Draft

9.3UltimateStrengthMethod 167

Figure9.3:FrequencyDistributionsof LoadQandResistanceR

Failurewouldoccurfornegative valuesofX

19 Theprobability of failurePf is equalto theratioof theshadedareato thetotalarea

underthecurve in Fig.9.4.

Figure9.4:De nitionof Reliability Index

20 IfXis assumedto follow aNormalDistributionthanit hasa meanvalueX=



ln

R

Q



m

anda standarddeviation.

21 We de nethesafety index(orreliability index) as =

X



22 For standarddistributionsandfor = 3:5, it canbe shownthattheprobability of failureis

Pf=

1

9 ; 091

or 1: 1  10

4

. Thatis 1 in every10,000structuralmembersdesignedwith = 3: 5

willfailbecauseof eitherexcessive loador understrengthsometimein itslifetime.

23 Reliability indicesarea relative measureof thecurrent conditionandprovidea qualitative

estimateof thestructuralperformance.

24 Structureswithrelativelyhighreliableindiceswillbe expectedto performwell.If thevalue

is too low,thenthestructuremay be classi edas a hazard.

25 Targetvaluesfor areshownin Table9.2, andin Fig.9.5