荷載課件 荷載chapt 8

LoadsandDesignPhilosophy

Ji

JingCEDepartmentofSCUTChapter8Fundamentalconceptsofstructuralreliability

8.1．Structureperformanceandlimitstate8.2．Statisticalanalysisofactioneffectand structuralresistance8.3.Degreeofreliabilityofstructure8.4.ReliabilityindexofstructureChapter8Fundamentalconceptsofstructuralreliability8.1．Structureperformanceandlimitstate

(結(jié)構(gòu)的功能及其極限狀態(tài))Structureperformance

Designpurpose:Anystructuresshouldmeetthespecifiedrequirementsduringthedesignworkinglifeundernormalcondition.designworkinglife:Itreferstotheperiodthatastructureorstructurememberworksasspecifiedwithoutheavyrepair.Fordifferenttypesofstructures,thedesignworkinglivesaredifferent.Seepage69.Chapter8FundamentalconceptsofstructuralreliabilityStructureperformance

undernormalcondition:Itreferstotheconditionfornormaldesign,normalconstructed,normaluse,andtheaccidentsandhumanerrorarenotincluded.specifiedrequirements(structureperformance):

(1)Safety(2)Serviceabilitystructureperformance

(3)Durability

(4)Integralstability

Theaboverequirementsaregenerallycalled“reliabilityofstructure”Chapter8Fundamentalconceptsofstructuralreliability1.Structureperformance

Question:What’sthedifferencebetweenthe“designworkinglife”and“designreferenceperiod”?Chapter8Fundamentalconceptsofstructuralreliability2.Limitstateofstructure

Limitstate:Whenastructureorstructuralelementexceedsaspecifiedstate,itcannotsatisfytheassignedrequirement,thespecifiedstateiscalled“l(fā)imitstate”.

Whenastructureorstructuralelementbecomesunfitforitsintendeduse,itissaidtohavereachedalimitstate.Chapter8Fundamentalconceptsofstructuralreliability2.Limitstateofstructure

AccordingtoChineseCode“UnifiedStandard”,thelimitstateofastructurecanbedividedintotwogroups:（1）Ultimatelimitstate（承載能力極限狀態(tài)）

Safety（2）Serviceabilitylimitstate（正常使用極限狀態(tài)）

Serviceability&DurabilityChapter8Fundamentalconceptsofstructuralreliability（1）Ultimatelimitstate（承載能力極限狀態(tài)）

Safety

When

astructureorstructuralelementattainsits

maximumbearingcapacityorthedeformationlimitthatthestructurecannotcarryloadinganymore,thusthestructureorstructuralelementisinultimatelimitstate.Someexamplesareasfollowing:Ruptureof

materialsincriticalpartsofastructure.(a)

(includefatiguefailure)Lossofequilibriumofapartorallofthestructureasarigidbody.(overturn,sliding)(b)Formationofaplasticmechanism.(makestructureunstable)Instability(columnbuckling)(d)(c)Progressivecollapse

Chapter8Fundamentalconceptsofstructuralreliability（2）Serviceabilitylimitstate（正常使用極限狀態(tài)）

Serviceability&Durability

When

astructureorstructuralelementattainsthecodelimitsofserviceabilityordurability,thusthestructureorstructuralelementisinserviceabilitylimitstate.Someexamplesareasfollowing:Excessivedeflectionsfornormalservice.Excessivecrackwidth.(corrosionofthereinforcement,gradualdeteriorationoftheconcrete)Undesirablevibrations.(maydisturbtheusers)Chapter8Fundamentalconceptsofstructuralreliability2.Limitstateofstructure

Summary:

Whenastructurereachesultimatelimitstate,itmayleadtolossoflifeandmajorfinanciallosses,thedamageisserious.Inpracticaldesign,suchalimitstateshouldhaveaverylowprobabilityofoccurrence.Whenastructurereachesserviceabilitylimitstate,itmay

disrupt

thefunctionaluse

ofthestructurebutnotcollapse.Sincethereislessdangeroflossoflife,ahigherprobabilityofoccurrencecanbetolerated.

