ATC 58 50percentDraft

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Guidelines for Seismic PerformanceAssessment of Buildings

ATC-58 50% Draft

Prepared by

APPLIED TECHNOLOGY COUNCIL201 Redwood Shores Parkway, Suite 240

Redwood City, California 94065www.ATCouncil.org

Prepared for

U.S. DEPARTMENT OF HOMELAND SECURITY (DHS)FEDERAL EMERGENCY MANAGEMENT AGENCY

Michael Mahoney, Project OfficerRobert D. Hanson, Technical Monitor

Washington, D.C.

PROJECT MANAGEMENT COMMITTEEChristopher Rojahn (Project Executive Director)Ronald O. Hamburger (Project Technical Director)John GillengertenPeter J. MayJack P. MoehleMaryann T. Phipps*Jon A. Heintz**William T. Holmes **

STEERING COMMITTEE

William T. Holmes (Chair)Roger D. BorcherdtAnne BostromBruce BurrKelly CobeenAnthony B. CourtTerry DooleyDan GramerMichael GriffinR. Jay LoveDavid MarSteven McCabeBrian J. Meacham

William J. Petak

* ATC Board Contact** ex-officio

STRUCTURAL PERFORMANCEPRODUCTS TEAM

Andrew S. Whittaker (Team Leader)Gregory DeierleinJohn D. HooperYin-Nan Huang

Nicolas LucoAndrew T. Merovich

NONSTRUCTURAL PERFORMANCEPRODUCTS TEAM

Robert E. Bachman (Team Leader)Philip J. CaldwellAndre FiliatraultRobert P. KennedyHelmut KrawinklerManos MaragakisEduardo MirandaKeith Porter

RISK MANAGEMENT PRODUCTS TEAMCraig D. Comartin (Team Leader)Mary ComerioGregory FenvesMahmoud HachemGee HecksherJudith Mitrani-ReiserFarzad NaeimHope Seligson

April 15, 2009
http://www.atcouncil.org/http://www.atcouncil.org/http://www.atcouncil.org/


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STRUCTURAL FRAGILITYDEVELOPMENT CONSULTANTS

Charles EkiertAndre FiliatraultAysegul Gogus

Kerem GulecDawn LehmanJingjuan LiLaura LowesEric LumpkinHussein OkailCharles RoederBenson ShingChristopher SmithVictor VictorssonJohn Wallace

FRAGILITY REVIEW PANEL

Bruce EllingwoodRobert KennedyStephen Mahin

NONSTRUCTURAL FRAGILITYDEVELOPMENT CONSULTANTS

Richard BehrJohn EidingerPaul Kremer

Ali M. MemariWilliam OBrienJohn OsteraasXin Xu

RISK MANAGEMENT PRODUCTSCONSULTANTS

Peter MorrisScott Shell

VALIDATION/VERIFICATION TEAMJack BakerDavid Bonneville

Charles Scawthorn

Notice

This document has been prepared by the ATC-58 Project Team to assist interested parties in

obtaining an understanding of the methodology as it is being developed, and to facilitatecomment and feedback to the project team on its further development. The guidelines presentedin this document are incomplete at this time. The data and procedures are not necessarilyappropriate for use in actual projects at this time, and should not be used for that purpose. Readernotes have been provided to describe the present status of development, and to identify portions

of the methodology that are not yet ready for implementation. The information contained hereinwill be subject to further revision and enhancement as the methodology is completed in futureyears.


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ATC-58 Contents i

Contents

List of Figures ............................................................................................... vii

List of Tables ............................................................................................... xiii

Glossary .................................................................................................... xvii

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

1.1 Purpose ..................................................................... 1-1

1.2 The Performance-Based Design Process ................. 1-1

1.3 Guideline Uses ......................................................... 1-3

1.4 Application ............................................................... 1-3

1.5 Performance Calculations ........................................ 1-4

1.6 Guideline Organization ............................................ 1-51.7 Limitations ............................................................... 1-6

Chapter 2 Performance Measures ....................................................... 2-1

2.1 Introduction .............................................................. 2-1

2.2 Factors Affecting Performance ................................ 2-1

2.3 Uncertainty in Performance Assessment ................. 2-1

2.4 Types of Performance Assessment .......................... 2-5

2.4.1 Intensity-Based Assessments ...................... 2-5

2.4.2 Scenario-Based Assessments ...................... 2-7

2.4.3 Time-Based Assessments ............................ 2-8

2.5 Use of Loss Distributions in Decision-making ........ 2-9

2.5.1 Typical Building Performance .................... 2-92.5.2 Probable Maximum Loss .......................... 2-10

2.5.3 Cost-Benefit Analysis ............................... 2-12

Chapter 3 General Methodology ........................................................ 3-1

3.1 Introduction .............................................................. 3-1

3.2 Step 1 Assemble Building Performance Model .... 3-1

3.3 Step 2 Define Earthquake Hazards ....................... 3-2

3.4 Step 3 Simulate Building Response ...................... 3-3

3.5 Step 4 Develop Collapse Fragility ........................ 3-4

3.6 Step 5 Damage and Loss Assessment ................... 3-6

3.6.1 Collapse Determination ............................... 3-7

3.6.2 Damage Assessment .................................... 3-7

3.6.3 Loss Calculation ........................................ 3-11

3.7 Loss Aggregation ................................................... 3-12

3.7.1 Intensity-Based Assessments .................... 3-13

3.7.2 Scenario-Based Assessments .................... 3-13

3.7.3 Time-Based Assessments .......................... 3-13

Chapter 4 Implementation .................................................................. 4-1

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


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ii Contents ATC-58

4.2 Building Performance Model ................................... 4-2

4.2.1 Occupancies................................................. 4-2

4.2.2 Population Models ....................................... 4-3

4.2.3 Normative Quantities .................................. 4-5

4.3 Characterize Ground Motion .................................. 4-12

4.4 Structural Analysis ................................................. 4-12

4.5 Develop Collapse Fragility ..................................... 4-124.6 Form Realizations .................................................. 4-13

4.7 Damage Determination ........................................... 4-14

4.7.1 Damage Correlation .................................. 4-14

4.7.2 Fragility Specifications.............................. 4-15

4.7.3 Damage States ........................................... 4-15

4.7.4 Component Fragility Functions ................. 4-18

4.7.5 Consequence Functions ............................. 4-18

4.7.6 Damage Aggregation ................................. 4-20

4.8 Repair Costs ........................................................... 4-20

4.9 Occupancy Interruption Time ................................ 4-21

4.10 Casualties ............................................................... 4-22

4.11 Loss Distributions .................................................. 4-224.11.1 Intensity- and Scenario-Based

Assessments ............................................... 4-22

4.11.2 Time-Based Assessments .......................... 4-24

Chapter 5 Ground Shaking Intensity .................................................. 5-1

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

5.2 Building Location and Site Conditions .................... 5-1

5.2.1 Seismic Environment and Hazard ............... 5-1

5.2.2 Location ....................................................... 5-2

5.2.3 Site Soil and Topographic Conditions ......... 5-2

5.3 Spectral Adjustments for Soil Conditions ................ 5-3

5.4 USGS-based Ground Motion Calculator .................. 5-45.4.1 Time-Based Hazard Calculations ................ 5-4

5.4.2 Intensity-Based Hazard Calculations .......... 5-7

5.5 Attenuation Relationships ........................................ 5-8

5.5.1 Introduction ................................................. 5-8

5.5.2 Functional Form .......................................... 5-9

5.5.3 Median Spectrum and Dispersion ............. 5-11

5.6 Hazard Characterization for Use with Nonlinear

Response-History Analysis .................................... 5-12

5.6.1 Introduction ............................................... 5-12

5.6.2 Selection of Earthquake Ground

Motions ...................................................... 5-14

5.6.3 Intensity-Based Assessment ...................... 5-145.6.4 Time-Based Assessments .......................... 5-15

5.6.5 Scenario-Based Assessments ..................... 5-18

5.7 Hazard Characterization for Use with Simplified

Analysis .................................................................. 5-19

5.7.1 Introduction ............................................... 5-19

5.7.2 Intensity-Based Assessment ...................... 5-20

5.7.3 Time-Based Assessment ............................ 5-20

5.7.3 Scenario-Based Assessment ...................... 5-21


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ATC-58 Contents iii

Chapter 6 Response Analysis ............................................................. 6-1

