Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

15.4 Calculation of Section Properties 457

15.4.2 Theorem of Perpendicular Axes

InFig.15.26,thesecondmomentsofarea,IxxandIyy,ofthesectionaboutOxandOyareknown.The
secondmomentofareaaboutanaxisthroughOperpendiculartotheplaneofthesection(i.e.,apolar
secondmomentofarea)isthen

Io=Ixx+Iyy (15.34)

15.4.3 Second Moments of Area of Standard Sections

Manysectionsmayberegardedascomprisinganumberofrectangularshapes.Theproblemofdeter-
miningthepropertiesofsuchsectionsissimplifiedifthesecondmomentsofareaoftherectangular
componentsareknownanduseismadeoftheparallelaxestheorem.Thus,fortherectangularsection
ofFig.15.27.

Ixx=

∫

A

y^2 dA=

∫d/^2

−d/ 2

by^2 dy=b

[

y^3

3

]d/ 2

−d/ 2

Fig.15.26

Theorem of perpendicular axes.

Fig.15.27

Second moments of area of a rectangular section.