Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

20.2 Open and Closed Section Beams 567

TheaxialloadPristhengivenby

Pr=(P^2 x,r+Py^2 ,r+P^2 z,r)^1 /^2 (20.11)

or

Pr=Pz,r

(δx^2 r+δy^2 r+δz^2 )^1 /^2

δz

(20.12)

TheappliedshearloadsSxandSyarereactedbytheresultantsoftheshearflowsintheskinpanelsand
webs,togetherwiththecomponentsPx,randPy,roftheaxialloadsinthebooms.Therefore,ifSx,wand
Sy,waretheresultantsoftheskinandwebshearflowsandthereisatotalofmboomsinthesection,

Sx=Sx,w+

∑m

r= 1

Px,r Sy=Sy,w+

∑m

r= 1

Py,r (20.13)

SubstitutinginEq.(20.13)forPx,randPy,rfromEqs.(20.10)and(20.9),wehave

Sx=Sx,w+

∑m

r= 1

Pz,r

δxr

δz

Sy=Sy,w+

∑m

r= 1

Pz,r

δyr

δz

(20.14)

Hence,

Sx,w=Sx−

∑m

r= 1

Pz,r

δxr

δz

Sy,w=Sy−

∑m

r= 1

Pz,r

δyr

δz

(20.15)

The shear flow distribution in an open section beam is now obtained using Eq. (19.6) in whichSxis
replaced bySx,wandSybySy,wfrom Eq. (20.15). Similarly for a closed section beam,SxandSyin
Eq.(19.11)arereplacedbySx,wandSy,w.Inthelattercase,themomentequation(Eq.(16.17))requires
modificationduetothepresenceoftheboomloadcomponentsPx,randPy,r.Thus,fromFig.20.5,we

Fig.20.5

Modification of moment equation in shear of closed section beams due to boom load.