet and studies of the replacement costs of 
structural and nonstructural systems indicate a building value of about $60 million or 
about $150 per square foot. Contents value is estimated as $15 million or about $10,000 
per employee. Contents includes such items as furniture, computers and 
telecommunication equipment.

There is no Business Inventory associated with the LACDPW Headquarters building. 
Business Income and Wages Paid are based on the economic rates given in Table 15.15 
of the HAZUS-MH Technical Manual for a GOV1 occupancy. In the case of Wages Paid, 
the $2.18 value of wages per square foot per day given in Table 15.15 assumes 0.025 
employees per square foot.

The $2.18 value is factored by (1,500/400,000)/0.025 to more realistically reflect the 
number of employees per square foot in the LACDPW Headquarters building. Relocation 
Disruption and Rental Costs are based on the economic rates given in Table 15.13 of the 
HAZUS-MH Technical Manual for a GOV1 occupancy. 

8.3.4. Defining Default AEBM Profile Data
The HAZUS software uses the Profile Name to link each building listed in the AEBM 
Inventory table to data that define an AEBM profile of capacity, damage and loss 
parameters. 
There must be at least one AEBM profile, but the same profile can be used for more than 
one building listed in the AEBM Inventory table. In the AEBM example, the Original 
Building and the CO Retrofit Scheme have different profiles since they have different 
capacity, damage and loss parameters.

AEBM profile data is voluminous, grouped into eight sets of AEBM Profiles databases: 
1. Building Characteristics 
2. Structural Fragility Curves 
3. Nonstructural Drift Fragility Curves 
4. Nonstructural Acceleration Fragility Curves 
5. Casualty Ratios (per occupant) 
6. Building Related Repair Cost Ratios 
7. Contents & Building Inventory Replacement Cost Ratios 
8. Loss of Function Parameters (# of days).

As a starting point, AEBM Profiles databases are populated with "default" capacity, 
damage and loss parameters of a GBS (General Building Stock) building. The process 
begins with the user's selection of the occupancy class, building type, design level and 
quality of construction that best represents the individual building of interest. Clicking on 
the AEBM Profiles option (of the Inventory pull-down menu) returns the dialog box 
shown in Figure 8.13.

Figure 8.13. Building Profile Name Dialog Box 
(screen capture)

After the user enters the Profile Name and selects appropriate occupancy class, building 
type, seismic design level and building quality parameters, the HAZUS software 
populates the eight AEBM Profiles databases with "default" data and displays the 
Building Characteristics table. A right click on the mouse will display an editing menu 
box with for adding new building profiles or editing existing profiles. Figure 8.14 shows 
a portion of the Building Characteristics table (and editing menu box) after addition of 
two records of the AEBM example.

Figure 8.14. AEBM Example Building Characteristics Table 
(screen capture)

The Profile Name, Occupancy, Building Type Design Level and Building Quality (with 
parameters shown by blue font) cannot be edited by the user. All other "default" profile 
data of 
the Building Characteristics table and the other seven tables of AEBM Profiles data can 
be edited to better reflect actual capacity, damage and loss parameters of the buildings. 
Section 8.4 describes editing of these tables to include data representing the Original 
Building and CO Retrofit Scheme.

8.3.5. Running the AEBM 
The AEBM may be run after the user has defined a scenario earthquake and building 
inventory and profile data. Clicking on the Run option of the Analysis pull-down menu 
returns the dialog box shown in Figure 8.15. The "Advanced Engineering Bldg Model" 
box should be checked before clicking on the OK button. The AEBM may be run without 
running other modules of the HAZUS software. Scenario earthquake ground shaking will 
be calculated for AEBM building sites even if the PESH module is not checked. 

8.3.6. Viewing and Printing AEBM Results 
Results of AEBM analyses may be viewed by clicking on the Advanced Engineering 
Bldg Model (AEBM) option of the Results pull-down menu. A results table includes 
response 
(intersection point) data, damage state probabilities and casualty and direct economic 
losses for each building in the AEBM Inventory. The same data may also be viewed (and 
printed) in HAZUS summary reports. Clicking on the Other tab of the Summary Reports 
option of the Results pull-down menu returns the dialog box shown in Figure 8.16. 

Figure 8.15. Analysis Options Dialog Box with AEBM Selected 
(screen capture)

Figure 8.16. HAZUS Summary Reports Dialog Box  
(screen capture)

Summary report options include an "AEBM - Individual Building Report" that 
summarizes results separately for each building in the AEBM Inventory and an "AEBM-
Portfolio Building Report" which averages damage and aggregates losses for all buildings 
in the AEBM Inventory. Figures 8.17 and 8.18 show individual summary reports for the 
Original Building and the CO Retrofit Scheme (based on default AEBM profile data), 
respectively. These reports may be printed (by clicking on the Printer icon shown at the 
top of the window) or exported in Word, Adobe or Excel format (by clicking on the 
Envelop icon at the top of the window).

Figure 8.17. Summary Report - Original Building Results (Default AEBM Profile Data) 
(screen capture of report)

Figure 8.18. Summary Report - CO Retrofit Scheme Results (Default AEBM Profile 
Data)
(screen capture of report)

8.4. Modifying Default AEBM Profile Data 
The results shown in Figures 8.17 and 8.18 for the Original Building and the CO Retrofit 
Scheme, respectively, are based on default AEBM Profile data corresponding to the 
occupancy class, building type, seismic design level and building quality that best 
represent the LACDPW Headquarters building before and after seismic retrofit.

Building occupancy is GOV1, since the building provides office space for Los Angeles 
County Department of Public Works. The building type is S1H, since the structural 
system is a steel moment-resisting frame and the building is over 7 stories in height (see 
Table 2.1). The seismic design level of Original Building is Moderate Code since it was 
designed and constructed between 1941 and 1975 (see Table 2.2) and is assigned a 
building quality of Inferior due to the weakness of the welded connections. After 
strengthening of the connections, the CO Retrofit Scheme is assumed to have strength 
comparable to a building of High Code seismic design level and Ordinary quality. 

Default AEBM Profile data are a good starting point, and can produce reasonable 
estimates of damage and loss (when based on the appropriate assumptions of occupancy, 
building type design level and quality). However, results of engineering (pushover) 
analyses and other building-specific data can be used to modify default data and produce 
more reliable estimates of damage and loss. This section illustrates modification of 
default data in AEBM Profiles databases for the Original Building and the CO Retrofit 
Scheme, respectively. The process begins with the user selecting the profile set (database) 
of interest by first clicking on the AEBM Profiles option of the Inventory pull-down 
menu and by then clicking on the one of the eight database sets shown in Figure 8.19.

