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Local Axial Load & Bending Moment in a Thin-Walled Cylinder

Local Axial Load & Bending Moment in a Thin-Walled Cylinder

Local Axial Load & Bending Moment in a Thin-Walled Cylinder

Hello all,

Linked figure with freebodies: https://imgur.com/C64SFjI

I am looking at a thin-walled cylinder with applied vertical and axial loads, simply supported at top-dead center at two bosses. The bosses are backed up by integral frames to carry local vertical loads into the body. (Section 1 of linked figure).

Balancing and sizing to vertical loads is easy (Section 2 of linked figure). The body is simply supported so I get local vertical reactions at the bosses. I can then balance the integral frames for the reaction loads using a q = V*Q/I shear flow distribution.

The global balance for the axial load is also simple (Section 3 of linked figure). Axial force is reacted at one of the bosses, and the induced moment is coupled out between vertical reactions at the frames.

The problem is how to locally work the axial reaction into the structure (Section 4 of linked figure). Most of the structures like this that I deal with have a local stiffener/beam running between the two integral frames, which provides a load path for the local offset-induced bending moment to couple out between the two frames (shown as "option 1"). Unfortunately due to non-structural systems & configuration issues I do not have that bending member. The only other ways that I can think of to carry this load are to dump it directly into the thin wall and size an effective arc length of the cylinder (maybe equal to the boss diameter?) to the bending moment (shown as "option 2"), or I could twist the moment around the integral frame and balance it with an M*c/I running load distribution at the cylinder wall (shown as "option 3").

Ideally I get the longitudinal bending member running between the frames--that will provide a loadpath to both carry the local bending as well as the local drag, which would then have plenty of space to shear into the skin. However that option is currently unavailable to me. And as much as I do not want to bend local skin, I think twisting all around the open-section frame is not realistic.

Any thoughts on how to intelligently balance this? I am also worried about what failure modes will become of concern when I do not provide the frame-to-frame loadpath--my effective arc length would be loaded in either tension or compression, plus bending, plus its portion of body bending stresses. Or is even considering this a bad idea, and should I press to get the local bending member?

Thanks in advance, and let me know if I can clear anything up.

RE: Local Axial Load & Bending Moment in a Thin-Walled Cylinder

I think you have a handle on the loads (FBD's do that like magic don't they?) but I would put the shear reaction in Case 3 on the near ring, not the far ring. In case 3 there is a bending on the vessel wall due to the reaction couple at the two rings.
I am picturing the rings as welded to the wall of the pressure vessel, but I'm not sure that's your intent. You called them "bosses", and to me that implies direct connection. The dotted line implies internally mounted.

IMO it's the potential failure mode you need to focus on.
This vessel seems to be prone to buckling failure. Specifically, a wrinkling of the sheet between the support rings, as you might expect.
The wrinkling can start long before the weight or pressure threaten the tank, however it does sometime help that internal pressure prevents the wrinkling from happening, so there's an interaction going on. Without pressure, and without a restraint to keep the rings from being overturned toward each other, the critical wrinkling stress could be quite poor, especially with thin skins. The critical wrinkling stress varies with the square of skin thickness.

This is thoroughly covered by a textbook by EF Bruhn, Analysis and Design of Flight Vehicle Structures. It's an old book and those chapters are based on even older test data, but this form of buckling has been studied and well understood ever since they started making aluminum skinned airplanes.

My hunch is that a stiffening member between the two rings is needed to keep it from collapsing, unless it's inflated to a high tensile stress (but then you have other problems). The whole thing would be easier if the lengthwise stiffening member is not internal or even fastened to the vessel. In fact it really should be a cradle so that the vessel can rest on it (under it) without having to put the attachment loads into the vessel skin. That would allow the tank to expand lengthwise and radially with internal pressure.

Please forgive me for choosing pictures that aren't of pressure vessels, but I thought these example will help where the cradle attachment is concerned:

Vessel strapped onto the cradle

Cradle welded to the vessel

Neither of these means of securing the vessel require installing internal rings (though they may be helpful for other reasons). The cradle in the lower photo is much must stiffer than the upper wall of the tank. If the walls are thick, this isn't a problem, but I get the impression your vessel has very thin walls (or you wouldn't be asking and wouldn't be putting those internal rings inside it).

No one believes the theory except the one who developed it. Everyone believes the experiment except the one who ran it.

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