Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

20.1 Tapered Wing Spar 563

or

Sy=Sy,w+Pz,1

δy 1

δz

+Pz,2

δy 2

δz

(20.4)

sothat

Sy,w=Sy−Pz,1

δy 1

δz

−Pz,2

δy 2

δz

(20.5)

Againwenotethatδy 2 inEqs.(20.4)and(20.5)isnegative.Equation(20.5)maybeusedtodetermine
theshearflowdistributionintheweb.Foracompletelyidealizedbeam,thewebshearflowisconstant
through the depth and is given bySy,w/h. For a beam in which the web is fully effective in resisting
directstresses,thewebshearflowdistributionisfoundusingEq.(19.6),inwhichSyisreplacedbySy,w
andwhich,forthebeamofFig.20.1,wouldsimplifyto

qs=−

Sy,w

Ixx

⎛

⎝

∫s

0

tDyds+B 1 y 1

⎞

⎠ (20.6)

or

qs=−

Sy,w

Ixx

⎛

⎝

∫s

0

tDyds+B 2 y 2

⎞

⎠ (20.7)

Example 20.1
DeterminetheshearflowdistributioninthewebofthetaperedbeamshowninFig.20.2,atasection
midwayalongitslength.Thewebofthebeamhasathicknessof2mmandisfullyeffectiveinresisting

Fig.20.2

Tapered beam of this example.