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HAZUS-MH MR1, Advanced Engineering Building Module

1. L4x3x 3 8 Sf 102 mm x 76 mm x 9 5 mm 13 mm 1 2 in Thk Doubler Plates 9 5 mm Typ 3 8 in 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 cost effective 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 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
2. oO iN 2 w 2 c O 2 Ke D O lt 0 2 O D oe 09 0 1 ro 12 18 24 30 36 42 48 Spectral Displacement inches Figure 8 20 Original Building and CO Retrofit Scheme Capacity Curves 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 indicat
3. 43 LOSS PUNCHONS js ssuxesvebsatiivh teed n See cay i EEE AAA N ene dia as 4 3 viii 43 1 Inventory Datas arroen eoor owes no e tea neees sz ae ee ea nceveren beues ne 4 3 Wd Ds Casualty Rates rar ren a Gite a E EEE taaeiys ney yee wae 4 6 4 3 3 Repair Cost Rates Loss Ratios o2s cccesceiveatesvyeyavnensavessevaneosasnan eves eins 4 7 4 3 4 Loss of Function and Recovery Time sssscssccsseerrrrrererreressrrrrrrreeeen 4 8 5 Development of Capacity Curves and Response Parameters esceeeeeee ence eens 5 1 5 1 Building Model and Pushover Criteria s 2cscuceeesceeciaveveysconessauexvieece wines ys ods 5 1 5 2 Development of Capacity Curve Control Points cc cece cece cece eee eee en ees 5 3 5 2 1 Conversion of Pushover Curve to Capacity Curve ceccceeceeee eee eee 5 3 5 2 2 Yield and Ultimate Capacity Control Points cece cece eens eee eee ee 5 5 5 3 Development of Response Parameters c cece ence ence eee eee eeeneeeaeeeaeeaee 5 7 5 3 1 Response Calculations sacskswarsiessayreaunswes tagensauyere ag ager p EE Ensete E SA 5 7 5 3 2 Elastic Damping Factors 2 scer scspep enana EEEE AE Ea Ne eee 5 10 5 3 3 Degradation PAClOIS sccrs seen nagar saneueascee des ee Gees heuatabense aucee Ea 5 10 5 3 4 Fraction of Nonstructural Components at Ground Level 0665 5 12 6 Development of Fragility Curvess 4 e505 teas uae ny geseas eocasy eens y decries m
4. N N 5 PAPS io ve i l i l Where w g mass assigned to the i degree of freedom Vip amplitude of pushover mode at i degree of freedom Typically the shape of the pushover mode is based on the I 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 1 mode shape may be used to calculate 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 factor in the commentary of the NEHRP Guidelines the modal factor O12 is defined by amplitude of the normalized pushover mode shape at the control point and the pushover mode participation factor E woe 1 f a 2 PEF kn ot 5 2 ae w io ip ve cpp i l Where w g mass assigned to the i degree of freedom Vip amplitude of pushover mode at i degree of freedom Opp amplitude of pushover mode at control point Typical
5. KL expressed as a fraction of nondegraded 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 amp 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 Le 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 Fyns of accelerationsensitive 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 ri
6. Mod Large Small Mod Large 0 2 0 4 0 6 0 2 0 4 0 6 0 2 0 4 0 6 Structural Systems with Very Small Capacity Curve Variability Be 0 1 Structure o s0 0 90 100 NSD oss 065 oso 075 oso 095 090 0 95 1 05 NSA 0 65 Structural Systems with Small Capacity Curve Variability Bo 0 2 Structure 0 60 0 65 0 80 0 70 oso oso 0 90 0 95 1 05 NSD oso 0 70 oso 075 085 095 095 100 1 10 Structural Systems with Moderate Capacity Curve Variability Be 0 3 Structure 0 60 0 70 oso 0 70 oso 090 0 95 1 00 11o nsp 0 60 0 70 oss 080 oss 0 95 095 105 115 Structural Systems with Large Capacity Curve Variability Be 0 4 Structure 0 60 070 0 85 0 75 oso 095 0 95 1 00 1 10 _ NSD oso 0 70 085 080 0 90 100 100 105 115 1 Building Systems include the Structure Nonstructural Drift Sensitive Components NSD and Nonstructural Acceleration Sensitive NSA components 6 18 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
7. 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 7 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 lsecond spectral response at the LACDPW Headquarters site 1 Peak Ground Acceleration 1 Second Spectral Acceleration Total Sierra Madre Total Sierra Madre Raymond Verdugo Verdugo uy 107 Annual Frequency of Exceedance 1078 0 25 5 79 1 125 1 5 1 75 2 Peak Ground Acceleration g Spectral Acceleration g at 1 Second 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 ev
8. nighttime populations of a study region to individual buildings 3 4 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
9. 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 modif
10. 2 describes pertinent building data including engineering pushover analysis results of the Black amp 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 8 1 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 O in except that the 2 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 WSMB
11. 91803 1331 Same as Record No 1 34 085 Same as Record No 118 15197 Same as Record No 1 Business Inventory J0 Same as Record No 1 Same as Record No 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 Daytime Occupants 1600 Same as Record No 1 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 8 13 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 Tec
12. AEBM are different than vi 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 WSMEF building in its current original building configuration and the calculation of damage and losses for the WSMEF 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 Vil TABLE OF CONTENTS Foreword Acknowledgements Executive Summary Section Page Vs Introduction xvgoy ee Sos bakes ends ieee ek eee bade eee EEEE E sy As oa TEN ee a bude nE eraa 1 1 LI SCO
13. 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 spe
14. 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 0 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 Normalized Base Shear V W 0 05 0 00 00 05 10 15 20 25 30 35 40 45 50 Roof Displacement ft Figure 8 7 Pushover Curve Connection Only Retrofit Scheme 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 7 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 334 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
15. Fracture Percentage 0 30 0 25 0 20 HH jenak Til 0 15 RINES RERE NERRIC RK 3 OKON AS 0 10 e ra LR nee DLSOTK NIN NN A Z B 0 05 ii sv vee Aw An Aw Aw A A An Ae UES 0 0 0 5 10 15 20 25 30 35 40 45 50 Roof Displacement feet Bottom Flange Fractures Normalized Base Shear V W Figure 8 6 Pushover Curves and Connection Damage Original Building 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 8 6 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
16. Installation Advanced Engineering Bldg Mode O User defined Structures O Transportation Systems CO Utility Systems C Induced physical damage C Direct Social Losses C Indirect economic impact C Contour maps OK ma Cancel Number of modules selected 1 Blue text indicates modules which need to be re analyzed since they are not current vis a vis the hazard scenario and or the analysis parameters Figure 8 15 Analysis Options Dialog Box with AEBM Selected Inventory Buildings Lifelines Induced Losses Other 3rd Party m Please select the summary report s to view Global Summary Report AEBM Individual Building Report AEBM Portfolio Building Report Quick Assessement Report 24M Quick Assessement Report 2PM Quick Assessement Report 5PM All Hazards Combined Losses Figure 8 16 HAZUS Summary Reports Dialog Box 8 16 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 Exc
17. J Lagorio R Scott Lawson Philip Schneider 1997 Development of a National Earthquake Loss Estimation Methodology Earthquake Spectra Vol 13 No 4 Oakland CA Earthquake Engineering Research Institute 9 2
18. Loss Pune Ons oeha2 5 coke wets bees E ae hehe beens eee PRE etree 2 12 3 Summary of Building Specific Data Provided by User cc ecceecc cence eee e een enees 3 1 Sell Amtroduct On sys ecacsseceeehes aa E NE E aA vous ws seeuen ees Seles 3 1 3 2 Site Souree Seismic Hazard Data cociasiy cee va a ass cava Cane yak ae See cab ed ts ee 3 1 3 9 4 Inventory Datani K hl 5 isn ie ee O Baas Shake Ne sets ue Aas A E eee 3 1 34 Performance Data orrara ienee sae E Ea E E E EAE E EEE ETEA EE E EAR 3 2 3 4 1 Building Failure Modes ssnnnnnnnnnueeerernereressssssssesessssssssssssseeete 3 2 3 4 2 Pushover Models and Modal Properties cceeeeeeee eens eeneee serren 3 3 3 4 3 Element Component Response Characteristics cceeeceeeeeeeeeeeeeees 3 4 3o Loss Data geo se ea Eae A E tate Goes EEA E A aoa ea eee ns 3 4 Jl Occupant Data ame ean E E AE E E E a E EES 3 4 33 27 Financial Data ooer aiea E oE a oats aw OE E RE eh 3 5 4 Summary of Damage and Loss Function Parameters ccccecee eee e eect ea eeene eee 4 4 1 Introductions vjsy 2s gee pis itin ve chovads EEE EE EEEE E EEES EEE EEEE Test 4 1 4 27 Damase FUNCHONS ereer de ea E EA i a O EEEE A ERE 4 1 421 Capacity Curve Parameters 2cseseece sy 5s eae nE EE EO EEE 4 1 4 2 2 REsponse Parameters cos icevcavaescnteeesndavecwkecees EE EELE EE EEEE 4 2 4 2 3 Fragility Curve Parameters sssssssssssseerrrrrererrerreressssssssrssssese 4 2
19. Slight Damage Threshold A Moderate Damage Threshold Extensive Damage Threshold Complete Damage Threshold OD 2 a 2 aS Ss s lt wT 5 i D Q op 10 15 20 Spectral Displacement inches Figure 2 7 Generic Building Type W1 Light Frame Wood lt 5 000 sq ft Capacity Curves and Structural Damage State Thresholds Fragility Medians for Five Seismic Design Levels Special High High Moderate Low and Pre Code Table 2 6 Generic Building Type W1 Light Frame Wood lt 5 000 sq ft Elastic Period Values and Average InterStory Drift Ratios of Capacity Curve Control Points and Structural Damage State Thresholds Fragility Medians Average Inter Story Drift Ratio Seismic Design Elastic Capacity Curve Structural Damage State Thresholds Level Period Control Points Fragility Medians sec Slight Moderate Extensive Complete Special High Code 0 0057 0 1371 0 0050 0 0150 0 0500 0 1250 1 A typical W1 building is 1 story i e 14 feet in height Spectral displacement is equal to 0 75 x roof displacement and base shear is equal to 0 75W x spectral acceleration 2 13 Capacity Yield Point Capacity Fully Plastic Point Slight Damage Threshold A Moderate Damage Threshold Extensive Damage Threshold Complete Damage Threshold wT 2 c 2 a l 5 lt wT a D lol ep Spectral Displacement inches Figure 2 8
