topic Re: Area moment of inertia...which axis is which? in Inventor Forum

Area moment of inertia...which axis is which?

dgilmoreJNGSW — Tue, 02 Sep 2025 20:11:01 GMT

I'm trying to determine the area moment of inertia for a long beam with constant cross section. What Inventor returns is values for "Ix" and "Iy". But it is extremely confusing which principal axes these refer to. I realize they pass through the centroid, but which axis is x and which is y?

Maybe it follows the main, colored axes? Nope. In my example, the y axis comes perpendicularly out of the page, which would be meaningless. So the Iy refers to some other axis.

Maybe y is the vertical axis relative to the way the sketch is shown on the screen? Nope. If I turn the sketch 90 degrees and re calculate, I get the same values in the same order.

When I look it up online, they say that the "larger" area moment of inertial is given first, as Ix. Well...which axis is larger? For a simple part it might be obvious, but what about a complex part where it might be ambiguous which axis is producing the larger moment of inertia?

In my case, I think I know which axis would be the weaker one, but it is still sideways to how the sketch is oriented. The larger moment is listed as "Ix", but the stronger axis appears to be the vertical one. How am I supposed to know which axis is which in the answer?

Re: Area moment of inertia...which axis is which?

dan_inv09 — Tue, 02 Sep 2025 22:15:06 GMT

Since you are using Region Properties then it is probably related to the sketch rather than the 3D model's coordinate system. If you go to the iProperties for the whole part then you can see inertia related to x, y, and z. (I must confess that I have never even see, let alone used, the region properties in a sketch.)

There is allegedly some logic to where horizontal and vertical are assigned for a sketch. You could probably try placing a horizontal constraint in your sketch to see where the x goes (or vertical for y).

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Wed, 03 Sep 2025 13:24:46 GMT

As I mentioned, the figures Ix and Iy do not appear to have any relation to any coordinate system. Creating the sketch with the cross section rotated 90 degrees and calculating again just results in the same Ix and Iy in the same order, not reversed as would be expected. If there is no way to tell the axes apart, this is a terrible flaw. It is vital that we know which axis is which to properly calculate buckling forces and directions.

Re: Area moment of inertia...which axis is which?

dan_inv09 — Wed, 03 Sep 2025 13:56:42 GMT

How did you create the sketch with the cross section rotated 90°?

Is there a reason you can't use the iProperties where Ixx, Iyy, Ixz, etc. are related to the parts 3D coordinate system?

When Inventor creates a sketch it assigns a coordinate system - I never know how it does it, it seems as if it waits until I try to make something horizontal and then decides that that must be vertical!

Maybe you could try this:

Right click when not in your sketch and Edit Coordinate System, then you should be able to make x or y whatever you would like (or at least see what it is).

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Wed, 03 Sep 2025 16:15:14 GMT

How do you tell what the sketch coordinate system is? I simply oriented the part view so that the sketch plane was rotated, then I selected it and the sketch came up sideways. What is x? What is y? Is there a way to tell? If not, what do the parameters Ix and Iy mean?

Re: Area moment of inertia...which axis is which?

dan_inv09 — Wed, 03 Sep 2025 21:51:52 GMT

Right click on your sketch in the browser, select Edit Coordinate System, the red arrow with the x next to it is the x the greenish arrow with the y is y.

You can pick a point to redefine the origin or move your axes to some edge or something. When you redefine an axis you can right click and flip the whole thing.

To see what it is: Right click on your sketch in the browser, select Edit Coordinate System (then you can esc out if you don't need to change it)

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Wed, 03 Sep 2025 22:08:05 GMT

This does not fix my issue. The problem is that the coordinate system does not appear to have any connection with the region properties. Regardless of what the coordinate axes are set to, the Region Properties gives me values of Ix and Iy that are always the same. They have no relationship with the x and y of the coordinate system whatsoever, nor do they have any connection with the vertical or horizontal directions. It appears that it simply makes Ix the larger of the two values, which is useless.

As I have stated before, it is crucial to know what area moment of inertia goes with what principal axis, otherwise it's meaningless. In my present sketch, what is listed as "Iy" appears to be the area moment of inertia about a horizontal axis. The horizontal axis of my sketch (and the model) is shown as the Z axis. This is all crazy.

I there no way to know?

