Lecture 23 - Moments of Inertia Area Moment of Inertia used...

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12/4/10 Moments of Inertia Area Moment of Inertia Mass Moment of Inertia - used in Dynamics to calculate the rotational motions of objects. - used to calculate stresses and deflections in beams. Can be thought of as a measure of the cross-sectional area’s resistance to bending. F F Much easier to bend the board in this orientation… …than this one.
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12/4/10 v.s. b h x y 3 12 1 bh I x = 4 3 95 . 1 ) 5 . 2 )( 5 . 1 ( 12 1 in I x = = We are taking the larger dimension to the third power, therefore we get a larger moment of inertia about the centroidal x- axis. b h x y …only for a rectangular cross- section… 4 3 70 . 0 ) 5 . 1 )( 5 . 2 ( 12 1 in I x = = By nature, the cross- section will try to rotate about its centroidal axis.
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12/4/10 = A x dA y I 2 = A y dA x I 2 Moment of inertia about x-axis Moment of inertia about y-axis A k I x x 2 = A k I y y 2 = kx ( rx ) is called the radius of gyration
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12/4/10 = A y dA x I 2 = A A dA xdA x 1st moment of an area 2nd moment of an area
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12/4/10 x y 400 2 = 100 mm 200 mm Determine the moment of inertia of the area bounded by the curve and the vertical line.
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