Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 497

Fig. P.16.2 Fig. P.16.3

P.16.3 DeterminethepositionoftheshearcenterSforthethin-walled,opencrosssectionshowninFig.P.16.3.
Thethicknesstisconstant.

Ans. πr/3.

P.16.4 FigureP.16.4showsthecrosssectionofathin,singlysymmetricalI-section.ShowthatthedistanceξSof
theshearcenterfromtheverticalwebisgivenby

ξS

d

=

3 ρ( 1 −β)

( 1 + 12 ρ)

whereρ=d/h.Thethicknesstistakentobenegligiblysmallincomparisonwiththeotherdimensions.

Fig. P.16.4 Fig. P.16.5

P.16.5 Athin-walledbeamhasthecrosssectionshowninFig.P.16.5.Thethicknessofeachflangevarieslinearly
fromt 1 atthetiptot 2 atthejunctionwiththeweb.Thewebitselfhasaconstantthicknesst 3 .Calculatethedistance
ξSfromthewebtotheshearcenterS.

Ans. d^2 (2t 1 +t 2 )/[3d(t 1 +t 2 )+ht 3 ].

P.16.6 FigureP.16.6showsthesinglysymmetricalcrosssectionofathin-walledopensectionbeamofconstant
wallthicknesst,whichhasanarrowlongitudinalslitatthecorner15.