Figure 8.19. Selection of AEBM Profiles Database Set 
(screen capture)

Each profile database set is shown by a table in the HAZUS software that has a similar 
format. Each table has the same number of records (e.g., two records in the AEBM 
example) and the first field of each table is always the Profile Name. Other fields contain 
various response, capacity, damage or loss parameters that are edited by directly by 
deleting existing (defa ult) values and typing in new data.

The following sections describe each of the eight AEBM Profiles databases, listing both 
default and modified data and discussing the basis for modified data (e.g., results of 
pushover analyses). 

8.4.1. Building Characteristics
Building characteristics are listed in Table 8.2 with values of default and modified data 
for the Original Building and the CO Retrofit Scheme, respectively. 

Table 8.2. Example AEBM Profiles Data - Building Characteristics
Parameter Field Name:
Record No. 1 (Default and Modified):
Record No. 2 (Default and Modified):

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Occupancy
Record No. 1 (Default and Modified):  GOV1
Record No. 2 (Default and Modified):  GOV1

Parameter Field Name:  Building Type
Record No. 1 (Default and Modified):  S1H
Record No. 2 (Default and Modified):  S1H

Parameter Field Name:  Design Level
Record No. 1 (Default and Modified):  M
Record No. 2 (Default and Modified):  H

Parameter Field Name:  Building Quality
Record No. 1 (Default and Modified):  I
Record No. 2 (Default and Modified):  S

Parameter Field Name:  Spectral Disp. @ Yield
Record No. 1 (Default):  1.164
Record No. 1 (Modified):  6.820
Record No. 2 (Default):  4.657
Record No. 2 (Modified):  6.850

Parameter Field Name:  Spectral Acc.. @ Yield
Record No. 1 (Default):  0.024
Record No. 1 (Modified):  0.142
Record No. 2 (Default):  0.098
Record No. 2 (Modified):  0.207

Parameter Field Name:  Spectral Disp. @ Ultimate
Record No. 1 (Default):  8.732
Record No. 1 (Modified):  17.150
Record No. 2 (Default):  55.884
Record No. 2 (Modified):  22.690

Parameter Field Name:  Spectral Acc. @ Ultimate
Record No. 1 (Default):  0.073
Record No. 1 (Modified):  0.195
Record No. 2 (Default):  0.293
Record No. 2 (Modified):  0.331

Parameter Field Name:  Duration Factor: Small EQ
Record No. 1 (Default):  0.60
Record No. 1 (Modified):  0.50
Record No. 2 (Default):  0.90
Record No. 2 (Modified):  0.90

Parameter Field Name:  Duration Factor: Moderate EQ
Record No. 1 (Default):  0.30
Record No. 1 (Modified):  0.30
Record No. 2 (Default):  0.60
Record No. 2 (Modified):  0.70

Parameter Field Name:  Duration Factor: Large EQ
Record No. 1 (Default):  0.10
Record No. 1 (Modified):  0.10
Record No. 2 (Default):  0.40
Record No. 2 (Modified):  0.50

Parameter Field Name:  Elastic Damping (%)
Record No. 1 (Default):  5
Record No. 1 (Modified):  5
Record No. 2 (Default):  5
Record No. 2 (Modified):  5

Parameter Field Name:  Ratio of Contents: Ground Level
Record No. 1 (Default):  0.2
Record No. 1 (Modified):  0.20
Record No. 2 (Default):  0.20
Record No. 2 (Modified):  0.20

Modified capacity curve parameters (i.e., spectral displacement acceleration 
corresponding to the yield and ultimate points) are based on the pushover curves of the 
Original Building and the CO Retrofit Scheme, shown in Figures 8.6 and 8.7, 
respectively. In the case of the Original Building, capacity curve properties are based on 
pushover strength consistent with UCSD test data. The pushover curves (plots of base 
shear versus roof displacement) were generated by SAP 2000 Nonlinear analyses of the 
structural systems. Capacity curves (plots of spectral acceleration versus spectral 
displacement) corresponding to these pushover curves were also generated by the SAP 
2000 analyses, using the conversion methods described in Section 5.2.1. Yield and 
ultimate "control" points are based on HAZUS compatible versions of these capacity 
curves in accordance with Section 5.2.2. HAZUS compatible capacity curves and their 
control points of the Original Building and the CO Retrofit Scheme are shown in Figure 
8.20 with the respective capacity curves based on pushover results.

Figure 8.20. Original Building and CO Retrofit Scheme Capacity Curves
Diagram displays Spectral Displacement (inches: 0, 6, 12, 18, 24, 30, 36, 42, 48) versus 
Spectral Acceleration (g: 0.0, 0.1, 0.2, 0.3, 0.4, 0.5) with HAZUS Compatible - Original 
Building, Pushover Results - Original Building, HAZUS Compatible - CO Retrofit 
Scheme, and Pushover Results - CO Retrofit Scheme points).

Default values of the duration factors are modified (slightly) to be consistent with the 
recommendations of Table 5.2. Default values of the elastic damping term and contents 
ratio are considered appropriate and are not modified. Note, in Table 8.2 and subsequent 
tables summarizing AEBM Profiles data, italics denote that default data are used without 
modification.

8.4.2. Structural Fragility Curves 
Structural fragility curve parameters (medians and betas) are listed in Table 8.3 with 
values of default and modified data for the Original Building and the CO Retrofit 
Scheme, respectively.

Modified values of structural damage-state medians are based on combination of 
recommendations of Appendix B of FEMA 351 [FEMA, 2000] and the pattern of damage 
predicted by the results of the pusho ver analyses. For the Original Building, damage 
states are based primarily on the extent of damage to welded connections as predicted by 
the pushover 
over analysis. Figure 8.6 includes a plot showing the number of damaged connections as 
a function of roof displacement. Based on the recommendations of Table B-4 of FEMA 
351, 
Slight damage corresponds to 2% of welded connections with damage and Figure 8.6 
indicates that this fraction of damaged weld occurs at about 10 inches of roof 
displacement. Using the same approach, Moderate damage occurs at about 13 inches, 
Extensive damage at about 18 inches and Complete damage at about 30 inches. Factoring 
these roof displacements by a2 = 0.74, as per Equation (6-1), the corresponding spectral 
displacements are Slight damage = 7.4 inches, Moderate damage = 9.6 inches, Extensive 
damage = 13.3 inches and Complete damage = 22.2 inches.

