mass prop moments of inertia
mass prop moments of inertia
(OP)
When doing a simple deflection of a beam calculation using the machinery's handbook it's using "I" moments of inertia in the formula. so rather than calculating this longhand I construct the model in Solidworks and do a mass properties on it. It reports moments of inertia values, but I'm not sure which values to use. Does it matter where the model sketch is relative to the origin? here is the mass prop I got from t shaped beam
Center of mass: ( inches )
X = 0.00000000
Y = 0.00000000
Z = -5.00000000
Principal axes of inertia and principal moments of inertia: ( pounds * square inches )
Taken at the center of mass.
Ix = (0.00000000, 0.00000000, 1.00000000) Px = 27.74575243
Iy = (1.00000000, 0.00000000, 0.00000000) Py = 83.23725729
Iz = (0.00000000, 1.00000000, 0.00000000) Pz = 101.73442558
Moments of inertia: ( pounds * square inches )
Taken at the center of mass and aligned with the output coordinate system.
Lxx = 83.23725729 Lxy = 0.00000000 Lxz = 0.00000000
Lyx = 0.00000000 Lyy = 101.73442558 Lyz = 0.00000000
Lzx = 0.00000000 Lzy = 0.00000000 Lzz = 27.74575243
Moments of inertia: ( pounds * square inches )
Taken at the output coordinate system.
Ixx = 430.05916266 Ixy = 0.00000000 Ixz = 0.00000000
Iyx = 0.00000000 Iyy = 448.55633095 Iyz = 0.00000000
Izx = 0.00000000 Izy = 0.00000000 Izz = 27.74575243
also, when I construct the same shape as a region in autoCad, it's massprop moments values are totally different. I don't know which to use.
any guidence is appreciated
Tom
Center of mass: ( inches )
X = 0.00000000
Y = 0.00000000
Z = -5.00000000
Principal axes of inertia and principal moments of inertia: ( pounds * square inches )
Taken at the center of mass.
Ix = (0.00000000, 0.00000000, 1.00000000) Px = 27.74575243
Iy = (1.00000000, 0.00000000, 0.00000000) Py = 83.23725729
Iz = (0.00000000, 1.00000000, 0.00000000) Pz = 101.73442558
Moments of inertia: ( pounds * square inches )
Taken at the center of mass and aligned with the output coordinate system.
Lxx = 83.23725729 Lxy = 0.00000000 Lxz = 0.00000000
Lyx = 0.00000000 Lyy = 101.73442558 Lyz = 0.00000000
Lzx = 0.00000000 Lzy = 0.00000000 Lzz = 27.74575243
Moments of inertia: ( pounds * square inches )
Taken at the output coordinate system.
Ixx = 430.05916266 Ixy = 0.00000000 Ixz = 0.00000000
Iyx = 0.00000000 Iyy = 448.55633095 Iyz = 0.00000000
Izx = 0.00000000 Izy = 0.00000000 Izz = 27.74575243
also, when I construct the same shape as a region in autoCad, it's massprop moments values are totally different. I don't know which to use.
any guidence is appreciated
Tom
Tom Malinski
http://www.okayind.com/
Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
SWorks Premium 2008 SP 3.1 & PDMWorks





RE: mass prop moments of inertia
Area: 24.0000
Perimeter: 28.0000
Bounding box: X: -3.0000 -- 3.0000
Y: 0.0000 -- 8.0000
Centroid: X: 0.0000
Y: 5.0000
Moments of inertia: X: 736.0000
Y: 40.0000
Product of inertia: XY: 0.0000
Radii of gyration: X: 5.5377
Y: 1.2910
Principal moments and X-Y directions about centroid:
I: 136.0000 along [1.0000 0.0000]
J: 40.0000 along [0.0000 1.0000]
none of these values match solidworks values? I am obviously doing something wrong. Any help is appreciated. I just want a reliable methos to extract moments of inertia for bem stress and deflection calculations.
Thanks,
Tom
Tom Malinski
http://www.okayind.com/
Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
SWorks Premium 2008 SP 3.1 & PDMWorks
RE: mass prop moments of inertia
This is not, exactly, rocket science.
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: mass prop moments of inertia
the T is esentially two rectangles 2" x 6" stacked on top of each other to form a T shape. So the overall size of the T is 6" wide x 8" tall
Tom
Tom Malinski
http://www.okayind.com/
Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
SWorks Premium 2008 SP 3.1 & PDMWorks
RE: mass prop moments of inertia
corus
RE: mass prop moments of inertia
I generally move all AutoCAD cross-sections to the origin. In your case, select all lines associated with the region, and move @(0,-5). The next time you run the mass props, it should show a centroid of (0,0). This is the lowest inertia value you will see.
If the section is actually attached to a plate, I use the parallel axis therom to increase the moment of inertia.
