Neutral Axis & Inertia

[Cobra17]

I'm hoping someone can help me determine the neutral axis and Inertia lx-x of a rolled plate (OD = 30"), but only for a specific angle (42.20981°).

the chord length is 10.6673" at an angel of 42.20981°. I've attached a sketch to make it more clear (I hope)

 

[rb1957]

MoI of an arc is a standard solution. Calculation of the NA is also a straight forward calculation.

The trick is these solutions will be about the principal axes, but I suspect you want about some arbitrary axes.
This is not so straight forward, but any mechanics of solids text will go through the procedure.
You can probably get there through YT.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Cobra17]

I can't seem to get the MoI and the radius of gyration.

Why I'm doing this:

I have a pressure vessel skirt (30" OD) that has a pair of rather large rectangular openings in it (12" @ 180° apart). I've run Compress calculations for the skirt and I converted the rectangular area into a circle with the equivalent area (Compress only does round openings) and put in skirt openings. Every thing is good except the P.Eng that is stamping the calculations (I am not a P.Eng.) wants the skirt to be calculated as if there were 4 openings in the skirt, so the skirt sections between the openings would be considered legs. The skirt is 14" long so there is only 2" of material connecting the skirt across the opening, and there is no base ring. The vessel is only 3 feet long and with seismic, no ring is required, and the fabricators don't want one/never had one.

so rather than create a new Compress file, do a bunch of work to figure out all the information required/needed to enter a new 'Structural Section' in compress I'd see if I could create a spreadsheet that did all/most of the work.

Basically from the attached files inputs (greyed out cells) I need to find:
Inertia lx-x
Inertia ly-y
radius of gyration

OR

Any other suggestions for a suitable way to prove the openings?

 

[cowski]

What CAD program are you using? Many of them have tools to help analyze the 2nd moment of area for arbitrary shapes.

 

[Cobra17]

I have autoCAD LT. I'm trying to make it so I don't have to drawing & dimension it every time I come across this type of skirt, which is on a semi regular basis.

 

[prex]

The formulae are in the Roark in the Properties of Plane Area chapter.
Those formulae are quite lengthy, though. You can more easily derive your result from:
- inertia J_x of a sector of a hollow circle wrt the diameter: (R⁴-r⁴)*(α+sinαcosα)/4
- neutral axis distance to the diameter of the same: y=2sinα(R³-r³)/(3α)/(R²-r²)
- knowing y you can easily reference back J_x to the neutral axis of your section

prex
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[rb1957]

that would be the I about the principal axis. what about when you have a "random" arc, like between 0deg and 30deg (as opposed between 45deg and 75 deg) ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.