Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

546 CHAPTER 19 Structural Idealization

Similarly,

q 34 =− 12 − 10 −^4 × 300 ×(− 200 )=−6N/mm

while,finally,attheoutsideofboom4,theshearflowis

− 6 − 10 −^4 × 300 ×(− 200 )= 0

asexpected.ThecompleteshearflowdistributionisshowninFig.19.8.
It can be seen from Eq. (i) in Example 19.3 that the analysis of a beam section which has been
idealizedintoacombinationofdirectstress-carryingboomsandshear-stress-only-carryingskingives
constantvaluesoftheshearflowintheskinbetweenthebooms;theactualdistributionofshearflows
isthereforelost.Whatremainsisinfacttheaverageoftheshearflow,ascanbeseenbyreferringto
Example19.3.Analysisoftheunidealizedchannelsectionwouldresultinaparabolicdistributionof
shearflowintheweb23whoseresultantisstaticallyequivalenttotheexternallyappliedshearloadof
4.8kN.InFig.19.8theresultantoftheconstantshearflowintheweb23is12× 400 =4800N=4.8kN.
Itfollowsthatthisconstantvalueofshearflowistheaverageoftheparabolicallydistributedshearflows
intheunidealizedsection.
Theresult,fromtheidealizationofabeamsection,ofaconstantshearflowbetweenboomsmay
beusedtoadvantageinpartsoftheanalysis.Supposethatthecurvedweb12inFig.19.9hasbooms
atitsextremitiesandthattheshearflowq 12 inthewebisconstant.Theshearforceonanelementδs
ofthewebisq 12 δs,whosecomponentshorizontallyandverticallyareq 12 δscosφandq 12 δssinφ.The
resultant,paralleltothexaxis,Sx,ofq 12 isthereforegivenby

Sx=

∫^2

1

q 12 cosφds

Fig.19.8

Shear flow in channel section of Example 19.3.