Square hollow column buckling 4

[cymeryss]

I have been trying to figure this out for a while and am having a problem with putting this together. Here is the setup. I have a long square hollow beam (L=2m, h=w=0.3m, t(wall)=0.5in), capped of on both side with the same thickness plates. Its loaded in compression as well as there is a force at the center of each side on all four faces. So it is loaded from all sides. I am not sure what is the best way to analyze it for buckling, since that is what I am worried about. It is not a simple Euler problem since in addition to the axial loading you have side loads from each side, which deflect all sides of the beam inwards. Any assistance would be appreciated.

I am attaching a pic for clarification.

http://files.engineering.com/getfil...-085a-4d2b-89e8-6902d625a287&file=loading.jpg

 

[saplanti]

cymeryss,

I do not think you will have an overall buckling with those dimensions on the column. However, you will have some local bending problems on four side of the column if the loads are directly go to the centers of the column webs by an web side plate. Using a web side plate with longer contact length with column web may reduce the problem, however does not eliminate the bending on the web.

I do not know how and what introduces the side loads onto the faces of the column. There may be a stability problem of the square cross section under four side loads as well. In case one of the connections introduces lateral bending the cross section mat have tendency to get into a diamond shape ultimately flatten if there is no other restraint. Therefore in the large column sizes there are always one or two levels of internal diaphragm plates used to eliminate this kind of instability.

If you can transfer the loads from each side to the two side webs, the webs are not going to be under local bending and this might be another way to solve the instability by using connected beam stiffnesses at the connections.

Hope it helps,

Ibrahim Demir

 

[swearingen]

I'm puzzled that nobody has asked what is causing these loads. It is a very odd loading and I'm curious. Part of my curiosity stems from the fact that to solve this problem, it would be nice to know if there is a stiffness associated with any of these loads, to wit:

- does the load stay the same as the deflection increases? (gravity-type loading)

- does the load reduce as the deflection increases? (spring-type loading)

Knowing this, I can also attempt to evaluate how much the side loads act as a brace point for my overall column buckling.

One other thing that I find lacking from the replies is the question of how much of the wall will contribute to resisting those lateral loads? inertia4u's spreadsheet is nice, but it doesn't mention this at all.

If this problem was on the borderline, a good FEA model may have been in order.

For the problem at hand, however, I think your walls are in trouble. If you assume that 16 times the thickness of your plate wall contributes to resisting the side loads, we get an 8" width. Using this and the 1/2" thickness, the moment of inertia for the section is 0.0833in^4 and the applied moment is about 31,900inlb which gives a max stress of over 95ksi. This does not consider the axial load from the two opposing walls, nor the axial stresses from the 137kN in the other direction. Unless this is a pretty exotic material, it's just not happening...

A possible solution: beef up the central section to resist the center wall stresses by either making the local portion much thicker, or installing a central plate for these loads to pass through. Once that problem is solved, if this is steel, there are no buckling issues (local or overall) with the assembly by my estimation. The axial stresses (from the 137kN load) are a good deal less than 2ksi and this is a pretty stocky column as has been mentioned.



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[inertia4u]

swearingen brings up some excellent points.

This is why I still firmly believe that it is good to have another set of eyes looking at a problem.

searingen,

I thought my buckling check of the walls did "resisting those lateral loads" as you say.

In other words, if the walls do not buckle, (bending + axial, beam column), then the section can be considered stable and the critical wall buckling load becomes Johnson-Euler (which limits the section to Fcy) - or maybe even a flat plate buckling - ss on all sides. What am I missing?

Cheers,
Nert

-----
Nert

 

[rb1957]

i don't think this is a beam-column type problem; i think you've got a column with pressure.

look at a slice of one face, the pressure load is reacted on the sides. the sides load up each other (in compression by the sound of it) so that each face is reacting the pressure as a beam (or a flat plate) and each side has a compression load from the adjacent sides. i think it's reasonable to say that the pressure load is reacted on two sides, that the shear load in the sides is reasonably constant along the length of the column.

