Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 421

P.14.2 AmoreaccurateestimateforthesaferangeofstressforthematerialofP.14.1isgivenbythenonlinear
formoftheGoodmanpredictioninwhichm=2.Calculateitsvalue.

Ans. 432N/mm^2.

P.14.3 Asteelcomponentissubjectedtoareversedcyclicloadingof100cycles/dayoveraperiodoftimeinwhich
±160N/mm^2 isappliedfor200cycles,±140 N/mm^2 isappliedfor200cycles,and±100N/mm^2 isappliedfor600
cycles.Ifthefatiguelifeofthematerialateachofthesestresslevelsis10^4 ,10^5 ,and2× 105 cycles,respectively,
estimatethelifeofthecomponentusingMiner’slaw.

Ans. 400days.

P.14.4 Aninfinitesteelplatehasafracturetoughnessof3320N/mm^3 /^2 andcontainsa4mmlongcrack.Calculate
themaximumallowabledesignstressthatcouldbeappliedroundtheboundaryoftheplate.

Ans. 1324N/mm^2.

P.14.5 A semi-infinite plate has an edge crack of length 0.4mm. If the plate is subjected to a cyclic
repeated stress loading of 180N/mm^2 , its fracture toughness is 1800N/mm^3 /^2 , and the rate of crack growth is
30 × 10 −^15 (K)^4 mm/cycle,determinethecracklengthatfailureandthenumberofcyclestofailure.

Ans. 25.4mm,7916cycles.

P.14.6 An aircraft’s cruise speed is increased from 200 to 220m/s. Determine the percentage increase in gust
damagethiswouldcause.

Ans. 65percent.

P.14.7 Theaverageblocklengthjourneyofanexecutivejetairlineris1000kmanditscruisespeedis240m/s.
Ifthedamageduringtheground–air–groundcyclemaybeassumedtobe10percentofthetotaldamageduringa
completeflight,determinethepercentageincreaseinthelifeoftheaircraftwhenthecruisingspeedisreducedto
235m/s.

Ans. 12percent.