Re: Area moment of inertia...which axis is which?

dan_inv09 — Wed, 03 Sep 2025 22:26:42 GMT

So you changed the coordinate system by using Edit Coordinate System and it did not change the values?

What did it give you when you got out of the sketch and got you moment of inertia from the iProperties?

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Thu, 04 Sep 2025 13:47:50 GMT

Area moment of inertia (not mass moment) is a property of a specific 2D cross section, not an intrinsic parameter of the solid. It won't be in the iProperties. The units are in length to the fourth power and have no relation to the mass, nor the rest of the part geometry for that matter. This is simple, undergraduate mechanics. The terms Ix and Iy can only apply to that sketch and, as principal axes, should pass through the centroid of that sketch (NOT the center of gravity of the model).

No matter what I do, the values are only reported as "Ix" and "Iy". There is never an Iz, no matter how the axes are arranged. The Ix value is always the larger of the two, regardless of how the sketch or the coordinate system are oriented. This is tantamount to listing the two properties at random. As I mentioned before, if this were a complex cross section it would be difficult or impossible to determine which axis is which, short of doing a laborious hand calculation. This needs to be fixed.

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Thu, 04 Sep 2025 21:36:54 GMT

OK, I guess I figured it out. In File>Options>Sketch>Display there is a check box to turn on the "sketch" coordinate system indicator, an auxiliary RBG indicator in each sketch. It is different than the global one and different than the center of gravity one, automatically assigned and probably not editable. I tried it out and no matter where you start a sketch, it always sets up x and y in the sketch plane and z coming out of the plane. Y is not always vertical, but the moments Ix and Iy appear to follow this UCS. I tried some simple rectangular sketches and Ix and Iy correspond to their proper axes. As long as I leave this box checked, I should be OK.

Re: Area moment of inertia...which axis is which?

dan_inv09 — Fri, 05 Sep 2025 18:51:15 GMT

"probably not editable"

Were the instructions more difficult than undergraduate mechanics?

Maybe this will help?

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Fri, 05 Sep 2025 19:26:03 GMT

Well, here we go again. I see that you can edit the sketch coordinate system...but I tried this and now the area moment of inertia is bogus. I rotated the xy axes and re-calculated the region properties and I get the same exact results as before I rotated it, which would not be correct. Apparently the properties are calculated based on the originally-assigned coordinate system.

Beware doing a Region Properties calculation on a sketch if you don't know, or don't remember, whether its coordinate system has been changed from the default.

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Fri, 05 Sep 2025 19:51:39 GMT

OK, I discovered something new. In a normal sketch, the coordinate axes shown on the center of gravity are the same as the universal ones in the lower-left corner of the screen. But when you change the coordinate system of a sketch, the cog axes turn gray. Then if you perform a Region Properties, the coordinate system that applies to the area properties is shown at the centroid, over the gray axes. Apparently you are limited to only those axes for your principal area moments. But at least this way you can tell what axes are being used, though it might be a little tricky if your sketch origin is in the same spot as the centroid.

Re: Area moment of inertia...which axis is which?

swalton — Fri, 05 Sep 2025 20:01:10 GMT

The Region Properties command reports the Area Moments of Inertia about two different coordinate systems. The Inertia Tensor results are calculated based on the sketch origin. The Principal Results are calculated at the centroid of the sketch loops. Inventor also calculates the rotation angle between the two results.

In your example, Inventor decided to rotate the Principle Axes 90 degrees when you redefined the Sketch Coordinate system. I don't know why.

Take a look at my example. I used a 2"x1" rectangle and Inventor's calculation with respect to the Principal Axes matches a hand calculation. If I rotate the sketch loop, then the Principal results are the same, but the Sketch Origin ones are different.

Note the color of the axes: X,Y,Z = R,G,B.

Re: Area moment of inertia...which axis is which?

dgilmoreJNGSW — Fri, 05 Sep 2025 20:40:43 GMT

Well, that's what I was saying. You get the same answer for Ix and Iy, no matter how you orient the sketch. If you want to know the area moment about a rotated axis, you just have to calculate it by hand, I guess. Perhaps, for a simple part, you could create the sketch for the original extrusion and fool it into using that as default. But for complex parts with many different possible cross sections this isn't practical.

But at least there is a coordinate system shown that corresponds to the calculations, which was my initial concern.