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Message No. 21962, Started by gordon43 on 03/13/13

Please disregard this posting shown below.  I seem to have used an incorrect formula for Iy, as can be seen from the units - - Iy must have the units of length**4.  There is no evidence that either of the formulae for Ix or Iy are incorrect.



If one goes to the Efunda formula for moments of inertia of planar figures, there is a formula for the area moment of inertia, Iy, of a trapezoid that contains 9 terms and involves (among others) the parameter c, which measures the offset of the top, left edge of the trapezoid from the Y axis.

The formula seems incorrect on two counts: (a) Iy should not depend on c, and (b) it seems awfully complicated.  More importantly, the defining relation for Iy is: Iy = Cy*Atrap, where Cy is the Y centroid, measured from the base of the trapezoid and Atrapis the area of the trapezoid (see the sketch on the web site).  Using this formula, and the published formula for Cy, we find:  Iy = [(h**2)/6]*(2a+b), a much simpler result that is independent of c.

Gordon Nelson

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Follow-up Messages (2)
Thanks for this.!!!
No. 23873, Posted by jorick1354 on 09/02/19, 01:52 PST.
Hello Gordon, It appears that your definition of Iy is different from ours...
No. 21963, Posted by dr funda on 03/13/13, 19:40 PST.
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