Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

410 CHAPTER 14 Fatigue

thedamagecausedbyonecycleisthen1/N(Su).Therefore,fromthePalmgren–Minerhypothesis,when
sufficientgustsofthisandallothermagnitudestogetherwiththeeffectsofallotherloadcyclesproduce
acumulativedamageof1.0,fatiguefailurewilloccur.Itisthereforenecessarytoknowthenumberand
magnitudeofgustslikelytobeencounteredinflight.
Gustdatahavebeenaccumulatedoveranumberofyearsfromaccelerometerrecordsfromaircraft
flyingoverdifferentroutesandterrains,atdifferentheights,andatdifferentseasons.TheESDUdata
sheets [Ref. 1] present the data in two forms, as we have previously noted. First,l 10 against altitude
curvesshowthedistancewhichmustbeflownatagivenaltitudeinorderthatagust(positiveornegative)
havingavelocity≥3.05m/sbeencountered.Itfollowsthat1/l 10 isthenumberofgustsencountered
inunitdistance(1km)ataparticularheight.Second,gustfrequencydistributioncurves,r(ue)against
ue,givethenumberofgustsofvelocityueforevery1000gustsofvelocity3.05m/s.
Fromthesetwocurves,thegustexceedanceE(ue)isobtained;E(ue)isthenumberoftimesagust
ofagivenmagnitude(ue)willbeequaledorexceededin1kmofflight.Thus,fromtheabove,

numberofgusts≥3.05m/sperkm= 1 /l 10

numberofgustsequaltoueper1000gustsequalto3.05m/s=r(ue)

Hence,

numberofgustsequaltouepersinglegustequalto3.05m/s=r(ue)/ 1000

ItfollowsthatthegustexceedanceE(ue)isgivenby

E(ue)=

r(ue)

1000 l 10

(14.17)

inwhichl 10 isdependentonheight.Agoodapproximationforthecurveofr(ue)againstueintheregion
ue=3.05m/sis

r(ue)=3.23× 105 u−e5.26 (14.18)

ConsidernowthetypicalgustexceedancecurveshowninFig.14.3.In1kmofflight,therearelikelyto
beE(ue)gustsexceedinguem/sandE(ue)−δE(ue)gustsexceedingue+δuem/s.Thus,therewillbe
δE(ue)fewergustsexceedingue+δuem/sthanuem/s,andtheincrementingustspeedδuecorresponds
toanumber−δE(ue)ofgustsatagustspeedclosetoue.Halfofthesegustswillbepositive(upgusts)
andhalfnegative(downgusts)sothatifitisassumedthateachupgustisfollowedbyadowngustofequal
magnitude,thenumberofcompletegustcycleswillbe−δE(ue)/2.Supposethateachcycleproduces
astressS(ue)andthatthenumberofthesecyclesrequiredtoproducefailureisN(Su,e).Thedamage
causedbyonecycleisthen1/N(Su,e),andoverthegustvelocityintervalδue,thetotaldamageδDis
givenby

δD=−

δE(ue)

2 N(Su,e)

=−

dE(ue)

due

δue

2 N(Su,e)

(14.19)