Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

280 CHAPTER 8 Columns

Example 8.3
Athin-walledpin-endedcolumnis2mlongandhasthecrosssectionshowninFig.8.17.Iftheends
ofthecolumnarefreetowarp,determinethelowestvalueofaxialloadwhichwillcausebuckling,and
specifythebucklingmode.TakeE=75000N/mm^2 andG=21000N/mm^2.

Since the cross section of the column is doubly symmetrical, the shear center coincides with the
centroidofarea,andxS=yS=0;Eqs.(8.74),(8.75),and(8.76)thereforeapply.Further,theboundary
conditionsarethoseofthecolumnwhosebuckledshapeisdefinedbyEqs.(8.71)sothatthebuckling
loadofthecolumnisthelowestofthethreevaluesgivenbyEqs.(8.77).
Thecross-sectionalareaAofthecolumnis

A=2.5( 2 ×37.5+ 75 )=375mm^2

ThesecondmomentsofareaofthecrosssectionaboutthecentroidalaxesCxyare(seeChapter15),
respectively,

Ixx= 2 ×37.5×2.5×37.5^2 +2.5× 753 / 12 =3.52× 105 mm^4

Iyy= 2 ×2.5×37.5^3 / 12 =0.22× 105 mm^4

ThepolarsecondmomentofareaI 0 is

I 0 =Ixx+Iyy+A(x^2 S+y^2 S) (seederivationofEq.(8.69))

Fig.8.17

Column section of Example 8.3.