31
Reliability and probability of failure in structural fire safety engineering An introduction Ruben Van Coile Structures in Fire Forum, April 12, 2016

Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Embed Size (px)

Citation preview

Page 1: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Reliability and probability of failure in structural fire safety engineeringAn introduction

Ruben Van Coile

Structures in Fire Forum, April 12, 2016

Page 2: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

2

I.Whyuseprobabilisticcalculations?

Page 3: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

3

I.Whyuseprobabilisticcalculations?

Perfectsafetydoesnotexist

Page 4: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

4

I.Whyuseprobabilisticcalculations?

It’sthebasisoftheEurocodes andBS

Page 5: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

5

I.Whyuseprobabilisticcalculations?

Perfectsafetydoesnotexist It’sthebasisoftheEurocodes andBS

Decisionmakingandcostoptimization

Page 6: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

6

I.Whyuseprobabilisticcalculations?

II.Basicconceptsforcalculatingfailureprobabilities

III.Discussion

Perfectsafetydoesnotexist It’sthebasisoftheEurocodes andBS

Decisionmakingandcostoptimization

Page 7: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

PerfectsafetydoesnotexistEverystructureorstructuralelement

hasaprobabilityoffailure

7

Page 8: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Theloadeffectexhibitsrandomvariations

(Baldwinetal.,1970)

8

Page 9: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Materialpropertiesexhibitrandomvariations

Figure II.2: Observed mean minus specified strength and standard deviation of standard cube strength of 88 production units of concrete grade C35 (Rackwitz 1983)

9

(Caspeele,2010)

Page 10: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Engineeringmodelsandcalculationtoolsareimperfect

10

(Soetens,2015)

Page 11: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Load E Resistance R

Situations with failure

Thus:Evenforagooddesign,theloadEmaybelargerthantheresistanceR

11

Boththe loadeffectE and the resistance R

exhibit randomvariations

Page 12: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Load E Resistance Rprior to fireResistance R

during fire

12

Thus:Evenforagooddesign,theloadEmaybelargerthantheresistanceR

Situations with failure

Page 13: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

13

LimitingtheprobabilityoffailurebydesignThebasisoftheEurocodes

Page 14: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

TheEurocodespecifiesatargetsafetylevel/failureprobability

Targetreliabilityindexinfunctionoftheconsequencesofstructuralfailure(normaldesignconditions)

• Eurocodepartialsafetyfactorsderivedfromthetarget

safetylevel

• ApplicationofEurocodedesignrulesresultsinasafety

levelof3.8

(generallyslightlyhigherbecauseofconservatism)

Page 15: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Unfortunately,notargetisspecifiedforstructuralfiresafety

• TargetreliabilitiesintheEuropean

NaturalFireSafetyConcept

(backgrounddocuments)

• Back-calculatingtheBStarget

reliabilityindexforspecificcases

Butoptions doexist

• Cost-optimization:

Whatistheoptimumlevelof

structuralfireresistance?

(VanCoile, 2015)

Page 16: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Isthereanoptimumlevelofinvestmentinstructuralfiresafety?Decisionmakingand

costoptimization

16

Page 17: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Isthereanoptimumlevelofinvestmentinstructuralfiresafety?

Utility function: ( ) ( ) ( ) ( )Y p B p C p D p= − −

Benefitfunction

Initial construction

cost

Expected costs due to failure

and partial damage

p =theoptimizationparameter

Includes• [Annual]Probabilityofafullydeveloped fire(λ*)

• Probabilityoffailure givenafullydeveloped fire(Pf,fi)

• Failurecostsandrepair/reconstructioncostsincaseofpartialdamage(ξ)

Optimizationcriterion:MaximizeY

Page 18: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Isthereanoptimumlevelofinvestmentinstructuralfiresafety?