Table 8.3. Example AEBM Profiles Data - Structural Fragility Curves
Parameter Field Name:
Record No. 1 (Default and Modified):
Record No. 2 (Default and Modified):

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Slight/Median
Record No. 1 (Default):  2.70
Record No. 1 (Modified):  7.60
Record No. 2 (Default):  3.37
Record No. 2 (Modified):  11.10

Parameter Field Name:  Slight/Beta
Record No. 1 (Default):  0.66
Record No. 1 (Modified):  0.75
Record No. 2 (Default):  0.64
Record No. 2 (Modified):  0.65

Parameter Field Name:  Moderate/Median
Record No. 1 (Default):  4.66
Record No. 1 (Modified):  9.70
Record No. 2 (Default):  6.74
Record No. 2 (Modified):  15.10

Parameter Field Name:  Moderate/Beta
Record No. 1 (Default):  0.70
Record No. 1 (Modified):  0.80
Record No. 2 (Default):  0.64
Record No. 2 (Modified):  0.65

Parameter Field Name:  Extensive/Median
Record No. 1 (Default):  10.56
Record No. 1 (Modified):  15.40
Record No. 2 (Default):  16.85
Record No. 2 (Modified):  30.00

Parameter Field Name:  Extensive/Beta
Record No. 1 (Default):  0.75
Record No. 1 (Modified):  0.85
Record No. 2 (Default):  0.65
Record No. 2 (Modified):  0.65

Parameter Field Name:  Complete/Median
Record No. 1 (Default):  26.96
Record No. 1 (Modified):  24.20
Record No. 2 (Default):  44.93
Record No. 2 (Modified):  42.50

Parameter Field Name:  Complete/Beta
Record No. 1 (Default):  0.94
Record No. 1 (Modified):  0.95
Record No. 2 (Default):  0.67
Record No. 2 (Modified):  0.70

The CO Retrofit Scheme does not fail connections. Rather, the pus hover curve indicates 
first yielding of elements and subsequent failure, leading to a loss of global strength. 
Referring to the CO Retrofit Scheme capacity curve in Figure 8.20, it may be seen that 
yielding does not occur until after about 10 inches of spectral displacement and that 
significant yielding but no loss of strength corresponds to about 15 inches of spectral 
displacement. At about 30 inches, some elements begin to fail and at about 42 inches 
more than one- half of the elements have failed. These spectral displacements represent 
reasonable values of Sight, Moderate, Extensive and Complete damage-state medians 
(that define the thresholds of damage states).

The modified damage-state medians of Table 8.3, although similar in value to those of 
the above discussion, are based on Equation (B-13) of FEMA 351 and assumptions of 
damage state interstory drift ratios of Table 8.4. Equation (B-13) is similar to Equation 
(6-1) with the addition of two additional terms, a3 and a4,ds, which adjust damage-state 
for higher-mode effects and non-uniform mode shape, respectively:

Equation B-13, FEMA 351:
Sd,ds = product of a2DdsHR | a3a4,ds

The a3 and a4,ds, factors are described in FEMA 351, including formulas for these 
factors that that are based on height (number of stories) of the building. Tables 8.4 and 
8.5 summarize pertinent factors and illustrate calculation of structural damage-state 
medians for the Original Building and CO Retrofit Scheme, respectively. 

Table 8.4. Calculation of Structural Damage State Medians - Original Building
Parameter:  
Structural Damage State (Slight, Moderate, Extensive, Complete):  

Parameter:  Drift ratio - Dds
Structural Damage State (Slight):  0.01
Structural Damage State (Moderate):  0.0125  
Structural Damage State (Extensive):  0.0175
Structural Damage State (Complete):  0.025

Parameter:  Building height (inches)
Structural Damage State (Slight, Moderate, Extensive, Complete):  1,848

Parameter:  Pushover modal factor, a2 - Equation 5-2
Structural Damage State (Slight, Moderate, Extensive, Complete):  0.73

Parameter:  Spectral Displacement (inches) - Equation 6-1
Structural Damage State (Slight):  13.6
Structural Damage State (Moderate):  17.0  
Structural Damage State (Extensive):  23.8
Structural Damage State (Complete):  34.0

Parameter:  Higher-mode factor, a3 - Equation B-14, FEMA 351
Structural Damage State (Slight, Moderate, Extensive, Complete):  1.4

Parameter:  Mode-shape factor, a4,ds - Equation B-15, FEMA 351
Structural Damage State (Slight):  1.27
Structural Damage State (Moderate):  1.25  
Structural Damage State (Extensive):  1.1
Structural Damage State (Complete):  1.0

Parameter:  Median spectral displacement of damage state, ds, Sd,ds - Equation B13, 
FEMA 351 (inches)
Structural Damage State (Slight):  7.6
Structural Damage State (Moderate):  9.7  
Structural Damage State (Extensive):  15.4
Structural Damage State (Complete):  24.2

Parameter:  Median spectral displacement of damage state based on results of pushover 
analyses
Structural Damage State (Slight):  7.4
Structural Damage State (Moderate):  9.6  
Structural Damage State (Extensive):  13.3
Structural Damage State (Complete):  22.2

Table 8.5. Calculation of Structural Damage State Medians - CO Retrofit Scheme 
Parameter:  
Structural Damage State (Slight, Moderate, Extensive, Complete):  

Parameter:  Drift ratio - Dds
Structural Damage State (Slight):  0.015
Structural Damage State (Moderate):  0.020  
Structural Damage State (Extensive):  0.035
Structural Damage State (Complete):  0.045

Parameter:  Building height (inches)
Structural Damage State (Slight, Moderate, Extensive, Complete):  1,848

Parameter:  Pushover modal factor, a2 - Equation 5-2
Structural Damage State (Slight, Moderate, Extensive, Complete):  0.74

Parameter:  Spectral Displacement (inches) - Equation 6-1
Structural Damage State (Slight):  19.8
Structural Damage State (Moderate):  26.4  
Structural Damage State (Extensive):  46.2
Structural Damage State (Complete):  59.2

Parameter:  Higher-mode factor, a3 - Equation B-14, FEMA 351
Structural Damage State (Slight, Moderate, Extensive, Complete):  1.4

Parameter:  Mode-shape factor, a4,ds - Equation B-15, FEMA 351
Structural Damage State (Slight):  1.27
Structural Damage State (Moderate):  1.25  
Structural Damage State (Extensive):  1.1
Structural Damage State (Complete):  1.0

Parameter:  Median spectral displacement of damage state, ds, Sd,ds - Equation B13, 
FEMA 351 (inches)
Structural Damage State (Slight):  11.1
Structural Damage State (Moderate):  15.1  
Structural Damage State (Extensive):  30.0
Structural Damage State (Complete):  42.5

Parameter:  Median spectral displacement of damage state based on results of pushover 
analyses
Structural Damage State (Slight):  10
Structural Damage State (Moderate):  15  
Structural Damage State (Extensive):  30
Structural Damage State (Complete):  42

Figure 8.21 illustrates the location of structural damage-state median points on the 
capacity curves of the Original Building and the CO Retrofit Scheme, respectively.