20. UBC Seismic Zone Design Vintage NEHRP Map Area Post 1975 1941 1975 Pre 1941 Zone 4 MA 7 High Code Moderate Code Zone 3 MA 6 Moderate Code Moderate Code 1 Assume Moderate Code design for residential wood frame buildings W1 1 1 F 2 2 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 Seismic Design Level Superior High Code Moderate Code Low Code Ordinary High Code Moderate Code Pre Code Inferior Moderate Code Pre Code 1 Special High Code includes essential f
21. a dynamics standpoint this requirement may also be thought of as including all degrees of freedom that significantly influence dynamic response of the 1 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 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 T
22. 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 component
23. 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 e 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 e 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 repa
24. 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 judgement 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 buil
25. 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 1 e Ra at periods of constant acceleration and Ry 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 5 Damped Response Spectrum Demand Spectrum w 2 c 2 5 2 Q lt T 5 ia D jor 09 Dema j Se Spectral Displacement inches 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 Ber as defined by Equations 5 8 and 5 9 Ra 2 12 3 21 0 68In Bor 5 8 Ry 1 65 2 31 0 411n Bos 5 9 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 5 8 levels expressed as a percentage of critical
26. 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 3 2 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 g
27. 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 Field Name Record No 1 Record No 2 Modified Modified street oa val oa oa ee e sreiesenive of val as E 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 acceleratiom 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 28 8 4 7 Contents amp 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
28. 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 acceleration sensitive 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 business income wage income relocation and temporary space rental Users should confirm or revise accordingly default values of HAZUS of the time required for cleanup and r
29. load carrying capacity and strengthening the concrete base to carry the loads from the steel frame to the ground 8 4 3 4 STIFF LEVEL 3 amp PL 1 7 8x8 LEVEL 3 amp 4 REMOVE E ASBEST PL 1 3 8x8 LEVEL 9 amp 10 CONTAINING FIRE PROOFING TO ACCESS CONN amp REPLACE 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 connectiomonly 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 8 5 The girder column connection was modeled to include the effects of shear deformation and shear yielding in the panel zone per
30. 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 amp Veatch during their seismic mitigation study or in 8 12 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 HIDNo iOW BS COT LACDPW Headquarters Building Same as Record No 1 Profile Name Original Building CO Retrofit Scheme 900 South Fremont Same as Record No 1 Alhambra Same as Record No 1 Same as Record No Zip Code
31. 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 Bp and the variability associated with the discrete threshold of each damage state Bras as described in Equation 6 5 Ba y CONV B cob ale B T ds 6 5 Where Bas is the lognormal standard deviation parameter that describes the total variability of damage state ds Be is the lognormal standard deviation parameter that describes the variability of the capacity curve Bp is the lognormal standard deviation parameter that describes the variability of the demand spectrum values of Bp 0 45 at short periods and Bp 0 50 at long periods were used to develop Tables 6 5 6 7 Bras 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 vari
32. 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 Ultimate Point A A DoS MD Yield Point D Loge To C Design Value T Building Period y A Overstrength u Ductility Spectral Acceleration g s Spectral Displacement inches Figure 2 3 Example Building Capacity Curve and Control Points 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 OAI fraction of building weight effective in the pushover mode 02 fraction of building height at the elevation where pushover mode di
33. 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 2 13 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 Bas
34. 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 6 5 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 stu
35. 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 02 and other terms Saas Fypas 2 a Hp a 6 2 Where Saas Median spectral displacement value of damage state ds inches Fopas Factor relating average inter story drift to the drift ratio of the component at damage state ds as defined by Equation 6 3 Ads Component drift ratio corresponding 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 6 11 The factor Fopas 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 Fop as is based on both the shape of the pushover mode and damage state loss ratio f pp 1 NSD F pas H NSD 6 3 Where rp Roof displacement of the pushover mode for damage state ds inches NSDgs Nonstructural drift sensitive component loss ratio of damage state ds expressed as a fracti
36. should be the true elastic fundamental mode period of the building T 0 32 2 eae 5 5 Ay e 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 1 e ignore additional straining at the point at which the structure becomes a mechanism e Ultimate capacity controlpoint displacement Dy 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 Au D 2 D 5 6 y 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 Tz 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 controlpoint displacement Du 5 5 which defines the d
37. 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 15 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 pulldown 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 n 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 Analysis Options E Advanced Engineering Bldg Mode Select All E L General Buildings O Essential Facilities Deselect All CO Military
38. the 1o 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 e 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 e Select specific values of building response that best represent the threshold of each discrete damage state e 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 6 3 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 damage state 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 nonstruc
39. 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 multilinear 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
40. 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 6 4 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
41. 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 GOV 1 buildings 8 29 Table 8 11 Example AEBM Profiles Data Loss of Function Parameters Parameter Field Name Record No 1 Record No 2 Modified Modified Function Loss Slight Days si o o o Function Loss Complete Days 0 03 0 03 C Recovery Timeone Day 0 o Co o Recovery Timesi Days 0 o 10 o C Recovery TimeModente ay 90 10 90 120 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
42. to have a replacement value of about 465 billion excluding contents based on 1994 dollar value Figure 8 11 shows a screen shot of Los Angeles County census tracts lt i alex File Edit Yiew Inventory Hazard Analysis Results Selection Tools Help QQ 2M OeD gt EROS edtog gt 9 Tost f me ol x lala B94 BBX o amp freer z g a 0 pE Eau e p amp Layers 8 Hazard Scenario Layer M eqTract_5a10 5a10 0 07528 0 21651 0 21651 0 35774 0 35774 0 49897 W 0 49897 0 6402 E 0 6402 0 78143 EW 0 78143 0 92267 Study Region Tract E M Study Region Boundary Display ee a eal eee gt drawing Oe A f Jamae zuja av srar 117 39 0 71 w 33 50 53 33 N PAstart A A A A Ghinbox microsoft outlook _ 827 ABM User s Manuali doc YHazus MH Earthquake 34 Virus update and introduc fi AEBM SCREEN SHOTS do HUPA 12 27PM Figure 8 11 Map of Los Angeles County and Scenario Earthquake Ground Shaking 8 3 2 Defining Scenario Earthquake Ground Shaking 8 10 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 user supplied map of ground motion The deterministic option will likely be the most useful and convenient method of defining AEBM ground sh
43. 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 si
44. 10 Example AEBM Profiles Data Contents Inventory Replacement Cost Ratios Parameter Field Name Record No 1 Record No 2 Modified Modified stnventory Stight 000 ooo ooo oo Tnvemory Moderate ooo ooo ooo ooo Tnventory Extensive Ooo oo ooo ooo Tnventory Complee 00o oo ooo oo 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
45. 7 1 the Collapse Factor is calculated P COL ISTR 0 50x0 0 0 40x0 1 0 10x1 0 14 8 2 8 26 Table 8 8 Example AEBM Profiles Data Casualty Ratios per Occupant Parameter Field Name Record No 1 Record No 2 Modified Modified 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 8 27 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
46. 8 19 AEBM Profiles Select the profile set to view edit Building characteristics z B uildi n q cha Spectral Disp Y 2 amp Table Profile Name Occupa 1 CORTFT GOoVvi 2 ORGBLDG Govt Structural fragility curves Non structural drift fragility curves Non structural acceleration fragility curves Indoor casualty ratios per occupant Building related repair cost ratios Contents amp business inventory replacement cost ratios Loss of function parameters of days Figure 8 19 Selection of AEBM Profiles Database Set 8 19 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 default 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
47. AZUS the NEHRP Guidelines represent a major multtyear 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 we 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
48. Attention Level 2 Requires Hospitalization Level 3 Life Threatening Injury Level 4 Death Economic Loss Building Exposure amp Economic Loss Loss Category j Exposure tito HJ Damage Ratio Building Structual 039 Building Nonstructual LB Ta 1500 2 2an Contents Business Interruption Total 8 32 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 Direct Economic Loss Business Interruption Daytime Casualties All 18 1 000 Ei 0 2 1 000 Daytime Casualties Immediate Deaths 1 600 AEBM Example Results CO Retrofit Scheme Direct Economic Loss Structural System 1 0 Direct Economic Loss Total Building 4 2 Direct Economic Loss Business Interruption 0 75 Daytime Casualties All 1 1 000 Daytime Casualties Immediate Deaths 160 o 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 res
