244_Problem CHAPTER 9

244_Problem CHAPTER 9 - PROBLEM 9.169 CONTINUED I z = I z)1...

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PROBLEM 9.169 CONTINUED ( ) ( ) 12 zz z I II =+ 2 2 11 1 12 2 2 2 WW a a gg    () 2 2 2 1 12 2 2 2 a aa ++ + 22 2 1 1 5 5 21 2 4 1 2 4 6 a  + + =   Now observe that the centroidal products of inertia, ,, x yy z I I ′′ and , zx I ′ ′ of both components are zero because of symmetry. Also, 1 0 y = Then 2 222 4 xy x y Wa W I Im x y m x y a a + = = = 2 28 yz y z Wa a W I y z m y z a g g + = = = ( ) 111 2 2 2 zx z x I z x m z x m z x + = + 2 3 2 8 W g = Substituting into Equation (9.46) O A xx x yxy y zyz z xzx I I I I I λ λλ =++− Noting that 1 3 xyzx x λλλλ = == = = = Have 2 5 32 6 OA W I a g + 113 2 488 WWW aaa ggg −+ + 2 4 3 2 36 4 W a g =− or 2 5 18 OA W I a g = W 0 0 0
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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