6.1 Scope ........................................................................ 6-1

6.2 Nonlinear Response-History Analysis ..................... 6-1

6.2.1 Introduction ................................................. 6-1

6.2.2 Mathematical Models of Components

and Elements ............................................... 6-1

6.2.3 Analysis Procedures .................................... 6-56.2.4 Residual Drift ............................................ 6-11

6.2.5 Response Data Input to PACT .................. 6-12

6.3 Simplified Analysis ................................................ 6-13

6.3.1 Introduction ............................................... 6-13

6.3.2 Mathematical Models of Components

and Elements ............................................. 6-14

6.3.3 Analysis Procedure ................................... 6-15

6.3.4 Response Data Input to PACT .................. 6-20

Chapter 7 Procedures for Collapse Assessment ................................. 7-1

7.1 Scope ........................................................................ 7-1

7.2 Collapse Analysis..................................................... 7-17.2.1 Introduction ................................................. 7-1

7.3 Mathematical Models for Collapse Analysis ........... 7-2

7.3.1 Introduction ................................................. 7-2

7.3.2 Best Estimate Models .................................. 7-2

7.3.3 Simplified Model ........................................ 7-3

7.4 Analysis and Modeling Considerations ................... 7-5

7.4.1 Three- and Two-Dimensional Models ........ 7-5

7.4.2 Mathematical Models of Structural

Components ................................................ 7-5

7.4.3 Damping ...................................................... 7-6

7.5 Ground Motion Characterization for Collapse

Assessment ............................................................... 7-67.6 Development of Collapse Fragility Curves .............. 7-8

7.6.1 Introduction ................................................. 7-8

7.6.2 Truncation of IDA Curves for Non-

Simulated Failure Modes and

Components ................................................ 7-8

7.6.3 Construction of a Collapse Fragility

Curve ........................................................... 7-9

7.6.4 Collapse Fragility Parameters ................... 7-10

7.6.5 Tools for Collapse Analysis of

Simplified, Planar Models ......................... 7-11

7.7 Collapse Descriptions for Casualty Assessments .. 7-13

Chapter 8. Example Applications ........................................................ 8-1

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

8.2 Example Building #1 ............................................... 8-1

8.2.1 Introduction ................................................. 8-1

8.2.2 Seismic Hazard Characterization ................ 8-3

8.2.3 Response-History Analysis and

Demand Parameter Matrices ..................... 8-13


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iv Contents ATC-58

8.2.4 Input of Data into the Performance

Assessment Calculation Tool (PACT) ...... 8-20

8.2.5 Loss Computations Using PACT .............. 8-25

Appendix A: Probability, Statistics & Distributions ............................... A-1

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

A.2 Statistical Distributions ........................................... A-1A.2.1 Finite Populations and Discrete

Outcomes .................................................... A-1

A.2.2 Combined Probabilities .............................. A-2

A.2.3 Mass Distributions ...................................... A-3

A.2.4 Continuous Distributions ............................ A-4

A.3 Common Forms of Distributions ............................. A-6

A.3.1 Normal Distributions .................................. A-6

A.3.2 Cumulative Probability Functions .............. A-8

A.3.3 Lognormal Distributions ............................ A-8

Appendix B: Fragility Group, Normative Quantity and Population

Models ............................................................................... B-1B.1 Fragility Group Classifications ............................... B-1

B.2 Occupancy Default Assignment Tables .................. B-1

B.3 Occupancy Default Normative Quantity Logic ....... B-1

B.3.1 Commercial Office ..................................... B-1

B.3.2 Residential .................................................. B-1

B.4 Population Models................................................... B-2

Appendix C: Default Structural Fragility Data ....................................... C-1

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

C.2 Vertical Seismic Framing Systems .......................... C-1

C.3 Horizontal Seismic Framing Systems

(Diaphragms) ........................................................... C-3C.4 Gravity Framing Systems ........................................ C-3

C.5 Default Fragility Data .............................................. C-4

Appendix D: Nonstructural Fragility specifications ............................... D-1

D.1 Default Nonstructural Fragility Data Tables ........... D-1

Appendix E: Ground Shaking Hazards .................................................. E-1

E.1 Scope ....................................................................... E-1

E.2 Attenuation Relationships ....................................... E-1

E.3 Fault Rupture Directivity and Maximum

Direction Shaking .................................................... E-3

E.4 Probabilistic Seismic Hazard Assessment ............... E-4E.4.1 Introduction ................................................ E-4

E.4.2 PSHA Calculations ..................................... E-5

E.4.3 Inclusion of Rupture Directivity Effects .. E-13

E.4.4 Deaggregation of Seismic Hazard Curves

and Epsilon ............................................... E-13

E.4.5 Conditional Mean Spectrum and Spectral

Shape ........................................................ E-16

E.5 Selection of Earthquake Ground Motions ............. E-19


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ATC-58 Contents v

E.5.1 Introduction ............................................... E-19

E.5.2 Earthquake Histories for Response

Analysis ..................................................... E-19

E.6 Vertical Earthquake Shaking ................................. E-19

E.6.1 Introduction ............................................... E-19

E.6.2 Procedure for Site Classes A, B and C ...... E-19

E.6.3 Procedure for Site Classes D and E ........... E-20E.7 Soil-Foundation-Structure Interaction ................... E-20

E.7.1 General ...................................................... E-20

E.7.2 Direct Soil-Foundation-Structure-

Interaction Analysis .................................. E-21

E.7.3 Simplified Soil-Foundation-Structure-

Interaction Analysis .................................. E-22

E.8 Alternate Procedure for Hazard Characterization

for Scenario-Based Assessment Using Nonlinear

Response-History Analysis .................................... E-25

Appendix F: Fragility Development ....................................................... F-1

F.1 Introduction .............................................................. F-1F.1.1 Purpose ........................................................ F-1

F.1.2 Fragility Function Definition ...................... F-1

F.1.3 Derivation Methods..................................... F-3

F.1.4 Documentation ............................................ F-4

F.2 Fragility Parameter Derivation................................. F-5

F.2.1 Actual Demand Data ................................... F-5

F.2.2 Bounding Demand Data .............................. F-6

F.2.3 Capable Demand Data................................. F-9

F.2.4 Derivation ................................................. F-11

F.2.5 Expert Opinion .......................................... F-11

F.2.6 Updating .................................................... F-13

F.3 Assessing Fragility Function Quality ..................... F-14F.3.1 Competing Demand Parameters ................ F-15

F.3.2 Dealing with Outliers using Pierces

Criterion .................................................... F-15

F.3.3 Goodness of Fit Testing ............................ F-16

F.3.4 Fragility Functions that Cross ................... F-17

F.3.5 Assigning a Single Quality Level to a

Fragility Function ...................................... F-18

Appendix G: Generation of Realizations for Loss Computations .......... G-1

G.1 Loss Computations.................................................. G-1

G.2 Realizations for Assessment Using Nonlinear

Response-History Analysis ..................................... G-1G.2.1 Introduction ................................................ G-1

G.2.2 Algorithm ................................................... G-2

G.2.3 Sample Application of the Algorithm ........ G-3

G.2.4 Matlab Code ............................................. G-10

G.3 Realizations for Assessment Using Simplified

Nonlinear Analysis ................................................ G-11

Appendix H: Residual Drift .................................................................... H-1