Figure 8.21. Structural Fragility - Damage-State Medians
Diagram displays Spectral Displacement (inches: 0, 6, 12, 18, 24, 30, 36, 42, 48) versus 
Spectral Acceleration (g: 0.0, 0.1, 0.2, 0.3, 0.4, 0.5), with capacity curves of the Original 
Building and the CO Retrofit Scheme.

Modified values of the structural damage-state betas medians are based on Table 6.7. The 
Original Building is assumed to have "moderate" to "large" capacity and damage 
variability due to uncertainty in the performance of connections. Interpolating between 
values, Table 6.7 suggests a beta of 0.75 for minor degradation (k  0.9), 0.85 for major 
degradation (k = 0.5) and to about 1.0 for extreme degradation (k less than or equal to 
0.1).

Extreme degradation is not expected since k = 0.30 for the duration of shaking associated 
with the scenario earthquake. Shaking duration applies to post- yield response and 
therefore applies primarily to Extensive and Complete damage states with little or 
minimal affect on Slight and Moderate damage states. The beta value of 0.75 selected for 
Slight damage assumes no degradation at this level of response. The beta values of other 
damage states increase progressively, Moderate damage - 0.80, Extensive damage - 0.85 
and Complete damage - 0.95. A beta value of 0.95 for Complete damage reflects 
degradation between major and extreme (k = 0.3).

The CO Retrofit Scheme is assumed to have "small" to "moderate" capacity and damage 
variability due to a reduction in uncertainty associated with the repair of welded 
connections. Further, repair of connections reduces the amount of degradation of the 
structural system that is expected to occur. Interpolating between values, Table 6.7 
suggests a beta of 0.65 for minor degradation that is used for Slight through Extensive 
damage states, with a small increase to a beta of 0.70 for Complete damage.

8.4.3. Nonstructural Drift Fragility Curves 
Nonstructural drift fragility parameters (medians and betas) are listed in Table 8.6 with 
values of default and modified data for the Original Building and the CO Retrofit 
Scheme, respectively.

Table 8.6. Example AEBM Profiles Data - Nonstructural Drift Fragility Curves 
Parameter:  
Record No. 1 (Default and Modified):  
Record No. 2 (Default and Modified):  

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Slight/Median
Record No. 1 (Default):  4.49
Record No. 1 (Modified):  5.70
Record No. 2 (Default):  4.49
Record No. 2 (Modified):  5.60

Parameter Field Name:  Slight/Beta
Record No. 1 (Default):  0.76
Record No. 1 (Modified):  0.80
Record No. 2 (Default):  0.72
Record No. 2 (Modified):  0.65

Parameter Field Name:  Moderate/Median
Record No. 1 (Default):  8.99
Record No. 1 (Modified):  9.70
Record No. 2 (Default):  8.99
Record No. 2 (Modified):  9.40

Parameter Field Name:  Moderate/Beta
Record No. 1 (Default):  0.87
Record No. 1 (Modified):  0.85
Record No. 2 (Default):  0.71
Record No. 2 (Modified):  0.65

Parameter Field Name:  Extensive/Median
Record No. 1 (Default):  28.08
Record No. 1 (Modified):  22.00
Record No. 2 (Default):  28.08
Record No. 2 (Modified):  21.50

Parameter Field Name:  Extensive/Beta
Record No. 1 (Default):  0.96
Record No. 1 (Modified):  0.90
Record No. 2 (Default):  0.74
Record No. 2 (Modified):  0.65

Parameter Field Name:  Complete/Median
Record No. 1 (Default):  56.16
Record No. 1 (Modified):  48.40
Record No. 2 (Default):  56.16
Record No. 2 (Modified):  47.20

Parameter Field Name:  Complete/Beta
Record No. 1 (Default):  1.04
Record No. 1 (Modified):  1.00
Record No. 2 (Default):  0.77
Record No. 2 (Modified):  0.75

Modified values of nonstructural drift damage-state medians are based on Equation (6-2) 
assuming drift to be essentially uniform over the height of the building (i.e., FfP,ds = 
1.0). Values of building height, HR, and modal factor, a2, are the same as those given in 
Table 8.4 and 8.5. Note, median values are slightly different for the Original Building and 
the CO Retrofit Scheme due a slight difference in the modal factor, a2.

Modified values of nonstructural drift damage-state betas are based on Table 6.7 
following the same approach and assumptions used to select structural damage-state betas 
(see discussion in the previous section).

8.4.4. Nonstructural Acceleration Fragility Curves 
Nonstructural acceleration fragility parameters (medians and betas) are listed in Table 8.7 
with values of default and modified data for the Original Building and the CO Retrofit 
Scheme, respectively.

Default values nonstructural damage-state medians (based on Moderate code design) are 
used for both the Original Building and the CO Retrofit Scheme on the basis that seismic 
upgrade of acceleration-sensitive components (e.g., seismic anchorage and bracing of 
equipment) is not part of the CO Retrofit Scheme. Modified values of nonstructural 
damage-state betas are based on Table 6.7 assuming a large variability (i.e., uncertainty) 
in damage variability of these components (since they are not being seismically 
upgraded). 

Table 8.7. Example AEBM Profiles Data - Nonstructural Acceleration Fragility Curves
Parameter:  
Record No. 1 (Default and Modified):  
Record No. 2 (Default and Modified):  

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Slight/Median
Record No. 1 (Default):  0.25
Record No. 1 (Modified):  0.25
Record No. 2 (Default):  0.30
Record No. 2 (Modified):  0.25

Parameter Field Name:  Slight/Beta
Record No. 1 (Default):  0.68
Record No. 1 (Modified):  0.65
Record No. 2 (Default):  0.69
Record No. 2 (Modified):  0.65

Parameter Field Name:  Moderate/Median
Record No. 1 (Default):  0.50
Record No. 1 (Modified):  0.50
Record No. 2 (Default):  0.60
Record No. 2 (Modified):  0.50

Parameter Field Name:  Moderate/Beta
Record No. 1 (Default):  0.68
Record No. 1 (Modified):  0.65
Record No. 2 (Default):  0.67
Record No. 2 (Modified):  0.65

Parameter Field Name:  Extensive/Median
Record No. 1 (Default):  1.00
Record No. 1 (Modified):  1.00
Record No. 2 (Default):  1.20
Record No. 2 (Modified):  1.00

Parameter Field Name:  Extensive/Beta
Record No. 1 (Default):  0.68
Record No. 1 (Modified):  0.65
Record No. 2 (Default):  0.67
Record No. 2 (Modified):  0.65

Parameter Field Name:  Complete/Median
Record No. 1 (Default):  2.00
Record No. 1 (Modified):  2.00
Record No. 2 (Default):  2.40
Record No. 2 (Modified):  2.00

Parameter Field Name:  Complete/Beta
Record No. 1 (Default):  0.68
Record No. 1 (Modified):  0.65
Record No. 2 (Default):  0.67
Record No. 2 (Modified):  0.65

8.4.5. Casualty Ratios (Per Occupant) 
Casualty ratio (per occupant) parameters are listed in Table 8.8 with values of default and 
modified data for the Original Building and the CO Retrofit Scheme, respectively. 
Default casualty rates are used for both the Original Building and the CO Retrofit 
Scheme. Only the parameter that defines the ratio of building area collapsed is modified 
using Equation (7-1) based on failure mode probabilities that distinguish between the 
collapse potential of the Original Building and that of the CO Retrofit Scheme.