49. Building height inches 1 848 Parameter Pushover modal factor amp 2 Equation 5 2 Spectral Displacement inches Equation 6 1 Higher mode factor 3 Eq B 14 FEMA 351 Mode shape factor 04 4 Eq B 15 FEMA 351 Median spectral displacement of damage state ds Saas Eq B13 of FEMA 351 inches Median spectral displacement of damage state based on results of pushover analyses 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 8 23 on ae a T T T Ge Curve Original Building Ton T T T Scheme 12 oo eae en oO IN w M z 2 2 D a Oo lt w 5 O D Q 09 O La o ro Figure 8 21 Structural Fragility Damage State Medians 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 2 0 9 0 85 for major degradation x 0 5 and to about 1 0 for extreme degradation k lt 0 1 Extreme degradation is not expected since 0 30 for the duration of shaking associated with the scenario earthquake Shaking duration applies to post yield respo
50. Characteristics Profile name unique and 40 chars or less LO O Occupancy class AGRI Aaqriculture gt Building type C1H Reinforced Cc Seismic design level Lio i Building quality bias iinei Figure 8 13 Building Profile Name Dialog Box 8 14 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 AEBM Profiles k Select the profile set to view edit Building characteristics z Table Profile Name Occupancy Building Type Design Level Gov1 2 NRGRLDG ANYI Add Profile Duplicate current profile Assign to default capacity amp Fragility curves Delete current profile Data Dictionary Figure 8 14 AEBM Example Building Characteristics Table 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
51. EBM Inventory Eoo Run HAZUS Define AEBM Profiles Open Create Study Region Hazard Menu Results Menu Open Define View Results Scenario Earthquake Print Results Figure 8 10 HAZUS Software Flowchart of AEBM Calculation of Damage and Loss 8 9 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 br 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
52. F 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 8 2 Figure 8 2 Typical Floor Framing of the DPW Building Chen et al 2001 meeeneeeenn td mee ry yt yt yl 4 j ad Se Fa a4 i Gewed bate Bod a bor 9 44 mitala nl Bae ia Figure 8 3 Elevation View at Perimeter of the DPW Building Chen et al 2001 8 3 9 5 mm 3 8 in 30 CP Typ 6 4 mm 1 4 in 45
53. Field Name Record No 1 Record No 2 Modified Modified Name CO Retrofit Scheme ating Type iP dS C see Pd a Dorion Facer Sma ea o0 oso 090 090 Paton For Modea eQ o0 o0 ow f omw 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 8 20 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 ther 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 HAZUS Compatible Original Building x Pushover Results Original Building HAZUS Compatible CO Retrofit Scheme x Pushover Results CO Retrofit Scheme o o
54. Generic Building Type URML Low Rise Unreinforced Masonry Bearing Walls Capacity Curves and Structural Damage State Thresholds Fragility Medians for the Pre Code Seismic Design Level Table 2 7 Generic Building Type URML Mid Rise URM Bearing Walls Elastic Period Values and Average InterStory Drift Ratios of Capacity Curve Control Points and Structural Damage State Thresholds Fragility Medians Average Inter Story Drift Ratio Seismic Design Elastic Capacity Curve Structural Damage State Thresholds Level Period Control Points Fragility Medians sec Slight Moderate Complete Special High Code 0 0057 0 1371 0 0050 0 0150 0 0500 0 1250 1 A typical URML building is 1 story i e 15 feet in height Spectral displacement is equal to 0 75 x roof displacement and base shear is equal to 0 50W x spectral acceleration 2 14 Capacity Yield Point o Capacity Fully Plastic Point Slight Damage Threshold A Moderate Damage Threshold Extensive Damage Threshold OD 2 a 2 aS Ss s lt wT 5 i D Q op 10 15 20 Spectral Displacement inches Figure 2 9 Generic Building Type C1L Low Rise Concrete Moment Frame Capacity Curves and Structural Damage State Thresholds Fragility Medians for Five Seismic Design Levels Special High High Moderate Low and Pre Code Table 2 8 Generic Building Type C1L Low Rise Concrete Moment Frame Elastic Period
55. Generic Building Types and Occupancies a Fraction of Total Building Cost Common Combinations of Occupancy and Building Type Nonstructural Systems Structural Occupancy Group Syse Percent of Total Nonstructural Cost Accel Sensitive 0 49 0 26 65 35 Single Family Residences RES1 W1 All Single Family Residences Retail Commercial COM1 S1M 0 25 0 37 All Commercial Buildings 40 60 0 11 0 62 15 85 Light Industrial IND2 PC1 All Industrial Buildings 0 25 Pl Mult Family Residences RES3 A F W1 0 41 All Non Single Family Residences 50 50 0 38 S a 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 e Slight damage would be a loss of 2 of building s replacement cost e Moderate damage would be a loss 10 of the building s replacement cost e Extensive damage would be a loss of 50 of the building s replacement cost e 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 con
56. Major Degradation Extreme Degradation Building x gt 0 9 Kk 0 5 kK lt 0 1 System Damage Variability Bras Damage Variability B r 4 Damage Variability B Small Mod Large Small Mod Large Small Mod Large 0 2 0 4 0 6 0 2 0 4 0 6 0 2 0 4 0 6 Structural Systems with Very Small Capacity Curve Variability Be 0 1 Structure 0 80 0 70 080 090 0 85 1 05 NSD 0 80 0 80 1 10 NSA 0 35 0 65 0 35 0 35 0 65 Structural Systems with Small Capacity Curve Variability Bo 0 2 Structure 0 65 0 85 0 75 0 95 1 10 NSD 0 65 0 85 0 80 0 95 1 10 Structural Systems with Moderate Capacity Curve Variability Be 0 3 Nsp 065 0 75 085 oso oso 100 095 1 05 1 15 Structural Systems with Large Capacity Curve Variability Be 0 4 Structure 070 0 75 0 90 080 0 90 100 100 105 115 _ Nsp_ 070 0 75 090 ogs oso 100 1 00 105 115 _ 1 Building Systems include the Structure Nonstructural Drift Sensitive Components NSD and Nonstructural Acceleration Sensitive NSA components 6 17 Table 6 7 High Rise Building Fragility Beta s Post Yield Degradation of Structural System Minor Degradation Major Degradation Extreme Degradation Building K gt 0 9 kK 0 5 K lt 0 1 System Damage Variability Bras Damage Variability B p 4 Damage Variability Bra Small Mod Large Small
57. Multi hazard Loss Estimation Methodology Earthquake Model HAZUS MH MRI 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 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 aAY e ie The National Institute of Building Sciences NIBS located in Washington DC is a nom governmental 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 Emergenc y Management Agency For information contact FEMA 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 ii ACKNOWLEDGMENTS HAZUS MH and HAZUS MH MRI Earthquake Committee Chairm
58. 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 e 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 1 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 e 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 1 4 building of the group These profile data define properties that represent the collective perfo
59. Values and Average Inter Story Drift Ratios of Capacity Curve Control Points and Structural Damage State Thresholds Fragility Medians Level Period Control Points Fragility Medians Special High Code 0 1000 1 A typical C1L building is 2 stories 1 e 20 feet in height Spectral displacement is equal to 0 75 x roof displacement and base shear is equal to 0 80W x spectral acceleration 2 15 Capacity Yield Point Capacity Fully Plastic Point Slight Damage Threshold A Moderate Damage Threshold Extensive Damage Threshold OD 2 c 2 aS S lt wT 5 a D Q op Spectral Displacement inches Figure 2 10 Generic Building Type C1M Mid Rise Concrete Moment Frame Capacity Curves and Structural Damage State Thresholds Fragility Medians for Five Seismic Design Levels Special High High Moderate Low and Pre Code Table 2 9 Generic Building Type C1M Mid Rise Concrete Moment Frame Elastic Period Values and Average Inter Story Drift Ratios of Capacity Curve Control Points and Structural Damage State Thresholds Fragility Medians Seismic Design Elastic Capacity Curve Level Period Control Points Fragility Medians Special High Code 0 0667 1 A typical C1M building is 5 stories i e 50 feet in height Spectral displacement is equal to 0 75 x roof displacement and base shear is equal to 0 80W x spectral acceleration 2 16 Capacity Yield P
60. ability Bras 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 1 e variability of ground shaking is a key parameter in the calculation of damage state variability The values of demand variability Bp 0 45 at short periods and Bp 0 50 at long periods are the same as those used to calculate the default fragility 6 13 curves of the HAZUS MH Technical Manual These values 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 Bag a Ba Beas 6 6 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 Equatio
61. acilities such as post 1973 California hospitals 2 4 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 accelerationsensitive 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 Acceleratio
62. aking 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 c
63. amage 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 1 5 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 settlemen
64. an William Holmes Rutherford amp 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 amp 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 amp Chekene San Francisco California Robert Whitman Massachusetts Institute of Technology Cambridge Massachusetts Shake Beta Subcommittee Chairman William Holmes Rutherford amp 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 Earth quake Engineering Richmond California Richard Eisner California Office o
65. apacity curve is the peak acceleration response at peak displacement D is a degradation factor that defines the fraction of the Area used to determine hysteretic damping Aro For a value of x 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 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 yy 0 5 and long k 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 dura
66. ate 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 6 1 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 di