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vi Contents ATC-58

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

H.2 Prediction of Residual Story Drifts ......................... H-2

H.3 Model to Calculate Residual Story Drifts ............... H-5

H.4 Proposed Damage States for Residual Story

Drifts ....................................................................... H-7

References .....................................................................................................I-1

ATC-58-1 Project Participants ..................................................................... J-1


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ATC-58 List of Figures vii

List of Figures

Figure 1-1 Performance-based design flow diagram ........................... 1-2

Figure 2-1 Example cumulative probability loss distributions for a

hypothetical building at four ground motion intensities .... 2-6

Figure 2-2 Example complimentary cumulative probability distributions

for loss at four ground motion intensities .......................... 2-7

Figure 2-3 Distribution of mean annual total repair cost ..................... 2-8

Figure 2-4 Cumulative loss function identifying a median (50th

percentile) loss ................................................................. 2-11

Figure 2-5 Annualized loss before and after proposed retrofit .......... 2-12

Figure 3-1 General Seismic Performance Assessment Procedure ....... 3-1

Figure 3-2 Representative collapse fragility for a hypotheticalbuilding structure ......................................................... 3-5

Figure 3-3 Loss calculation flow chart ........................................... 3-7

Figure 3-4 Example family of fragility curves for special steel

moment frames................................................................. 3-10

Figure 3-5 Sample consequence function for cost of repair .............. 3-12

Figure 3-6 Seismic hazard curve and time-based loss calculations ... 3-14

Figure 4-1 Graph illustrating the percent of peak occupancy, by

hour and day present .......................................................... 4-5

Figure 4-2 Representative Fragility Specification ............................. 4-17

Figure 4-3 Sample repair/replacement losses for a scenario or

intensity-based assessment ............................................... 4-23

Figure 4-4 Direct losses deaggregated by performance group for a

scenario or intensity-based assessment ............................ 4-23

Figure 4-5 Sample loss calculations for a time-based assessment ..... 4-24

Figure 5-1 Representative seismic hazard curve for a site in

San Francisco with T = 1 second, plotted in semi-log

format ................................................................................. 5-5

Figure 6-1 Generalized force-displacement behavior of

structural components ........................................................ 6-3


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viii List of Figures ATC-58

Figure 6-2 Definition of floor and story numbers and story height ... 6-16

Figure 7-1 Force-displacement relationships ....................................... 7-4

Figure 7-2 Results of Incremental Dynamic Analysis ......................... 7-6

Figure 7-3 Transforming results of IDA to a collapse fragilitycurve ................................................................................. 7-10

Figure 7-4 Global force-displacement relationship in the SPO2IDA

space ................................................................................. 7-12

Figure 7-5 Sample SPO2IDA results for the example of

Figure 7-4 ......................................................................... 7-13

Figure 8-1 Photograph of the example building .................................. 8-2

Figure 8-2 Schematic structural framing plan for example building

(no scale) ............................................................................ 8-2

Figure 8-3 Elevation of typical steel moment frame for example

building (no scale) .............................................................. 8-3

Figure 8-4 Spectral accelerations for Bin I ground motions ................ 8-4

Figure 8-5 Spectral accelerations per the Chiou-Youngs NGA

relationship forWM =7, r= 1 km, strike-slip faulting

and30v = 760 m/s, and varying as 0.47 T ........................ 8-6

Figure 8-6 Spectral accelerations for Bin S1 ground motions, 16th,

50th and 84th percentiles of spectral acceleration and the

11 target spectral ordinates for Bin S1 motions ................. 8-7

Figure 8-7 Sixteenth, 50th and 84th percentiles of spectral

acceleration for Bin S1 motions and demands predicted

by the Chiou-Youngs NGA relationship ............................ 8-7

Figure 8-8 Screen capture from USGS ground motion calculator for

generating a one-second hazard curve for the site of the

building .............................................................................. 8-8

Figure 8-9 One-second seismic hazard curve ...................................... 8-8

Figure 8-10 Seismic hazard curves for the site of the building .............. 8-9

Figure 8-11 Characterizing seismic hazard for time-based

assessment ........................................................................ 8-11

Figure 8-12 Target spectral ordinates for Bins T1 through T8 and

spectra for scaled ground motions in Bins T1 and T8 ...... 8-11

Figure 8-13 PACT Input Hub .............................................................. 8-20


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ATC-58 List of Figures ix

Figure 8-14 PACT General Info Screen .............................................. 8-21

Figure 8-15 PACT Building Information Screen ................................ 8-22

Figure 8-16 PACT Performance Group Quantity Screen (s) ............... 8-23

Figure 8-17 PACT View Analysis Cases Screen................................. 8-25

Figure 8-18 PACT Intensity and Scenarios Based Loss Screen .......... 8-26

Figure 8-19 PACT Time-Based Assessment Loss Screen ................... 8-27

Figure A-1 Probability mass function indicating the probability

of n numbers of heads-up outcomes in four

successive coin tosses ....................................................... A-4

Figure A-2 Distribution of possible concrete cylinder strengths for

a hypothetical mix design ................................................. A-5

Figure A-3 Calculation of probability that a member of thepopulation will have a value within a defined range ........ A-6

Figure A-4 Probability density function plots of normal distributions

with mean values of 1.0 and coefficients of variation of

0.1, 0.25 and 0.5 ................................................................ A-7

Figure A-5 Cumulative probability plots of normal distributions

with coefficients of variation of 0.1, 0.25, and 0.5 ........... A-8

Figure A-6 Probability density function plots of lognormal

distributions with median values of 1.0 and dispersions

of 0.1, 0.25 and 0.5 ........................................................... A-9

Figure A-7 Cumulative probability plots of lognormal distributions

with median values of 1.0 and dispersions of 0.1, 0.25,

and 0.5 ............................................................................... A-9

Figure C-1 Fragility specification for post-1994 welded steel

moment frame ..................................................................C-11

Figure C-2 Fragility specification for exterior wall with structural

sheathing and cement plaster ........................................... C-12

Figure C-3 Fragility specification for interior wall with wood studs

and gypsum board sheathing ............................................C-13

Figure D-1 Fragility for interior partitions .......................................... D-1

Figure D-2 Fragility for unitized glazed curtainwall ........................... D-2

Figure D-3 Fragility for suspended acoustic ceiling systems .............. D-3

Figure D-4 Fragility for gypsum ceiling on wood joists ..................... D-4


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x List of Figures ATC-58

Figure D-5 Fragility for concrete tile roofs.......................................... D-5

Figure D-6 Fragility for hydraulic elevators ........................................ D-6

Figure D-7 Fragility for roof-mounted mechanical equipment ........... D-7

Figure D-8 Fragility for miscellaneous housewares and art objects .... D-8

Figure D-9 Fragility for home entertainment equipment ..................... D-9

Figure D-10 Fragility for desktop computer equipment............................ D-10

Figure D-11 Fragility for servers and network equipment .................. D-11

Figure D-12 Fragility for tall filing cabinets ....................................... D-12

Figure D-13 Fragility for unanchored bookcases ................................ D-13

Figure E-1 Site-to-source distance definitions (Abrahamson and

Shedlock, 1997)................................................................. E-3

Figure E-2 Fault rupture directivity parameters (Somerville et al.,

1997) ................................................................................. E-4

Figure E-3 Steps in probabilistic seismic hazard assessment

(Kramer, 1996) .................................................................. E-6

Figure E-4 Source zone geometries (Kramer, 1996) ........................... E-7

Figure E-5 Variations in site-to-source distance for three source

zone geometries (Kramer, 1996) ....................................... E-7

Figure E-6 Conditional probability calculation (Kramer, 1996) ......... E-9

Figure E-7 Seismic hazard curve for Berkeley, California

(McGuire, 2004) .............................................................. E-12

