Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

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

whichgives

Ixx=

bd^3

12

(15.35)

Similarly,

Iyy=

db^3

12

(15.36)

Frequently,itisusefultoknowthesecondmomentofareaofarectangularsectionaboutanaxiswhich
coincideswithoneofitsedges.Thus,inFig.15.27andusingtheparallelaxestheorem

IN=

bd^3

12

+bd

(

−

d

2

) 2

=

bd^3

3

(15.37)

Example 15.13
DeterminethesecondmomentsofareaIxxandIyyoftheI-sectionshowninFig.15.28.

UsingEq.(15.35),

Ixx=

bd^3

12

−

(b−tw)d^3 w

12

Alternatively,usingtheparallelaxestheoreminconjunctionwithEq.(15.35)

Ixx= 2

[

btf^3

12

+btf

(

dw+tf

2

) 2 ]

+

twdw^3

12

Fig.15.28

Second moments of area of anI-section.