mass prop moments of inertia 1

[tmalinski]

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

Tom Malinski

http://www.okayind.com/

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[tmalinski]

Here is the massprop data from Autocad using the same t beam constructed as a region and located exactly the same position as Solidworks model relative to the origin in Autocad

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

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[GregLocock]

How about you tell us the dimensions of the section that you used?

This is not, exactly, rocket science.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[tmalinski]

Yes,
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

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[corus]

The difference is that one is rotary inertia (mass x distance^2) whereas the other is the second area thingy moment of inertia (length^4), I think. If you're wanting deflection then use the latter. NASA take note.

corus

 

[GBor]

You have to locate your centroid (center of mass) at the same location in each model if you want the numbers to be the same.

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.

 

[GregLocock]

well, first up you don't need mass moment 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

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[tmalinski]

Ok, here is a simple rectangle 2" x 6" converted to a region in autocad center of rec is on Autocad 0,0

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

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[GregLocock]

Congratulations. One of those numbers for each of those two sections is what I would expect you to use in a beam calculation.

The Solidworks numbers seem odd, but as I said, they are in the wrong units for your purposes.




Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GBor]

Simple rectangle: I = 1/12 b*h^3

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

 

[tmalinski]

Thanks guys, it looks like Autocad is the way to go for now, or just use GBor's formula for a simple rectangle. But for complex shapes in autocad I guess I should always move the geometry so the centroid of the shape is on 0,0 then do the mass prop. What about the neutral bend axis location, which is not always the centroid. Does it's location influence this method?

Tom

Tom Malinski

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[GBor]

If the bending axis is not at the centroid, you use the parallel axis theorem, which basically means you add A*d^2 where A is the area of the section and d is the distance from the centroidal axis to the bending axis.

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.

 

[tmalinski]

Thanks GBor

Tom Malinski

http://www.okayind.com/

Dell Prec 670, Xeon 3.8,2GB Ram, Nvidia Quadra FX 3450/4000 SDI
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[rb1957]

sorry guys, but when doesn't the neutral axis go thru the centroid ?

 

[GBor]

When you aren't dealing with a single, simple beam, or a construction made of just beams. The bending axis may be about another part of your "sandwich".

 

[EdR]

Someone needs to answer rb1957's question before proceeding!!!!.....

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.

 

[EdR]

Gbor:

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.

 

[GBor]

The original question involved a simple beam deflection. For that calculation, depending on end conditions of the beam, the deflection calculation is generally in the form of PL^3/XEI, where P is the load, L is the length, X is a constant for the given boundary conditions, E is the modulus of the elasticity of the material, and I is the area moment of inertia for the cross-section...I'm not shooting blindly...I've done this before -- at least twice.

 

[GBor]

Ed,

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.

 

[rb1957]

agreed that there is a difference between the area (or mass) centroid and the centroid of the transformed section, but i haven't seen any mention of multiple materials (which is mostly why i'd transform a section).