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Panel under Bi-axial Compression Stress and Shear

Panel under Bi-axial Compression Stress and Shear

I have been looking (text books & stress manuals I can access) to see if I could find an interaction curve dealing with a panel buckling under bi-axial compression and simultaneous shear without success.
I have seen many interaction curves, but this one I have not come across.
From what I have found, it suggests that the bi-axial stress situation alone is not a topic for an interaction curve.
However, uni-axial stress and shear is easily found.

Could anybody suggest a possible source?


RE: Panel under Bi-axial Compression Stress and Shear

I believe there are interaction MS design curves available for the loading condition you are interested in but unfortunately the source is proprietary. I just wanted to let you know that such curves are available. Let me look at some of the open source materials I possess and if I come across such a curve, I will share it with you.

Other option is to model using FEM :)

RE: Panel under Bi-axial Compression Stress and Shear

Thanks for the input.

I have done a set of FE analysis of bi-axial stress for one panel size to see what the outcome may be.
They generate a curve which looks plausible but has no simple relationship.
I will have to look at another panel size(s) and I maybe something will gel.
It will take a little time.
I will eventually make it public here.

RE: Panel under Bi-axial Compression Stress and Shear

interaction should be easy enough, why not principal stress ? the difficult part is the allowable ... what structure are we looking at ? sheet ? plate ? thick (stable) section ?

another day in paradise, or is paradise one day closer ?

RE: Panel under Bi-axial Compression Stress and Shear

I want to mention that the design curves for the loading condition of interest is for simple supported (hinged) edge support on all 4 sides.

RB, as you might be familiar, Nastran provides SOL 105 output usually in terms of Buckling Factor which is a ratio of Critical Load/Applied Load i.e. Pcr/Papplied. I guess Pcr kinda becomes allowable! See below for my justification and you can provide inputs if it makes sense.

This is what we have done in the past. Since we do not have a sophisticated in-house testing facility, we usually FE model panels, loading & support conditions for which Critical load analytical solutions are available. For Ex: Panels with uniaxial compression along with bending etc. We then establish the "procedure" as accurate and scale it to more complex conditions.

RE: Panel under Bi-axial Compression Stress and Shear

I haven't worked too much with SOL105; I'd be interested to see how it matches up with NACA 2661 (diagonal tension analysis); I don't even know if it matches basic panel compression (ie 30t effective width).

another day in paradise, or is paradise one day closer ?

RE: Panel under Bi-axial Compression Stress and Shear

Thanks for all comments.

I will comment on the comments in turn.

Considering the principal stress against ftu would give over optimistic results. Comparing to fbuckling (min of two values) would not be much better I think.
The situation is panel biaxial compression. The elastic buckling condition is normally considered as the Ultimate allowable as long as RF > 1.
The real logic is that the panel will intially buckle. At this point the panel stiffness will reduce and the load will then distribute to adjacent panels if they exist. The panel will continue to carry a limited amount of load (plastic state), where the calcs are not so simple. The normal practice is then to move the excess (above buckling) compression loads out of the panel into the panel edge supports. Failure is then considered when the edges quit. Not a reality, but normally works in practice. At design time you can always up the panel thickness to solve the problem.
If you have many loading cases to consider, the problem can become a nightmare.

It is common practice to accept the SOL105 analysis as the point of the elastic buckling. All checks I am aware of show that SOL105 predicts the buckling stresses for uniaxial and shear loads very well when compared to the standard mathematically derived curves that you can find in most text books. Mixtures of loading when there is no standard curves to compare, are usually accepted unless you can test. Exactly as you describe.

I think SOL105 will not be able to be compared to diagonal tension curves. Diagonal tension analysis is much more than simple elastic buckling.

Further, I have looked at ONE geometric panel for biaxial compression. The results are attached.
As you can see that RF = 1/(Rx + Ry) produces slightly conservative results.

RE: Panel under Bi-axial Compression Stress and Shear

Hi again

A comment to the deleted post of Burner2K.

In the past I have had to deal with a very thin curved shear panel (only) in the post elastic buckled state. Nastran SOL 105 was used.
The analysis showed that the stiffness changed at the elastic buckled state but the panel continued to carry shear load until the panel deflections (effectively panel stiffness) became obviously nonsense. You had to interpret the panel deflection curves for a shear "failure" load (stress). This "failure" occurring well before the panel shear stress was reached. The edge rivet loading peaked at the panel ends I believe, but was not very different from the central area.

RE: Panel under Bi-axial Compression Stress and Shear

sure a panel in isolation can approach elastic buckling, without failing the entire structure.

possibly have two models, one with an effective panel, and one with a very thin (ineffective) panel. then figure out that the panel buckles at X% of the load so superimpose the two models ... X% of (fully effective panel model) + (100-x)% of (ineffective panel model). hopefully you have a fine gird model.

but the other side of the coin is to say that the panel is effective for 30t up to your other buckling limits (inter-rivet, crippling, etc) so you take the model gridpoint loads and revise the section to account for the reduced effectivity of the skin (the model assumes fully effective skin, like in tension, so the effective section/stresses need to be revised).

but I'd've thought that compression and shear = diagonal tension. there is an issue with bi-axial compression as diagonal tension, but I don't think there's much research on the matter; usually use the highest compression. and curved shells adds another wrinkle to the problem.

another day in paradise, or is paradise one day closer ?

RE: Panel under Bi-axial Compression Stress and Shear

ROARK 7th_edition, Page 732. Table 15.2 (Statement 5)
There you will see bi-axial compression and shear combined equation.

(excuse me if you are already aware, just as a warning to the difference between Bruhn and Roark K coefficients) :

RE: Panel under Bi-axial Compression Stress and Shear

Also I came across this which is basically the calculus of the panel buckling for a couple of different cases.