67. ation Fragility Curves cece eeeee eee e eee eere 8 25 8 4 5 Casualty Ratios Per Occupant cece eec cece e ence eee eee eeeeeeeneneeenes 8 26 8 4 6 Building Related Repair Cost Ratios cece cece eee e eee eneeeeee ee nees 8 27 8 4 7 Contents amp Building Inventory Replacement Cost Ratios 64 8 29 8 4 8 Loss of Function Parameters c cece ence eeeeee eee eeeeeeeeeeneeeeeeaenes 8 29 boo Example AEB M Results icc cvcnnsde es ecevs sas amas eeu nonetadenssa ones REAREA ATN EEE SA 8 30 8 3 1 Interpr tation sirae eerdere eera a aE tye xendccavereime wees EAE ERTO 8 33 8 3 2 Sensitivity Analysis serrer oee sen erroei KERAS PESEE ARENE ETNE EEE ESSEN 8 34 9 URCISTENCES eene aeaa a e E le dupe dune re Ees aS EE eEG 9 1 CHAPTER 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 amp 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
68. bability of 0 40 at 6 inches of spectral displacement in the example shown in Figure 6 1 pol S2 72 D o I gt 2 Fo 2 _ o Extensive Damage Curve O Complete Damage Curve 15 20 Spectral Displacement inches Figure 6 1 Example Fragility Curves Calculation of Damage State Probability 6 2 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 nore 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 building specific fragility curves jej a 2 D A i gt y Q O kos A Ti lo 5 exp 0 8 2 25 in 10 15 Spectral Displacement inches Figure 6 2 Example Lognormal Fragility Curves Beta 0 4 0 6 0 8 1 0 and 1 2 and Calculation of 16 Spectral Displacement Figure 6 2 illustrates the calculation of spectral displacement at 1 standard deviation 10 probability levels for a typical Beta value of 0 8 In this example the lo level of spectral displacement is more than twice the median value and
69. bability of no injury or death to equal 1 0 The Collapse Factor P COLISTRs 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 W1 W2 SIH S2H S3 S4H SSH and MH 3 SIM S2M S4M S5M C1H C2H and RM2H 5 SIL S2L S4L and SSL 8 CIM C2M C3H PC2H RMIM and RM2M 10 CIL C2L C3M PC2M RMIL and RM2L C3L PC1 PC2L URML and URMM 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 COLISTRs is expressed by Equation 7 1 P COL ISTR PIC Fso 7 1 Where P Ci Probability of Collapse failure mode i Fso 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 wis
70. 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 3 3 4 3 Element Component Response Characteristics HAZUS methods estimate building damag
71. cheme cece eee cence eee e ee eee 8 4 8 2 4 Engineering Pushover Analyses eeceeeee eee cent eeneeeeaeeeeeeaes 8 5 8 2 5 Original Building OB Performance ce cece cece eee ene teen eeene ees 8 6 8 2 6 Connection Only CO Retrofit Scheme Performance 0054 8 7 o 227 Ground Shaking Hazard gcc suicacsyddenieipceys was Ge Selene bee oie Ren geese 8 8 8 3 HAZUS Software Getting Started 72200 551s cap oriaenes tedees ie pesp ean aeh ves uaeene 8 9 8 3 1 Defining a Study Region oo ciccnisses sav evigaiuiueseyanedesGnensvemer erase eee awens 8 10 8 3 2 Defining Scenario Earthquake Ground Shaking cceeeeeeee eee 8 11 8 3 3 Defining AEBM Inventory Data cece cece ence ence ence eee eeeeeenees 8 11 8 3 4 Defining Default AEBM Profile Data ccc cee cece eee e eee eee ees 8 14 8 39 Runie the AEBM yino hae a E EE vane E eye RE 8 15 8 3 6 Viewing and Printing AEBM Results cc cee ce cece nee e ee enee eee aeaaee 8 15 8 4 Modifying Default AEBM Profile Data 2 0 0 0 cece e eee e eee ee ee nee cette es 8 19 8 4 1 Building Characteristics c 5 ss nsevetisetesseisauneeaeiapeeean snes eeyernsuencnenes 8 20 1x 8 4 2 Structural Fragility Curves 26 si cceeseysnsecees ss yeewaeneeatayseeuusedseadedendae 8 21 8 4 3 Nonstructural Drift Fragility Curves cc cece eee ence ee eneeeeeaeenees 8 25 8 4 4 Nonstructural Acceler
72. cific 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 1 1 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 H
73. d 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
74. d 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 1 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 Degradation Kappa Factor Seismic Design Level Ata At Cio os o7_ os 07 fos os os or 00 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 Inferi
75. 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 Br damping Equations 5 8 and 5 9 yield reduction values of Ra 1 0 and Ry 1 0 respectively for a value of Ber 5 of critical Effective damping Perr is defined as the total energy dissipated by the building during peak earthquake response and is the sum of an elastic damping term Bg and a hysteretic damping term By associated with post yield inelastic response Bet Pe Bu 5 10 The elastic damping term Bg 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 By 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 By is defined in Equation 5 11 Area K 5 11 Bu E D z 5 11 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 is the peak displacement response of the c
76. dies 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 1 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 InterStory Drift Ratios of Structural Damage State Medians Damage Component Criteria Set No 2 Fraction Slight Moderate Extensive 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 d
77. ding 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 STRDas the fractions of the total cost of nonstructural drift sensitive components NSDDgzs and the fractions of the total cost of nonstructural acceleration sensitive components NSADags respectively associated with repair of
78. ding 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 3 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 Inventory Menu i Analysis Menu Define AEBM Inventory Ana ysis Menu Run HAZUS Define AEBM Profiles Open Create Study Region Hazard Menu Results Menu Open Define View Results Scenario Earthquake Print Results Figure 1 1 HAZUS Software Flowchart of AEBM Calculation of Damage and Loss 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 performance characteristics including damage and loss function parameters Each building in the AEBM Inventory must be linked to one of the AEBM
79. e 6 4 Example Damage State Medians of Saw Tooth Pushover Curve 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 6 7 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 buildi
80. e 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 n 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 co
81. 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 FVsrr is the fraction of the total replacement value of the building RVs associated with the value of the structural system The Fractional Value FVnsp is the fraction of the total replacement value of the building RVpg associated with the value of nonstructural systems sensitive to drift The balance of the total replacement value of the building RVs is associated with the value of nonstructural systems sensitive to acceleration Four Loss Ratios specify fractions of the total cost of contents CDas 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 build
82. ed 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 bss 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
83. efined 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 62 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 1 set of criteria of Table 6 2 i e limits of 24 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 6 6 Normalized Force Deformation or Deformation Ratio Figure 6 3 Idealized Component Load versus Deformation Curve from Figure 2 5 of the NEHRP Guidelines HAZUS Compatible Capacity Curve Moderate Base Shear Capacity Curve from Slight Pushover Analysis Average Inter Story Drift Ratio Figur
84. el 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 HAZUS AEBM Individual Building Report 2 2004 Building Information ki Number usw Bulkihg Name LAC DPW Heaxkjiarers Bulking Ackitess S00 South Fremoat Latitude Long itach 340a4118 15 Bulkihg Pronk ORGBLDG Ground Motion Building Intersection Points SA O3seconk a 076 Dispkaceme at M 13 13 SA 1Dsecork 4 O5t Aocek ration 0 0 13 PGA a ox Soll Tye Building Damage Gamage State Damage State Probabilities Structural Non Structural Drift Non Structural Acceleration None 10 70 640 Slight 60 20 12 Moderate 320 30 2 Extensive 30 120 5 Complete 20 290 17 Casualties Imated Number ecupants amp Casualties Level Description Day Time Scenario Night Time Scenario Occupants of people in building 1600 a Level 1 Requires Medical Attention 3 Level 2 Requires Hospitalization 6 0 Level 3 Life Threatening Injury 1 0 Level 4 Death 1 0 Economic Loss Building Exposure amp Economic Loss Loss Category Exposure Loss Damage Ratio Building Structual 4255 a Building Nonstructual 60 000 12 008 05 Contents 1500 1513 100 Business Interruption 412 l Total 75 000 2a 8 17 Figure 8 18 Summary Report CO Retrofit Scheme Results Default AEBM Profile Data HAZUS AEBM Individual Building Report 2 3 2004 Build
85. eneral 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 nom 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
86. ents 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 BSE2 probabilistic definition and maximum magnitude events on the Verdugo and Sierra Madre faults are shown in Figure 8 9 8 8 e ii sa Verdugo Fault M6 9 S E Q w D a oO oO O lt w 5 O oO Qa ep Period Seconds Figure 8 9 Site Specific Response Spectra DPW Building 8 3 HAZUS Software Getting Started Before the AEBM can be used to evaluate building specific damage 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 Inventory Menu i Analysis Menu Define A
87. epair construction time considering the extent of damage determined from pushover analysis and evaluation of damage to building components 3 5 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 1 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 Func
88. epair of the structural system dollars Loss due to repair of nonstructural drift sensitive components dollars Loss due to repair of nonstructural acceleration sensitive components dollars Probability of building being in structural damage state ds Probability of building being in nonstructural drift sensitive damage state ds Probability of building being in nonstructural acceleration sensitive damage state ds Structural system repair cost of damage state ds expressed as a fraction of the total cost of the structural system Nonstructural repair cost of damage state ds expressed as a fraction of the total cost of nonstructural drift sens itive components Nonstructural repair cost of damage state ds expressed as a fraction of the total cost of nonstructural acceleration sensitive components Fraction of total building replacement value RVpg associated with the structural system Fraction of the fraction of total building replacement value RVs associated with nonstructural drift sensitive components Replacement value of building dollars The Replacement Value of the building RVg may be estimated as the product of the Total Floor Area FA and the total cost per square foot of structural and nonstructural systems 44 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 dol
