213_Problem CHAPTER 9

# 213_Problem CHAPTER 9 - PROBLEM 9.152 Determine the...

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PROBLEM 9.152 Determine the products of inertia , xy I , yz I and zx I of the steel machine element shown. (The specific weight of steel is 3 0.284 lb/in . ) SOLUTION First compute the mass of each component m V g γ = Then ( ) 3 2 1 2 0.284 lb/in 5 in. 4.5 in. 0.9 in. 0.1786 lb s /ft 32.2 ft/s m = × × = ( ) 3 2 2 2 0.284 lb/in 3 in. 2.5 in. 0.8 in. 0.05292 lb s /ft 32.2 ft/s m = × × = ( ) 3 2 2 3 2 0.284 lb/in 0.6 in. 0.5 in. 0.0049875 lb s /ft 32.2 ft/s m π = × = Now observe that the centroidal products of inertia, , , x y y z I I ′ ′ ′ ′ and , z x I ′ ′ of each component are zero because of symmetry. Now uv u v I I muv ′ ′ = + so that ( ) body . uv I mu v = Σ 2 , lb s /ft m , ft x , ft y , ft z 2 lb ft s
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