2nd moment of area for an arbitrary beam section
2nd moment of area for an arbitrary beam section
(OP)
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.
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.





RE: 2nd moment of area for an arbitrary beam section
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.
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RE: 2nd moment of area for an arbitrary beam section
Cheers
RE: 2nd moment of area for an arbitrary beam section
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.
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RE: 2nd moment of area for an arbitrary beam section
RE: 2nd moment of area for an arbitrary beam section
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.
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RE: 2nd moment of area for an arbitrary beam section
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 = 18.867962264www.nxjournaling.com
RE: 2nd moment of area for an arbitrary beam section
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!
RE: 2nd moment of area for an arbitrary beam section
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.
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