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Calculating Ixy ?

by phydis
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Jul22-13, 03:22 AM
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Here as shown in the diagram,

(1)Is Ixy zero for plane ABCD symmetrical along X axis? If yes, how it happens?
(2)How can we calculate Ixy for the plane PQRS ?

Ixy = the product of moment of area.

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Jul22-13, 06:58 AM
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For any plane figure with an axis of symmetry, Ixy = 0 for coordinate axes thru the centroid of the figure.

To confirm this, examine the definition of Ixy = Int(x*y)dA For every element of area dA which lies on one side of the axis of symmetry, there will be a corresponding element of area lying on the opposite side which is the same distance from the axis. When you add up all of these elements of area multiplied by x*y, the integral is necessarily equal to zero.

To calculate the Ixy of rectangle PQRS, apply the parallel axis theorem.

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