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How to calculate the principal axis of an area

How to calculate the principal axis of an area

How to calculate the principal axis of an area

(OP)
I am trying to develop an excel calculator for a single aluminum angle in flexure.

It is pretty similar to steel - if the shape is unrestrained (as mine is) bending will occur about the principal axis instead of the geometric axis.

So, I am trying to calculate the principal axis for an arbitrary area - one would think that a solution to this problem would be readily available via google, but I can't find anything - no calculation examples nor execl calculators.

Do you know where I can find the appropriate equations for this?

RE: How to calculate the principal axis of an area

The principal axes of an area are the axes where the product of inertia is zero. For a doubly symmetrical shape, the principal axes are the X and Y axes.

For an unsymmetrical shape, if theta is the angle measured counterclockwise from the X axis to one of the the principal axes then tan(2*theta) = 2K/(Iy-Ix) where K is the product of inertia about the X and Y axes and Ix, Iy are the moments of inertia about the X and Y axes respectively. The other principal axis is normal to the first.

For an angle, the expression may be found in the CISC Handbook of Steel Construction and, although I cannot be certain, I would bet that it is also in the AISC manual.

BA

RE: How to calculate the principal axis of an area

look up principal axes in any text.

like BA says, you need the three moment of inertia of the section ... Ixx, Iyy, and Ixy

Quando Omni Flunkus Moritati

RE: How to calculate the principal axis of an area

You can cross-check your results with this program, which calculates all properties for custom defined sections.
A relative example can be found here.

Regards

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