Chapter8Fundamentalconceptsofstructuralreliability

8.1．Structureperformanceandlimitstate8.2．Statisticalanalysisofactioneffectand structuralresistance8.3.Degreeofreliabilityofstructure8.4.ReliabilityindexofstructureChapter8Fundamentalconceptsofstructuralreliability

8.2．Statisticalanalysisofactioneffectand structuralresistance

(荷載和結(jié)構(gòu)抗力的統(tǒng)計(jì)分析)The

factorsaffectingthereliabilityofstructureanduncertaintyNormaldistributioncurveProbabilityofconfidenceThecharacteristicvaluesoffunctionsofrandomvariable

Chapter8Fundamentalconceptsofstructuralreliability

8.2．Statisticalanalysisofactioneffectand structuralresistance

(荷載和結(jié)構(gòu)抗力的統(tǒng)計(jì)分析)The

factorsaffectingthereliabilityofstructureanduncertainty

Thefactorsaffectingthereliabilityofstructurecanbeconcludedintotwocategories:ActioneffectStructuralresistanceChapter8Fundamentalconceptsofstructuralreliability

Actioneffect

isthereactionofastructuretotheaction.Itinvolvesinternalforces,suchasbendingmoment,

shearingforce

andaxialforce,deformation,crackandvibrationofthestructure.Structuralresistanceisthe

capacity

ofastructuretoresisttheactioneffect.Itdependsonthestrengthofthematerial,thedimensionofthestructureandtheaccuracyofthecalculatingequation.Chapter8FundamentalconceptsofstructuralreliabilityAsthe

actioneffectandthe

structuralresistanceareallrandomvariables,itisdifficulttodeterminetheirvaluesbyfixedvaluemethod.Earthquakeactionisarandomvariable.Occupancyload,windload,snowloadareallrandom.Theself-weightofthestructureisalsosomewhatrandom.

action

actioneffect

witharandom

Chapter8Fundamentalconceptsofstructuralreliability

Thefactorsaffectingthe

structuralresistance:

thestrengthofthematerial,thedimensionofthestructure,theaccuracyofthecalculatingequation.Forthestrengthofthematerial,itsvalueisaffectedbythematerialqualityandproductiontechnics.Itisveryhardtoavoidtheerrorsfrommanufactureprocess.

Chapter8Fundamentalconceptsofstructuralreliability

Duetothevariabilityinthestrengthofthematerial,thetoleranceinthemanufactureanderection,andtheassumptionandapproximationofthecalculatingequation,noneofabovefactorsisdefiniteintheirvalues.Sothe

structuralresistanceisalsotreatedastherandomvariable.

Summary:Wecanuse

probabilitytheoryandstatisticssurveytodeterminethevaluesoftheactioneffectandthestructuralresistance.Chapter8Fundamentalconceptsofstructuralreliability

2.Normaldistributioncurve（正態(tài)分布曲線(xiàn)）

Foraction,actioneffect,andstructuralresistance,theirprobabilitydistributioncurvesaredifferentandcomplicatedbasedonstatisticsurvey.However,inreliabilityanalysis,theirdistributioncurvesallcanbetransformedinto

normaldistributioncurvebysimplification.

randomvariablesymmetryaxisinflectionpointprobabilitydensityChapter8Fundamentalconceptsofstructuralreliability

(1)Fourfeaturesofnormaldistributioncurve

Thecurvehasonlyonepeakvalue.Thecurvehasonesymmetryaxis.Whenthevariablexistendingtoward＋∞or－∞,thedensityfunctionf(x)is

tendingtoward0.Thereisaninflection

pointateachsideofsymmetryaxis.

Chapter8Fundamentalconceptsofstructuralreliability

(2)Threecharacteristicvaluesofnormaldistributioncurve

Arithmeticmean(μ)

μ=wherexi—thevalueofrandomvariablei

n—thenumberofrandomvariables.

Fromthecurve,wecanseethatthearithmeticmeanrepresentsthe

concentratedpositionofthevariablevalues.Chapter8Fundamentalconceptsofstructuralreliability

(2)Threecharacteristicvaluesofnormaldistributioncurve

Standarddeviation(σ)

Fromthecurve,wecanseethestandarddeviationσ

isthehorizontaldistanceformthepeaktotheinflectionpoint.

Thestandarddeviationσ

isexpressedthedispersiondegreeofthevariablevalues.(離散程度）Chapter8Fundamentalconceptsofstructuralreliability

(2)Threecharacteristicvaluesofnormaldistributioncurve

Standarddeviation(σ)

Figure8-5showsagroupofcurveswiththesameμ

anddifferentσ.

Whenσ

islarger,

thevaluesaremoredispersed.

