hurricane damage prediction model for residential structures：住宅建筑结构震害预测模型的飓风

HURRICANEDAMAGEPREDICTIONMODELFORRESIDENTIALSTRUCTURESJEANPAULPINELLI1,EMILSIMIU2,KURTGURLEY3,CHELAKARASUBRAMANIAN4,LIANGZHANG5,ANNECOPE6,ANDJAMESJFILLIBEN71ASSOCIATEPROFESSOR,DEPARTMENTOFCIVILENGINEERING,FLORIDAINSTITUTEOFTECHNOLOGY,150WESTUNIVERSITYBOULEVARD,MELBOURNE,FL329016975,TEL3216748085,FAX3216747565,EMAILPINELLIFITEDU2NISTFELLOW,BUILDINGANDFIRERESEARCHLABORATORY,BUILDING226,ROOMB264,NATIONALINSTITUTEOFSTANDARDANDTECHNOLOGY,GAITHERSBURG,MD208993ASSISTANTPROFESSOR,DEPARTMENTOFCIVILANDCOASTALENGINEERING,UNIVERSITYOFFLORIDA,POBOX116580,GAINESVILLE,FL,326116580,TEL3523925947,FAX3523923394,EMAILKGURLCEUFLEDU4ASSOCIATEPROFESSOR,DEPARTMENTOFMECHANICALANDAEROSPACEENGINEERING,FLORIDAINSTITUTEOFTECHNOLOGY,150WUNIVERSITYBOULEVARD,MELBOURNE,FL3290,TEL3216747614,FAX3216748813,EMAILSUBRAMANFITEDU5GRADUATERESEARCHASSISTANT,DEPARTMENTOFCIVILENGINEERING,FLORIDAINSTITUTEOFTECHNOLOGY,150WESTUNIVERSITYBOULEVARD,MELBOURNE,FL329016975,TEL3216747562,EMAILLZHANGFITEDU6GRADUATERESEARCHASSISTANT,DEPARTMENTOFCIVILANDCOASTALENGINEERING,UNIVERSITYOFFLORIDA,POBOX116580124YONHALL,GAINESVILLE,FL326116580,TEL3523922347,EMAILCOPEADUFLEDU7GROUPLEADER,STATISTICALENGINEERINGDIVISION,INFORMATIONTECHNOLOGYLABORATORY,NISTNORTH,ROOM353,NATIONALINSTITUTEOFSTANDARDANDTECHNOLOGY,GAITHERSBURG,MD208990001ABSTRACTTHEPAPERREPORTSPROGRESSINTHEDEVELOPMENTOFAPRACTICALPROBABILISTICMODELFORTHEESTIMATIONOFEXPECTEDANNUALDAMAGEINDUCEDBYHURRICANEWINDSINRESIDENTIALSTRUCTURESTHEESTIMATIONOFTHEDAMAGEISACCOMPLISHEDINSEVERALSTEPSFIRST,BASICDAMAGEMODESFORCOMPONENTSOFSPECIFICBUILDINGTYPESAREDEFINED,ANDTHEIRPROBABILITIESOFOCCURRENCEASFUNCTIONSOFWINDSPEEDSAREESTIMATEDSECOND,THEDAMAGEMODESARECOMBINEDINPOSSIBLEDAMAGESTATES,WHOSEPROBABILITIESOFOCCURRENCEARECALCULATEDFROMTHEPROBABILITIESOFTHEBASICDAMAGEMODESANDESTIMATEDCONDITIONALPROBABILITIESASMEASURESOFTHEMUTUALDEPENDENCEBETWEENTHOSEMODESTHEPAPERDESCRIBESTHECONCEPTUALFRAMEWORKFORTHEPROPOSEDMODEL,ANDILLUSTRATESITSAPPLICATIONFORASPECIFICBUILDINGTYPEWITHHYPOTHETICALPROBABILISTICINPUTACTUALPROBABILISTICINPUTMUSTBEBASEDONLABORATORYSTUDIES,POSTDAMAGESURVEYS,INSURANCECLAIMSDATA,ENGINEERINGANALYSESANDJUDGMENT,ANDMONTECARLOSIMULATIONMETHODSTHEPROPOSEDCOMPONENTBASEDMODELISFLEXIBLEANDTRANSPARENTITISTHEREFORECAPABLEOFBEINGREADILYSCRUTINIZEDTHEMODELCANBEUSEDINCONJUNCTIONWITHHISTORICALLOSSDATA,TOWHICHITCANREADILYBECALIBRATED1INTRODUCTIONWITHINTHEUS,WINDSTORMSAREONEOFTHECOSTLIESTNATURALHAZARDS,FAROUTPACINGEARTHQUAKESINTOTALDAMAGEWINDENGINEERING,1997LANDSEAETAL,1999FOREXAMPLE,THE22BILLIONINSUREDLOSSESOFHURRICANEANDREWEXCEEDEDBYABOUT7BILLIONTHEINSUREDLOSSESOFTHENORTHRIDGECALIFORNIAEARTHQUAKEARECENTANALYSISOFWINDSTORMDAMAGEFORTHEUSEASTANDGULFCOASTSBYPIELKEETAL1998SUGGESTSTHATTHEAVERAGEANNUALECONOMICLOSSISABOUT5BILLIONTHISAGREESCLOSELYWITHNATIONALOCEANICANDATMOSPHERICADMINISTRATIONNOAAESTIMATESOF84BILLIONDOLLARSINHURRICANERELATEDDAMAGESINCE1980ACCORDINGTOSTATISTICSPUBLISHEDBYTHEMUNICHREGROUPFORTHEYEAR2001,WINDSTORMSWERERESPONSIBLEWORLDWIDEFOR55OFTHE36BILLIONINECONOMICLOSSESAND88OFTHE115BILLIONININSUREDLOSSESDUETOALLNATURALDISASTERSCOMBINEDSIMILARPERCENTAGESWERERECORDEDFORTHEUSTOPICS,2002OVERHALFOFTHEHURRICANERELATEDDAMAGEINTHEUSOCCURSINTHESTATEOFFLORIDA,WHICHHAS15TRILLIONINEXISTINGBUILDINGSTOCKCURRENTLYEXPOSEDTOPOTENTIALHURRICANEDEVASTATIONWITHAPPROXIMATELY85OFTHERAPIDLYINCREASINGPOPULATIONSITUATEDONORNEARTHE1200MILESOFCOASTLINE,FLORIDALOSSESWILLCONTINUETOMOUNTINPROPORTIONTOCOASTALPOPULATIONDENSITYITISTHEREFORECRITICALFORTHESTATEOFFLORIDA,ANDTHEINSURANCEINDUSTRYOPERATINGINTHATSTATE,TOBEABLETOESTIMATEEXPECTEDLOSSESDUETOHURRICANESANDTHEIRMEASUREOFDISPERSIONFORTHISREASONTHEFLORIDADEPARTMENTOFINSURANCEASKEDAGROUPOFRESEARCHERSTODEVELOPAPUBLICHURRICANELOSSPROJECTIONMODELTHISPAPERDESCRIBESAMODELFORTHEESTIMATIONOFTHEDAMAGETORESIDENTIALBUILDINGSDUETOHURRICANEORSEVERESTORMSALTHOUGHANUMBEROFCOMMERCIALLOSSPROJECTIONMODELSHAVEBEENDEVELOPED,ONLYAHANDFULOFSTUDIESAREAVAILABLEINTHEPUBLICDOMAINTOPREDICTDAMAGEFORHURRICANEPRONEAREASMOSTSTUDIESUSEPOSTDISASTERINVESTIGATIONSORAVAILABLECLAIMDATATOFITDAMAGEVERSUSWINDSPEEDVULNERABILITYCURVESFOREXAMPLE,ARELATIONSHIPBETWEENHOMEDAMAGEFROMINSURANCEDATAANDWINDSPEEDWASPROPOSEDFORTYPHOONSMIREILLEANDFLOMITSUTAETAL1996ASTUDYBYHOLMES1996PRESENTSTHEVULNERABILITYCURVEFORAFULLYENGINEEREDBUILDINGWITHSTRENGTHASSUMEDTOHAVELOGNORMALDISTRIBUTION,BUTCLEARLYINDICATESTHENEEDFORMORETHOROUGHPOSTDISASTERINVESTIGATIONSTOBETTERDEFINEDAMAGEPREDICTIONMODELSAMETHODFORPREDICTINGTHEPERCENTAGEOFDAMAGEWITHINANAREAASAFUNCTIONOFWINDSPEEDANDVARIOUSOTHERPARAMETERSWASPRESENTEDBYSILLANDKOZLOWSKI1997THEPROPOSEDMETHODWASINTENDEDTOMOVEAWAYFROMCURVEFITTINGSCHEMES,BUTITSPRACTICALVALUEISINOUROPINIONQUESTIONABLEOWINGTOINSUFFICIENTCLARITYANDTRANSPARENCYHUANGETAL2001PRESENTEDARISKASSESSMENTSTRATEGYBASEDONANANALYTICALEXPRESSIONFORTHEVULNERABILITYCURVETHEEXPRESSIONISOBTAINEDBYREGRESSIONTECHNIQUESFROMINSURANCECLAIMDATAFORHURRICANEANDREWALTHOUGHSUCHANAPPROACHISSIMPLE,ITISHIGHLYDEPENDENTONTHETYPEOFCONSTRUCTIONANDCONSTRUCTIONPRACTICESCOMMONTOTHEAREASREPRESENTEDINTHECLAIMDATARECENTCHANGESINBUILDINGCODESORCONSTRUCTIONPRACTICESCANNOTBEADEQUATELYREFLECTEDBYHUANGETALSVULNERABILITYCURVEINADDITION,DAMAGECURVESOBTAINEDBYREGRESSIONFROMOBSERVEDDATACANBEMISLEADING,BECAUSEVERYOFTEN,ASWASTHECASEFORHURRICANEANDREW,FEWRELIABLEWINDSPEEDDATAAREAVAILABLEINCONTRAST,ACOMPONENTAPPROACHEXPLICITLYACCOUNTSFORBOTHTHERESISTANCECAPACITYOFTHEVARIOUSBUILDINGCOMPONENTSANDTHELOADEFFECTSPRODUCEDBYWINDEVENTSTOPREDICTDAMAGEATVARIOUSWINDSPEEDSINTHECOMPONENTAPPROACHTHERESISTANCECAPACITYOFABUILDINGCANBEBROKENDOWNINTOTHERESISTANCECAPACITYOFITSCOMPONENTSANDTHECONNECTIONSBETWEENTHEMDAMAGETOTHESTRUCTUREOCCURSWHENTHELOADEFFECTSFROMWINDORFLYINGDEBRISAREGREATERTHANTHECOMPONENTSCAPACITYTORESISTTHEMONCETHESTRENGTHCAPACITIES,LOADDEMANDS,ANDLOADPATHSAREIDENTIFIEDANDMODELED,THEVULNERABILITYOFASTRUCTUREATVARIOUSWINDSPEEDSCANBEESTIMATEDESTIMATESAREAFFECTEDBYUNCERTAINTIESREGARDINGONONEHANDTHEBEHAVIORANDSTRENGTHOFTHEVARIOUSCOMPONENTSAND,ONTHEOTHER,THELOADEFFECTSPRODUCEDBYHURRICANEWINDSADAMAGEPREDICTIONMODELTHATINCORPORATESELEMENTSOFACOMPONENTAPPROACHISBEINGIMPLEMENTEDFORTHEHAZUSPROJECTMINORANDSCHNEIDER,2001THEPURPOSEOFTHISPAPERISTOPRESENTANDILLUSTRATETHEPRINCIPLEOFAPROBABILISTICCOMPONENTAPPROACHTOTHEPREDICTIONOFWINDINDUCEDDAMAGEANDOFCORRESPONDINGREPAIR/REPLACEMENTCOSTSOURAPPROACHMAKESUSEOFPROBABILISTICINFORMATIONONBASICDAMAGEMODESTHISINFORMATIONISUSEDTOCALCULATEPROBABILISTICINFORMATIONONCOMBINEDDAMAGESTATESTHELATTERCONSISTOFCOMBINATIONSOFBASICDAMAGEMODES,DETERMINEDBYENGINEERINGJUDGMENT,POSTDISASTEROBSERVATIONS,AND/ORANALYSISTHENEXTSECTIONDISCUSSESBASICDAMAGEMODESANDTHEIRPROBABILISTICCHARACTERIZATIONWETHENCONSIDERCOMBINEDDAMAGESTATESANDTHEDERIVATIONOFTHEIRPROBABILISTICCHARACTERISTICSONCETHISISDONEITISPOSSIBLETOESTIMATEREPAIR/REPLACEMENTCOSTSASSOCIATEDWITHBUILDINGDAMAGEINDUCEDBYWINDSTORMSSUCHCOSTSAREREFERREDTOASWINDINDUCEDBUILDINGDAMAGE,ORFORSHORTDAMAGENOTETHATWEWILLOCCASIONALLYREFERTOSOMETYPESOFDAMAGEINAPHYSICAL,ASOPPOSEDTOMONETARYSENSEFOREXAMPLE,WEWILLREFERTOTHEPHYSICALDAMAGEOF,SAY,SHINGLESWEWILLOMITTHEADJECTIVE“PHYSICAL”ANDREFERTOPHYSICALDAMAGEMOREBRIEFLYASDAMAGEWHENEVERTHECONTEXTISSUFFICIENTLYCLEARTHATNOCONFUSIONCANRESULTFROMTHISUSETHECALCULATIONOFDAMAGEREPAIR/REPLACEMENTCOSTSALLOWSTHEESTIMATIONOFBUILDINGVULNERABILITIESINAWINDENGINEERINGCONTEXTWEWILLDEFINEVULNERABILITYASAMEASUREOFTHESUSCEPTIBILITYTODAMAGE,EXPRESSEDASAFUNCTIONOFTHEWINDSPEEDFINALLY,WEDISCUSSANDILLUSTRATETHEESTIMATIONOFEXPECTEDDAMAGEFORGROUPSOFBUILDINGS,INCLUDINGREGIONALEXPECTEDANNUALDAMAGE,ANDEXPECTEDDAMAGEINDUCEDBYAHURRICANEEVENTUNCERTAINTIESASSOCIATEDWITHSUCHESTIMATESWILLBEDEALTWITHINASUBSEQUENTPAPERACOMPANIONTEAMOFRESEARCHERSFORTHISPROJECTISDEVELOPINGTHEWINDFIELDMODELTHATWILLPROVIDETHISDAMAGEMODELWITHTHEPROBABILITIESOFOCCURRENCEOFVARIOUSWINDSPEEDS,THUSALLOWINGTHEESTIMATIONOFANNUALIZEDINSURABLELOSSDEVELOPMENTOFTHEWINDFIELDMODELISNOTAPARTOFTHISPAPER,ANDWILLBETHESUBJECTOFAFORTHCOMINGSEPARATEDOCUMENT2BASICDAMAGEMODESTHISRESEARCHISCURRENTLYFOCUSEDONRESIDENTIALLOWRISESTRUCTURESOFDIFFERENTTYPESTHATMAKEUPTHEOVERWHELMINGBULKOFTHEFLORIDABUILDINGSTOCKFORPURPOSESOFILLUSTRATION,THEPAPERPRESENTSTHEAPPROACHFORABUILDINGBELONGINGTOASPECIFIEDTYPEANUNREINFORCEDMASONRYHOUSEWITHTIMBERGABLEROOFCOVEREDWITHSHINGLESITSMOSTVULNERABLETYPESOFCOMPONENTSARESHOWNINFIG1THEYCORRESPONDTOTHEFOLLOWINGFIVESIGNIFICANTBASICDAMAGEMODES1BREAKAGEOFOPENINGSO2LOSSOFSHINGLEST3LOSSOFROOFORGABLEENDSHEATHINGS4ROOFTOWALLCONNECTIONDAMAGECAND5MASONRYWALLDAMAGEWFORASPECIFIEDWINDSPEEDVTHEBUILDINGWILLEITHERNOTEXPERIENCEDAMAGE,OREXPERIENCESEVERALOFTHESEFIVEBASICDAMAGEMODESSOMEDAMAGEMODESAREINDEPENDENTOFEACHOTHEREG,LOSSOFSHINGLESANDBREAKAGEOFOPENINGSOTHERSARENOTEG,GIVENTHATTHEBUILDINGHASEXPERIENCEDWINDOWBREAKAGE,THEPROBABILITYOFITSLOSINGSHEATHINGINCREASESTHEMODELISFURTHERREFINEDBYDIVIDINGEACHBASICDAMAGEMODEINTOSEVERALSUBDAMAGEMODESEG,OI,I0,1,2,3ACCORDINGTOTHEDEGREEOFDAMAGENODAMAGE,LIGHT,MODERATE,ORHEAVYDAMAGEFOREXAMPLE,WECANDEFINEO0ASZEROLOSSOFOPENINGNODAMAGE,O1ASLOSSOFLESSTHAN25OFOPENINGSLIGHT,O2ASLOSSOF25TO50OFOPENINGSMODERATE,ANDO3ASLOSSOFINEXCESSOF50OFOPENINGSHEAVYSUBDAMAGEMODESCANSIMILARLYBEDEFINEDFORTHEOTHERBASICDAMAGEMODES,DENOTEDBYTJ,SK,CL,WM,J,K,L,M0,1,2,3THESUBDAMAGEMODESCORRESPONDINGTOADAMAGEMODEMUSTBESODEFINEDTHATTHEYAREMUTUALLYEXCLUSIVEEG,THEUNIONOFTHESUBEVENTSOII1,2,3ISEQUALTOTHEEVENTO,ANDTHESUMOFTHEIRPROBABILITIESISEQUALTOTHEPROBABILITYOFOAFIRSTSTEPTOWARDTHEESTIMATIONOFWINDINDUCEDDAMAGEISTHEPROBABILISTICCHARACTERIZATIONOFTHEBASICDAMAGEORSUBDAMAGEMODESTHISREQUIRESESTIMATESOF1PROBABILITIESTHAT,UNDERWINDSPEEDSCONTAINEDINSPECIFIEDINTERVALSDEFINED,FORSHORTHANDPURPOSES,BYASPEEDV,ABUILDINGOFASPECIFIEDTYPEWILLEXPERIENCEDAMAGESUBDAMAGEMODESOFVARIOUSKINDS,AND2MEASURESOFSTATISTICALDEPENDENCEBETWEENTHEEVENTSASSOCIATEDWITHTHOSEMODESFORPURPOSESOFILLUSTRATION,TABLE1LISTSASSUMEDPROBABILITIESOFOCCURRENCEOFTHESUBDAMAGEMODESFORTHEEXAMPLEOFFIGURE1,CONDITIONALONWINDSPEEDSBELONGINGTO5M/SINTERVALSCENTEREDONVALUESOFVVARYINGFROM40TO70M/STABLE1STATESTHATFORVINTHEINTERVAL575M/SV625M/S,PT2|60M/S50ISTHEPROBABILITYTHATABUILDINGWILLEXPERIENCEMODERATESHINGLEDAMAGE,ANDPS3|60M/S10ISTHEPROBABILITYTHATTHEBUILDINGWILLEXPERIENCEHEAVYROOFSHEATHINGDAMAGETOSIMPLIFYTHENOTATIONWEWILLOMITTHENOTATION“|V”INALLSUBSEQUENTDEVELOPMENTS,THATIS,WEWILLUSETHESHORTHANDNOTATIONPXINLIEUOFPX|VFOREACHDAMAGEMODETHEEVENT“NODAMAGE”I0ISUNITYMINUSTHESUMOFTHEPROBABILITIESOFTHETHREESUBDAMAGEMODESI1,2,3FOREXAMPLE,FORV40M/STHEPROBABILITYFORNOOPENINGDAMAGEISPO01PO1PO1PO2PO3100595THEREQUISITEPROBABILITIESOFBASICDAMAGEMODESCANINPRINCIPLEBEOBTAINEDDIRECTLYFROMLABORATORYTESTSEG,BASKARANANDDUTT,1995,AFTERTRANSLATINGPHYSICALDAMAGEUSUALLYREPORTEDINLABORATORYTESTSINTOMONETARYTERMSFROMPOSTDISASTEROBSERVATIONSOFDAMAGE,DULYACCOUNTINGFORTHEFACTTHATREPORTEDDAMAGEINCLUDESDAMAGEDUETOEFFECTSOTHERTHANWINDFOREXAMPLESTORMSURGEANALYTICALSTUDIESENTAILINGSIMULATIONSAND,LASTBUTBYNOMEANSLEAST,ENGINEERINGJUDGMENTNEEDEDTOSUPPLEMENTORINTERPOLATEBETWEENSPARSEDATATHECHOICEOFBASICDAMAGEMODESISINGENERALDETERMINEDBYPRACTICALCONSIDERATIONSSUCHASTHETYPEOFSTRUCTURE,THEFORMATOFTHEREQUISITEPROBABILISTICINFORMATIONANDTHEEXTENTTOWHICHITISAVAILABLE,THENEEDFORKEEPINGTHEMODELREASONABLYSIMPLE,ANDTHEREQUISITEACCURACYOFTHELOSSESTIMATIONTHEMETHODOLOGYDESCRIBEDINTHISPAPERISINDEPENDENTOFTHEBASICDAMAGEMODESBEINGCONSIDEREDINTHECALCULATIONS3COMBINEDDAMAGESTATESWHENAWINDSTORMCAUSESDAMAGETOASTRUCTURE,ITWILLUSUALLYCAUSEDIFFERENTDAMAGEMODESTODIFFERENTCOMPONENTSATTHESAMETIMEWESHALLREFERTOTHESECOMBINATIONSOFDAMAGEMODESASCOMBINEDDAMAGESTATESSINCETHERESULTINGCOMBINEDDAMAGESTATESREQUIRENOTONLYSETTHEORETICALBUTALSOARCHITECTURALANDSTRUCTURALENGINEERINGSCRUTINY,ITISAPPROPRIATETOUSEANENGINEERINGAPPROACHTOTHEIRDEFINITIONTHEDAMAGESTATESBEINGCONSIDEREDMUSTSATISFYTHEFOLLOWINGREQUIREMENTSTHEYMUSTBECOMBINATIONSOFTHEDAMAGEMODESDESCRIBEDPREVIOUSLYTHEYMUSTBECHOSENWITHAVIEWTOENABLINGDAMAGEESTIMATESTOBEMADECORRECTLY,INTHESENSETHATNOPOSSIBLEDAMAGESTATEISOMITTED,ANDNODOUBLEORMULTIPLECOUNTINGOFDAMAGESTATESOCCURSTHEYMUSTMAKESENSEFROMANARCHITECTURALANDSTRUCTURALENGINEERINGPOINTOFVIEWFOREXAMPLE,FORABUILDINGCOVEREDBYCONVENTIONALSHEATHING,ITMAYBEASSUMEDTHATWALLDAMAGEWILLNOTOCCURWITHOUTSOMELOSSOFSHEATHINGSIMILARLY,ALTHOUGHSHINGLEANDOPENINGFAILURESDONOTNECESSARILYCAUSEROOFTOWALLCONNECTIONDAMAGE,ITISREASONABLETOASSUMETHATNOROOFTOWALLCONNECTIONDAMAGEWILLOCCURWITHOUTSOMESHINGLELOSSANDOPENINGBREAKAGETHEBASICDAMAGEMODESAREREPRESENTEDINTHEDIAGRAMOFFIGURE2THEPARTIALORTOTALOVERLAPOFTHEBASICDAMAGEMODESISBASEDONENGINEERINGJUDGMENTFIGURE2ISTHEPOINTOFDEPARTUREINTHEPROCESSOFDEFININGCOMBINEDDAMAGESTATESASSOCIATEDWITHTHEBASICDAMAGEMODESO,T,S,WANDCAREEVENTSCOMBINEDDAMAGESTATESWHOSEUNIONREPRESENTSTHETOTALDAMAGEUNIVERSESHOWNINFIGURE2COMBINEDDAMAGESTATESCANSIMILARLYBECONSIDEREDTHATINVOLVESUBDAMAGEMODESWECONSIDERTHEEVENTSASSOCIATEDWITHTHEOCCURRENCEOFTHEFOLLOWINGCOMBINATIONSOFSUBDAMAGEMODESEVENT1O0T0NODAMAGESEEHATCHEDAREAINFIG3ASINCEITISASSUMEDTHATALLDAMAGEINVOLVESFIRSTSOMEOPENINGBREAKAGEAND/ORSHINGLELOSS,THELACKOFBOTHOFTHESEISEQUIVALENTTONODAMAGEEVENTS2,3,4OIT0OPENINGFAILUREANDNOSHINGLELOSSI1,2,3SEEHATCHEDAREAINFIG3BRECALLTHATEACHAREAOIISASUBSETOFTHESETOFORCONVENIENCETHISISNOTSHOWNINANYOFTHEGRAPHSOFFIG3THEPROBABILITIESOFTHESESUBSTATESWILLHELPTOESTIMATETHECOSTOFREPAIROFHOMESTHATHAVEONLYOPENINGFAILURESEVENT5,6,7O0TJS0SHINGLEFAILUREANDNOOPENINGORSHEATHINGLOSSI1,2,3SEEHATCHEDAREAINFIG3CTHEPROBABILITIESOFTHESESUBSTATESWILLHELPTOESTIMATETHECOSTOFREPAIROFHOMESTHATHAVEONLYROOFCOVERFAILURESEG,HOMESWITHEFFECTIVELYBOARDEDOPENINGSANDSTRONGGARAGEDOORSEVENTS8THROUGH