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88_Problem CHAPTER 9 - PROBLEM 9.77 Using the parallel-axis...

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PROBLEM 9.77 Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes. SOLUTION Have xy x y I I x yA ′ ′ = + Where 0 x y I ′ ′ = for each rectangle Then ( ) ( ) ( ) 1 2 3 xy xy xy xy I I I I = + + x yA = Σ Now ( ) 1 178.4 mm 160 mm 18.4 mm x = − = − 1 60 mm 12.2 mm 47.8 mm y = = 2 1 320 mm 120 mm 38400 mm A = × = and ( ) 2 178.4 mm 30 mm 208.4 mm x = − + = − 2 40 mm 12.2 mm 27.8 mm y = = 2 2 60 mm 80 mm 4800 mm A = × = and ( ) 3 320 mm 178.4 mm 40 mm 101.6 mm x = = ( ) 3 12.2 mm
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