Figure E-8 Sample de-aggregation of a hazard curve (from

www.usgs.gov) ................................................................ E-15

Figure E-9 Sample geometric-mean response spectra for

negative-, zero- and positive- record sets with each

record in the sets scaled to a) (0.8 )a

S s = 0.5 g and

b) (0.3 )aS s = 0.5 g (Baker and Cornell 2006) ................. E-16

Figure E-10 UHS for a 2% probability of exceedance in 50 years

and original and scaled CMS for a rock site in

San Francisco .................................................................. E-18

Figure E-11 Analysis for soil foundation structure interaction

(FEMA, 2005) ................................................................. E-21


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ATC-58 List of Figures xi

Figure E-12 Reductions in spectral demand due to kinematic

interaction ........................................................................ E-24

Figure E-13 Calculation of spectral accelerations given a lognormal

distribution ....................................................................... E-26

Figure F-4 Illustration of (a) fragility function, and (b) evaluatingindividual damage-state probabilities ................................ F-2

Figure F-2 Form for soliciting expert judgment on component

fragility ............................................................................ F-13

Figure G-1 Generation of vectors of correlated demand parameters

(Yang 2006) ...................................................................... G-3

Figure G-2 Relationships between demand parameters ...................... G-4

Figure G-3 Joint probability density functions .................................... G-5

Figure H-1 Idealized incremental dynamic analysis presentingtransient and residual story drift ratios.............................. H-3

Figure H-2 Idealized response characteristics for elastic-plastic (EP),

general inelastic (GI) and self-centering (SC) systems ..... H-3

Figure H-3 Idealized model to estimate residual story drift from

peak transient drift ............................................................ H-6


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ATC-58 List of Tables xiii

List of Tables

Table 4-1 Recommended Default Peak Population Models .............. 4-4

Table 4-2 Example Fragility Groups for Moment-resisting Steel

Frame Office Structure ...................................................... 4-8

Table 5-1 Representations of Seismic Hazard for Intensity-

Based assessments ........................................................... 5-10

Table 4-3 Example Performance Groups and Quantities for

3-story, Moment-resisting Steel Frame Office Structure .. 4-9

Table 5-1 Representations of Seismic Hazard for Intensity-Based

Assessments ....................................................................... 5-8

Table 6-1 Default descriptions and values for c ............................. 6-7

Table 6-2 Default descriptions and values for q

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

Table 6-3 Default Dispersions for Record-to-Record Variability,

Modeling Uncertainty and Ground Motion Variability ..... 6-9

Table 6-4 Story-Drift and Floor-Acceleration Correction Factors .. 6-19

Table 7-1 Sample probabilities that the specified portion of a

building will be involved in the collapse ......................... 7-14

Table 8-1 Seed Ground Motions for Response-History Analysis ...... 8-4

Table 8-2 Spectral Demand Per the Chiou-Youngs Relationship ...... 8-5

Table 8-3 Mean Hazard Curve ......................................................... 8-10

Table 8-4 Spectral Accelerations and MAFE (i

) for Boundaries

on the Seismic Hazard Curve........................................... 8-12

Table 8-4 Spectral Accelerations and MAFE (i

) for Boundaries

on the Seismic Hazard Curve........................................... 8-13

Table 8-6 Demand Parameters for Intensity-Based Assessment...... 8-14

Table 8-7 Demand Parameters for Scenario-Based Assessment ..... 8-15

Table 8-8 Demand Parameters for Time-Based Assessment ........... 8-16

Table B-1 Default Fragility Groups .................................................... B-3


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xiv Contents ATC-58

Table B-2 Default Assignment Commercial Office ......................... B-45

Table B-3 Default Assignment Multi-family Residential ................ B-45

Table B-4 Normative Quantities for Commercial Office

Occupancies .................................................................... B-46

Table B-5 Normative Quantities for Residential Occupancy .......... B-46

Table B-6 Default Time of Day and Day of Week Population

Variations (relative to Expected Peak Population) for

Office and Residential Occupancies ............................... B-47

Table B-7 Monthly Population Variations (Relative to Expected

Peak Population) for Office and Residential

Occupancies .................................................................... B-48

Table C-1 Classification System for Vertical Seismic Framing

Systems ............................................................................. C-5

Table C-2 Classification System for Horizontal Seismic Framing

Systems (Diaphragms) ...................................................... C-9

Table C-3 Classification System for Gravity Framing Systems ...... C-10

Table E-1 Ground Motion Attenuation Relationships ....................... E-2

Table E-2 Values ofi for Generating a Distribution of ( )aiS T .... E-26

Table F-1 Values of z....................................................................... F-10

Table F-2 Parameters for Applying Peirce's Criterion ..................... F-16

Table F-3 Critical Values for the Lilliefors Test .............................. F-17

Table F-4 Fragility Function Quality Level...................................... F-19

Table G-1 Matrix of Demand Parameters, X ................................... G-4

Table G-2 Mean and Variance ofX ................................................. G-4

Table G-3 Demand Parameters, Y .................................................... G-6

Table G-4 Matrix YD

for the Sample Problem ................................. G-6

Table G-5 MatrixYY

R for the Sample Problem ................................ G-7

Table G-6 MatrixY

L for the Sample Problem .................................. G-8

Table G-7 Matrix of Simulated Demand Parameters

(first 10 vectors) ................................................................ G-9


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ATC-58 Contents xv

Table G-8 Ratio of Simulated to Original Logarithmic Means ......... G-9

Table G-9 Ratio Of Entries in Simulated and OriginalYY

R

Matrices ............................................................................ G-9

Table H-1 Damage states for residual story drifts ............................. H-8

Table H-2 Sample transient story drift ratios, / h , associated

with the residual story drift damage states of Table H-1 .. H-9


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ATC-58 Glossary xvii

Glossary

Annualized loss over a period of many years, the average annual value of

loss,

Casualties loss of life, or serious injury to persons, typically requiring

hospitalization

Component one of many parts, structural and nonstructural, that together

comprise a building

Consequence function - a relationship that indicates the conditional

probability of incurring loss as a function of building damage

Correlation - a mathematical relationship that defines the extent that the

value of one parameter is dependent on the value of one or more otherparameters

Damage function for a specific damage state, a detailed description of the

significant effects of the damage in terms of what is damaged, the repair

actions that it necessitates, the effect on occupancy, and the effects that could

result in casualties

Damage State an extent of damage associated with a particular building

component and damage function.

Demand a parameter, such as floor (ground) acceleration, component

deformation, story displacement, floor (ground) velocity, or component force(stress) that is correlated with the occurrence of damage to one or more

components

Discount rate a factor used to indicate the time-value of money in

economic analysis

Downtime the amount of time, following an earthquake, that a building

cannot be used for its normal intended function

Earthquake Scenario - a specific earthquake event, defined by a magnitude

and geographic location

Fragility Functiona mathematical function that indicates the conditional

probability of incurring damage associated with a particular damage state as

a function of a demand parameter

Fragility Group the set of building components that can be assigned the

same fragility specification


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xviii Glossary ATC-58

Fragility Specification a detailed description of damage states, damage

functions and fragility functions associated with a particular type of

component or collection of componentsGeomean abbreviation of geometric mean. In characterization of ground

motion intensity, the square root of the product of the value of a ground

motion parameter in each of two orthogonal directions

Intensity the severity of ground shaking as represented by a 5%-damped,

elastic acceleration response spectrum

Intensity-based Assessment an assessment of a buildings probable

performance given that the building is subjected to a specific intensity of

ground shaking

Net present value the present value of one or more expenditures incurred

or benefits received in the future, discounted for the time value of moneyNon-structural Component a building component that is not part of thestructural system

Performance the consequences of a buildings response to earthquake

shaking expressed in terms of the probable number of casualties, downtime

and direct economic loss.

