Curved plate with normal load 1

[jetmaker]

I'm looking for some information on the effect of curvature of a plate when subjected to a normal load.

Here is the structure description:

Curved C-Channel beam (3" deep) with tight curvature (r=4") about the stong axis. A uniform pressure is applied on the upper flange causing a bending of the flange at the channel web.

At this time, I assume that the upper flange acts as a plate in bending with 3 edges simply supported and 1 free. However, I am having problems rationalizing the length to use. I know that the curvature of the beam will add some additional stiffness to the plate and I am assuming that I could switch to a S/C/S/F boundary condition for the plate. However, I am still at a loss for the length to use. I figure the segment length could be reduced due to the tight curvature and the assumption that it is equal to a flat plate.

Anybody else have an idea or suggestion to tackel this problem. Also literature on the effect of curvature would be beneficial.

Thanks,

jetmaker

 

[rb1957]

won't curved beam analysis be appropriate ?

 

[jetmaker]

rb1957,

That's what's causing the problem. The transverse loading is so high that it results in a failure. However, I have intermediate flange stiffeners spaced at intervals of 2.5" and need to prove that this spacing is adequate to provide enough fixity to the flange that the transverse stress predicted by curved beam analysis is not valid.

Hopefully you can shed more light here.

Thanks,

jetmaker

 

[rb1957]

practically i can see the web stiffeners helping by providing support to the outer flange, and providing another loadpath into the web (improving the web's ability to react the in-plane shears induced by the pressure load). I see the outer flange as a curved plate loading in compression, and the inner flange loaded in tension, and i'd expect the tension loads to be quite a bit higher than the compression (i expect a nett tension reaction, reacting the applied pressure). I'd also expect that this is probably a fairly substantially sized relatively small fitting ... ideal for FEA

 

[jetmaker]

Ok... I'm open to FEA. However, what is the approach to this? What would you suggest? Obviously must be a non-linear analysis to capture the secondary bending effects of the flanges.

I'm looking for as much info as possible as this is a type of analysis I am not overly familiar with.

Thanks,

jetmaker

 

[rb1957]

it might be non-linear, if by that you mean material non-linear (plastic stresses, yielding) or it might be that the displacements are large (compared to the size of the structure (doubt that).

throwing gizzillions of elements at it will detect the non-linear stress field well enough (and these days it'll solve quickly enough). with the size of the model, i'd expect a solid model (3D brick elements) would do the job; 2D plate elements also.

basically you have to set up the geometry of the model, using CAD files is good, or you can simplify the design to simple curves and surfaces then you can work from that. support the model where the frame is supported, apply the pressure load to the flange, and "let it rock". these days you get really nice looking pictures that beat the crap out of impressing people you don't know better !

 

[RPstress]

Jetmaker - might it be possible to submit a text-style sketch of the section?

 

[jetmaker]

RP

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Top flange measures 0.72" x 0.060", same for Bottom flange. Height is 3". Curvature for Top flange is 4.54" and for lower flange 1.00". Centers of curvature are not the same. Structure is 7000 series aluminum.

Hope this provides what you are requesting.

jetmaker

 

[rb1957]

you're arcing through about 90deg ?

you've got some pretty thin gauge flange, particularly for a sharply curved beam with radial pressure applied to the flange.

i figure you've got a crippling stress of about 33ksi, not accounting for the curved shape.

strongly recommend the ribs you were talking about earlier.

 

[jetmaker]

rb1957,

The arc is about 45 degrees. I agree with your assessment of the crippling strength.

That's the problem, how do I determine the appropriate spacing for the flange stiffeners/ribs? I've looked at the FEM as suggested, and the transverse bending stress went way down. However, our DER is skeptical about FEM and I'd prefer a hand technique to show satisfactory.

