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77_Problem CHAPTER 9

# 77_Problem CHAPTER 9 - PROBLEM 9.67 Determine by direct...

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PROBLEM 9.67 Determine by direct integration the product of inertia of the given area with respect to the x and y axes. SOLUTION First note 2 2 1 4 x y a a = 2 2 1 4 2 a x = Have EL EL xy x y dI dI x y dA ′ ′ = + where ( ) EL 0 symmetry x y dI x x ′ ′ = = 2 2 EL 1 1 4 2 4 y y a x = = 2 2 1 4 2 dA ydx a x dx = = Then 2 2 2 2 2 0 1 1 4 4 4 2 a xy xy I dI x a x a x dx  = =
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