Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

19.3 Effect of Idealization on the Analysis 549

19.3.3 Shear Loading of Closed Section Beams

Argumentsidenticaltothoseintheshearofopensectionbeamsapplyinthiscase.Thus,theshearflow
at any point around the cross section of a closed section beam comprising booms and skin of direct
stress-carryingthicknesstDis,bycomparingEqs.(19.6)and(16.15),

qs=−

(

SxIxx−SyIxy

IxxIyy−Ixy^2

)⎛

⎝

∫s

0

tDxds+

∑n

r= 1

Brxr

⎞

⎠

−

(

SyIyy−SxIxy

IxxIyy−Ixy^2

)⎛

⎝

∫s

0

tDyds+

∑n

r= 1

Bryr

⎞

⎠+qs,0

(19.11)

Note that the zero value of the “basic” or “open section” shear flow at the “cut” in a skin for which
tD=0extendsfromthe“cut”totheadjacentbooms.

Example 19.4
Thethin-walledsinglecellbeamshowninFig.19.11hasbeenidealizedintoacombinationofdirect
stress-carryingboomsandshear-stress-only-carryingwalls.Ifthesectionsupportsaverticalshearload
of10kNactinginaverticalplanethroughbooms3and6,calculatethedistributionofshearflowaround
thesection.

Boomareas: B 1 =B 8 =200mm^2 ,B 2 =B 7 =250mm^2
B 3 =B 6 =400mm^2 ,B 4 =B 5 =100mm^2
Thecentroidofthedirectstress-carryingarealiesonthehorizontalaxisofsymmetrysothatIxy=0.
Also,sincetD=0andonlyaverticalshearloadisapplied.

Fig.19.11

Closed section of beam of Example 19.4.