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181_Problem CHAPTER 9

# 181_Problem CHAPTER 9 - PROBLEM 9.138 A 3-mm-thick piece of...

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PROBLEM 9.138 A 3-mm-thick piece of sheet metal is cut and bent into the machine component shown. Knowing that the density of steel is 3 7850 kg / m , determine the moment of inertia of the component with respect to each of the coordinate axes. SOLUTION First compute the mass of each component. Have s ts t mV t A ρρ == () ( ) 3 1 7850 kg/m 0.003 m 0.70 m 0.780 m 12.858 kg m 2 3 2 7850 kg/m 0.003 m 0.39 m 5.6265 kg 2 m π       ( ) 3 3 1 7850 kg/m 0.003 m 0.780 m 0.3 m 2.7554 kg 2 m Using Fig. 9-28 for component 1 and the equations derived above for components 2 and 3 have () () () 123 x xx x I III =++ 2 2 2 10 . 7 8 12.858 kg 0.78 m 12 2 =+ 2 22 2 2 11 6 4 0 . 3 9 5.6265 kg
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