Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

568 CHAPTER 20 Wing Spars and Box Beams

seethatEq.(16.17)becomes

Sxη 0 −Syξ 0 =

∮

qbpds+ 2 Aqs,0−

∑m

r= 1

Px,rηr+

∑m

r= 1

Py,rξr (20.16)

Equation(20.16)isdirectlyapplicabletoataperedbeamsubjectedtoforcespositionedinrelationto
themomentcenterasshown.Caremustbetakeninaparticularproblemtoensurethatthemomentsof
theforcesaregiventhecorrectsign.

Example 20.2
ThecantileverbeamshowninFig.20.6isuniformlytaperedalongitslengthinbothxandydirections
and carries a load of 100kN at its free end. Calculate the forces in the booms and the shear flow
distributioninthewallsatasection2mfromthebuilt-inendiftheboomsresistallthedirectstresses
whilethewallsareeffectiveonlyinshear.Eachcornerboomhasacross-sectionalareaof900mm^2 ,
whilebothcentralboomshavecross-sectionalareasof1200mm^2.

Theinternalforcesystematasection2mfromthebuilt-inendofthebeamis

Sy=100kN Sx= 0 Mx=− 100 × 2 =−200kNm My= 0

ThebeamhasadoublysymmetricalcrosssectionsothatIxy=0andEq.(15.18)reducesto

σz=

Mxy

Ixx

(i)

Fig.20.6

(a) Beam of Example 20.2; (b) section 2m from built-in end.