16OITJS0OPENINGANDSHINGLEFAILUREANDNOSHEATHINGLOSSI,J1,2,3SEEHATCHEDAREAINFIG3DEVENTS17THROUGH25O0TJSKSHINGLEANDSHEATHINGFAILUREANDNOOPENINGFAILUREJ,K1,2,3SEEHATCHEDAREAINFIG3EEVENTS26THOUGH52OITJSKW0C0OPENING,SHINGLEANDSHEATHINGLOSSANDNOWALLANDCONNECTIONFAILUREI,J,K1,2,3SEEHATCHEDAREAINFIG3FEVENTS53THROUGH133OITJSKCLW0OPENING,SHINGLE,SHEATHINGANDCONNECTIONFAILUREANDNOWALLFAILURESEEHATCHEDAREAINFIG3GEVENTS134THROUGH214OITJSKWMC0OPENING,SHINGLE,SHEATHINGANDWALLFAILUREBUTNOCONNECTIONFAILURESEEHATCHEDAREAINFIG3HEVENTS215THROUGH457OITJSKCLWMOPENING,SHINGLE,SHEATHING,WALL,ANDCONNECTIONFAILURESEEHATCHEDAREAINFIGURE3ITHEREAREATOTALOF457DAMAGESTATEEVENTSHOWEVER,NOTALLOFTHESEEVENTSAREOFINTERESTFROMADAMAGEESTIMATIONPOINTOFVIEWENGINEERINGCONSIDERATIONSALLOWTHEELIMINATIONOFANUMBEROFEVENTSTHEREARESEVERALSCENARIOSWHENROOFCOVERDAMAGETANDSHEATHINGDAMAGESOCCURATTHESAMETIME,THEDAMAGEDAREAOFTHEROOFCOVERMUSTBELARGERTHANTHEDAMAGEDAREAOFSHEATHINGWECANTHEREFOREELIMINATEALLTHEDAMAGESTATESWHICHPERTAINTODAMAGEDAREAOFROOFCOVEREQUALTOORSMALLERTHANTHEDAMAGEDAREAOFSHEATHING,IEELIMINATEEVENTSTHATCONTAINTJSKWHENJKWHENROOFCOVERDAMAGETORSHEATHINGDAMAGESOROPENINGDAMAGEOOCCURTOGETHERWITHWALLDAMAGEWORCONNECTIONDAMAGEC,THELEVELOFDAMAGEFORTORSOROSHOULDBELARGERTHANFORWORCTHATIS,THEREISONLYASMALLPROBABILITYTHATAWALLWOULDSUFFERHEAVYDAMAGEWHILETHEROOFCOVERHASSUFFEREDLIGHTDAMAGETHUSWECANELIMINATEALLTHEDAMAGESTATESWHICHCONTAINLOWERLEVELSOFROOFCOVERINGDAMAGEANDDECKINGDAMAGEANDOPENINGDAMAGETHANWALLDAMAGEANDCONNECTIONDAMAGEIEELIMINATEEVENTSCONTAININGOI,TJ,SK,WM,ANDCNWHENI,J,KM,NINPARTICULAR,WHENSEVEREWALLDAMAGEANDSEVEREROOFTOWALLCONNECTIONDAMAGEOCCURTOGETHER,THEWHOLESTRUCTURECOLLAPSESSOIFROOFTOWALLCONNECTIONANDWALLDAMAGEAREBOTHHEAVYIE,IFW3ANDC3OCCUR,THEONLYSIGNIFICANTDAMAGEEVENTWILLBEO3T3S3W3C3,SOTHATWECANELIMINATEALLEVENTSOITJSKW3C3FORWHICHI,J,K1,2THESEENGINEERINGCONSIDERATIONSALLOWTHEELIMINATIONOF240DAMAGESTATES,LEAVING217DAMAGESTATES4CONDITIONALPROBABILITIESASETOFCONDITIONALPROBABILITIES,INCLUDINGPS|O,PSK|O,PS|OI,PSK|OI,PW|C,PW|CL,PWM|C,PWM|CL,ISNECESSARYTOCOMPUTETHEPROBABILITIESOFOCCURRENCEOFANYOFTHEEVENTSLISTEDINTHEPREVIOUSSECTIONTHESECONDITIONALPROBABILITIESAREANENGINEERINGINPUTTOTHEPROBLEMTHEYWERESELECTEDBYTAKINGINTOACCOUNTTHEFEASIBILITYANDSEQUENCEOFOCCURRENCEOFTHEEVENTSFOREXAMPLE,ITISMORELIKELYTHATASHEATHINGFAILURESWOULDRESULTFROMANOPENINGFAILUREORATHERTHANTHEOPPOSITETABLE2PROVIDESILLUSTRATIVEEXAMPLESNOTETHATTHECONDITIONALPROBABILITIESOFONESUBDAMAGEMODEOCCURRINGGIVENTHATANOTHERSUBDAMAGEMODEHASOCCURREDAREALSOCONDITIONALONTHEWINDSPEEDASWASTHECASEFORTHEPROBABILITIESOFTABLE1,THECONDITIONALDEPENDENCEONVISOMITTEDFROMTHENOTATIONWITHREGARDTOTHESTATISTICALDEPENDENCEBETWEENBASICDAMAGEMODES,NOTECASESATHROUGHDBELOWTHESEAREILLUSTRATEDBYUSINGTHEDAMAGEMODESOFTHEEXAMPLETABLE1,ANDTHEYCANFACILITATEORCIRCUMSCRIBEINFORMEDENGINEERINGJUDGMENTA100DEPENDENCETHEPROBABILITYOFTSHINGLELOSSGIVENTHATSSHEATHINGLOSSHASOCCURREDISUNITYIE,PT|S1IFTHESTRUCTUREHASLOSTSHEATHINGPANELSTHENTHESHINGLESHAVENECESSARILYBEENLOSTFORTHISCASEITFOLLOWSFROMBASICDEFINITIONSTHATPTSPT|SPSPS1SIMILARLY,IFTHESTRUCTUREHASLOSTANYPARTOFTHECONNECTIONTHENTHESHEATHINGDIAPHRAGMHASNECESSARILYBEENDAMAGEDPSCPS|CPCPC2ALSO,ITISASSUMEDTHATIFTHEWINDISSTRONGENOUGHTODAMAGEANYPARTOFTHEWALLSTHENTHESHEATHINGDIAPHRAGMWILLALSOBEDAMAGEDPWSPS|WPWPW3BINDEPENDENCE0DEPENDENCEFOREXAMPLE,OPENINGBREAKAGEDOESNOTDIRECTLYAFFECTTHEROOFSHINGLESINTHISCASEPT|OPT,THATIS,PTOPTPO4CPARTIALDEPENDENCEFORTHISSUBCASEITISREQUIREDTOSPECIFYTHECONDITIONALPROBABILITYONTHEBASISOFSTRUCTURALENGINEERINGCONSIDERATIONSTHISWOULDAPPLY,FOREXAMPLE,TOTHEPROBABILITYOFROOFSHEATHINGDAMAGEGIVENTHATOPENINGBREAKAGEHASOCCURRED,PS|OTHEEXISTENCEOFANOPENINGONTHEWINDWARDSIDEOFTHESTRUCTUREWILLINCREASETHELIKELIHOODOFROOFSHEATHINGDAMAGEDUETOGREATERINTERNALPRESSURIZATIONTHEDEGREEOFDEPENDENCEBETWEENTWODAMAGEMODESWILLDEPENDONSTRUCTURALTYPEOFTHEBUILDING,DAMAGEMECHANISM,LOADPATHANDSTRENGTHCAPACITYOFBUILDINGCOMPONENT,ETCFOREXAMPLE,THESIGNIFICANTDIFFERENCEOFGABLEROOFANDHIPROOFINSTRENGTHRESISTANCEFORUPLIFTFORCEWILLAFFECTPARTIALDEPENDENCECONCERNINGTHEROOFFAILUREWHETHERTHEFAILUREOFROOFISDUETOTHETURBULENCEUNDERANOVERSIZEDEAVE,ORAWEAKROOFTRUSSTOWALLCONNECTION,ORAGREATERINTERNALPRESSURE,WILLRESULTINDIFFERENTPARTIALDEPENDENCEBETWEENROOFFAILUREANDOPENINGFAILURETHEDEGREEOFDEPENDENCEISAFUNCTIONOFSTRUCTURALTYPE,LOADPATH,ANDFAILUREMODEDMUTUALLYEXCLUSIVESTATESFORMUTUALLYEXCLUSIVESTATESA,B,WEHAVEPA|B0,SOPAB0INTHISMODEL,THEREARENOMUTUALLYEXCLUSIVEDAMAGEMODESINPRACTICE,THECONDITIONALPROBABILITIES,ASWELLASTHEPROBABILITIESL