Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 349

Problems..............................................................................................

P.10.1 Describe a simple tensile test and show, with the aid of sketches, how measures of the ductility of the
materialofthespecimenmaybeobtained.Sketchtypicalstress–straincurvesformildsteelandanaluminumalloy
showingtheirimportantfeatures.

P.10.2 A bar of metal 25mm in diameter is tested on a length of 250mm. In tension, the results shown in
TableP.10.2(a)wererecorded.

Table P.10.2(a)

Load (kN) 10.4 31.2 52.0 72.8

Extension (mm) 0.036 0.089 0.140 0.191

AtorsiontestgavetheresultsshowninTableP.10.2(b).

Table P.10.2(b)

Torque (kN m) 0.051 0.152 0.253 0.354

Angle of twist (degrees) 0.24 0.71 1.175 1.642

RepresenttheseresultsingraphicalformandhencedetermineYoung’smodulus,E;themodulusofrigidity,
G;Poisson’sratio,ν;andthebulkmodulus,K,forthemetal.

Ans. E 205000N/mm^2 ,G 80700N/mm^2 ,ν 0.27^2 ,K 148500N/mm^2.

P.10.3 Theactualstress–straincurveforaparticularmaterialisgivenbyσ=Cεn,whereCisaconstant.Assuming
that the material suffers no change in volume during plastic deformation, derive an expression for the nominal
stress–straincurveandshowthatthishasamaximumvaluewhenε=n/( 1 −n).

Ans. σnom=Cεn/( 1 +ε).

P.10.4 Astructuralmemberistobesubjectedtoaseriesofcyclicloadswhichproducedifferentlevelsofalternating
stressasshowninTableP.10.4.Determinewhetherornotafatiguefailureisprobable.

Ans. Notprobable(n 1 /N 1 +n 2 /N 2 +···=0.39).

Table P.10.4

Number of Cycles

Loading Number of Cycles to Failure

1104 5 × 104

2105 106

3106 24 × 107

4107 12 × 107