Performance group the subset of components within a fragility groupthat

will experience the same demand and which will produce similar

consequences

Realization - one possible outcome of a particular earthquake scenario or

intensity including a unique set of demands, damage and consequences

Repair cost the cost, in present dollars, necessary to restore a building to

pre-earthquake condition, or in the case of total loss, to replace the building

with a new structure of similar type.

Return on investment the annual income that can be derived from an

investment divided by the value of the investment

Scenario-based Assessment an assessment of a buildings probable

performance given that the building is subjected to a specific earthquake

scenario

Structural Component a building component that is part of the intended

vertical or lateral force resisting system, or that provides measurable

resistance to earthquake-induced building deformations

Time-based Assessment an assessment of probable building performance

over a specified period of time, considering all earthquake scenarios that

could occur during that period of time, and the probability of occurrence of

each.


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ATC-58 1: Introduction 1-1

Chapter 1

Introduction

1.1 Purpose

This report describes a basic methodology and recommended procedures to

assess the probable earthquake performance of individual buildings based on

their unique site, structural, nonstructural and occupancy characteristics. It

was developed as a product under a contract between the Applied

Technology Council (ATC) and the Federal Emergency Management

Agency (FEMA) to develop next-generation Performance-Based Seismic

Design Guidelines for buildings, termed the ATC-58 Project. The program

for developing this and other products is defined in the FEMA 445 report,

Next-Generation Performance-Based Seismic Design Guidelines, Program

Plan for New and Existing Buildings (FEMA, 2006). As currently

envisioned, future products may include publications that suggest appropriate

performance characteristics for buildings of differing occupancy and use;

procedures to design new buildings or upgrade existing buildings to obtain

desired performance; and publications intended to assist design professionals,

building regulators, developers, owners, tenants, lenders, insurers and other

stakeholders to take advantage of the benefits of performance-based design

approaches.

1.2 The Performance-Based Design Process

Performance-based design is a process that explicitly considers building

performance in the design process. This is in contrast to the typical building

design process in which building components and systems are proportioned

and detailed to satisfy prescriptive criteria contained within the building code

without direct consideration of the buildings performance. In the

performance-based design process, the designers and other stakeholders

jointly identify the desired building performance characteristics at the outset

and these performance goals then guide the many design decisions that must

be made. Figure 1-1 illustrates the key steps in the performance-baseddesign process.

The process initiates with selection of one or more performance objectives.

Each performance objective is a statement of the acceptable risk of incurring

damage or loss for identified earthquake hazards. Building

developers/owners, design professionals, and building officials will typically

participate in the selection of performance objectives, and may also consider


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1-2 1: Introduction ATC-58

the needs and desires of a wider group of stakeholders. These can include

prospective tenants, lenders, insurers and others who have impact on a

buildings value, but who generally do not have an opportunity to participate

in the design process directly.

Figure 1-1 Performance-based design flow diagram

Next, design professionals must develop a preliminary design to a sufficient

level of detail to allow determination of the buildings performancecharacteristics. For new buildings, this will include, as a minimum,

identification of: (1) the location and characteristics of the site; (2) building

size, configuration and occupancy; (3) type, location and character of

finishes and nonstructural systems; and (4) estimates of the strength, stiffness

and ductility of the structural system. In the case of existing buildings, these

characteristics are already defined, and it is only necessary to determine what

they are, and then define preliminary concepts for retrofit measures, if

needed.

Performance assessment (the shaded box in Figure 1-1) is the process used to

determine if a design is capable of achieving the desired performance

objectives. In this step, which is the subject of these Guidelines, the engineer

conducts a series of simulations (analyses) to predict the buildings response

when subjected to the earthquake hazards identified as part of the

performance objectives. Following performance assessment, the engineer

compares the predicted performance with the desired performance. If the

assessed performance matches or exceeds the stated performance objectives,


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the design is adequate and the project can be completed. If the assessed

performance does not meet the performance objectives, the engineer revises

the design, or alters the performance objectives in an iterative process, until

the assessed performance meets the desired objectives.

1.3 Guideline Uses

These Guidelines can be used by engineers for performance-based seismic

design or retrofit of buildings, as described in Section 1.2. The methodology

and procedures presented herein can also be used in the following ways:

Engineers can determine the probable performance of buildings (e.g.,probable maximum loss, business continuity, life safety protection) in

support of real estate transactions and occupancy decisions.

Building product suppliers can determine the seismic performancecapability of their products.

Building code developers can determine the performance consequencesof building code requirements to guide the improvement of these

requirements

Researchers can identify areas where additional building performanceresearch is needed.

Educators can use this informationas instructional materials inearthquake engineering curricula.

Software developers can develop applications that implement theperformance assessment methodology either coupled with, or

independent of, structural analyses

1.4 Application

These Guidelines present a general methodology for seismic performance

assessment of individual buildings and one set of recommended procedures

to implement this methodology. Nothing contained in these Guidelines is

intended to prevent or discourage the use of alternative procedures that

produce unbiased assessments of probable building performance, and that

appropriately consider and portray the uncertainties inherent in the

assessment of future building performance.

The methodology and recommended procedures presented herein can be

applied to the performance assessment of any building type, regardless of

age, construction type or occupancy. However, application requires basic

data on structural and nonstructural component fragilities and the

consequences of component damage in terms of potential casualties, repair


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costs, and downtime. The data required is dependent on structural system

type; the specific details of construction; the type, location and means of

installation of nonstructural components and systems; and building

occupancy and use. Sources of such data can include laboratory testing of

individual building components, analytical evaluation, statistical information

on the actual performance of buildings in past earthquakes, and expert

judgment.

At the present time, the availability of such data is limited. This report

includes a set of such data gathered by the project development team. This

data set is sufficient to allow performance assessment of buildings with the

following structural systems:

light wood frame, moment-resisting steel frame, moment-resisting concrete frame, braced steel frame, concrete shear wall, and masonry shear wall construction;and conforming to one of the following occupancies:

commercial office, education (k-12), general hospital, hotel/motel, multi-family residential, research, retail, and warehouse uses.In order to perform assessments of buildings of other construction types or

occupancies, it may be necessary to obtain additional fragility andconsequence data. These Guidelines include recommended procedures for

deriving such data.

1.5 Performance Calculations

Companion software, termed thePerformance Assessment Calculation Tool

(PACT) accompanies this report. PACT includes databases of typical


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component and contents inventories, fragility and consequence data for

buildings of the construction types and occupancies described above. PACT

also automates the repetitive calculations necessary to assess probable

building performance as described later in this report. Individual users can

enhance, expand and modify the PACT databases using routines embedded

within the PACT software. In addition, for individual building assessments,

users can modify default values obtained from the databases with building-

specific values. PACT is provided as a developmental tool and to facilitate

implementation of the recommended procedures. As currently planned,

PACT will not be maintained by either the Applied Technology Council or

the Federal Emergency Management Agency, however, its code is open

source and available for use as the basis of either individually maintained or

commercially developed software.

1.6 Guideline Organization

Chapter 2 introduces the building performance measures used in these

guidelines and the uncertainties associated with performance assessment. It

also describes some ways to use the information obtained from performance

assessments to guide decision making processes. Chapter 3 presents the

general performance assessment methodology. Chapters 4 through 8

introduce a set of recommended procedures to implement this methodology.

Chapter 4 provides an overview of these procedures. Chapter 5 presents

detailed information on representation of seismic hazards for use in these

procedures. Chapter 6 presents recommended methods of structural analysis

for performance assessment. Chapter 7 presents analytical procedures fordetermining the collapse fragility of individual buildings. Chapter 8 presents

example applications of these procedures to representative buildings.

