Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

284 CHAPTER 8 Columns

Fig.8.20

Determination of torsion bending constant for column section of Example 8.5.

Thetorsionbendingconstantisthenthe“momentofinertia”ofthe“wire”andis

= 2 td

1

3

(d^2 )^2 +

td

3

(

d^2

2

) 2

× 2 +td

(

d^2

2

) 2

fromwhich

=

13

12

td^5

Also,thetorsionconstantJisgivenby(seeSection3.4)

J=

∑st^3

3

=

5 dt^3

3

Theshearcenterofthesectionandthecentroidofareacoincidesothatthetorsionalbucklingloadis
givenbyEq.(8.76).Rewritingthisequation

d^4 θ

dz^4

+μ^2

d^2 θ

dz^2

=0(i)

where

μ^2 =(σI 0 −GJ)/E(σ=P/A)

ThesolutionofEq.(i)is

θ=Acosμz+Bsinμz+Cz+D (ii)