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222_Problem CHAPTER 9 - PROBLEM 9.157 A section of sheet...

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PROBLEM 9.157 A section of sheet steel 3 mm thick is cut and bent into the machine component shown. Knowing that the density of the steel is 3 7860 kg/m , determine the mass products of inertia , xy I , yz I and zx I of the component. SOLUTION First compute the mass of each component Have.. sT sT m V tA ρ ρ = = Then ( ) ( )( )( ) 3 3 1 7860 kg/m 0.003 0.7 0.78 m 12.785 kg m = = ( ) ( ) 3 2 3 2 7860 kg/m 0.003 0.39 m 5.6337 kg 2 m π = × = ( ) ( ) 3 3 3 1 7860 kg/m 0.003 0.78 0.3 m 2.7589 kg 2 m = × × = Now observe that because of symmetry the centroidal products of inertia of components 1 and 2 are zero and ( ) ( ) 3 3 0 x y z x I I ′ ′ ′ ′ = = Also ( ) ( ) 3,mass 3,area y z sT
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