Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

574 CHAPTER 20 Wing Spars and Box Beams

Themomentresultantoftheinternalshearflows,togetherwiththemomentsofthecomponentsPy,r
oftheboomloadsaboutanypointinthecrosssection,isequivalenttothemomentoftheexternally
appliedloadaboutthesamepoint.WenotefromExample20.2thatformomentsaboutthecenterof
symmetry,

∑^6

r= 1

Px,rηr= 0

∑^6

r= 1

Py,rξr= 0

Therefore,takingmomentsaboutthecenterofsymmetry

100 × 103 × 600 = 2 q 12 × 600 × 300 + 2 (q 12 −43.8) 600 × 300

+(q 12 −76.65) 600 × 600 +(q 12 +32.85) 600 × 600

fromwhich

q 12 =62.5N/mm

fromwhich

q 23 =19.7N/mm q 34 =−13.2N/mm q 45 =19.7N/mm,

q 56 =63.5N/mm q 61 =96.4N/mm

sothatthesolutionisalmostidenticaltothelongerexactsolutionofExample20.2.
Theshearflowsq 12 ,q 23 ,andsooninducecomplementaryshearflowsq 12 ,q 23 ,andsooninthe
panelsinthelongitudinaldirectionofthebeam;theseare,infact,theaverageshearflowsbetweenthe
twosectionsconsidered.Foracompletebeamanalysis,theaboveprocedureisappliedtoaseriesof
sections along the span. The distance between adjacent sections may be taken to be any convenient
value;foractualwings,distancesoftheorderof350to700mmareusuallychosen.However,forvery
smallvalues,smallpercentageerrorsinPz,1andPz,2resultinlargepercentageerrorsin P.Onthe
otherhand,ifthedistanceistoolarge,theaverageshearflowbetweentwoadjacentsectionsmaynot
bequiteequaltotheshearflowmidwaybetweenthesections.

Problems..............................................................................................

P.20.1 AwingsparhasthedimensionsshowninFig.P.20.1andcarriesauniformlydistributedloadof15kN/m
alongitscompletelength.Eachflangehasacross-sectionalareaof500mm^2 withthetopflangebeinghorizontal.
Iftheflangesareassumedtoresistalldirectloadswhilethesparwebiseffectiveonlyinshear,determinetheflange
loadsandtheshearflowsinthewebatsections1and2mfromthefreeend.

Ans. 1mfromfreeend:PU=25kN(tension),PL=25.1kN(compression),q=41.7N/mm.

2mfromfreeend:PU=75kN(tension),PL=75.4kN(compression),q=56.3N/mm.