Based on engineering evaluations (and judgement) and reflecting a high degree of 
uncertainty, the Original Building is assumed to be equally likely of having no collapse, 
partial collapse of a single story or global collapse of the entire structure, given that it has 
reached a state of Complete structural damage. Partial collapse would affect about 1/10 of 
total building area. Using Equation (7-1), the Collapse Factor is calculated:

Equation 8-1:
P[COL|STR5] = 0.33 x 0.0 + 0.33 x 0.1 + 0.33 x 1.0 = 36%

With strengthening of connections, the CO Retrofit Scheme is assumed to be much less 
likely of global collapse (i.e. only a 10% probability), but still likely to have some form 
of collapse (i.e., 50% probability), given that it has reached a state of Complete structural 
damage. Again using Equation (7-1), the Collapse Factor is calculated:

Equation 8-2:
P[COL|STR5] = 0.50 x 0.0 + 0.40 x 0.1 + 0.10 x 1.0 = 14%

Table 8.8. Example AEBM Profiles Data - Casualty Ratios (per Occupant) 
Parameter:  
Record No. 1 (Default and Modified):  
Record No. 2 (Default and Modified):  

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Slight/Level 1
Record No. 1 (Default):  0.00050
Record No. 1 (Modified):  0.00050
Record No. 2 (Default):  0.00050
Record No. 2 (Modified):  0.00050

Parameter Field Name:  Slight/Level 2
Record No. 1 (Default):  0.00000
Record No. 1 (Modified):  0.00000
Record No. 2 (Default):  0.00000
Record No. 2 (Modified):  0.00000

Parameter Field Name:  Slight/Level 3
Record No. 1 (Default):  0.00000
Record No. 1 (Modified):  0.00000
Record No. 2 (Default):  0.00000
Record No. 2 (Modified):  0.00000

Parameter Field Name:  Slight/Level 4
Record No. 1 (Default):  0.00000
Record No. 1 (Modified):  0.00000
Record No. 2 (Default):  0.00000
Record No. 2 (Modified):  0.00000

Parameter Field Name:  Moderate/Level 1
Record No. 1 (Default):  0.00200
Record No. 1 (Modified):  0.00200
Record No. 2 (Default):  0.00200
Record No. 2 (Modified):  0.00200

Parameter Field Name:  Moderate/Level 2
Record No. 1 (Default):  0.00025
Record No. 1 (Modified):  0.00025
Record No. 2 (Default):  0.00025
Record No. 2 (Modified):  0.00025

Parameter Field Name:  Moderate/Level 3
Record No. 1 (Default):  0.00000
Record No. 1 (Modified):  0.00000
Record No. 2 (Default):  0.00000
Record No. 2 (Modified):  0.00000

Parameter Field Name:  Moderate/Level 4
Record No. 1 (Default):  0.00000
Record No. 1 (Modified):  0.00000
Record No. 2 (Default):  0.00000
Record No. 2 (Modified):  0.00000

Parameter Field Name:  Extensive/Level 1
Record No. 1 (Default):  0.01000
Record No. 1 (Modified):  0.01000
Record No. 2 (Default):  0.01000
Record No. 2 (Modified):  0.01000

Parameter Field Name:  Extensive/Level 2
Record No. 1 (Default):  0.00100
Record No. 1 (Modified):  0.00100
Record No. 2 (Default):  0.00100
Record No. 2 (Modified):  0.00100

Parameter Field Name:  Extensive/Level 3
Record No. 1 (Default):  0.00001
Record No. 1 (Modified):  0.00001
Record No. 2 (Default):  0.00001
Record No. 2 (Modified):  0.00001

Parameter Field Name:  Extensive/Level 4
Record No. 1 (Default):  0.00001
Record No. 1 (Modified):  0.00001
Record No. 2 (Default):  0.00001
Record No. 2 (Modified):  0.00001

Parameter Field Name:  Complete/Level 1
Record No. 1 (Default):  0.05000
Record No. 1 (Modified):  0.05000
Record No. 2 (Default):  0.05000
Record No. 2 (Modified):  0.05000

Parameter Field Name:  Complete/Level 2
Record No. 1 (Default):  0.01000
Record No. 1 (Modified):  0.01000
Record No. 2 (Default):  0.01000
Record No. 2 (Modified):  0.01000

Parameter Field Name:  Complete/Level 3
Record No. 1 (Default):  0.00010
Record No. 1 (Modified):  0.00010
Record No. 2 (Default):  0.00010
Record No. 2 (Modified):  0.00010

Parameter Field Name:  Complete/Level 4
Record No. 1 (Default):  0.00010
Record No. 1 (Modified):  0.00010
Record No. 2 (Default):  0.00010
Record No. 2 (Modified):  0.00010

Parameter Field Name:  Complete with Collapse/Level 1
Record No. 1 (Default):  0.40000
Record No. 1 (Modified):  0.40000
Record No. 2 (Default):  0.40000
Record No. 2 (Modified):  0.40000

Parameter Field Name:  Complete with Collapse/Level 2
Record No. 1 (Default):  0.20000
Record No. 1 (Modified):  0.20000
Record No. 2 (Default):  0.20000
Record No. 2 (Modified):  0.20000

Parameter Field Name:  Complete with Collapse/Level 3
Record No. 1 (Default):  0.05000
Record No. 1 (Modified):  0.05000
Record No. 2 (Default):  0.05000
Record No. 2 (Modified):  0.05000

Parameter Field Name:  Complete with Collapse/Level 4
Record No. 1 (Default):  0.10000
Record No. 1 (Modified):  0.10000
Record No. 2 (Default):  0.10000
Record No. 2 (Modified):  0.10000

Parameter Field Name:  Ratio of Building Area Collapsed
Record No. 1 (Default):  0.03
Record No. 1 (Modified):  0.36
Record No. 2 (Default):  0.03
Record No. 2 (Modified):  0.14

8.4.6. Building Related Repair Cost Ratios 
Building related repair cost ratio parameters are listed in Table 8.9 with values of default 
and modified data for the Original Building and the CO Retrofit Scheme, respectively.

