Appendix 13-11 Reinforced Obround Vessel

[FoxRox]

I'm trying to design a reinforced obround vessel per appendix 13-11. I'm stuck on trying to calculate 'I11' (moment of inertia of combined reinforcing member and effective width of plate w of thickness 't1').

The vessel will be designed just like figure 13-2(b)(2).

I have 'w'. I have 'p'. I have 't1'. I have every other variable figured out besides 'I11'. I don't see how any of the given equations for moment of inertia incorporate the wall and the reinforcing member, such as in 13-4(k). Am I supposed to sum multiple moments of inertia or something? I have not done this before.

Please help!

 

[JStephen]

That sounds like the "Parallel Axis" approach from Strength of Materials class.

 

[FoxRox]

Hi JStephen. Thank you for your reply.

So, with your approach, I would essentially be combining the MOI of the shell with the MOI of the reinforcing member into one MOI through the centroid of combined cross-sectional area. I can see the logic.

But logic doesn't make it code compliant. Does the code tell us to do this? If so, where? Is it just supposed to be understood? Have you done Appendix 13-11 calculations before and successfully applied the parallel axes theorem? It seems like it would at least be referenced. Most of the code is quite explicit, and where it's not it usually says U-2(g).

I'm really hoping I'm just missing something in the code.

 

[JStephen]

I'm assuming that when they calculate the moment of inertia of a composite section, that they do so in the standard way, and that's using the parallel axis theorem.

No, I don't see where the code tells you to do it that way.
I'm assuming that's supposed to be understood.
I think I've designed an obround opening one time, and don't remember if it involved that specific section or not.
I'm not sure how I would apply the parallel axis theorem unsuccessfully.
In the example in 13-17g, if you check the moment of inertia of the combined section using the parallel axis theorem, you do get their number for I-11, though.

 

[FoxRox]

Apologies if my response was not toned well. It was not my intent. I appreciate your help very much. When I said "successful", I was referring to having your calcs accepted by a third party, not questioning your mathematical abilities. If anyone's math needs questioned, it's mine.

Unfortunately, I do not have access to PTB-4 to see the example.

It's been a while since I was in Strength of Materials, so just to make sure I understand correctly...

Step 1.) Find the MOI of the shell and the reinforcing member individually, about their respective centroids.
Step 2.) Find the centroid of the cross-section of the combined area of the shell and reinforcing member.
Step 3.) Use the parallel axes theorem to "convert" the MOIs of the shell and reinforcing member to the centroid of the combined cross-section (Iz=Ix+Ar^2).
Step 4.) Sum the converted MOIs to get the total MOI.

Does that sound right?

 

[FoxRox]

I'm actually getting more confused as I work on this further. Area moment of inertia is supposed to have units of length^4.

The equation for moment of inertia in Appendix 13-4(k) (I = pt2/12) does not yield these units. Also, it includes a component of length. The typical equations for area moment of inertia do not.

I guess I'm not understanding the context or purpose of this equation in 13-4(k).

Any guidance would be appreciated. Thanks!