297_Problem CHAPTER 9

297_Problem CHAPTER 9 - PROBLEM 9.196 Determine the moments...

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PROBLEM 9.196 Determine the moments of inertia and the radii of gyration of the steel machine element shown with respect to the x and y axes. (The density of steel is 7850 kg/m 3 .) SOLUTION First compute the mass of each component. Have st mV ρ = Then () 33 1 7850 kg/m 0.24 0.04 0.14 m m × 10.5504 kg = 2 23 7850 kg/m 0.07 0.04 m 2.41683 kg 2 mm π  == × =   ( ) 2 45 7850 kg/m 0.044 0.04 m 1.90979 kg × = Using Figure 9.28 for components 1, 4, and 5 and the equations derived above (before the solution to Problem 9.144) for a semicylinder, have () () () () () ( ) ( ) 12345 2 3 where x xx xx x x x I IIIII I I =+++− = ( ) ( ) 22 2 11 10.5504 kg 0.04 0.14 m
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