Modified structure (STR) repair cost ratios are based on Table B-9 of FEMA 351. "Pre-
Northridge" ratios are used for the Original Building and "Post-Northridge" ratios are 
used for the CO Retrofit Scheme. Cost ratios are adjusted to reflect that about one- half of 
the value of the structural system (i.e., $12 million = 1/2 x 0.40 x $60 million) of the 
LACDPW Headquarters building is associated with basement and foundation structures 
that are not susceptible to ground shaking damage. For the Original Building, the repair 
cost ratios for Slight, Moderate and Extensive damage states are 0.04, 0.10 and 0.40, 
respectively, based on one-half of the "Pre-Northridge" ratios given in Table B-9 of 
FEMA 351. "Pre-Northridge" repair cost ratios of FEMA 351 reflect actual costs of 
repair to buildings damaged during the 1994 Northridge earthquake, including costs of 
post-earthquake inspection of connections. The repair cost of Complete damage is 100% 
assuming that basement and foundation structures could not be salvaged if the building 
was a total loss.

Table 8.9. Example AEBM Profiles Data - Building Related Repair Cost Ratios 
Parameter:  
Record No. 1 (Default and Modified):  
Record No. 2 (Default and Modified):  

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  STR/Slight
Record No. 1 (Default):  0.3
Record No. 1 (Modified):  0.6
Record No. 2 (Default):  0.3
Record No. 2 (Modified):  0.3

Parameter Field Name:  STR/Moderate
Record No. 1 (Default):  1.8
Record No. 1 (Modified):  1.8
Record No. 2 (Default):  1.8
Record No. 2 (Modified):  0.9

Parameter Field Name:  STR/Extensive
Record No. 1 (Default):  9
Record No. 1 (Modified):  7.2
Record No. 2 (Default):  9
Record No. 2 (Modified):  4.5

Parameter Field Name:  STR/Complete
Record No. 1 (Default):  17.9
Record No. 1 (Modified):  17.9
Record No. 2 (Default):  17.9
Record No. 2 (Modified):  17.9

Parameter Field Name:  NSD/Slight
Record No. 1 (Default):  0.7
Record No. 1 (Modified):  0.7
Record No. 2 (Default):  0.7
Record No. 2 (Modified):  0.7

Parameter Field Name:  NSD/Moderate
Record No. 1 (Default):  3.3
Record No. 1 (Modified):  3.3
Record No. 2 (Default):  3.3
Record No. 2 (Modified):  3.3

Parameter Field Name:  NSD/Extensive
Record No. 1 (Default):  16.4
Record No. 1 (Modified):  16.4
Record No. 2 (Default):  16.4
Record No. 2 (Modified):  16.4

Parameter Field Name:  NSD/Complete
Record No. 1 (Default):  32.8
Record No. 1 (Modified):  32.8
Record No. 2 (Default):  32.8
Record No. 2 (Modified):  32.8

Parameter Field Name:  NSA/Slight
Record No. 1 (Default):  1
Record No. 1 (Modified):  1
Record No. 2 (Default):  1
Record No. 2 (Modified):  1

Parameter Field Name:  NSA/Moderate
Record No. 1 (Default):  4.9
Record No. 1 (Modified):  4.9
Record No. 2 (Default):  4.9
Record No. 2 (Modified):  4.9

Parameter Field Name:  NSA/Extensive
Record No. 1 (Default):  14.8
Record No. 1 (Modified):  14.8
Record No. 2 (Default):  14.8
Record No. 2 (Modified):  14.8

Parameter Field Name:  NSA/Complete
Record No. 1 (Default):  49.3
Record No. 1 (Modified):  49.3
Record No. 2 (Default):  49.3
Record No. 2 (Modified):  49.3

Parameter Field Name:  Ratio:STR to Building Value
Record No. 1 (Default):  0.18
Record No. 1 (Modified):  0.40
Record No. 2 (Default):  0.18
Record No. 2 (Modified):  0.40

Parameter Field Name:  Ratio:NSD to Building Value
Record No. 1 (Default):  0.33
Record No. 1 (Modified):  0.20
Record No. 2 (Default):  0.33
Record No. 2 (Modified):  0.20

Default repair cost ratios are used for both nonstructural drift-sensitive (NSD) and 
nonstructural acceleration-sensitive (NSA) systems.

Modified ratios of structural system value and nonstructural drift-sensitive system value 
to total building value are based on estimates of the actual costs of these systems 
developed during the engineering evaluation of seismic upgrade options. The modified 
ratios reflect an approximate $24 million replacement value of the structural system, one-
half of which is associated with basement and foundation structures, as mentioned above. 
Nonstructural drift-sensitive systems have a replacement value of about $12 million and 
nonstructural acceleration-sensitive systems have a replacement value of about $24 
million. These system replacement costs sum to the total building replacement cost of 
$60 million.

8.4.7 Contents & Building Inventory Replacement Cost Ratios

Contents and inventory replacement cost ratio parameters are listed in Table 8.10 with 
values of default and modified data for the Original Building and the CO Retrofit 
Scheme, respectively. Default values of these parameters are used in all cases. 

Table 8.10. Example AEBM Profiles Data - Contents/Inventory Replacement Cost Ratios
Parameter:  
Record No. 1 (Default and Modified):  
Record No. 2 (Default and Modified):  

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Contents/Slight
Record No. 1 (Default):  0.01
Record No. 1 (Modified):  0.01
Record No. 2 (Default):  0.01
Record No. 2 (Modified):  0.01

Parameter Field Name:  Contents/Moderate
Record No. 1 (Default):  0.05
Record No. 1 (Modified):  0.05
Record No. 2 (Default):  0.05
Record No. 2 (Modified):  0.05

Parameter Field Name:  Contents/Extensive
Record No. 1 (Default):  0.25
Record No. 1 (Modified):  0.25
Record No. 2 (Default):  0.25
Record No. 2 (Modified):  0.25

Parameter Field Name:  Contents/Complete
Record No. 1 (Default):  0.50
Record No. 1 (Modified):  0.50
Record No. 2 (Default):  0.50
Record No. 2 (Modified):  0.50

Parameter Field Name:  Inventory/Slight
Record No. 1 (Default):  0.00
Record No. 1 (Modified):  0.00
Record No. 2 (Default):  0.00
Record No. 2 (Modified):  0.00

Parameter Field Name:  Inventory/Moderate
Record No. 1 (Default):  0.00
Record No. 1 (Modified):  0.00
Record No. 2 (Default):  0.00
Record No. 2 (Modified):  0.00

Parameter Field Name:  Inventory/Extensive
Record No. 1 (Default):  0.00
Record No. 1 (Modified):  0.00
Record No. 2 (Default):  0.00
Record No. 2 (Modified):  0.00

Parameter Field Name:  Inventory/Complete
Record No. 1 (Default):  0.00
Record No. 1 (Modified):  0.00
Record No. 2 (Default):  0.00
Record No. 2 (Modified):  0.00

8.4.8 Loss of Function Parameters 
Loss of function parameters are listed in Table 8.11 with values of default and modified 
data for the Original Building and the CO Retrofit Scheme, respectively.

