Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

19.3 Effect of Idealization on the Analysis 551

Fig.19.12

Shear flow distribution N/mm in walls of the beam section of Example 19.4.

Inanywall,thefinalshearflowisgivenbyqs=qb+qs,0sothat

q 21 =−18.1+5.4=−12.7N/mm=q 87

q 23 =−5.4N/mm=q 67

q 34 =−34.3N/mm=q 56

q 45 =−37.9N/mm

and

q 81 =17.0N/mm

givingtheshearflowdistributionshowninFig.19.12.

19.3.4 Alternative Method for the Calculation of Shear Flow Distribution

Equation(19.4)mayberewrittenintheform

q 2 −q 1 =

∂Pr

∂z

(19.12)

inwhichPristhedirectloadintherthboom.Thisformoftheequationsuggestsanalternativeapproach
tothedeterminationoftheeffectofboomsonthecalculationofshearflowdistributionsinopenand
closedsectionbeams.
Letussupposethattheboomloadvarieslinearlywithz.Thiswillbethecaseforalengthofbeam
overwhichtheshearforceisconstant.Equation(19.12)thenbecomes

q 2 −q 1 =− Pr (19.13)

inwhich Pristhechangeinboomloadoverunitlengthoftherthboom. Prmaybecalculatedbyfirst
determiningthechangeinbendingmomentbetweentwosectionsofabeamaunitdistanceapartand
thencalculatingthecorrespondingchangeinboomstressusingeitherofEq.(15.18)orof Eq.(15.19);
thechangeinboomloadfollowsbymultiplyingthechangeinboomstressbytheboomareaBr.Note
thatthesectionpropertiescontainedinEqs.(15.18)and(15.19)refertothedirectstress-carryingarea
of the beam section. In cases where the shear force is not constant over the unit length of beam, the
methodisapproximate.