Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

8.6 Flexural–Torsional Buckling of Thin-Walled Columns 283

Itcanbeseenthatthisvalueofflexural–torsionalbucklingloadislowerthananyoftheuncoupled
bucklingloadsPCR(xx),PCR(yy),orPCR(θ);thereductionisduetotheinteractionofthebendingand
torsionalbucklingmodes.

Example 8.5
Athin-walledcolumnhasthecrosssectionshowninFig.8.19,isoflengthL,andissubjectedtoan
axialloadthroughitsshearcenterS.Iftheendsofthecolumnarepreventedfromwarpingandtwisting,
determinethevalueofdirectstresswhenfailureoccursduetotorsionalbuckling.

Thetorsionbendingconstantisfoundusingthemethoddescribedin(seeRef.3).Thepositionof
theshearcenterisgivenbutisobviousbyinspection.Thesweptarea2λAR,0isdeterminedasafunction
ofs,anditsdistributionisshowninFig.8.20.Thecenterofgravityofthe“wire”isfoundbytaking
momentsaboutthesaxis.
Then,

2 A′R 5 td=td

(

d^2

2

+

5 d^2

4

+

3 d^2

2

+

5 d^2

4

+

d^2

2

)

whichgives

2 A′R=d^2

Fig.8.19

Section of column of Example 8.5.