Modified values of the time to restore loss of function are based on the mean repair time 
values and loss-of- function multipliers given in Table B-10 of FEMA 351 for 9-story 
WSMF buildings, limited to a maximum of 30 days. "Pre-Northridge" values are used for 
the Original Building and "Post-Northridge" values are used for the CO Retrofit Scheme. 
The values given in Table B-10 acknowledge differences in repair time based on building 
height (i.e., building size). However, these values represent commercial building 
occupancy and do not recognize that government services are expected to be restored in a 
relatively short period of time (even if the building is closed). Thus, the maximum time to 
restore loss of function is set at 30 days.

Modified values of the time to make all repairs and full recovery are based on the mean 
repair time values given in Table B-10 of FEMA 351 for 9-story WSMF buildings, 
factored by 
recovery time multipliers. "Pre-Northridge" values are used for the Original Building and 
"Post-Northridge" values are used for the CO Retrofit Scheme. Recovery time multipliers 
are 1.0 for Slight damage, 3.0 for Moderate and Extensive damage states, and 2.0 for 
Complete damage, consistent with the ratios of recovery times to repair times given in 
Tables 15.11 and 15.10, respectively, of the HAZUS-MH Technical Manual for 
government (GOV1) buildings.

Table 8.11. Example AEBM Profiles Data - Loss of Function Parameters
Parameter:  
Record No. 1 (Default and Modified):  
Record No. 2 (Default and Modified):  

Parameter Field Name:  Name
Record No. 1 (Default and Modified):  Original Building
Record No. 2 (Default and Modified):  CO Retrofit Scheme

Parameter Field Name:  Function Loss/None (Days)
Record No. 1 (Default):  0.5
Record No. 1 (Modified):  0.5
Record No. 2 (Default):  0.5
Record No. 2 (Modified):  0.5

Parameter Field Name:  Function Loss/Slight (Days)
Record No. 1 (Default):  0.1
Record No. 1 (Modified):  0.1
Record No. 2 (Default):  0.1
Record No. 2 (Modified):  0.1

Parameter Field Name:  Function Loss/Moderate (Days)
Record No. 1 (Default):  0.02
Record No. 1 (Modified):  0.02
Record No. 2 (Default):  0.02
Record No. 2 (Modified):  0.02

Parameter Field Name:  Function Loss/Extensive (Days)
Record No. 1 (Default):  0.03
Record No. 1 (Modified):  0.03
Record No. 2 (Default):  0.03
Record No. 2 (Modified):  0.03

Parameter Field Name:  Function Loss/Complete (Days)
Record No. 1 (Default):  0.03
Record No. 1 (Modified):  0.03
Record No. 2 (Default):  0.03
Record No. 2 (Modified):  0.03

Parameter Field Name:  Recovery TIme/None (Days)
Record No. 1 (Default):  0
Record No. 1 (Modified):  0
Record No. 2 (Default):  0
Record No. 2 (Modified):  0

Parameter Field Name:  Recovery Time/Slight (Days)
Record No. 1 (Default):  10
Record No. 1 (Modified):  0
Record No. 2 (Default):  10
Record No. 2 (Modified):  0

Parameter Field Name:  Recovery Time/Moderate (Days)
Record No. 1 (Default):  90
Record No. 1 (Modified):  150
Record No. 2 (Default):  90
Record No. 2 (Modified):  120

Parameter Field Name:  Recovery Time/Extensive (Days)
Record No. 1 (Default):  360
Record No. 1 (Modified):  540
Record No. 2 (Default):  360
Record No. 2 (Modified):  540

Parameter Field Name:  Recovery Time/Complete (Days)
Record No. 1 (Default):  480
Record No. 1 (Modified):  720
Record No. 2 (Default):  480
Record No. 2 (Modified):  720

Parameter Field Name:  Recapture Factor/Business Income
Record No. 1 (Default):  0.80
Record No. 1 (Modified):  0.80
Record No. 2 (Default):  0.80
Record No. 2 (Modified):  0.80

Parameter Field Name:  Recapture Factor/Wages
Record No. 1 (Default):  0.80
Record No. 1 (Modified):  0.80
Record No. 2 (Default):  0.80
Record No. 2 (Modified):  0.80

Default recapture factors are used for both business income and wages.

8.5. Example AEBM Results
After the modification of default AEBM Profiles data, the AEBM may be run, as 
described in Section 8.3.5 and the results viewed and printed, as described in Section 
8.3.6.

Figures 8.22 and 8.23 show individual summary reports for the Original Building and the 
CO Retrofit Scheme, respectively. These reports are the same as those shown Figures 
8.17 and 8.18, respectively, except that results are now based on modified AEBM profile 
data and represent the most reliable estimates of damage and losses for LACDPW 
Headquarters building due to scenario earthquake ground shaking. Summary results 
indicate that the CO Retrofit Scheme would substantially reduce structural damage (and 
associated structural losses by more than a factor of 15), virtually eliminate serious 
injuries and deaths, and reduce total direct economic loss by about a factor of 5 for 
scenario earthquake ground shaking (e.g., a magnitude M7.2 event on the Sierra Madre 
fault).

A note of caution to users, ground motion (spectral acceleration) values may not be 
accurately reported in individual building reports. Users can verify suspicious values of 
spectral acceleration (e.g., the 1-second spectral acceleration of 0.07 g shown in Figures 
8.22 and 8.23 seems low) with ground motion results of HAZUS for the census tract(s) 
where buildings are located. In this example, the LACDPW Headquarters building is 
located in Census Tract 06037480802 and HAZUS shows a 1-second spectral 
acceleration of 0.43 g for this census tract.

Figure 8.22. Summary Report - Original Building Results
(screen capture of report)

Figure 8.23. Summary Report - CO Retrofit Scheme Results 
(screen capture of report)

8.5.1 Interpretation 
Individual building results from AEBM analyses may be evaluated (and better 
understood) by comparison with the results of regional studies for the same scenario 
earthquake. Table 8.12 provides such a comparison of AEBM example results with 
building-related losses of the Los Angeles County study region due to a magnitude M7.2 
earthquake on the Sierra Madre fault.

