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242_Problem CHAPTER 9 - PROBLEM 9.168 Determine the moment...

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PROBLEM 9.168 Determine the moment of inertia of the steel machine element of Problems 9.147 and 9.151 with respect to the axis through the origin which forms equal angles with the x , y , and z axes. SOLUTION From Problem 9.147: 3 2 9.8821 10 lb ft s x I = × 3 2 11.5344 10 lb ft s y I = × 3 2 2.1878 10 lb ft s z I = × Problem 9.151: 3 2 0.48776 10 lb ft s xy I = × 3 2 1.18391 10 lb ft s yz I = × 3 2 2.6951 10 lb ft s zx I = × Now x y z λ λ λ = = and 2 2 2 1 x y z λ λ λ + + = Therefore, 2 3 1 x λ = or 1 3 x y z λ λ λ = = = Equation 9.46 2 2 2 2 2 2 OL x x y y z z xy x y yz y z zx z x I I I I I I I λ λ λ λ λ λ λ λ λ = + + ( ) 2 2 2 1 1 1 1 1 9.8821 11.5344 2.1878
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