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

 

[inertia4u]

Maybe try the following:

1. Determine resultant load from all four directions. This will give you a load at some angle (let's say theta) perpendicular to your cross-section.

2. Find the geometric properties with an axis that has at least one axis perpendicular to that applied load.

3. Solve as either Euler or Johnson-Euler depending on if it is considered long/short column (This is important).

4. If loads are variable, then come up with a spreadsheet or mathcad (tm) sheet that will account for that.

5. Profit.

Good Luck.


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Nert

 

[inertia4u]

Shoot, sorry, I typed before I though!

Euler and J-E are not beam-columns,which is what you have.


What you have is a beam-column. So you will need to use Beam-Column equations.

However, Steps 1&2 are still applicable. Then, find a beam-column equation for a point load (where the resultant is) and the axial load that you have.

Good luck.



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Nert

 

[cymeryss]

Yeah I see what you saying, but the loads that come from the four directions from the four beam phases are 90deg apart and with the same magnitude, sort of squishing the beam. Then the second part is the axial (compression) loading from both sides with different magnitude than the first four. I am worried that the structure will buckle, and that is what I am trying to solve for.

 

[GregLocock]

The problem as I see it is that the 4 loads will destabilise the skins, softening the structure. I did something rather similar for my final year project, however that was far too long ago for me to remember anything helpful.


Are the 4 loads symmetrical? are they small in comparison to the axial load?




Cheers

Greg Locock

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

 

[cymeryss]

The loads are symmetrical, and they are 48kN, where the axial load is 137kN.

 

[inertia4u]

So the net result is "0" Newtons?

Then, if you are worried about the "squishing", then I would think you can do (conservatively) the following:

Assuming that the applied loads are not on the "corners" of the square, but rather somewhere between them, then try the following:

1. Calculate the maximum deflection (delta) of a simply-supported beam of length = to one of the sides (.3 mm) with a point load somewhere along the length (where your side loads are applied).

2. Assume that the "square" shrinks the amount of "delta" for each "leg" of the square. I would think that you can then whip up an "artificial" geometric properties of the "deformed" section and run a beam column equation.







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Nert

 

[cymeryss]

THanks for the help inertia4u. From what I undestand the first step would be to do a simple beam deflection calculation with the beam length set up to half of the length (1m) and a 48kN load, but I am not sure I understand the second part and how to apply that to the buckling analysis using the axial loading. The johnson or euler equiations are for straight columns, unless I am missing something here. Thanks for the prompt response.

 

[desertfox]

Hi cymeryss

If the four loads of 48kN are all directly opposite then you don't have a bending load over the 2m length of the beam,what you do have is local bending on each side of the tube ie:- over the 0.3m length.
Then the axial loads you have make the tube act like a strut.
Slight correction:- you do have bending over the 2m length
of the the tube but due to the tubes own mass and not from the external loads.
what inertia4u is trying to say is do the beam calculation over the length of the 0.3m (width of box section) using the thickness of 0.5" as the depth of beam to check for local bending.
I would do the following determine deflection of the tube as a beam column using the beams weight as the transverse load for bending.
I would then check for local deflection or buckling across the width of the beam as suggested by inertia4u.

regards

desertfox

 

[zekeman]

First off, you do not have a buckling problem since your L/k is significantly less than 100. So the only loading is compressive in the "short" beam plus the stresses due to perhaps the point loading at the sides; those can be done by simple plate theory of a point load on a simply supported plate; that solution is readily available in Rourke or Timoshenko "Plates and Shells". You can use superposition for the final result, but I don't see buckling as a problem.

 

[inertia4u]

cymeryss,

I spent a little time this morning drawing up what I was talking about (a picture is worth a thousand words). If you can't view excel, I'll see if I can convert it to another format.

Cheers,
Nert

http://files.engineering.com/getfil...-3684-4781-a8da-c13bd7175be6&file=engtips.xls

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Nert

 

[inertia4u]

Oh, and zekeman reminded me of something.

