Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

20.3 Beams Having Variable Stringer Areas 571

Fig.20.8

Shear flow (N/mm) distribution in beam section of Example 20.2.

20.3 BeamsHavingVariableStringerAreas............................................................

Inmanyaircraft,structuralbeams,suchaswings,havestringerswhosecross-sectionalareasvaryinthe
spanwisedirection.Theeffectsofthisvariationonthedeterminationofshearflowdistributioncannot
therefore be found by the methods described in Section 19.3 which assume constant boom areas. In
fact, as we noted in Section 19.3, if the stringer stress is made constant by varying the area of cross
section,thereisnochangeinshearflowasthestringer/boomiscrossed.
Thecalculationofshearflowdistributionsinbeamshavingvariablestringerareasisbasedonthe
alternativemethodforthecalculationofshearflowdistributionsdescribedinSection19.3andillustrated
inthealternativesolutionofExample19.3.ThestringerloadsPz,1andPz,2arecalculatedattwosections
z 1 andz 2 ofthebeamaconvenientdistanceapart.Weassumethatthestringerloadvarieslinearlyalong
itslengthsothatthechangeinstringerloadperunitlengthofbeamisgivenby

P=

Pz,1−Pz,2

z 1 −z 2

Theshearflowdistributionfollowsaspreviouslydescribed.

Example 20.3
SolveExample20.2byconsideringthedifferencesinboomloadatsectionsofthebeameithersideof
thespecifiedsection.

Inthisexample,thestringerareasdonotvaryalongthelengthofthebeam,butthemethodofsolution
isidentical.
We are required to find the shear flow distribution at a section 2m from the built-in end of the
beam.Wethereforecalculatetheboomloadsatsections,say0.1meithersideofthissection.Thus,at
adistance2.1mfromthebuilt-inend,

Mx=− 100 ×1.9=−190kNm

The dimensions of this section are easily found by proportion and are of width=1.18m and
depth=0.59m.Thus,thesecondmomentofareais

Ixx= 4 × 900 × 2952 + 2 × 1200 × 2952 =5.22× 108 mm^4