Chapter8Fundamentalconceptsofstructuralreliability

(2)Threecharacteristicvaluesofnormaldistributioncurve

Coefficientofvariation(δ)

Inordertocomparethedispersiondegreeofdifferentgroupsofdatawithdifferentmeanμ,thecoefficientofvariationisintroducedandisdefinedasδ=Thecoefficientofvariationδisexpressedtherelativedispersiondegreeofthevariablevalues.(相對(duì)離散程度）Whenabovethreecharacteristicvalues

aredetermined,thedensityfunctionf（x）canbedefinedasThenthenormaldistributioncurvecanbedetermined.

Chapter8Fundamentalconceptsofstructuralreliability3.Probabilityofconfidence(正態(tài)分布曲線(xiàn)的保證率)

Anintegraloffunctionf（x）iscalled

probability,thesumoftheprobabilityforthecurveisequalto1.

When

xisgivenbyx0,wecancomputetheprobability

ofrandomvariable

x>x0

asfollowing:

P（x>x0

）=

Ifxisstructuralresistance,Piscalledprobabilityofconfidence.Chapter8Fundamentalconceptsofstructuralreliabilityx0:μ-σμ-1.645σμ-2σP(保證率)：84.13%

95%97.73%保證率系數(shù)

1 1.6452失效概率

15.9%

5%2.3%分位值

0.1590.05 0.023

3.Thecharacteristicvaluesoffunctionsofrandomvariable(隨機(jī)變量函數(shù)的特征值)

Thefunctionofrandomvariableisalsorandom,sothecharacteristicvaluesofthefunctioncanbecomputedbasedonprobabilitytheory.

IffunctionZincludesseveralrandomvariablesXi（i=1,2,…n），

When

Z=X1±X2，…，±Xn,thecharacteristicvaluesare

Chapter8FundamentalconceptsofstructuralreliabilityChapter8Fundamentalconceptsofstructuralreliability

8.1．Structureperformanceandlimitstate8.2．Statisticalanalysisofactioneffectand structuralresistance8.3.Degreeofreliabilityofstructure8.4.ReliabilityindexofstructureChapter8Fundamentalconceptsofstructuralreliability

8.3．Degreeofreliabilityofstructure

(結(jié)構(gòu)的可靠度)Itistheprobabilitythatastructureorstructuralelementfulfillthespecifiedperformancesduringthedesignworkinglifeundernormalcondition.Itisthequantitativemeasureforreliabilityofstructure.

TheprobabilityofreliabilityisexpressedasPs,--可靠概率

TheprobabilityoffailureisexpressedasPf,--失效概率

then

Ps

＋Pf

＝1complementaryrelation

UsuallyweusePftomeasurethereliabilityofstructureinpractice.

Nostructurescanbedeignedtoabsolutelyreliable.Whatcanbeachievedistodesignthestructuresothattheprobabilityoffailureissufficientlylowortheprobabilityofreliabilityissufficientlyhigh.TheperformancefunctionZisassumedtoberelatedtotwovariablesactioneffectS

andstructuralresistanceR:

Z=R-S(1)IfZ>0，orR>S，thestructureisinreliablestate

；(2)IfZ<0，orR<S，thestructureisinfailurestate

；(3)IfZ=0，orR=S，thestructureisinlimitstate.

Thebasicrequirementforstructuralreliabilityis

Z≥0orR≥S

IftheperformancefunctionZhasprobabilitydensityfunctionf(z),then

Theprobabilityofreliabilitycanbeexpressedas

TheprobabilityoffailurecanbeexpressedasChapter8Fundamentalconceptsofstructuralreliability

TheprobabilityoffailurePfisusuallydeterminedbyintegration.IftheperformancefunctionZ

hasprobabilitydensityfunction

,andthentheprobabilityoffailurePfis

thevolumeoftheareawithZ<0

，seeFig.8-12.

ItisdifficulttocalculatethePfusingaboveequationbecauseweshouldconductmultipleintegration.Exceptveryimportantstructuresornewtypeofstructures,weusuallyusereliabilityindexβ

insteadofPfindesignwork.Chapter8FundamentalconceptsofstructuralreliabilityChapter8Fundamentalconceptsofstructuralreliability

8.1．Structureperformanceandlimitstate8.2．Statisticalanalysisofactioneffectand structuralresistance8.3.Degreeofreliabilityofstructure8.4.ReliabilityindexofstructureChapter8Fundamentalconceptsofstructuralreliability

8.4．Reliabilityindexofstructureβ

Inpractice，weusereliabilityindexβ