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mass prop moments of inertia

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

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

(OP)
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
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

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

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

(OP)
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
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 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

RE: mass prop moments of inertia

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.

RE: mass prop moments of inertia

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

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

(OP)
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
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

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

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

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

RE: mass prop moments of inertia

(OP)
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
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

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.

 

RE: mass prop moments of inertia

(OP)
Thanks GBor

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

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

RE: mass prop moments of inertia

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".

RE: mass prop moments of inertia

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.

RE: mass prop moments of inertia

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.

RE: mass prop moments of inertia

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.

RE: mass prop moments of inertia

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.

RE: mass prop moments of inertia

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).

 

RE: mass prop moments of inertia

I will like to add the following to the point raised by rb1957 as to the difference between centroid axis and neutral axis.

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.
 

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