Calculating Ixy ?

  1. 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.


    Attached Files:

    • Ixy.jpg
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  2. jcsd
  3. SteamKing

    SteamKing 10,309
    Staff Emeritus
    Science Advisor
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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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