89. ermination 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 inpu
90. es 8 21 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 2 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 Record No 2 Modified Default Modified O siema os os oa os The CO Retrofit Scheme does not fail connections Rather the pushover 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 t
91. es 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 Capacity Yield Point Capacity Fully Plastic Point
92. f Emergency Services Oakland California William Holmes Rutherford amp Chekene San Francisco California Robert Olson Robert Olson amp Associates Inc Sacramento California Henry Lagorio University of California at Berkeley Berkeley California Earthquake Model Methodology Development PBS amp J Atlanta Georgia Jawhar Bouabid Program Manager Scott Lawson il 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 amp 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 amp R Directorate FEMA Information Services Technology Division Washington D C Dirk Vandervoort POWER Engineers Inc Boise Idaho Leslie Weiner Lea
93. g before and after seismic retrofit Building occupancy is GOV since the building provides office space for Los Angeles County Department of Public Works The building type is SIH 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 datain 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
94. 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 econo mic 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 l 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 8 30 Figure 8 22 Summary Report Original Building Results HAZUS AEBM Individual Building Report Building Information Ki Number usoa Bulking Name LAC DPW Heackyrarers Balkllig Ackiress 900 Sorti Fremont Latitude Long tick S4094118 15 Balkllig Pronk ORGBLDG Ground Motion Building Intersection Points SAM O3 second yy O76 Displacement Ih 10 23 SA 1Oseoork my ost Accek ration 02 PGA ity ow Soll Type Building Damage Damage State Damage State Probabilities o Structural Non Strict
95. h to consider the following four general types e Co No Collapse Building is a complete loss but does not threaten life safety e C Local Collapse Localized collapse of building elements or components e g out of plane collapse of infill walls e Cs Story Collapse Collapse of an individual story or portion thereof e g soft story e Cg Global Collapse Collapse over multiple stories e g pancake collapse 7 3 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 Fgoj 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 e P Co 0 Fgoi 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 e P CL 0 5 Fgoi 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 e P Cs 0 5 Fgoi 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 e P Cc 0 0 Fgoi 1 0 Building is assumed to have no significan
96. 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 5 12 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 1 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 d
97. he 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 Q and Oz 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 De Ac Provided the pushover curve was developed using a push force pattern based on the 1 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 T e 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 Capacity Curve S DoAg Spectral Acceleration g s Pushover Curve Normalized by Building Weight Spectral Displacement inches Figure 5 1 Example Conversion of Pushover Curve to Capacity Curve Using Pushover Mode Factors HAZUS defines the two pushover mode factors Oly fraction of building weight effective in pushover mode 2 fraction of building height at the elevation where pushover mode displacement is equal to spectral displacement 5 3 Consistent with ATC 40 methods and terms 0 is defined by the distribution of building mass and pushover mode shape Sow ip ve a bei o e 5 1
98. 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 x 0 9 minor degradation K 0 5 major degradation and lt 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 Bc and the variability of the threshold of the damage state Bras 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 value
99. hnical 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 Building Characteristics Structural Fragility Curves Nonstructural Drift Fragility Curves Nonstructural Acceleration Fragility Curves Casualty Ratios per occupant Building Related Repair Cost Ratios Contents amp Building Inventory Replacement Cost Ratios Loss of Function Parameters of days o ST Ov Ee eS 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 Building Profile name 4 x m Building Profile
100. ia need eee 6 1 6 1 Building Response and Performance Criteria 2 2 0 0 0 cece cee ee eee e nee ee eee eee ences 6 1 6 2 Development of Damage State Medians 0 cece ccc e cece ence eens eens eeaeeenaes 6 3 6 2 1 Stra Cuural Sy stem oi eraai EE UREE SENE TEE EEEE E eE RESY 6 4 6 2 2 Nonstructural Components ssri EE E EE E 6 10 6 3 Development of Damage State Variability ccc eee ece cece eee e eee eeneneee ees 6 13 7 Development of Loss Functions 23 2 73i25 555509 do dence 9 2a es eae ea meas dea ee 7 1 T L Building Loss Criteria 2 oidgeien okie ccaga ce iyans an venta shnnienscdadacsawta sees EE AARE opeests 7 1 7 2 Direct Social Losses Casualties s 0 3 ic tscveiecck acdsee eed end vet dee doee eae Seas 7 1 23 Direct Economie LOSSES acca itv seshusariee ver ere ia AEE AE IN pes ausis hie E i 7 4 Teel WNEDAIN CG OSIG 5250 notch setnacteyaeeae o sexed a Na eas neue eae ads hameauanee 7 5 Dio LOSS Ob PUNCHON sariat en AEE EAE E AR EE EE ETE EAR 7 7 8 Example Estimation of Building Damage and Loss Using the AEBM 8 1 Bel Backsound ss cies tes Byer sores abesa acts A vals antune esa eared pc iss 8 1 8 2 Example Building Data nosis cies voce eis pan eaves a ve ok ae Le ew a eng aeae 8 1 8 2 1 LACDPW Headquarters Building 022202s00c 2025 decease aise eed 8 1 8 2 2 Original Building OB Structure 2 0 0 0 cece cee cree ne eee ene e ences 8 2 8 2 3 Connection Only CO Retrofit S
101. ical 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
102. ications 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 A 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 Total Direct Economic Loss Structural Direct Economic Loss dollars in millions dollars in millions Original CO Retrofit Original CO Retrofit Building Scheme Building Scheme 8 34 Default Profile 22 57 9 6 4 8 2 9 HAZUS GBS Data Modified Profile s220 om 7 4 22 3 9 19 1 1 62 Capacity Data Only Modified Profile 94 40 8 9 1 sm 44 8 13 55 Loss Data Only Modified Profile gi9 5 13 3 6 62 3 3 31 0 2 93 All Data Modified Profile gig7q 17 95 1 46 4 1 15 1 2 58 Fragility Data Only 8 35 SECTION 9 REFERENCES California Se
103. ield Name Record No 1 Record No 2 Modified Modified O siema ose os o 00s O Mosememesian oso ow ow ow 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 P COL ISTR 0 33x0 0 0 33x0 1 4 0 33x1 0 36 8 1 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
104. ifferent 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 estim
105. iform Building Code Whittier CA ICBO International Conference of Building Officials ICBO 1994 Uniform Building Code Whittier CA ICBO Kennedy R P C A Cornell R L Campbell S Kaplan and H F Perla 1980 Probabilistic Seismic Safety of an Existing Nuclear Power Plant Nuclear Engineering and Design Vol 59 2 pp 315 38 Kircher Charles A Aladdin A Nassar Onder Kustu and William T Holmes 1997a Development of Building Damage Functions for Earthquake Loss Estimation Earthquake Spectra Vol 13 No 4 Oakland California Earthquake Engineering Research Institute Kircher Charles A Robert K Reitherman Robert V Whitman and Christopher Arnold 1997b Estimation of Earthquake Losses to Buildings Earthquake Spectra Vol 13 No 4 Oakland CA Earthquake Engineering Research Institute Jabobsen L S 1930 Steady Forced Vibration as Influenced by Damping Trans ASME APM 52 15 1930 New York New York American Society of Mechanical Engineers Newmark N M and W J Hall 1982 Earthquake Spectra and Design Earthquake Engineering Research Institute EERI Monograph Oakland CA EERI Reis Evan 2000 Pilot Testing of Procedures for Developing HAZUS Compatible Building Specific Damage and Loss Functions Report prepared for the National Institute of Building Sciences Palo Alto CA Comartin Reis Whitman Robert V Thalia Anagnos Charles A Kircher Henry
106. ights 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 differences 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 an
107. ing Information ki Number usome Bulking Name LAC DPW Heackytare rs Bulkihg Address 00 Sorts Fremont Lattice Long tick 340A4118 15 Bulking Pronk CORTFT Ground Motion Building Intersection Points SA 03sen My 076 Dkpl mert i 12 45 SA 1Dsecords ost Aoce ration on PGA wy ow Soll Tye Building Damage Damage State Probabilities a Damage State Structural Non Structural Drift Non Structural Acceleration None 20 80 60 Slight 150 240 5 Moderate 510 540 6 Extensive 20 110 1 Complete 30 30 z Casualties Tmated Number ccupants amp Casualties Level Description Day Time Scenario Night Time Scenario Occupants of people in building 1 600 a Level 1 Requires Medical Attention 9 G Level 2 Requires Hospitalization 0 Level 3 Life Threatening Injury 0 0 Level 4 Death 0 0 Economic Loss Building Exposure amp Economic Loss Loss Category Exposure Loss Damage Ratio Building Structual 2486 Lii Building Nonstructual 60 000 3873 6 45 Contents 15 000 25 10 Business Interruption 2531 Total 71500 9 155 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 8 18 class building type seismic design level and building quality that best represent the LACDPW Headquarters buildin
108. ing occupancy type Four Loss Ratios specify fractions of the total cost of business inventory INVaqs 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 onstruction 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 BCTas 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 LOFgs 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 Techn
