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87_Problem CHAPTER 9 - PROBLEM 9.76 Using the parallel-axis...

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PROBLEM 9.76 Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes. SOLUTION Symmetry implies ( ) 1 0 xy I = Using Sample Problem 9.6 and Equation 9.20, note that the orientation of A 2 corresponds to a 90° rotation of the axes; thus ( ) 2 2 2 1 72 x y I b h ′ ′ = Also, the orientation of A 3 corresponds to a 270° rotation of the axes; thus ( ) 2 2 3 1 72 x y I b h ′ ′ = Then ( ) ( ) ( ) 2 2 4 2 1 9 in. 6 in. 40.5 in 72 x y I ′ ′ = = and ( )( ) 2
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