Moment of Inertia for hollow circle sector

[monkeyeng]

I am trying to calculate the moment of inertia for a 'sector of hollow circle'. I have found the formula in Roarks formulas for stress and strain page 808. This formula works out but my problem has parallel slots(which do not pass through the centerline)that are 0.188" either side. Can anyone help with what I should do or point me in the right direction showing where the formula can be found.

I have attached a screen dump of the problem that I have.

Thanks

Phil

 

[GregLocock]

To save on confusion do you want the second moment of area about the centroid?



Cheers

Greg Locock


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[Ron]

Include the 0.188 slots in your calculation, then subtract the slots. (assuming I'm understanding your issue correctly).

 

[GregLocock]

However unless you have frequent bulkheads or the slots are short then the classical approach will wildly overestimate the rigidity of the section, as you will get lateral instability on the compression side.

Cheers

Greg Locock


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[BAretired]

It seems like a straightforward issue. I don't understand the problem.

The formula for the hollow circle sector can be found in CISC Handbook of Steel Construction, eighth edition, page 7-62. Then apply two negative rectangular areas of 0.188 x t where t is the thickness of the section. Subtract the slots as Ron suggested. It's a bit messy, but easily done.

There are other approximate methods which are probably close enough for your purposes.

BA

 

[GregLocock]

That assumes that plane surfaces remain plane. In practice tubes, with longitudinal slots in, stop behaving like that rather quickly.



Cheers

Greg Locock


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[iv63]

psaum:
This is easily done in AutoCAD using MASSPROP command. As you can see from the attachment Ix=0.0058in^4 and Iy=0.0740in^4.
IV

 

[monkeyeng]

Thanks for the posts......I have done this by using the mass properties in Solidworks but I was just trying to get this done in MathCAD. I will just be simple in my approch to this and use Solidworks