Table 8.12. Comparison of AEBM Example and Los Angeles County Study Region 
Losses for a Magnitude M7.2 Earthquake on the Sierra Madre Fault
Parameter:  
Exposure:  
Loss:  
Ratio:  

(AEBM Example Results - Original Building)
Parameter:  Direct Economic Loss - Structural System
Exposure:  $24 million
Loss:  $1.71 million
Ratio: 4.9%

Parameter:  Direct Economic Loss - Total Building
Exposure:  %60 Million
Loss:  $4.67 million
Ratio:   7.8%

Parameter:  Direct Economic Loss - Building Interruption
Exposure:  1 x building value
Loss:  $2.24 million
Ratio:  3.7%

Parameter:  Daytime Casualties - All
Exposure:  1,600
Loss:  25
Ratio: 18/1,000

Parameter:  Daytime Casualties Immediate Deaths
Exposure:  1,600
Loss:  0
Ratio:  0.2/1,000

(AEBM Example - CO Retrofit Scheme)
Parameter:  Direct Economic Loss - Structural System
Exposure:  $24 million
Loss:  $0.23 million
Ratio: 1.0%

Parameter:  Direct Economic Loss - Total Building
Exposure:  %60 Million
Loss:  $2.5 million
Ratio:   4.2%

Parameter:  Direct Economic Loss - Building Interruption
Exposure:  1 x building value
Loss:  $0.45 million
Ratio:  0.75%

Parameter:  Daytime Casualties - All
Exposure:  1,600
Loss:  1
Ratio: 1/1,000

Parameter:  Daytime Casualties Immediate Deaths
Exposure:  1,600
Loss:  0
Ratio:  0.2/1,000

Table 8.12 includes loss ratios that are calculated as losses divided by exposure. These 
ratios provide a basis to compare individual building results of the AEBM example with 
average (or typical) losses for the study region. Comparison of loss ratios given in Table 
8.12 indicate that Original Building losses exceed average losses for Los Angeles 
County, in part due to the higher than average level of ground shaking at the LACDPW 
Headquarters building site. The CO Retrofit Scheme has substantially lower loss ratios 
that are comparable to or less than those of Los Angeles County.

Damage-state probabilities are based on best estimates of damage considering the 
inherent variability of ground shaking, building capacity and damage states. Losses based 
on "best estimates" of damage may be thought of as "expected" losses, recognizing that 
actual losses could be substantially higher or lower. Direct economic loss is based on the 
combination of many states of damage to structural and nonstructural systems that 
effectively create a continuous distribution of possible dollar losses. Economic losses 
reported by the AEBM represent the center values of these continuous distributions.

Casualties, in particular, deaths are based on a much more discrete set of possibilities. 
Table 8.12 reports 9 immediate (daytime) deaths that are based on the assumption that 
there is a 1/3-probability of no collapse, a 1/3-probability partial (single-story) collapse 
and a 1/3-probability of full collapse. Full collapse is expected to immediately kill 160 
people, based on the daytime population of 1,600 and the 0.10 immediate death rate 
given collapse (Table 8.8). Partial collapse of a single-story is expected to immediately 
kill 16 people, 1/10 of full collapse deaths. Thus, the expected number of immediate 
deaths (9 deaths) represents an approximate 5% chance (i.e., 1/3 of the 0.16 probability of 
Complete structural damage) of full collapse that would immediately kill 160 people and 
an approximate 5% chance of a single-story collapse that would immediately kill 16 
people. The expected number of 9 deaths tends to understate the number of deaths that 
could occur if the building actually collapses.

8.5.2. Sensitivity Analyses 
Users are required to input a large amount of data in the AEBM based on engineering 
judgement and assumptions that are inherently uncertain, and thus affect the reliability of 
the results. While uncertainty in capacity, fragility and loss parameters is unavoidable, 
the AEBM may be used to test the sensitivity of results to input parameters. 
As an example of sensitivity analyses, the AEBM example is run for five different sets of 
Profile data:
* Default AEBM Profiles data (All Default Data)
* Default AEBM Profiles data with modified Capacity parameters (Capacity Only) 
* Default AEBM Profiles data with modified Fragility parameters (Fragility Only) 
* Default AEBM Profiles data with modified Loss parameters (Loss Only) 
* Modified AEBM Profiles data (All Modified Data).

These AEBM example runs test the sensitivity of results to modifications of default 
Profile data, indicating which modifications have the greatest affect on estimated losses. 
Direct economic loss results are summarized in Table 8.13 for the Original Building and 
CO Retrofit Scheme, respectively. Table 8.13 includes a "%D" column that provides a 
measure of the change in result values when modified parameters are used in lieu of 
default parameters.

Table 8.13 suggests that default data produces reasonable estimates of losses for the 
Original Building that are only modestly different from those based on modified 
properties. Conversely, there are significant differences (improvements) to estimates of 
CO Retrofit Scheme losses when default data is modified, particularly with respect to 
losses to the structural system. 

Table 8.13. Comparison of Economic Losses 
Profile Name
Total Direct Economic Loss (dollars in millions) - Original Building and CO Retrofit 
Scheme:
Structural Direct Economic Loss (dollars in millions) - Original Building and CO Retrofit 
Scheme:

Default Profile - HAZUS GBS Data
Total Direct Economic Loss (dollars in millions) - Original Building: Value = $22.57; 
%D = --
Total Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = $9.6; 
%D = --
Structural Direct Economic Loss (dollars in millions) - Original Building: Value = $4.8; 
%D = --
Structural Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = 
$2.9; %D = --

Modified Profile - Capacity Data Only
Total Direct Economic Loss (dollars in millions) - Original Building: Value = $22.0; %D 
= 0%
Total Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = $7.4; 
%D = -22%
Structural Direct Economic Loss (dollars in millions) - Original Building: Value = $3.9; 
%D = -19%
Structural Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = 
$1.1; %D = -62%

Modified Profile - Fragility Data Only
Total Direct Economic Loss (dollars in millions) - Original Building: Value = $18.70; 
%D = -17%
Total Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = $5.1; 
%D = -46%
Structural Direct Economic Loss (dollars in millions) - Original Building: Value = $4.1; 
%D = -15%
Structural Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = 
$1.2; %D = -58%

Modified Profile - Loss Data Only
Total Direct Economic Loss (dollars in millions) - Original Building: Value = $24.4; %D 
= 8%
Total Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = $9.1; 
%D = -5%
Structural Direct Economic Loss (dollars in millions) - Original Building: Value = $4.4; 
%D = -8%
Structural Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = 
$1.3; %D = -55%

Modified Profile - All Data
Total Direct Economic Loss (dollars in millions) - Original Building: Value = $19.5; %D 
= -13%
Total Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = $3.6; 
%D = -62%
Structural Direct Economic Loss (dollars in millions) - Original Building: Value = $3.3; 
%D = -31%
Structural Direct Economic Loss (dollars in millions) - CO Retrofit Scheme: Value = 
$0.2; %D = -93%

SECTION 9 
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