109. ings for which properties are not well known 6 15 Table 6 5 Low Rise Building Fragility Beta s Post Yield Degradation of Structural System Minor Degradation Major Degradation Extreme Degradation Building x gt 0 9 Kk 0 5 kK lt 0 1 System Damage Variability Bras Damage Variability Br 4 Damage Variability B Small Mod Large Small Mod Large Small Mod Large 0 2 0 4 0 6 0 2 0 4 0 6 0 2 0 4 0 6 Structural Systems with Very Small Capacity Curve Variability Be 0 1 Structure 0 70 0 85 0 90 1 00 0 95 1 10 NSD 0 65 0 85 0 90 1 00 0 95 1 10 NSA 035 0 50 0 65 0 35 0 35 0 65 Structural Systems with Small Capacity Curve Variability Be 0 2 Structure 0 70 0 85 0 90 1 00 0 95 1 15 NSD 0 70 0 85 0 90 1 00 0 95 1 10 Structural Systems with Moderate Capacity Curve Variability Be 0 3 xsp_ 070 oso 090 0 85 095 10s 100 105 115 Structural Systems with Large Capacity Curve Variability Be 0 4 Structure 080 085 0 95 0 90 100 110 105 110 120 Nsp_ 075 oss 095 0 90 100 1 05 1 00 105 115 1 Building Systems include the Structure Nonstructural Drift Sensitive Components NSD and Nonstructural Acceleration Sensitive NSA components 6 16 Table 6 6 Mid Rise Building Fragility Beta s Post Yield Degradation of Structural System Minor Degradation
110. ir 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 7 1 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
111. ismic Safety Commission CSSC 1996 Seismic Evaluation and Retrofit of Concrete Buildings Products 1 2 and 1 3 of Proposition 122 commonly known as ATC 40 SSC Report No 96 01 Sacramento CA Seismic Safety Commission State of California Chen T Albert Chia Ming Uang Brandon Chi and Joe Ungerer 2001 Application of FEMA 351 Seismic Upgrade of the Los Angeles County Public Works Headquarters Proceedings of the 2001 ASCE Structures Congress Washington D C ASCE Chi Brandon and Chia Ming Uang 2000 Seismic Retrofit Study on Steel Moment Connections for the Los Angeles Department of Public Works Headquarters Building Report No TR 2000 14 La Jolla CA University of California San Diego Chopra Anil K 1995 Dynamics of Structures Engelwood Cliffs New Jersey Prentice Hall Computer and Structures Inc CSI 2000 SAP2000 Integrated Finite Element Analysis and Design of Structures Version 7 4 CSI Berkeley California Earthquake Engineering Research Institute EERI 1994 Expected Seismic Performance of Buildings Oakland CA EERI EQE International EQE 2000 Pilot Study Building Specific HAZUS Compatible Damage and Loss Functions Report prepared for the National Institute of Building Sciences Oakland CA EQE Federal Emergency Management Agency FEMA 1994 Reducing the Risks of Nonstructural Damage A Practical Guide Washington D C FEMA 74 Federal Emergency Manage
112. isplacement 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 HAZUS Compatible Capacity Curve Ultimate Capacity Control Point Yield Capacity Control Point Capacity Curve from Pushover Analysis Spectral Acceleration g s Spectral Displacement inches Figure 5 2 Example Development of the Capacity Curve for a Structure with Saw Tooth Force Deflection Behavior 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 HAZUS Compatible Capacity Curve Ultimate Capacity Control Point Capacity Curve from Pushover Analysis Yield Capacity Control Point Spectral Acceleration g s Spectral Displacement inches Figure 5 3 Example De
113. lars of contents RVc and business inventory RVinc are used in calculations of direct economic loss due to the replacement of these contents or inventory 5 EL_CCD RV PNSA CD ds 2 5 EL _INV RV wv PNSA INVD ds 2 where EL_CCD Loss due to replacement of damaged contents dollars EL_INV Loss due to replacement of business inventory dollars PNSAg Probability of building being in nonstructural acceleration sensitive damage state ds CDa Contents replacement cost of damage state ds expressed as a fraction of the total cost of contents INVDas 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 RVpg 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 5 EL _ INC 1 RFBI BINC PSTR LOF ds 1 whe
114. ly the roof is used as the location of the control point The shape of the pushover mode is typically based on the 1 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 term the most appropriate pushover shape would be the amplitude dependent shape at the amplitude of interest but the pre yield 1 mode shape may be used to calculate z 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 5 4 SD a 5 3 V W SA MW 5 4 a 1 Where Ap 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 e 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 e The expected period Te of the building at or just below yield
115. ly 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 S ICOL In such cases casualty rates for Severity 3 and 4 should be increased by a factor 7 2 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 pro
116. ment Agency FEMA 1995 NEHRP Recommended Provisions for the Seismic Regulations for New Buildings Washington D C FEMA 222A Federal Emergency Management Agency FEMA 1997 NEHRP Guidelines for the Seismic Rehabilitation of Buildings Washington D C FEMA 273 Federal Emergency Management Agency FEMA 1998 Handbook for the Seismic Evaluation of Buildings A Prestandard Washington D C FEMA 310 Federal Emergency Management Agency FEMA 1999 Case Studies An Assessment of the NEHRP Guidelines for the Seismic Rehabilitation of Buildings Washington D C FEMA 343 Federal Emergency Management Agency FEMA 2000 Recommended Seismic Evaluation and Upgrade Criteria for Existing Welded Steel Moment Frame Buildings Washington D C FEMA 351 Federal Emergency Management Agency FEMA 200la HAZUS99 for MapInfo Service Release 2 December 2001 Western U S CD ROM Washington D C FEMA Federal Emergency Management Agency FEMA 2001b HAZUS99 Technical Manual Service Release 2 Washington D C FEMA 9 1 Federal Emergency Management Agency FEMA 2001c HAZUS99 User s Manual Service Release 2 Washington D C FEMA Geomatrix Consultants Inc Geomatrix 1999 Site Specific Earthquake Response Spectra Los Angeles County DPW Headquarters Building 900 South Fremont Avenue Alhambra California Oakland CA Geomatrix International Conference of Building Officials ICBO 1967 Un
117. n 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 Bp but such can be ignored in the calculation of total damage state variability Bas when substantially less than both capacity curve variability Bc and damage state threshold variability Bras 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 acceleratiom sensitive components The Beta values of these tables are a function of the following building characteristics and criteria e Building Height Group Low Rise Buildings Table 6 5 Mid Rise Buildings Table 6 6 and High Rise Buildings Table 6 7 e Post Yield Degradation of the Structural System Minor Major and Extreme Degradation e Damage State Threshold Variability Small Moderate or Large Variability e Capacity Curve Variability Very Small Small Moderate or Large Variability The Beta values of the tables are applicable to all model b
118. n Architectural Mechanical and Electrical 2 6 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 1 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 Sae Small plaster cracks at corners of d
119. nd 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 Sa or other seismic demand parameter is defined by Equation 2 2 1 S Plds S amp In 4 2 2 B ds S d ds where Saas is the median value of spectral displacement at which the building reaches the threshold of damage state ds Bas is the standard deviation of the natural logarithm of spectral displacement for damage state ds and cc is the standard normal cumulative distribution function 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 includ
120. ndro DHS EP amp 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 amp 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 iv Beta Test Subcommittee HAZUS MH MRI 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 Y
121. ng 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 ob
122. ng 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 as of Structural Damage States Model Building Type Structural Damage States Slight Extensive Complete Low Rise Buildings High Code Design Level 0 100 0 080 0 080 0 080 0 070 Low Rise Buildings Moderate Code Design Level 0075 0 060 0 060 0 060 0 053 Low Rise LR Buildings Low Code Design Level 0 075 0 050 0 050 0 050 0 044 0 035 Low Rise LR Buildings Pre Code Design Level 0 060 0 040 0 040 0 040 0 0835 0 028 All High Rise Building Types 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 6 9 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 02 and other terms Saas a Hp a 2 6 1 Where Sads Median spectral displacement value of damage state ds inches Ag Average inter story drift ratio at the threshold of damage s
123. ngle 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 5 1 building corners All three segments have flexible diaphragms Possible building response and failure modes include the following there may be others e 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 e Full collapse of center section in weak direction perpendicular to tilt up panels e Partial collapse of end sections in the weak direction near joints with center section accentuated by torsion response The user w
124. nomic 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 Floor Area Wood Residential Steel Commercial Concrete Occupancy Class ee Masonry Model Building Type Mobile Home Figure 2 2 Example Inventory Relationship of Model Building Type and Occupancy Class Table 2 1 Model Building Types of HAZUS Height Description Wood Light Frame lt 5 000 sq ft All 1 14 Wood Greater than 5 000 sq ft rap pt Steel Moment Frame Low Rise Mid Rise High Rise Steel Braced Frame Low Rise Mid Rise High Rise S3 Steel Light Frame E S4L Steel Frame with Cast in Place Low Rise S4M_ Concrete Shear Walls Mid Rise S4H High Rise SSL Steel Frame with Unreinforced Low Rise S5M_ Masonry Infill Walls Mid Rise S5H High Rise CIL Concrete Moment Frame Low Rise CIM Mid Rise n Yis cda Da eID wn eens n oN q N of A faa ee perce fr ToT blt ay dof A od ab T n So C1H High Rise C2L Concrete Shear Walls Low Rise A e i i N U C2M Mid Rise High Rise Concrete Frame with Unreinforced Low Rise Masonry Infill Walls Mid Rise High Rise PCI fe Precast Concrete Frames with Low Rise Concrete Shear Walls Mid Rise High Rise Reinforced Masonry Bearing Walls Low Rise with Wood or Metal Deck Mid Ri
