92_Problem CHAPTER 9

92_Problem CHAPTER 9 - PROBLEM 9.80 Determine the moments...

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PROBLEM 9.80 Determine the moments of inertia and the product of inertia of the area of Problem 9.72 with respect to new centroidal axes obtained by rotating the x and y axes 45° clockwise. SOLUTION From the solution to Problem 9.72 4 501.1875 in xy I = 2 23 20.25 in AA == First compute the moment of inertia () ( ) ( ) ( ) ( ) 123 2 3 with x xx x x x I II I I I =++ = ( ) ( ) 33 11 12 in. 9 in. 2 9 in. 4.5in. 12 12  =+   ( ) 44 729 136.6875 in 865.6875 in = and ( ) ( ) ( ) ( ) ( ) 2 3 with yy y y y y I I I = ( ) ( ) 2 2 9 in. 12 in. 2 4.5 in. 9 in. 20.25 in
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