StructuralReliability&RiskAssessment4 -8 July 2016Wuhan, ChinaLecture 4 & 5: Structural Reliability Analysis-l & 1lProfessorPurnendu K.DasB.E., M.E., PhD, CEng, CMarEng, FRINA, FIStructE, FIMarEST
Structural Reliability & Risk Assessment 4 – 8 July 2016 Wuhan, China Lecture 4 & 5: Structural Reliability Analysis-I & II Professor Purnendu K. Das B.E., M.E., PhD, CEng, CMarEng, FRINA, FIStructE, FIMarEST 1
eOxfordRISKHAZARDThe chance of bad consequences,lossWebsterThe chance of injury, damage or loss
Oxford RISK HAZARD The chance of bad consequences, loss Webster • The chance of injury, damage or loss 2
Two aspects thrust themselves forward:FIRST, Chance &SECOND, the unwantedconsequences involved in riskDecision making involves:PROBABILITIES(Chance)&UTILITIES (Consequences)
Two aspects thrust themselves forward: FIRST, Chance & SECOND, the unwanted consequences involved in risk Decision making involves: PROBABILITIES (Chance) & UTILITIES (Consequences) 3
RISK= PROBABILITYOFFAILUREXCONSEQUENCESOFFAILURE
RISK = PROBABILITY OF FAILURE CONSEQUENCES OF FAILURE 4
If you risk nothing, then you risk everythingTheR-101isassafeasahouseexceptforthemillionthchance.Lord Thomson, Secretary of State for Air, shortly beforeboardingthe airship headed to India for its first flight.Oct 4,1930
If you risk nothing, then you risk everything. The R-101 is as safe as a house except for the millionth chance. Lord Thomson, Secretary of State for Air, shortly before boarding the airship headed to India for its first flight. Oct 4, 1930 5
IntroductionStructural design istraditionallybasedon deterministic analysisHowever,fluctuationsofloads,variabilityofmaterialpropertiesuncertainty in analysis models etc. all contribute to a generally smalprobability that the structure does not perform as intended. This smallprobabilityisdefinedasthefailureprobability.Thereliability,defined asthecomplementofthefailureprobability,isarational measureof safetyReliabilitymethodsdealwith theuncertainnatureof loads.resistanceetc.andleadtoassessmentof thereliability.Reliabilitymethodsarebasedonanalysismodelsforthestructureinconjunctionwithavailableinformationaboutloadsandresistancesandtheirassociateduncertainties.Theanalysis models areusuallyimperfect,andtheinformationaboutloadsandresistancesisusuallyincomplete.Thereliabilityasassessedbyreliabilitymethodsisthereforegenerallynotapurelyphysicalpropertyofthestructureinitsenvironmentofactions,butratheranominalmeasureofthesafetyofthestructure,givenacertainanalysismodelandacertainamountandqualityofinformation
Introduction • Structural design is traditionally based on deterministic analysis. However, fluctuations of loads, variability of material properties, uncertainty in analysis models etc. all contribute to a generally small probability that the structure does not perform as intended. This small probability is defined as the failure probability. The reliability, defined as the complement of the failure probability, is a rational measure of safety. • Reliability methods deal with the uncertain nature of loads, resistance etc. and lead to assessment of the reliability. Reliability methods are based on analysis models for the structure in conjunction with available information about loads and resistances and their associated uncertainties. The analysis models are usually imperfect, and the information about loads and resistances is usually incomplete. The reliability as assessed by reliability methods is therefore generally not a purely physical property of the structure in its environment of actions, but rather a nominal measure of the safety of the structure, given a certain analysis model and a certain amount and quality of information. 6
Correspondingly,alsotheestimatedfailureprobabilityisdependentonthe analvsis model and the level of information,and it can thereforeusuallynotbeinterpreted asthefreguencyof occurrenceoffailureforthatparticulartvpeofstructure.Anidealfreguentisticinterpretationoftheestimated failureprobability would require a large population of theparticular type of structure in conjunction with perfect analysis modelsand full knowledge about the governing uncertainties.This will practicallyneverbefulfilled..Measuringthe safetyof a structurebyits reliability makesthereliabilityauseful decision parameter.Fulfillmenf of a requirement to the reliability isthennecessaryinordertoensureasufficientsafetylevelindesign.Sucha requirement can eitherbe derived by a utility optimisation in a decisionanalysis,orbyreguiringthatthesafetylevelasresultingfromthedesignbya reliability analysis shall bethesameasthesafetylevel resultingfromcurrentdeterministicdesignpractice.Thelatterapproachisbasedonthepostulationthatcurrentdesignpracticeisoptimalwithrespecttosafetyandeconomyor,atleast,leadstoalevelofsafetyacceptedbysociety.In bothcasesthe requirement to thereliabilityis atargetreliability whichis dependent on the analysis model aswell asthedistribution assumptions made for representation of the uncertainties inloadsandresistances
• Correspondingly, also the estimated failure probability is dependent on the analysis model and the level of information, and it can therefore usually not be interpreted as the frequency of occurrence of failure for that particular type of structure. An ideal frequentistic interpretation of the estimated failure probability would require a large population of the particular type of structure in conjunction with perfect analysis models and full knowledge about the governing uncertainties. This will practically never be fulfilled. • Measuring the safety of a structure by its reliability makes the reliability a useful decision parameter. Fulfillment of a requirement to the reliability is then necessary in order to ensure a sufficient safety level in design. Such a requirement can either be derived by a utility optimisation in a decision analysis, or by requiring that the safety level as resulting from the design by a reliability analysis shall be the same as the safety level resulting from current deterministic design practice. The latter approach is based on the postulation that current design practice is optimal with respect to safety and economy or, at least, leads to a level of safety accepted by society. In both cases the requirement to the reliability is a target reliability which is dependent on the analysis model as well as the distribution assumptions made for representation of the uncertainties in loads and resistances. 7
Structural Reliability Analysis·Uncertainty·Consistentlevelof safety
• Uncertainty • Consistent level of safety Structural Reliability Analysis 8
CLASSIFICATIONNOTES&NO.30.6DNVSTRUCTURALRELIABILITY ANALYSISOFMARINESTRUCTURESJULY1992
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Target ReliabilityClass of FailureConseguence of failureLess SeriousSerious10-e3-10-e4·Redundantstructure10-e4-10-e5Non-redundantstructure(significantwarning)Non-redundant structure10-e5- 10-e6(no warning)10
Target Reliability • Redundant structure 10-e3 - 10-e4 • Non-redundant structure 10-e4 - 10-e5 (significant warning) • Non-redundant structure 10-e5 - 10-e6 (no warning) Class of Failure Consequence of failure Less Serious Serious 10