125. nse 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 24 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 Field Name Record No 1 Record No 2 Modified Modified OO eee o ow on os Modified values of nonstructural drift damage state median
126. nstructural 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 S A region of constant spectral displacement exists at very long periods although this region does not usually affect calculation of building 5 7 damage Amplification of ground shaking to account for local site conditions is based on the short period Fa and velocity domain Fy 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
127. o those of the above discussion are based on Equation B 13 of FEMA 351 and assumptions of damage state inter story drift ratios of Table 8 4 Equation B 13 is similar to Equation 6 1 with the addition of two additional terms 3 and 4 as which adjust damage state for higher mode effects and non uniform mode shape respectively R _ OA He Sig B 13 FEMA 351 Q 304 as The 03 and 4as 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 8 22 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 Structural Damage State Structural Damage State Drift ratio Ags 0 01 0l a Building height inches 1 848 Parameter Pushover modal factor amp 2 Equation 5 2 Spectral Displacement inches Equation 6 1 Higher mode factor 3 Eq B 14 FEMA 351 Mode shape factor O44 Eq B 15 FEMA 351 Median spectral displacement of damage state ds Saas Eq B13 of FEMA 351 inches Median spectral displacement of damage state based on results of pushover analyses Table 8 5 Calculation of Structural Damage State Medians CO Retrofit Scheme cae Damage State Drift ratio Ags 015 0 020 0 035 0 045
128. of known commonly as a pushover curve In order to facilitate direct comparison with spectral demand base shear is 2 7 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
129. 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
130. 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 eco
131. oint Capacity Fully Plastic Point Slight Damage Threshold A Moderate Damage Threshold Extensive Damage Threshold Complete Damage Threshold OD 2 c 2 aS S lt wT 5 i D Q op Spectral Displacement inches Figure 2 11 Generic Building Type C1H High Rise Concrete Moment Frame Capacity Curves and Structural Damage State Thresholds Fragility Medians for Five Seismic Design Levels Special High High Moderate Low and Pre Code Table 2 10 Generic Building Type C1H High Rise Concrete Moment Frame Elastic Period Values and Average Inter Story Drift Ratios of Capacity Curve Control Points and Structural Damage State Thresholds Fragility Medians Seismic Design Elastic Capacity Curve Level Period Control Points Fragility Medians Sec Extensive Complete Special High Code 0 0500 1 A typical C1H building is 12 stories i e 120 feet in height Spectral displacement is equal to 0 60 x roof displacement and base shear is equal to 0 75W x spectral acceleration 2 17 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 det
132. on Hr Height of building at the roof level inches AmaxP Maximum inter story drift ratio considering torsion over the height of the building corresponding to the roof displacement orp The factor F p as 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 1 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 t
133. 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_ENDO N po PIS COL PICOL PsTR PSTR where SL_ENDO Expected number of daytime casualties of Severity Level i P S ICOL Probability of Severity Level i given full building collapse P COLISTRs Probability of full building collapse given Complete structural damage STRs PSTRs Probability of Complete structural damage Npo 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 R Vg 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 5 EL _ STR FV r RV PSTR STRD ds 2 5 EL L NSD FV sp RV PNSD NSDD ds 2 5 EL _ NSA 1 FVop FVysp RV PNSA NSAD where EL_STR EL NSD EL_NSA PSTRas PNSDas PNS Aas STRDas NSDDas NSADas FVstr FVnsp RV ds 2 Loss due to r
134. onservative 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 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 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 o
135. oor and window openings and wall Slight 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 Large plaster or gypsum board cracks at corners of door and window Moderate 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 Large diagonal cracks across shear wall panels or large cracks at plywood Extensive 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 Structure may have large permanent lateral displacement or be in Complete 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 ro
136. or I KA 5 5 11 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 aceleration 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
137. ork HAZUS MH and HAZUS MH MRI1 Shell Development PBS amp J Atlanta Georgia Mourad Bouhafs Program Manager HAZUS MH Pushpendra Johari Program Manager HAZUS MH MRI Sandeep Mehndiratta Special thanks to ESRI for its assistance in coordinating ArcGIS with HAZUS MH Earthquake Model Software Development PBS amp J Atlanta Georgia Pushpendra Johari Program Manager Mourad Bouhafs Foued Bouhafs Sandeep Mehndiratta Eduardo Escalona Nabil Bouhafs Department of Homeland Security Emergency Preparedness amp 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 curren
138. ould 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
139. pe and Backeround oi 6 eos 2ens r A Basa ea E E E 1 1 1 2 AP UTPOSE ANA PPG dC sass eects Pag he Salis SUG sso eRe gies ANG dea teeta Se 1 2 1 3 Pilot Testing and Revision of Methods ccc cee ceee seen eee ee eee ene enenaeens 1 3 1 4 Individual Buildings and Groups of Buildings of a Specific Type 05 1 3 LS AERBM Overview me eiee re aa OEE ounces been Saud A EE oh ot cians bower 1 4 LG Man al Oreqnizaon sence E T sacs hs nat ese aay pas pene ag neuen N 1 5 2 Summary of HAZUS Earthquake Loss Estimation Methods ccseeeee cence eens 2 1 2 1 Overview Of Methodology cs cideccseseesanierccaeawsdatesos vent aswenransenadis ooveansaan ages 2 1 22 Building Classification asean iene ae pave onnes teense eee oe ae okt eee 2 2 2 3 Seismic Design Levels and Construction Quality cece eee eee cence ee eeaeeeees 2 4 2 4 Structural and Nonstructural Systems and Contents ccceeceeene eens sesse 2 6 Doe Damate States Steet hes eG ates St Oi ase Wt er ree le NRG Seat atte R 2 7 2 6 Building Capacity Curves o 5 3 caudslareveensa sn anand sens deantaweviddacs oda seeadaesauteues 2 7 2 7 Building Response Calculation cece cece cence cee eee eee e ene eneeeaeeneeneens 2 9 2 9 Building Fragility Curves o 8 c vdenesteee soli teste cel ees See sedans ey dees 2 10 2 9 Example Capacity and Fragility Data ccceceecceseseestenncenseeeanenneeness 2 12 29 Buildins
140. quake 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 amp 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 amp 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
141. r 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 1 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 Npo and Nighttime Occupants Nyno 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 structural damage and casualty severity levels However serious injuries and fatalities tend to be dominated by
142. r 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 Advanced Engineering Building Model Inventory Zz oj x m Table ld eadebmid Tract Name uso00001 Uso00001 06037480802 LACDPW Headquarters Building ORGBLDG USo00002 FUSO00002 06037480802 LACDPW Headquarters Building CORTFT Start Editing Stop Editing Add New Record Delete Selected Records Import Export Data Dictonary Meta Data Close Map Print Figure 8 12 AEBM Example Inventory Table 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
143. re EL_INC Loss of business income dollars PSTRgs Probability of building being in structural damage state ds LOF 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 5 EL _ WAGE 1 RFW WAGE PSTR LOF ds 1 where EL_WAGE Loss of wages dollars PSTRgs Probability of building being in structural damage state ds LOFg 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 5 5 EL _ REL DISC PSTR OO RENT PSTR RT ds 3 ds 3 5 EL _ RENT 1 O0 RENT PSTR RT ds 3 where EL_REL Loss due to business relocation expenses dollars EL_RENT Loss due to rental of temporary space dollars PSTRas Probability of building being in structural damage state ds RT gs Recovery time for damage state d
144. rivial equation summarizing conversion peak floor acceleration of each damage state to the corresponding amount of spectral acceleration is S was Arak 6 4 Where Saas 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 upper floor 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 6 12 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 2 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
145. rmance of the group 1 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 Sof
146. s 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 default 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 46 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 Sj 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 COLISTRs 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 buil
147. s 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 e Determining the total replacement cost of building systems contents and business inventory e 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 7 5 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
148. s are based on Equation 6 2 assuming drift to be essentially uniform over the height of the building i e F p as 1 0 Values of building height Hg and modal factor 2 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 2 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 8 25 Table 8 7 Example AEBM Profiles Data Nonstructural Acceleration Fragility Curves Parameter F
149. s of variability c and Bras 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 e Uncertainty in capacity curve properties and the thresholds of damage states and e Building population 1 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 Bc 0 3 and damage state threshold variability Bras 0 3 Structure Bras 0 5 NSD and Bra 0 6 NSA The generic model building types represent large populations of build