Appendices to this report present background information that may be useful

for some readers. Appendix A provides a basic tutorial on probability and

statistics and the types of probabilistic distributions used to represent

uncertainty in these performance assessment procedures; Appendix B lists

the types and default quantities of nonstructural components and contents

contained in the PACT databases for the several building occupancy types; as

well as the building population models for each of these occupancies;

Appendix C contains the structural system and Appendix D the nonstructural

component fragility specifications contained in the PACT databases;

Appendix E provides detailed information on seismic hazard evaluation and

attenuation relationships; Appendix F summarizes methods for development

of fragility functions for structural and nonstructural components; Appendix

G describes the mathematical procedure used by PACT to derive earthquake


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response realizations; and Appendix H provides background on assessment

of residual story drift.

A separate PACT users manual provides instructions on running the

electronic performance assessment calculation tools (PACT).

1.7 Limitations

This report provides a general methodology and recommended procedures to

assess the probable performance of individual buildings when subjected to

future earthquake shaking. Specifically, the methodology assesses the

likelihood that building structural and nonstructural components and systems

will be damaged by earthquake shaking, and estimates the potential

casualties, repair costs, and interruption of beneficial building occupancy that

could occur as a result of such damage.

Earthquake shaking can cause other significant effects including loss ofoffsite power, water and sewage, initiation of fires, inundation, and release of

hazardous materials. Similarly, earthquake effects other than ground shaking

including ground fault rupture, landslide, liquefaction, seiches and tsunamis,

and lateral spreading can significantly affect building performance.

While these effects can have significant impact on earthquake losses and the

general methodology presented in this report could be used to assess these

effects, assessment of these losses is beyond the scope of the recommended

procedures contained in this report. When conducting seismic performance

assessments of buildings using these procedures engineers should, as a

minimum perform qualitative evaluation of these other effects, and, if these

effects appear significant, report this.

Assessment of the probable performance of a building in future earthquakes

inherently entails significant uncertainty. The methodology and procedures

presented herein use state of art methodologies to assess future building

earthquake performance with explicit consideration of these uncertainties.

Regardless, it is possible that the performance of individual buildings in

actual earthquakes may either be better or worse than indicated by

assessments conducted in accordance with the procedures presented herein.

Further the accuracy of performance assessments depends in large part on

data and calculations generated by individual users. Neither the Federal

Emergency Management Agency, the Applied Technology Council, their

employees, nor their consultants, present any warranty expressed or implied

as to the accuracy of performance assessments made using these procedures.


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ATC-58 2: Performance Measures 2-1

Chapter 2

Performance Measures

2.1 Introduction

The methodology presented in these Guidelines uses three fundamental

measures of earthquake performance:

casualties defined as deaths and serious injuries that would normally

require hospilization

repair cost defined as the cost of repairing or replacing damaged

buildings, and their contents

downtime defined as the period of time during which a building is not

useable for its intended purpose or function as a result of earthquake-

induced damage

It is impossible to precisely quantify the losses that a building will

experience in future earthquakes, before events actually occur. The

methodology, therefore, expresses performance using probabilistic measures.

2.2 Factors Affecting Performance

Building earthquake performance is dependent on:

the intensity of ground shaking and other seismic hazards at the buildingsite;

the manner in which the building responds to the ground shaking and

other hazards, and the amount of force, deformation, acceleration and

velocity experienced by the various structural and nonstructural

components, contents and occupants

the vulnerabiltiy of the building and its systems to damage;

the number of people, their location in the building, and the type,

location and amount of contents present when the earthquake occurs;

the actions people take in response to the damage that occurs.

2.3 Uncertainty in Performance Assessment

Each of the individual factors that affect seismic performance is difficult, if

not impossible, to predict precisely. For example, it is not presently possible

to determine which fault the next earthquake will originate on, where along

the fault the surface the rupture will initiate, or what magnitude it will be, let


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2-2 2: Performance Measures ATC-58

alone the direction in which the fault rupture will propagate or the exact

character of the ground shaking that will result at a particular site. Similarly,

it is not possible to predict the day of the week or time of day at which the

earthquake will occur, which tenants and people will be present in the

building, what contents and furnishings they may have within the building,

what condition the building will be in, or the economic conditions that will

prevail at the time of the earthquake. The result of these uncertainties and

many others is that it is not possible to predict precisely the losses that will

occur, whether casualties, repair costs or downtime.

Although these uncertainties make it impossible to make a precise

assessment of building performance, in terms of a specific number of

casualties, repair cost or time of occupancy interruption, it is possible to

assess these performance measures in the form of probability distributions

that indicate the probability that losses of specified or larger magnitude will

be incurred. The methodology and procedures presented in this reportdescribe the means of determining these loss probability distributions.

Each step in the performance assessment process entails uncertainty. The

primary steps and the associated uncertainties are defined below.

Building Definition. In order to assess a buildings future performance it is

necessary to completely define the state the building will be in at the time the

earthquake occurs. This includes the configuration, strength, and detailing of

its structural elements; the location, make, model number, and means of

installation of each of the nonstructural components and systems; the

location, value and means of installation of all the buildings contents, and

the location of all people within the building.

Even if the drawings and specifications for a building are available, these

only define the specified, rather than actual building construction. Structural

drawings define the intended strength and ductility of the structural system.

Variability in material strength, workmanship, inspection, and condition can

result in a structure that is either more or less vulnerable to earthquake

effects. Similarly, nonstructural components will be described on the

drawings as to type and size, however, the make and model number of

individual items likely will not be described. Further, these components maybe anchored and braced to the structure or not. Even if they are initially

installed with appropriate bracing and anchorage, over the years, as tenants

make modifications to these systems, they may either improve or reduce the

effectiveness of these measures. As different tenants move in and out of a

building, they will change the configuration of ceilings, lighting systems,

partitions, and other features. Some tenants will have high value contents


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and others will not. Some tenants will have persons present in a building 24

hours a day, seven days a week, while other buildings will be occupied only

a few hours a week.

Uncertainty in building definition can be reduced by obtaining a set of

updated drawings and specifications for the building, performing surveys toassure that the inventory of components and their means of installation are

understood; performing materials testing to quantify the strength of structural

materials, and interviewing tenants to determine their patterns of occupancy

and the value of their contents.

Intensity of Earthquake Effects. The more intense the earthquake effects at a

site, the more damage and loss is likely to occur. These Guidelines focus

principally on earthquake performance associated with ground shaking,

though other earthquake effects including landslide and liquefaction could

also be considered. Earth scientists and geotechnical engineers useattenuation relationships to predict the intensity of ground shaking at a site

from future earthquakes. These attenuation relationships predict the

amplitude of spectral response acceleration at various structural response

periods, as a function of earthquake magnitude, fault and rupture

characteristics, distance of the rupture surface from the site, and the geologic

and soil conditions along the path of travel of earthquake energy from the

fault to the site and at the site and other factors. Seismologists develop

attenuation relationships by performing statistical analysis on data sets of

ground motion recordings obtained in past earthquakes with known rupture

characteristics, at sites having known geotechnical conditions and distancefrom the fault ruptures. The factors used in the statistical analysis do not

correlate perfectly with the recorded motions and as a result, even if the exact

magnitude, fault rupture type, distance, and soil conditions associated with a

specific site and earthquake are known, actual ground motions recorded at a

particular site may be somewhat more or less intense than predicted by the

statistical fit to the data. To account for this, modern attenuation

relationships incorporate an error term that indicates the possible variability

of actual motions from those predicted by the relationship. This form of

uncertainty cannot be reduced, except by improvement of the ground motion

prediction equations that reduce their inherent error. Appendix E providesmore information on this topic.

Structural Response. The amount of damage a structure will incur when it is

subject to a particular ground motion is, in part, a function of the buildings

response, that is, how much it displaces and how much stress and

deformation are induced in its various elements. This is a function of the

strength of the individual elements and their connections, the overall strength


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and stiffness of the structural system, its configuration, and detailing. It is

also quite dependent on the spectral shape of the shaking that affects the

structure and the exact character of the ground motion, as represented by an

accelerogram.

