Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

500 CHAPTER 16 Shear of Beams

Fig. P.16.11 Fig. P.16.12

P.16.12A thin-walled closed section beam of constant wall thicknesst has the cross section shown in
Fig.P.16.12.
Assumingthatthedirectstressesaredistributedaccordingtothebasictheoryofbending,calculateandsketch
theshearflowdistributionforaverticalshearforceSyappliedtangentiallytothecurvedpartofthebeam.

Ans. qO1=Sy(1.61cosθ−0.80)/r

q 12 =

Sy

r^3

(

0.57s^2 −1.14rs+0.33r^2

)

.

P.16.13A uniform thin-walled beam of constant wall thicknessthas a cross section in the shape of an isosce-
les triangle and is loaded with a vertical shear forceSyapplied at the apex. Assuming that the distribution of
shear stress is according to the basic theory of bending, calculate the distribution of shear flow over the cross
section.
Illustrateyouranswerwithasuitablesketch,markingincarefullywitharrowsthedirectionoftheshearflows
andnotingtheprincipalvalues.

Ans. q 12 =Sy( 3 s^21 /d−h− 3 d)/h(h+ 2 d)

q 23 =Sy(− 6 s^22 + 6 hs 2 −h^2 )/h^2 (h+ 2 d).

P.16.14FigureP.16.14 shows theregular hexagonal cross section of athin-walled beamof sidesaand constant
wallthicknesst.ThebeamissubjectedtoatransverseshearforceS,itslineofactionbeingalongasideofthe
hexagon,asshown.