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Unformatted text preview: k = k MOMENTS OF INERTIA Moment of Inertia 2D = Second Moment of an Area = dA y I x 2 where Ix, Iy are the axes about which the second moment of inertia is to be taken = dA x I y 2 y = distance from the xaxis x = distance from the yaxis Polar Moment of Inertia ( ) + = + = = y x o I I dA y x dA r J 2 2 2 Moments of Inertia by Integration x 2 x 1 f 1 (x) x dx y x f 2 (x) tall thin strips ( ) ( ) [ ] = 2 1 1 2 2 x x y dx x f x f x I ( ) ( ) [ ] = 2 1 3 3 1 3 2 x x x dx x f x f I Radius of Gyration A I k x x = A I k y y = Parallel Axis Theorem for Moments of Inertia of Composite Areas (n discrete shapes) = = + = n i i i n i x x d A I I i 1 2 1 ' where ' x I = moment of inertia of shape i about its own centroid A i i = area of shape i d i = distance between centroidal axis of i and reference axis....
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This note was uploaded on 09/19/2009 for the course CEE 372 taught by Professor Siddharthan during the Spring '08 term at Nevada.
 Spring '08
 SIDDHARTHAN

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