 

[cymeryss]

I am glad I can count on you guys to have a look at this problem with another set of eyes as ineria4u has mentioned. Basically, let me spill some more input so we can eliminate some of the questions. This short column (strut) is basically in a vertical position. so the weight factor is minimal. The four side loads are actually magnetic forces on this structure which initially is made from Al6061-T6. These four forces are actually distributed over the whole length of the column and about 10" wide, on all four sides. The column is also encapsulated on top and bottom with the same material. The top plate which carries the 137kN load is actually thicker - 1". So that is the structure. From my preliminary calcs it looks like I am marginal but I assume final design will incorporate some internal ribs, since I need to minimize side wall deflections due to my system constraints. I just wanted to be sure that this thing will not crush under the loads and needed some guidance on the right approach to the problem. I really appreciate all the ideas and welcome more suggestions. Thanks.

 

[saplanti]

cymeryss,

I guess you need an engineer to do the job for you. Obtaining information without a proper background can make you disappointed in the end.

From the beginning we are trying to solve puzzles, every puzzle brings another one. I suggest you to consult a structural/mechanical engineer to solve your problem by presenting all the details you have to consider.

Hope it helps.

Ibrahim Demir

 

[GregLocock]

Yes, saplanti's post is about 10/10 on the pissiness scale, but he has a point. Any road up, there is a whole area of structural analysis that concerns the elastic buckling of pressure vessels, which seems to be a much better approximation to your problem than some horrible bodges trying to work out the effect of side loads on beams.


Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rb1957]

how do you have "magnetic forces" on 6061 Aluminium ?

are you welding this strut together ?

 

[unclesyd]

Aside from the approach taken above you might want to research papers similar to this one. Look at the related articles section on this page for some other approaches.

http://www.sciencedirect.com/scienc...serid=10&md5=a4c9a992ebfe1755e6b64283dea37d73

 

[inertia4u]

It is interesting to me how much the problem has changed from your original sketch in post no. 1! Maybe, in the future it would be more beneficial to state a problem similar to the description like you posted above- rather than, what I believe to be somewhat of a misleadind FBD!
Regardless, it looks like there may be enough information provided now to get a better understanding of what you have, and at least get a better FBD developed!

Good luck!

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Nert

 

[swearingen]

The distributed load issue really is some critical information. Obviously a point load of 5 tons is a little different than if it is spread over 5 1/2 square feet.

If we take a 1" wide strip of the wall, it would have a distributed load of 13.7lb/in. The moment becomes approximately 13.7*11.8^2/8 = 239inlb. Using my previously calculated moment of inertia, this gives a stress due to local bending of 0.7ksi - much more manageable. Add to this a local axial stress on our strip of 13.7*10/2/(1*1/2) = 0.14ksi and I don't think you'll have any local beam-column buckling of the wall. Again, since your global column axial stress is less than 2ksi as stated in my last post, it appears this column is just fine - unless, of course, you pull another odd constraint out of your hat...



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[rb1957]

i'm with swearingen ... the column stress is Very low, the pressure induces small stresses (a bit of a red herring)

i'd be more interested in the analysis that showed it "marginal". possibly the problem was that you can't (shouldn't) separate the loading on one face from the other (faces), and once you have that thought out you see these loads are self-reacting.

still like to know how you get magnetic loads on an Aluminium structure ...

 

[Timelord]

Magnetic forces from aluminum come from induced eddy currents. For example, it is how the damper on a triple beam scale works. See

http://en.wikipedia.org/wiki/Eddy_current

 

[cymeryss]

That's right, the magnetic forces produce magnetic pressure which is distributed along the surface. It looks like I am getting some heat for not presenting the problem to its fullest, although my initial intent was to show, what I believed was a simplified version of the problem, as I was just looking a first order approximation to the stresses and any possibility of bucking. I am an engineer but its been a while since I have done structural analysis since I am mostly involved in testing. Eventually, this be done in FEA since there are local stress issues which have to be looked at.
You guys did help me a whole lot and just the discussion brought a lot of good points which is what I was looking for. Can anybody recommend any other books in addition to Roarks which have additional solution to plate/beam problems, since I have couple of cases which are not present in Roarks?

 

[inertia4u]

Well you know the adage - give one problem to 15 engineers and you'll end up with 18 different ways of trying to solve it



-----
Nert

 

[saplanti]

ASME Sect VIII Div 1 - Appx 13 - Section on the design of "Vessels of Non-circular Cross Section".

Ibrahim Demir

 

[chicopee]

cymeryss-before you start asking questions about your problem,you should present your problem accurately. It is quiet different to have point loads at the center than having them uniformely distributed along its length. Also you do not really state whether or not the loads are like a guide to the colum or would sway in the direction of column bend.