Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

570 CHAPTER 20 Wing Spars and Box Beams

The shear flow distribution in the walls of the beam is now found using the method described in
Section19.3.Since,forthisbeam,Ixy=0andSx=Sx,w=0,Eq.(19.11)reducesto

qs=

−Sy,w

Ixx

∑n

r= 1

Bryr+qs,0 (iv)

Wenow“cut”oneofthewalls,say16.Theresulting“opensection”shearflowisgivenby

qb=−

66.6× 103

5.4× 108

∑n

r= 1

Bryr

or

qb=−1.23× 10 −^4

∑n

r= 1

Bryr (v)

Thus,

qb,16= 0

qb,12= 0 −1.23× 10 −^4 × 900 × 300 =−33.2N/mm

qb,23=−33.2−1.23× 10 −^4 × 1200 × 300 =−77.5N/mm

qb,34=−77.5−1.23× 10 −^4 × 900 × 300 =−110.7N/mm

qb,45=−77.5N/mm(fromsymmetry)

qb,56=−33.2N/mm(fromsymmetry)

giving the distribution shown in Fig. 20.7. Taking moments about the center of symmetry, we have,
fromEq.(20.16),

− 100 × 103 × 600 = 2 ×33.2× 600 × 300 + 2 ×77.5× 600 × 300

+110.7× 600 × 600 + 2 × 1200 × 600 qs,0

fromwhichqs,0=−97.0N/mm(i.e.,clockwise).Thecompleteshearflowdistributionisfoundbyadding
thevalueofqs,0totheqbshearflowdistributionofFig.20.7andisshowninFig.20.8.

Fig.20.7

“Open section” shear flow (N/mm) distribution in beam section of Example 20.2.