Your case is on page 9. There is a complete solved example about exactly what you were looking for.


RE: Panel under Bi-axial Compression Stress and Shear

Hallo aerostress82

I thank you very much for the information.

First, I have never noticed the solution that you indicate in Roarke. It is shown in edition 2 & 3 also. Theses are the earliest versions I have. When Warren C Young changed so many of the table formats in edition 5, I began to use Roarke less and less for hand calcs, as it was much more effort to use the formula (unless you used Mathcad which was not always made available in the times of DOS only). I always had other sources for buckling situations, but that is no excuse for not being aware of of the offered solution though.
I will make a comparison of the FE I have shown and Roarke, then upload it.

For the INCAS Bulletin I am very grateful. It looks very interesting indeed. This is the first time I have seen a clear definition of "simply supported". (buckling values are very different when you fix the edges in the plane of the panel (see ESDU, it is clearly indicated) as you could have with a panel in a group of panels).

Many thanks again.

RE: Panel under Bi-axial Compression Stress and Shear

You are very welcome stresscalcs, and good catch on the INCAS "simply support" boundary condition for that problem solution. (I hadn't checked that actually)
I try to find pdf versions of those books where I can search the text inside. So, it allows me to scan them too. (I know we have so many reference books and it adds up to a significant amount of time to do research in them most of the time)

You can have this clear version here too (I found it via google search): (remove the space in the middle when you copy-paste) Roark's%20formulas%20for%20stress%20and%20strain.pdf

I take aerospace very seriously as people are flying in those structures (especially commercial aerospace) and would try to be of help if I see any posts that I have had experience on.
That being said, per your case, clamped boundary is a non-conservative approach for panel buckling (ONLY IF that's what you are using and if there is more to it around "your panel of interest". ie, vertical, horizontal stiffeners, stiffener landings etc.).

What I've seen in my past experience is that there would be a scale factor per panel boundary conditions. And if you could verify your vertical/horizontal stiffeners' and stiffener landings' torsional/flexural instability, inertia check criteria, you could use a boundary condition between simply support and clamped support (but that's only if "all your verification methods for boundary conditions" passed these checks).

You guys probably have a lead/principal stress in your office, you could discuss the clamped/simply support assumption for the panel if this structure is going to fly. If not, or if you are already aware of all the clamped/simply support conditions in your design, please ignore this message. Hope this adds up more insight to the problem. All the best!


RE: Panel under Bi-axial Compression Stress and Shear

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RE: Panel under Bi-axial Compression Stress and Shear

Hello Compositepro. Thanks for the support. I want to ask some change to Eng-Tips sub-sections format:
(in your profile it is mentioned you are a member of Eng-Tips Round Table - hope you have the connections for this purpose here)

I already wrote this in the most recent Eng-Tips survey, but just wanted you to have the info if you could have a more direct effect:

For Aerospace especially, could we create an Aerospace Structural/Stress Engineering section in Structural Engineers area? (
I think this area has so much coming up due to past/current developments in aerospace especially considering the future commercial hypersonic technology that's knocking on our doors recently. I think the aerospace stress/structural guys (including me) would have a better guide of applying correct practices if we were to have all these discussions in one place.

Also, it would add value to the website to have a Automotive Structural/FEA engineering section in Structural Engineers area as well.


RE: Panel under Bi-axial Compression Stress and Shear

Aerostress82, you can always get a message to site management by using the red flag feature. I appreciate the logic of your suggestion, but do not completely agree with it. I watch all the forums you mention and it works pretty well. There really is not a great deal of commonality between aerospace structural engineering and building structural engineering. There is no perfect system to organize these fora, so it is always open to discussion. It is apparent that you will be one of the more valuable contributors to this site. Welcome.

RE: Panel under Bi-axial Compression Stress and Shear

Thanks for the response Compositepro. I checked Aircraft Engineering subtitle only and it looks like most of it is here, but there are also other parts in other forum subtitles. I guess I'll use search for something that I can't come up with from Aircraft Engineering subtitle.

The explanation to why I look like I'm new to here (per my posts so far) is as follows:
I've been a member of Eng-Tips for more than 7 years and have checked it so many times for Patran/Nastran and aerospace structural/stress engineering issues that I faced at the time as a junior aircraft stress engineer, but have gone off the grid for 4-5 years as I've been working day and night on my aircraft stress analysis projects in my previous job and also as I switched to automotive FEA/structural analysis for the last 1 year - so really had to deal with the animal there for a whole year. But from here on, I should be contributing more whenever I see open ends in discussions if it is within my expertise. But I also see so many valuable senior stress engineers here and I believe this will be a nice gathering here now since I've had more experience in the last 7 years as well :)
Thanks for the welcome too! All the best..


RE: Panel under Bi-axial Compression Stress and Shear

looking at the INCAS report, it seems to set failure as the onset of buckling, and doesn't permit post-buckled behaviour (diagonal tension). For me the structure (the skin/stringer panel) will keep working so long as the stringers are not buckled

another day in paradise, or is paradise one day closer ?

RE: Panel under Bi-axial Compression Stress and Shear

I feel like the INCAS paper is just an introduction to onset of buckling per Calculus, too.
Then would come the stiffener instability, edge member flexibility, stiffener inertia checks for boundary conditions and a post-buckling analysis would also be necessary. At the final step a load redistribution to stiffeners assuming the panel has failed.

This post in this forum is merely a start of all the analysis on a stiffened panel I think. There is a lot more to it that I've seen in my past experience as well. All my explanations above were only about "a simple panel onset of buckling calculation". Just as a warning too..


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