Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 471

FromEqs.(15.50)and(15.53),

MxT=Eα 2 T 0 at(a)+

∫a

−a

Eα

T 0

a

(a+y)ytds

thatis,

MxT=EαT 0

{

2 a^2 t+

1

a

[

ay^2

2

+

y^3

3

]a

−a

}

fromwhich

MxT=

8 Eαa^2 tT 0

3

Alternatively,theaveragetemperaturechangeT 0 inthewebmaybeconsideredtoactatthecentroidof
thetemperaturechangedistribution.Then,

MxT=Eα 2 T 0 at(a)+EαT 02 at

(a

3

)

thatis,

MxT=

8 Eαa^2 tT 0

3

asbefore

ThecontributionofthetemperaturechangeinthewebtoMyTremainszero,sincethesectioncentroid
isintheweb;thevalueofMyTistherefore−Eαa^2 tT 0 asinExample15.14.

Reference

[1] Megson,T.H.G.,StructuresandStressAnalysis,2ndedition,Elsevier,2005.

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

P.15.1 FigureP.15.1showsthesectionofananglepurlin.Abendingmomentof3000Nmisappliedtothepurlin
inaplaneatanangleof30◦totheverticalyaxis.Ifthesenseofthebendingmomentissuchthatitscomponents
MxandMyboth produce tension in the positivexyquadrant, calculate the maximum direct stress in the purlin,
statingclearlythepointatwhichitacts.

Ans. σz,max=−63.3N/mm^2 atC.