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SecondMomentsofAreaOverview9a

# SecondMomentsofAreaOverview9a - Second Moments of...

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Second Moments of Area (a.k.a. Area Moments of Inertia) KML 7/17/09 Second moments of area represent the distributions of areas with respect to axes and determine the stiffnesses and load capacities of beams in bending and torsion. Second moments of area are positive and have units of in 4 , m 4 , or mm 4 . x I is the SMA with respect to the centroidal x-axis. The nominal formulas for calculating second moments of area are: = dA y I 2 x and = dA x I 2 y . These formulas apply to differential strips of area that are parallel to the given axes. For x I and y I , the subscript means: “with respect to the _ axis”. h/2 h/2 b/2 b/2 axis x - axis y - dy 12 hb I 3 y = 12 bh 2 h 2 h 3 b I 3 3 3 x = - - = 3 y b dy y b dy 2 b 2 b y I 3 2 / h 2 / h 2 2 / h 2 / h 2 x = = - - = - - Other common shapes: r h b 4 r I I 4 y x π = = axis x - 36 bh I 3 x =

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