2nd moment of area for an arbitrary beam section 1

[disbecknell]

Hi -

I'm attempting to teach my junior undergraduate Structures students how to check their calculations for the 2nd moments of area (i.e. area moments of inertia, Iy and Iz) and area product of inertia (Iyz) of beams using NX 8.5 (it's what's available through our university). Problem is, I'm having trouble doing this myself.

What's the most straightforward way for students to sketch a cross section and have NX calulate the following quantities : Location of centroid, principal axes, and the 2nd moment of area about both the y- and z- axes as well as the principal axes? The fewer steps the better.

See the attached HW problem for further explanation of what they should be able to verify via NX.

 

[cowski]

Use the sketcher to draw your section, go to Analysis -> section inertia... use the "existing section" type, select the sketch, turn on the desired outputs, and press OK. If you chose the "principle axes" option, 2 lines will be drawn to indicate the principle axes, the intersection will be the COG. A PMI note will be added to the layer of your choosing to give some limited information about the section properties.

For more complete output, use the Analysis -> advanced mass properties -> area using curves command. The dialog that pops up is older, not overly user friendly, but it works. Choose "boundary (temporary)", select the section curves, and enter your desired tolerance for the calculations. At this time temporary objects representing the principle axes and COG point will be displayed on screen. Press "create centroid/axes" if you want to create objects that will stick around after a display refresh. Press "list all" to get a text window listing all the calculated values of the section.

www.nxjournaling.com

 

[disbecknell]

Thanks for your help. Both of those methods I had already tried and was not satisfied with the results. If you can follow the steps you listed and get the same numbers that my students should get by hand (as shown in the .pdf at the top of the thread), please let me know. For the benefit of others (and my students, of course) I've put together the attached tutorial to show how these values can be obtained in a way that is straightforward and agrees with the basic theory we teach in 200 and 300-level engineering courses.

Cheers

 

[JohnRBaker]

Creating a sketch (part file attached), based on your PDF, but in the XY plane with the 0,0 origin at the bottom-left corner and using the 'Area Using Curves' method, I got the following results:

X(cg) = 3.1538 cm
Y(cg) = 5.4615 cm

Ix = 1238.2564 cm^4
Iy = 512.1026 cm^4

My results, with the exception of the Iy Area Moment of Inertia, are dead on to yours.

John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Digital Factory
Cypress, CA
Siemens PLM:
UG/NX Museum:

To an Engineer, the glass is twice as big as it needs to be.

 

[disbecknell]

Thanks John, I was able to get your same results using your .prt file. Any idea why, when I draw the same section in the YZ plane, NX doesn't play nice?

 

[cowski]

The NX convention is to work on the XY plane; if the curves you specify are not on the XY plane it will project them to the XY plane and then attempt the analysis.

I question the posted result (in the pdf) of the principal axes. In part C the angle is calculated to be 25°; the usual convention is that positive angles represent a CCW rotation, but the pdf reports a CW rotation. I believe this leads to an incorrect diagram for part D.

www.nxjournaling.com

 

[cowski]

I should mention that you can specify the units for the analysis functions by going to Analysis -> units and choosing your desired units (if they are not in the list, you can create your own). The following is the result of the area using curves command after choosing g - cm as the reported units.

[pre]
Information Units Grams - Centimeters

Perimeter = 56.000000000
Area = 52.000000000

First Moments
MY = 164.000000000
MX = 284.000000000

Center of Mass
Xbar = 3.153846154
Ybar = 5.461538462

Moments of Inertia (Work)
Ixxw = 2789.333333333
Iyyw = 1029.333333333

Moments of Inertia (Centroidal)
Ixx = 1238.256410256
Iyy = 512.102564103

Moment of Inertia (Polar)
= 1750.358974359

Product of Inertia (Work)
Pxyw = 460.000000000

Product of Inertia (Centroidal)
Pxy = -435.692307692

Radii of Gyration (Work)
Rgxw = 7.324003389
Rgyw = 4.449142816

Radii of Gyration (Centroidal)
Rgx = 4.879817955
Rgy = 3.138172435

Radii of Gyration (Polar)
= 5.801788475

Principal Axes
Xp(X) = 0.905589421
Xp(Y) = 0.424155396
Yp(X) = -0.424155396
Yp(Y) = 0.905589421

Principal Moments of Inertia
Ixxp = 1442.323771338
Iyyp = 308.035203021

Circle Size
Center
XC = 5.000000000
YC = 8.000000000
Diameter = 18.867962264
[/pre]

www.nxjournaling.com

 

[disbecknell]

Thanks cowski and John, I corrected the HW solutions and updated my NX tutorial to include the simplified method by sketching in the XY plane.

One last question; in the Simulation-based method (creating a custom 1-D beam element using the sketched cross section, as shown at the end of the attached tutorial), when NX outputs the section properties it supplies the location of the Shear Center. Since this is another quantity we cover in my course, does anyone know if the simple area by curves... method of analyzing an XY sketch can be made to output this Shear Center location?

Please see the attached tutorial .pdf if it's not clear exactly what I mean.

Thanks!

 

[cowski]

I don't have a definitive answer, but I have a theory that you can test.

If you look carefully at the yellow coordinate system in the preview window, I think it is placed at the shear center. The results are then reported w.r.t. this coordinate system. This would explain why the shear center is reported at (0,0) and the centroid location differs from the previously calculated value.

www.nxjournaling.com