You have to know, as Greg indicates, the shape of the section, how it is oriented, and how it is used to calculate the actual inertia. For this comparison, however, just make sure you are comparing "apples to apples", which you are not at the moment.
RE: mass prop moments of inertia
For a beam calculation we are primarily interested in the second moment of area.
Therefore your units should be inch^4
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: mass prop moments of inertia
Area: 12.0000
Perimeter: 16.0000
Bounding box: X: -3.0000 -- 3.0000
Y: -1.0000 -- 1.0000
Centroid: X: 0.0000
Y: 0.0000
Moments of inertia: X: 4.0000
Y: 36.0000
Product of inertia: XY: 0.0000
Radii of gyration: X: 0.5774
Y: 1.7321
Principal moments and X-Y directions about centroid:
I: 4.0000 along [1.0000 0.0000]
J: 36.0000 along [0.0000 1.0000]
here is the mass prop for Solidworks with the same rectangle sketch with center on the origin. extruded into a solid
Center of mass: ( inches )
X = 0.0000
Y = 0.0000
Z = 0.5000
Principal axes of inertia and principal moments of inertia: ( pounds * square inches )
Taken at the center of mass.
Ix = (1.0000, 0.0000, 0.0000) Px = 1.4451
Iy = (0.0000, 1.0000, 0.0000) Py = 10.6937
Iz = (0.0000, 0.0000, 1.0000) Pz = 11.5607
Moments of inertia: ( pounds * square inches )
Taken at the center of mass and aligned with the output coordinate system.
Lxx = 1.4451 Lxy = 0.0000 Lxz = 0.0000
Lyx = 0.0000 Lyy = 10.6937 Lyz = 0.0000
Lzx = 0.0000 Lzy = 0.0000 Lzz = 11.5607
Moments of inertia: ( pounds * square inches )
Taken at the output coordinate system.
Ixx = 2.3121 Ixy = 0.0000 Ixz = 0.0000
Iyx = 0.0000 Iyy = 11.5607 Iyz = 0.0000
Izx = 0.0000 Izy = 0.0000 Izz = 11.5607
The values are totally different.
Again, I'm sorry for my lack of knowledge in this area, but I am confused as to which I can or should use?
Tom
Tom Malinski
http://www.okayind.com/
Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
SWorks Premium 2008 SP 3.1 & PDMWorks
RE: mass prop moments of inertia
The Solidworks numbers seem odd, but as I said, they are in the wrong units for your purposes.
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: mass prop moments of inertia
For the way your beam is oriented in AutoCAD, b = 2 and h = 6
1/12 * 2 * 6^3 = 36
FOr the other direction where b = 6 and h = 2:
1/12 * 6 * 2^3 = 4
RE: mass prop moments of inertia
Tom
Tom Malinski
http://www.okayind.com/
Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
SWorks Premium 2008 SP 3.1 & PDMWorks
RE: mass prop moments of inertia
You should be able to find a spread sheet that will calculate all of this for you. I'm attaching a simple one that works for me. It may help you to understand how to do it, but this one works for limited cross-sections.
RE: mass prop moments of inertia
Tom Malinski
http://www.okayind.com/
Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
SWorks Premium 2008 SP 3.1 & PDMWorks
RE: mass prop moments of inertia
RE: mass prop moments of inertia
RE: mass prop moments of inertia
Also it seems to me that there needs to be some basic checking going on with simple models against theoretical results so we understand what we are doing (mass moments vs. second moments, etc.)....Seems like we are just taking results from programs and jamming them into other programs and expecting good and accurate results...
Ed.R.
RE: mass prop moments of inertia
Didn't see your last post before mine went out.....
Even in the case of a "sandwich" bending still occurs about the centroid of the equivalent "transformed" section....
Ed.R.
RE: mass prop moments of inertia
RE: mass prop moments of inertia
Didn't see your response before I "popped off"...
Agreed that it still bends about the centroid of the "transformed" section, but no necessarily about the centroid of a beam within that section.
RE: mass prop moments of inertia
RE: mass prop moments of inertia
Centroid axis of a cross-section is a line such that the moment of the upper part of the area about the line is same as the moment of the lower part of the section area about the same line. It is a property of the cross-section and independent of the stresses in the section.
Neutral axis is a line such that that the forces on the cross-section (external and internal) above the line is exactly same as those below the line.
Where the cross-section is subjected to external applied force which is applied at an eccentricity to the centroid axis, the neutral axis is different to the centroid axis. In fact if the force is applied through the centroid, it will be under pure compression or tension -- there will be no neutral axis. But of course it will have a centroid axis as calculated from the cross-section geometry. Such situations are common in pre-stressed concrete, high-strength friction grip bolts, ground anchors etc.
In tmalinski's case the T-cross-section is asymmetric but as far as I make out has not got any axial compression. So the 2nd moment of inertia shoud be about the centroid axis, as mentioned by some others before me. This axis will also be the neutral axis.