Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

462 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams

Fig.15.31

(a) Actual thin-walled channel section; (b) approximate representation of section.

Fig.15.32

Second moments of area of an inclined thin section.

Expandingthecubedterm,wehave

Ixx= 2

[

(b+t/ 2 )t^3

12

+

(

b+

t

2

)

th^2

]

+

t

12

[

( 2 )^3

(

h^3 − 3 h^2

t

2

+ 3 h

t^2

4

−

t^3

8

)]

whichreduces,afterpowersoft^2 andupwardareignored,to

Ixx= 2 bth^2 +t

( 2 h)^3

12

ThesecondmomentofareaofthesectionaboutCyisobtainedinasimilarmanner.
Wesee,therefore,thatforthepurposeofcalculatingsectionproperties,wemayregardthesection
asbeingrepresentedbyasingleline,asshowninFig.15.31(b).
Thin-walledsectionsfrequentlyhaveinclinedorcurvedwallswhichcomplicatethecalculationof
sectionproperties.ConsidertheinclinedthinsectionofFig.15.32.Itssecondmomentofareaabout