Always open for more suggestions.

jetmaker

 

[rb1957]

i suspect your DER has a lot of experience and something about the design is bugging him. i would have thought that the loaded (and compression) flange needed to be more substantial than the unloaded (and tension) flange or the web, ie a constant thickness piece looks odd; but more on this later.

as an unstiffened piece, i'd've thought that this would have lent itself ideally to a curved beam analysis. you mentioned that the curved beam stresses were "too high". why do you think this ? 'cause they exceeded your allowable ? and did this analysis consider the 2ndry bending of the loaded flange ?

i figure the piece is only about 4" long (maybe 6"), which would indicate only 3 (just maybe 4) stiffeners, before the riveting gets excessive.

basically i think your loaded flange is undercooked, and i think your DER doesn't like the piece (nor any way of "showing it good"). i'd ...
1) consider reinforcing the loaded flange with a strap or ,better, an angle, say 0.063" thick;
2) add 3 stiffeners (closing out the ends and one in the middle);
3) if you're trying to "optimise" the part, consider reducing the thickness to 0.05" (but how much weight are you saving ? (1oz, maybe, is it worth it ?)
4) consider making this a machined part (and get rid of all those rivets !)
5) it makes sense to me that there is some long column failure mode (afterall, crippling is the most you can get out of the flange). i see something like the flange would get wavy, which is why i think stiffeners would help. maybe consider the flange as a curved plate in compression (but that is probably conservative)
6) if you've done both FE and curved beam hand calc on this, did you get different results ? why do you think ?? i'd've thought that the internal stresses in the piece are quite defined (or definable) and that the question lies in the allowable.

 

[jetmaker]

rb1957,

Thanks for your comments. I'll provide my take on them, but the problem lies in that these parts are already in production and a design change at this time is not the answer we're looking for.

As to the analysis, the curved beam stresses are very high, and yes they do exceed the plastic allowable for the material. However, the curved beam analysis is conservative as it ignores the effect of the flange/web stiffeners, it assumes the transverse flange stress to be based upon a 1" long arc segment which is "flat", the transverse stress is based upon a cantilever beam theory. The high curvature over the small arc means that for a 1" arc segment, my flange is considerably curved. It is this curvature that I believe will help stiffen the flange thus reduce it's stress. Also, the stiffner does something similar, plus adds some additional end constraints. Finally, as the section is a C-Channel, the assumption of a fixed end is not quite valid as the web will deflect, thereby allowing a reduced stiffness and hence bending stress.

Now with all that said, the answer to your points are:
1) the upper and lower flanges both would need reinforcement as the applied loads are reversing, but not equal. If they were equal, then the smaller radius would require greater reinforcement.

2) already have 1, would like the other 2 you suggest, but that is not what I have to work with.

3) just trying to show what is there good.

4) already hogged out of plate stock.

5) long column failure is already addressed and the part has considerable later restraint.

6) the results from FEA are an order of magnitude smaller. However, the model includes the stiffener.

I think you can see my problem, which is why I am looking for a way to show that the single stiffener is adequate to reduce the flange bending (which is a secondary effect due to the radial load induced by the curvature).

Again, thanks for your insight. Let me know if you have any other ideas/questions/comments.

jetmaker

 

[rb1957]

sometimes pigs won't fly, no matter how much you hope.

a single stiffener ... you don't have end ribs, closing the section ... does it attach to the rest of the world via the flanges and a shear clip on the web ?

you're right about the reversed loading.

"in production" ? ... delivered, or still in the shop ... this is only a small part; re-manufacturing it shouldn't be that big of a problem, but you know the situation better.

"show it good" ... sometimes a dodgy thing to do, particularly if the DER is suspicious of it

how hard would it be to test it ? ... if the bosses are pushing for it, and technically you're uncomfortable with it, this can be a way to satisfy everyone (if it works) ... but it's much better to know it doesn't work before the lawyers come aknocking.

 

[jetmaker]

rb1957,

Interesting statement about the pigs.

The area of interest has only 1 stiffener. This section is part of a larger beam that has closed ends and multiple stiffeners and lateral attachment locations.

The comment about testing is a good one. Maybe I can purse that route if the DER won't buy. I do not feel the present design is a problem for the loads that it will see; however, what I feel and what I can prove are 2 different things. And we all know that what I can feel means diddly for the DER.

Thanks for your help.

jetmaker

 

[desertfox]

Hi jetmaker

Don't know if this site will help its got theory for
thick and thin curved beams.
As your radius of curvature is small with depth of beam my
link is to the thick curved beam theory.

http://www.mech.uwa.edu.au/DANotes/MST/thick/thick.html

regards

desertfox