How to calculate the principal axis of an area

[dreber]

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?

 

[BAretired]

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

 

[rb1957]

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

 

[johnbridge231]

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