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MASSPROP command vs Parallel Axis Theorem
Hello,
I've been trying to calculate the Moment of Inertia of this compound section:
Here below some data that I have used for my calculations. The centre-to-centre distance between the 2 trapezoids is 25 mm:
As you can see, Ixg calculated with the equation and Ixg calculated with the MASSPROP command of AutoCAD aren't the same. Both trapezoids have been drawn with polylines and I used the REGION command before using the MASSPROP command to give them a solid feature.
Can anyone please shed some light on this?
Thank you
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It is difficult to check the AutoCAD values you are using in your calculation from the images you provide. I would check the location of the centroids for the shapes as they are relative to the World UCS and the distance used in the Parallel Axis Theorem should be the distance between the axes passing through the centroids and the reference axis.
Please post your drawing.
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Thank you for your prompt reply,
I've attached the DWG drawing for your perusal. Would you be so kind having a closer look and telling me if the centroids are correctly placed in the right location when i run the MASSPROP command?
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Your equation is calculating the moment about the centroid of the combined shapes whereas AutoCAD is calculating it about the x-axis.
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Thank you very much for your insights. Is it possible then to calculate the moment about the centroid of the combined shapes with Autocad?
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Yes. Calculate the mass properties of the combined shapes and note the location of the centroid then create a UCS located at the centroid and give the massprop command again.
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@leeminardi has explained the discrepancy and process well. Note that the principal moments of inertia are always about the centroid but about rotated axes that result in the maximum and minimum moments of inertia. Here is a screencast.