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 2 3 20.25 in A A = = First compute the moment of inertia ( ) ( ) ( ) ( ) ( ) 1 2 3 2 3 with x x x x x x I I I I I I = + + = ( )( ) ( )( ) 3 3 1 1 12 in. 9 in. 2 9 in. 4.5in. 12 12 = + ( ) 4 4 729 136.6875 in 865.6875 in = + = and ( ) ( ) ( ) ( ) ( ) 1 2 3 2 3 with y y y y y y I I I I I I = + + = ( )( ) ( )( ) ( ) ( ) 3 3 2 2 1 1 9 in. 12 in. 2 4.5 in. 9 in. 20.25 in 9 in. 12 36 = + +
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