Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

19.3 Effect of Idealization on the Analysis 545

Fig.19.7

Idealized channel section of Example 19.3.

Theeffectivedirectstress-carryingthicknesstDofthewallsofthesectioniszerosothatthecentroid
ofareaandthesectionpropertiesrefertotheboomareasonly.SinceCx(andCyasfarastheboom
areasareconcerned)isanaxisofsymmetry,Ixy=0;also,Sx=0andEq.(19.6)therebyreducesto

qs=−

Sy

Ixx

∑n

r= 1

Bryr (i)

inwhichIxx= 4 × 300 × 2002 = 48 × 106 mm^4 .SubstitutingthevaluesofSyandIxxinEq.(i)gives

qs=−

4.8× 103

48 × 106

∑n

r= 1

Bryr=− 10 −^4

∑n

r= 1

Bryr (ii)

Attheoutsideofboom1,qs=0.Asboom1iscrossed,theshearflowchangesbyanamountgivenby

q 1 =− 10 −^4 × 300 × 200 =−6N/mm

Hence,q 12 =−6N/mm,since,fromEq.(i),itcanbeseenthatnofurtherchangesinshearflowoccur
untilthenextboom(2)iscrossed.Hence,

q 23 =− 6 − 10 −^4 × 300 × 200 =−12N/mm