Engineers use structural analysis to predict the response of a structure toground shaking. To perform this analysis, it is necessary to build a

mathematical model that represents the structures important response

properties including stiffness, strength and hysteretic behavior. Since the

precise strength, stiffness and ductility of real structural elements in a

building are never known with a certainty, due to inherent variability in

materials and workmanship, the models used to predict structural response

typically incorporate errors that may either over predict or under predict the

buildings actual response.

Even with perfect models, which never exist, some methods of analysis arebetter at predicting response than others. Nonlinear response history

analyses that use appropriate ground shaking records and models that

accurately represent the structures characteristics can provide excellent

estimates of response. Linear static procedures using coarse elastic spectra

as the basis for loading often provide inaccurate assessments of response.

Even the best models and most sophisticated analytical procedures cannot

produce accurate assessments of response if the characteristics of the ground

motion are not accurately represented in the loading. Thus, structural

analysis may either under- or over-predict the true strength and deformation

demands experienced by structural elements.

Damage. These procedures predict the amount of damage that occurs to

structural and nonstructural elements using the value of peak demand

parameters, including acceleration, drift, plastic rotation and element force,

obtained from structural analysis. Laboratory data, and where such data s

unavailable, judgment is used to project the level of demand at which

damage of different types will occur. However, even if laboratory data is

available, test specimens seldom precisely represent the actual components in

a building or the boundary conditions that the building places on the

components; nor do loadings applied in the laboratory closely resemble the

actual shaking demands placed on building components during earthquakes.

As a result, even if the demands predicted by analysis are exact, we may over

or under-predict the amount of damage that occurs. When judgment, rather

than laboratory data is used to determine the demand levels at which damage

occurs, even greater is inaccuracy is likely.


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Loss. The amount of loss that occurs as a result of damage is dependent on a

number of factors. These include:

Casualties the number of people present at the time of the earthquake,

their locations in the building, whether debris falls towards or away from

them, and the actions they take as the building shakes

Repair Costs the means used to repair the building, the efficiency of the

contractor, the availability of labor and materials and the contractors

desire for profit

Downtime whether the building is red or yellow tagged, by post-

earthquake inspectors; the owners efficiency in retaining consultants and

contractors; whether or not the building is occupied while repairs are

made

The methodology and procedures presented herein attempt to account for

each of these uncertainties and others, and rigorously portray their effect on

the probable value of losses.

2.4 Types of Performance Assessment

The methodology and procedures can be used to develop three types of

performance assessment: intensity-based, scenario-based and time-based.

2.4.1 Intensity-Based Assessments

Intensity-based assessments provide a distribution of probable losses, given

that the building experiences a specified intensity of shaking. Groundshaking intensity is represented by a 5% damped, elastic acceleration

response spectrum. Intensity could also include representation of permanent

ground displacements produced by fault rupture, landslide, liquefaction, and

compaction/settlement, although procedures for doing this are not included

herein. This type of assessment could be used to answer such questions as:

What is the probability that repair cost will be greater than $1million, if

the building experiences ground motion represented by a smoothed

spectrum with a peak ground acceleration of 0.5 g?

How long is the building likely to be closed for occupancy if itexperiences ground shaking matching the design spectrum contained in

the building code?

What is the probability of incurring one or more casualties, if the

building experiences a ground motion with intensity corresponding to the

maximum considered earthquake spectrum described by the building

code?


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The results of intensity-based performance assessment are cumulative

probability distributions that express the probability that loss will exceed

various values, given that the building experiences a particular intensity of

shaking. Figure 2-1 presents four such cumulative probability distributions

for repair cost for a hypothetical building. Each of the four curves plotted in

the figure represents the distribution of possible loss for different intensity

levels, labeled I1 through I4, where I1 represents the lowest intensity and I4

the highest. In the figure, the probability that total repair costs exceed a

specified value of total repair cost (trc) is plotted as a function of total repair

cost. For shaking intensity I4, the figure shows a 50% probability that repair

cost will exceed $1.8million and a 10% probability that repair cost will

exceed $3.5 million. For intensity I1, there is a 50% probability that repair

cost will exceed $0.6million and only a 10% chance it will exceed $0.9

million.

0 1 2 3 4 5 6 7 8 9 10Total repair cost (trc), Million dollars

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(TRC

trc)

I1

I2

I3

I4

Figure 2-1 Example cumulative probability loss distributions for ahypothetical building at four ground motion intensities

The results of intensity-based performance assessments can also be presented

as complementary distribution curves. Complementary distributions present

the probability that loss will be less than a given value. Figure 2-2 plots the

same data shown in Figure 2-1 except in complementary form.


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0 1 2 3 4 5 6 7 8 9 10Total repair cost (trc), Million dollars

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(TRC

trc)

I1

I2

I3

I4

Figure 2-2 Example complementary cumulative probability distributions for

loss at four ground motion intensities

2.4.2 Scenario-Based Assessments

Scenario-based performance assessments provide distributions of possible

loss, given that the building experiences a specific earthquake scenario,

defined as a combination of earthquake magnitude and distance of the

building from the fault on which the earthquake occurs. This type of

assessment can be used to answer the following types of questions:

What is the probable maximum loss (repair cost with a 10% chance of

exceedance) if there is a magnitude 6.5 earthquake on a fault located 10

miles from the building site?

What is the likelihood of casualties in a building, if we experience a

repeat of a historic event (e.g. 1811-12 New Madrid, 1964 Anchorage,

1906 San Francisco)

Scenario assessments may be useful for decision makers with buildings

located close to one or more known active faults. Scenario-based assessments

are very similar to intensity-based assessments except that uncertainty in the

earthquake intensity, given the scenario, is considered. The results of

scenario-based assessments aresingle cumulative or complementary loss

distributions, such as one of the loss curves in either Figure 2-1 or Figure 2-

2. Such curves show the probability that loss will either be more or less than

different values, given that the building is subjected to the effects of the

particular scenario earthquake.


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2.4.3 Time-Based Assessments

Time-based performance assessments provide a distribution of probable

earthquake loss, considering all earthquakes that may affect the building in a

given time period, and the probability of occurrence of each. Time-based

assessments can be used to answer the following types of questions:

What is the probability that my building will experience repair costs with

a net present value exceeding $3,000,000 in the next 30 years?

What is the chance, during any year, of incurring interruptions of

occupancy in my building that exceed 30 days?

What is the probability of having at least one earthquake-caused casualty

in my building over a fifty-year period?

For time-based assessments earthquake-intensity is described by a seismic

hazard curve, which plots the relationship between earthquake intensity, e,

and the mean annual probability of exceedance ofe, ( )e . To form time-

based assessments, a series of intensity-based assessments are performed at

for a series of intensities of earthquake shaking that span the intensity range

of interest and are then integrated (summed) over the hazard curve to

construct an annualized loss curve of the type shown in Figure 2-3. This

curve shows for example, that for the hypothetical building, there is

approximately a 0.2% chance per year that an earthquake will produce repair

costs exceeding $1.5 million.

0 0.5 1 1.5 2 2.5 3 3.5 4Total repair cost (trc), Million dollars

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Annualrateofexceedingtrc

Figure 2-3 Distribution of mean annual total repair cost

Using such curves, it is possible to compute a mean annual loss, sometimes

called an average annualized loss, by integrating the area under the loss


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curve. For this example, the annualized loss is $37,900. While it is not

actually expected that an earthquake producing $37,900 of loss will occur

each year, in theory, if the owner of the building could self-insure, by placing

this amount of money in an interest bearing account each year, over a very

long period of time, he should be able to pay for any actual earthquake repair

costs using the money in this account. In essence, the annualized loss for

repair costs represents the premium that one should be willing to pay for an

insurance policy. In reality, insurance companies will not charge this amount

for insurance premiums. This is because they rarely actually calculate the

annualized loss for a building and even if they did, can spread their risks over

a large number of buildings, under-charging for some policies, and over-

charging for others. Also, insurance companies must cover their

administrative costs and want to make a profit, and must operate in a

competitive environment that affects the prices they can charge.

