Moment of inertia units

[conveyordude]

Hi,

I have a track section composed of structural members to analyze. I drew the member completely in 3D using AutoCad and used mass properties to obtain the moment of inertia. That being said, my question is this... Why are the units given in lbs*in^2 and what, if any, conversion is there back to in^4?


Thanks in advance,

 

[austim]

Hi, conveyordude.

The simple answer to converting from lb*in^2 to in^4 is that it can't be done. You are trying to convert between two entirely different types of physical property (converting from apples to oranges etc).

The value that you have is a genuine moment of inertia (inertia being related to mass and geometry). It may sometimes be called the 'second moment of mass', and is only used in dynamic calculations.

The value that you appear to be seeking as in^4 is not a moment of inertia at all (although practically every text on strength of materials refers to it as such). The correct terminology for the geometric property is 'second moment of area'; it is used in deriving the flexural stiffness of a structural member.

 

[conveyordude]

Hi autism,

Thanks for the clarification. Can the second moment of mass be used to find the defection in the member under a load? If so, where can I find the equations?

Again, thanks for your help!

 

[austim]

Hi again, conveyordude.

Sorry, but the value that you have from mass properties is no use to you in working out beam deflections.

My knowledge of AutoCad is negligible, so I am unlikely to be able to help you much, but...

I suggest that you go hunting for a menu for 'geometric properties' and see whether that gives you what you are looking for. 'Mass properties' cannot help you.

Don't hang on to my 'second moment of mass' as a recognised term - I invented it on the spur of the moment to differentiate the two common uses of the widely used 'moment of inertia'. I am not intending to change world-wide common usage of M of I in bending formulae.

Even Timoshenko refers to the 'moment of inertia' OF AN AREA when describing the meaning of the factor I that you find in the beam stiffness EI.

 

[austim]

Third time lucky?

I have just had a quick look at 'Autocad for Dummies quick reference' (bought when I had good intentions of trying to learn to use Autocad). This may be more helpful.

Stick with MASSPROP. I think that you have got the mass properties of a solid. For what you are trying to do, you need the properties of a REGION.

To quote the book, "Regions are created by the REGION command, more or less for the purpose of analysis... MASSPROP provides the following information for regions - area, perimeter,...centroid, moments of inertia, products of inertia, radii of gyration and principal moments of inertia"

All of those are pure geometric properties. Finding them under MASSPROP is rather like having to click on Start to shut down Windows .

 

[brad]

FYI-
The terms that I have typically heard used to readily differentiate between the two 'moments of inertia' are 'mass moment of inertia' and 'area moment of inertia'.
Brad

 

[ishvaaag]

Whatever the case, Autocad 12 AME module readily gives moments of inertia for the calculation ot the mechanical properties of regions, cm4, in4 and so on.

 

[butelja]

Use the SECTION command to cut a slice of the cross section of your beam. Use the REGION command to convert the section to a region. Then, use MASSPROP to get the moment of inertia of the section.

 

[ljr]

The simplest way is to draw a rectangle of known breadth and depth say 100mm x 300mm. The second moment of area is bd^3/12, which equals 225000000mm^4.

Then use massprops to determine which value of the geometrical properties equates to the second mom of area. Then you can draw any complicated shape in the knowledge that you are looking at the correct value to be used in flexural stiffness calcs.


i.e. Draw a test section

 

[ljr]

addendum to above

you can then move the test section around in autocad and repeat the massprop command to see how the geometrical properties alter.
The values of second moment of area will not alter. Moment of inertia will alter

if u then put the centroid of section on the global coordinates 0,0 the value of moment of inertia will equal that of the second moment of area.

 

[nolan51]

I don't think you want a mass moment of inertia. You probably want the area moment of inertia. That's why the units are wrong. Area I is in^4 and mass Mom. of inertia is lb-in^2.

 

You can simply use free Secpro.exe program at

http://www.lanxun.com/pce

to calculate the properties.