Safetyinvestmentcostfactor

ISO834fire exposure,given λ* 120minISO834fireexposure

Page 19: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Butcost-optimizationisnosilverbullet

• Parametersofcost-optimizationareuncertain

• Stakeholdersmaynotallagreeoneachinputparameter

• Casespecificevaluationsarenotalwaysfeasible needforgeneralrules

DetermineanAcceptableRangeforthestructuralfireresistancetime

Basedonresultsofcost-optimization,i.e.

• failureprobabilities• fireignition frequencies

• failurecosts…

Page 20: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

ξ =350

Anacceptablerangeforthestructuralfireresistancetime

ξ failurecostratio

Avoidingoverinvestment

Avoidingunderinvestment

Acceptable Range20

Page 21: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

BasicconceptsforcalculatingfailureprobabilitiesAconceptualintroduction

21

Page 22: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

ThelimitstatefunctionZHowdoyoudefinefailure?

22

! = # − %Generalformula ! = # − % < 0Failure

! = # − % ≥ 0Safe/Success

“Load” E “Resistance” R

Situations with failure

UseMonteCarlomethods

Orevaluate/knowthePDF

)* = + ! = # − % < 0

Page 23: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

ThelimitstatefunctionZApplicationtofire-exposedstructuralmembers:cross-sectionbased

23

! = # − %Generalformula PureBending

! = ,-.-,*0,1 − ,2 .3 +.5

10000MonteCarlo

andMixedLNapproximation

Page 24: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

ThelimitstatefunctionZApplicationtofire-exposedstructuralmembers:advancedmodels(2nd ordereffects)

24

! = # − %Generalformula

6)ButthemomentmE depends

onthedeflection…

Doomedtocomputationally

expensiveMonteCarlo?

Page 25: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Adetourtoafeasiblecalculationmethod…Evenforverycomplexmodels,thePDFofascalarmodeloutputY canbeapproximated“quickly”

25

Simpleexample

7 = 29:9;9<With:

X1 :LN(3;0.3)

X2 :LN(4;0.5)

X3 :LN(2;0.2)

Y:LN(12.48;0.646)

10000MCS

Page 26: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

ThelimitstatefunctionZApplicationtofire-exposedstructuralmembers:advancedmodels(2nd ordereffects)

26

! = # − %Generalformula

6)

Asthereascalarmodeloutput

whichisrepresentativeforthe

resistanceR?

Foreverycolumnrealizationthereisa

maximumloadPmax

(takingintoaccount2nd ordereffects)

=runmodeltofailure10000MCS

Page 27: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

ThelimitstatefunctionZApplicationtofire-exposedstructuralmembers:advancedmodels(2nd ordereffects)

27

! = # − %Generalformula

6)

Eccentricloadingincl.2nd order

! = ,-)=>?,*0,1 − ,2 )3 + )5

Failureprobabilityevaluationfeasible

withPDFofPmax approximated

Page 28: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

DiscussionHowtodefine“failure”forstructuralsystemsexposedtofire?

Page 29: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

4.Other…

NeedtodefinealimitstatefunctionZAnddeterminearepresentativescalarmodeloutputY

29

! = # − %Generalformula Options

! = ,-@- − ,[email protected] tR

! = ,-A=>? − ,2A22.Runthemodelforincreasingfireloadtillfailure qmax

! = ,-B=>? − ,2BC0=013.Determinearepresentativefailureindicator e.g vmax

Toapplyreliabilityconceptstostructuralsystemsexposedto

fire,weneeda“performanceindicator/criterion”

Page 30: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

30

Summary/Conclusions

StandardreliabilitycalculationsarebasedonalimitstatefunctionZ

Perfectsafety doesnot exist.

Everystructure orstructural elementhasaprobability offailure

Needtodefineperformanceindicators/criteriaforstructuralfire

Limiting the probability offailureisthe very goalofthe Eurocodes

Probabilisticcalculationsforcost-optimizationanddecisionmaking

Page 31: Reliability and probability of failure in structural fire ...fire-research.group.shef.ac.uk/steelinfire/downloads/RVC2016.pdf · Reliability and probability of failure in structural

Thank you for your attention !

31