Nevertheless, annualized loss can be a valuable tool to assess the value of

insurance as well as other uses. Section 2.5 illustrates additional uses for the

data provided by performance assessments.

2.5 Use of Loss Distributions in Decision-making

A diverse group of stakeholders and decision-makers have impact on

selection of the appropriate seismic performance objectives for both new and

existing buildings. These include owners/developers, building officials,

tenants, lenders, insurers and design professionals. Different decision-

makers may use very different decision processes to determine acceptable

building performance. The loss distributions generated by these performanceassessment procedures can be used in different ways to satisfy the needs of

these different decision-makers.

2.5.1 Typical Building Performance

Many building officials, owners/developers and design professionals will

choose performance equivalent to that expected of a typical building

designed in conformance with the building code as the minimum acceptable

performance objective for a performance-based design. Life safety protection

is often the primary concern. In the past, life safety was often considered an

absolute goal, with zero tolerance for life endangerment, regardless of how

low the risk. In reality, no building can be designed with zero risk of

earthquake-induced life loss. In order to use the procedures contained in

these Guidelines to obtain equivalent performance to that attainable by

typical code-designed buildings, it is necessary to determine the risk of life

loss for such buildings. Recently, in an effort associated with development

of national seismic hazard maps for use in the building codes, the Building


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April 15, 2009


Seismic Safety Councils Seismic Design Procedures Group set a life-safety

related goal for ordinary buildings conforming to Occupancy Category II as

defined in ASCE 7-05. This goal, relates to the probability of building

collapse as opposed to the probability of life loss. The Seismic Design

Procedures Group suggests that a conditional probability of collapse of 10%

given that the building is subjected to Maximum Considered Earthquake

shaking is an acceptable goal. For most sites in the United States, Maximum

Considered Earthquake shaking has an annual frequency of exceedance of 1

in 2,500 or 4x10-4 per year. When integrated with the hazard curve, this

typically results in an annual probability of collapse of approximately 0.001

per year.

The procedures used in this guideline can be used to determine the annual

probability of collapse for an individual building design, which can then be

compared with the values suggested by the Building Seismic Safety Council

as a means of demonstrating compliance with the capability of typicalbuildings. However, the procedures presented herein can also consider the

annual frequency of casualty generation, and in the process, provide more

collapse resistant design for buildings with large occupancies, as intended by

the Occupancy Group requirements of the building code. In order to do this,

it will be necessary to determine the risk of life loss in typical code-

conforming buildings of different occupancies. This task is beyond the scope

of this document, but could be performed by individual users or building

code developers.

2.5.2 Probable Maximum Loss

Decisions regarding the degree of initial investment in seismic protection for

a new building and the appropriate level of retrofit for existing buildings can

be made with the aid of cumulative loss distributions or loss functions.

Figure 2-4 presents a sample loss function for a hypothetical building. It plots

the probability (y-axis) that the costs associated with post-earthquake repair

and/or replacement will be less than a dollar amount as function of the dollar

amount (x-axis). This particular loss curve presents the probability of loss

for a specific intensity of shaking with a return period of 475 years. Scenario

loss curves present the probability of loss for a particular earthquake

magnitude and distance. Annualized loss curves present the frequency of

loss considering all earthquakes that might occur and the probability of each

such earthquake.

The shape of the loss function will vary as a function of earthquake intensity

and the vulnerability of the building to damage. Reducing the vulnerability of


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April 15, 2009


a new or retrofitted building will shift the curve in Figure 2-4 to the left, such

that there is reduced risk of incurring loss.

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DV(capital loss, $M)

P(losses = (3-1)

where the term ( )P L l E e> = is the product of an intensity based assessmentfor intensity e . Equation (3-1) will generally be solved by numerical

integration.

In order to perform this integration, the spectral range of interest is divided

into n intervals, ie . The spectral range of interest will typically range fromvery low intensity that results in no damage, to very large intensity that

produces a high probability of collapse. The midpoint intensity in each

interval is Iie , and the annual frequency of earthquake intensity in the range

ie is j where the parameters ie , Iie and j are defined in Figure 3-5

for the sample hazard curve using n = 4. This small value forn is chosen for

clarity. In real time-based assessments, a much larger number, n, of

intensities will typically be necessary.

An intensity-based assessment is performed at each of the n midpoint

intensities, 1Ie through Ine , The number, n of intensities required toimplement this process will vary from structure to structure, and will depend

on the steepness of the hazard curve and the ability of the structure to survive

a wide range of ground shaking intensities. Earthquake intensity at intensity

1Ie is assumed to represent all shaking in the interval 1e . The product of the

n intensity-based assessments is n loss curves of the type shown in Figure 2-

1. The annual probability of shaking of intensity Ije , j , is calculated


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ATC-58 3: General Methodology 3-15

directly from the seismic hazard curve. A sample calculation is shown in

Figure 3-5 for interval 1e for which 1 0.054 = . Figure 2-3 is constructed

by: (1) multiplying each loss curve by the annual frequency of shaking in the

interval of earthquake intensity used to construct the loss curve; and (2)

summing the annual frequencies for a given value of the loss.


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ATC-58 4: Implementation 4-1

Chapter 4

Implementation

4.1 Introduction

This chapter presents an overview of a recommended set of procedures that

can be used to implement the general methodology described in Chapter 3.

These are not the only acceptable implementation procedures. Other

procedures that appropriately account for the uncertainties inherent in

assessment of ground motions, structural response to these ground motions,

damage to structural and nonstructural systems and components given this

response, and the consequences of this damage are acceptable.

These procedures address three types of performance assessments:

Intensity-based assessments that indicate the probability of incurring

casualties, repair costs and occupancy interruption as a resulting from a

specific ground motion intensity, defined by a linear acceleration

response spectrum

Scenario-based assessments that indicate the probability of incurring

casualties, repair costs and occupancy interruption as a result of a

specific earthquake event, defined by a magnitude and site distance

Time-based assessments that indicate the probability of incurring

casualties, repair costs and occupancy interruption over a period of time,considering all earthquakes that could occur in that time, and the

probability that they will occur.

The procedures employed for each type of assessment have differences, as

defined in the sections below and Chapters 5, 6 and 7. As described in

Chapter 3, and illustrated in Figure 3-1, the basic steps contained in these

procedures include the following steps:

1. Assemble the building performance model. This is a systematic and

quantitative description of the building components and systems at risk,

of damage as a result of building exposure to earthquake effects, the

damage states that can occur to these systems and components, and the

time-dependent distribution of people exposed to injury in the building.

Section 4.2 provides guidelines on assembling building performance

models.


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4-2 4: Implementation ATC-58

2. Characterize the earthquake ground shaking hazard for which building

performance is to be assessed following the guidelines of Section 4.3 and

Chapter 5.

3. Perform structural analysis of the building for shaking as defined in step

2 following the guidelines of Section 4.4 and chapter 6.

4. Develop a collapse-fragility and a collapse mode-identification for the

building following the guidelines of Section 4.5 and chapter 7.

5. Based on the results of the structural analysis, form a series of

realizations. Each realization is one possible outcome of the buildings

response to earthquake shaking, developed as described in Section 4.6.

6. For each realization, determine:

o the damage sustained by the building as described in Section 4.7

o the repair/replacement costs per Section 4.8, the occupancyinterruption time per Section 4.9 and the casualties, per Section 4.10

7. For each of the individual performance measures (repair/replacement

costs, down time, and casualties), order the re

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