150. screte 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 Sg that defines the threshold of a particular damage state ds is given by Equation 2 1 2 10 Sq Saas Eds 2 1 where Saas is the median value of spectral displacement of damage state ds Eds is a lognormal random variable with a unit median value and a logarithmic standard deviation Bas 0 6 D 5 0 4 None Re Slight 0 2 A Moderate 0 Extensive _ Weak Complete Shaking Med Damage t Level rg State Figure 2 6 Example Damage State Probabilities for Weak Medium and Strong Shaking Levels 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 a
151. se Diaphragms nN Q N T ioe i N REFER mer gt W Reinforced Masonry Bearing Walls Low Rise with Precast Concrete Diaphragms Mid Rise High Rise Unreinforced Masonry Bearing Low Rise Walls Mid Rise W N Ne H Mobile Homes gt i E Pt do do do x do P Gc vs aw a lt Ale e2 22 1888 W W g S 2 3 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 he
152. se 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 Saas in inches of each structural and nonstructural drift sensitive damage state or median spectral acceleration Sas in units of acceleration g of each nonstructural acceleration sensitive damage state 4 2 Damage State Beta Lognormal Standard Deviation Ba 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 1la through 5 11d of the HAZUS MH Technical Manual fo
153. 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 S COL are conditional on the Collapse Factor P COLISTRs 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 Severity Injuries requiring basic medical aid but without hospitalization treat and release Severity 2 Injuries requiring medical attention and hospitalization but not considered to be life threatening Severity 3 Casualties that include entrapment and require expeditious rescue and medical treatment to avoid death Severity 4 Immediate deaths Casualty rates given collapse P Sj COL apply on
154. served 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 6 8 interest For structural systems with very stiff components e g URM buildings average inter story drift ratios developed from pushover analysis usi
155. spectrum Background on the 5 damped response spectrum of ground shaking is provided in Section 5 Spectral Acceleration g s Spectral Displacement inches Figure 2 4 Example Intersection of Demand Spectra and Building Capacity Curves 2 9 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 1 0 Extensive gt Ur Probability 0 0 Weak Medium Strong Shaking Shaking Shaking Spectral Response Figure 2 5 Example Fragility Curves for Slight Moderate Extensive and Complete Damage The fragility curves distribute damage among Slight Moderate Extensive and Complete damage states For any given value of spectral response di
156. splacement is equal to spectral displacement not shown in Figure 2 3 Yy overstrength factor relating true yield strength to design strength overstrength factor relating ultimate strength to yield strength and u ductility ratio relating ultimate displacement to 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 level 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
157. splacements represent a range of plausible estimates resulting in moderate damage to elements and comporents 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 pro
158. sts 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
159. t 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 1 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 3 1 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
160. t HAZUS MH Software Kircher amp 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 b
161. t 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 Ground Shaking Ground Failure e Response Spectra e PGD Settlement e PGA e PGD Lateral Spread Induced Damage Buildin gs Lifelines ee Essential Facilities Transportation e Debris e Utility Casualties Economic Shelter Emergency e Fatalities e Capital e Households e Loss of Function e Injuries e Income e Short Term e Restoration Time Figure 2 1 Building Related Modules of the FEMA NIBS Methodology 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
162. t probability of total building collapse that would expose all building occupants to collapse The calculation of the Collapse Factor PI COLISTRs for this example is shown in Equation 7 2 P COL ISTR 0 00 04 0 5x0 1 0 5x0 2 0 0x1 0 15 7 2 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 componen
163. tate ds determined by user consistent with generic values of Table 6 2 Hr Height of building at the roof level inches OQ 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 sensi
164. tents are not vulnerable to ground shaking and could be salvaged even if the building were severely damaged Building specific contents damage loss ratios CDas should be based on an appropriate fraction e g one half of the loss ratios of acceleration sensitive nonstructural components 7 6 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 Proportional 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 7 7 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 earth
165. 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 0 50 100 Upper Bound Pushover Response ae t Lower Bound Pushover Response 0 40 gt Pushover based on UCSD Tests 0 35 Bottom Flange
166. tion of ground shaking for buildings that have reached yield 5 9 foe Design Spectrum Demand Short Duration Demand Moderate Duration Demand Long Duration Building Capacity Curve Spectral Acceleration g s Spectral Displacement inches 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 Damping of Critical Steel Buildings Reinforced Concrete and Pre cast Concrete Buildings 7 Reinforced Masonry Buildings 7 10 Unreinforced Masonry Bearing Wall and In Fill Buildings Wood Buildings 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 le
167. tions 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 Ay 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 Br expressed as a percentage of critical damping Degradation Kappa Factors Ks Km
168. tive 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 Nonstructural Damage States All Building Types Inter Story Drift Ratio Ags Drift Sensitive Components 0 004 0 008 0 025 0 050 Peak Floor Acceleration Amax ds Acceleration Sensitive Components Contents g s Special HighCode oas o9 i8 36 HighCode 0o30 o6 12 24 tow caie oa 04 os 6 PreCode 020 04 08 6 10 HAZUS default values of peak floor acceleration defining the threshold of each damage state are summarized in Table 6 3 for accelerationsensitive 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 req
169. ts 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 7 4 Earthquake repair and strengthening of historical buildings can be extremely expensive due to preservation of historical features even though the damage triggering such 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
170. tural 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 Likely Amount of Damage Direct Economic Loss or Building Condition Damage State Range of Probability of Probability of Immediate Possible Loss Long Term Partial or Full Post Earthquake Ratios Building Closure Collapse Inspection 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 25 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
171. tware 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 value and variability of damage states Median values of structural damage states are also based on the results of the building s pushover analysis while damage state 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 WSMEF building in its current original building configuration and the calculation of d
172. uilding 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
173. uilding types For example a low rise concrete frame building CIL 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 6 14 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
174. uire 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 anchorage 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 acceleratiom sensitive components at which different nonstructural components would begin to fail and require repair or
175. ults 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 8 33 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
176. urs Drift Non Structural Acceleration None 310 Text Object Wo Slight 130 m0 5 Moderate 20 20 7 Extensive 140 130 5 Complete wo w0 16 Casualties Imated Number ccupants asualties Level Description Day Time Scenario Night Time Scenario Occupants of people in building 1 500 a Level 1 Requires Medical Attention 80 3 Level 2 Requires Hospitalization 1 Level 3 Life Threatening Injury 6 0 Level 4 Death 12 1 Economic Loss Building Exposure amp Economic Loss Loss Category Exposure Loss Damage Ratio Building Structual 3055 50 Building Nonstructual 60 000 11 332 1889 Contents 15 000 1461 974 Business Interruption 365 Total 75 000 19 544 8 31 Figure 8 23 Summary Report CO Retrofit Scheme Results HAZUS AEBM Individual Building Report Building Information kI Namber uso Bulking Name LAC DPW Hexkjiarers Bulkilig Ackess 900 South Fremont Lattin Long tuck 340A4118 15 Bulkllig Pronk CORTFT Ground Motion Building Intersection Points SAM O3secondk A 076 Displacement M 803 SAM 1Dsecondks 0 o5 Aocekration Q 025 PGA o3 Soll Type Building Damage Damage State Probabilities Structural Non Structural Drift Non Structural Acceleration None 690 Slight 140 310 Moderate 140 Extensive 10 Complete 15 Damage State Casualties Lewel Description Occupants of people in building 1 800 Level 1 Requires Medical
177. vel of ground shaking which is different for each building site and scenario earthquake The default values of 5 10 the Kappa factor developed for generic building analysis assume that the building would have ground shaking strong enough b 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 woul
178. velopment of the Capacity Curve for a Structure with Brittle Force Deflection Behavior 5 6 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 HAZUS Compatible Capacity Curve gt Wes Ultimate Capacity Control Point at a fully plastic state Capacity Curve from Pushover Analysis Spectral Acceleration g s Yield Capacity Control Point Spectral Displacement inches Figure 5 4 Example Development of the Capacity Curve for a Structure with Ductile Force Deflection Behavior Both the initial stiffness 1 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 no

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