When you do your final column check - verify if you are in long column or short column range. If you are in the short column range, then you will be limited to either the crippling of the tube (Fcc) or Fcy of the material. I say cripping only because you have 4 corners on the square tube.

Peace

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Nert

 

[inertia4u]

Grrr,
Let me clarify, once again
If you have a short column, you will use Johnson-Euler equation. The limiting term will be either Fcc or Fcy in the J-E equation.


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Nert

 

[cymeryss]

I really appreciate everybody's help, especially ineria4u. I will crunch some numbers and get back later on if I am still puzzled, but at least now I see the light. THanks.

 

[inertia4u]

No problem.

A couple of other things that I've been thinking about and rereading some of the responses here.

You may want to account for weight as pointed out by desertfox - (us aero guys typically don't do this because our stuff is so darn small, relatively speaking).

In the final step of that excel file I posted, you may need to account for the deflection of the beam under its own weight, which will introduce eccentric loading into the column, thus turning it into once again a "beam-column" (we can't just seem to get away from that!!) - the equation that comes to mind is typically called the "secant formula for beam columns" (see the link below) and will allow you to calculate the maximum stress in the beam.



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Nert

 

[cymeryss]

I think what I am missing is an equations for critical force for a beam-column problem. My Timoshenko book on mechanical of material only refers me to his other book on theory of elasticity which I don't have. Can anybody point me to a web site which has the equation, or post in on the forum. Its basically a beam in compression (with center loading) and a perpendicular point load at the center of the beam, for a pinned-pinned scenario.

 

[cymeryss]

I was also thinking of another approach, man this is getting long. What if simply use just the 48KN side load with a simply supported beam and calculate the deflection. Then, convert the deflection to column problem with an eccentric axial load by deriving the eccentricity, following with the secant formula to calc my max stress. Anything wrong with that reasoning??

 

[desertfox]

Hi again cymeryss

Why not just workout the deflection in bending due to the weight of the beam, then use this formula that inertia4u posted in the link. the offset for the applied axial load can be the beam deflection.
The other local bending calculation can be done afterwards to see if the tube wall will collaspse.

http://www.efunda.com/formulae/solid_mechanics/columns/eccentric.cfm

regards

desertfox

 

[cymeryss]

I have found the right beam-column formulas and looks like everything looks good. As zekeman has mentioned I should not have a bucking problem of the main column because my slenderness ratio is 13.5. I have yet to include the weight of the system.

 

[inertia4u]

cymeryss,


This is by no means a simple problem, for sure - but it is very interesting.

I'm not sure I quite follow your 16:29 post - but if you are saying what I think you are saying, I would not advise neglecting the axial loads for determining the deflection of the wall. As desertfox noted, the deflection for the beam-column is on that efunda website link (look for the boxed equation).

A beam-column is essentially a column problem where the transverse load actually subjects your column to a bending moment. This bending will ALWAYS cause your column to fail before it can reach the pure column buckling load because of the eccentricity of the load path.

Note that the secant formula only gives you max stress, it will not tell you if the section is stable or not. You will have to locate a reference which will show you how to write a safety margin for the interaction of the "bending moment" and the "column allowable."


If you are going to be working a lot of these kinds of problems, I would recommend you find a good reference book which contains tables for beam-columns, deflections and how to calculate safety margins.

For my work, I use "Engineering Column Analysis, The Analysis of Compression Members" by William F. McCombs. He covers a lot of the different types of columns/ beam-columns, stepped columns, buckling crippling yadda yadda. The data and equations, I believe should be applicable for all Engineers, regardless of background
[In fact, when I went to a website that sells it, it is listed as a Civil Engineers book, although McCombs is more known in the Aero industry]

This book really is nothing more than a photocopy of work that Mr. McCombs finished before passing away several years ago. It isn't pretty, but it contains a ton of *USEFUL* information that you can reference in your stress notes.

If you are still having trouble, then I would recommend maybe hitting a technical library. I've actually had

http://www.lindahall.org/

email me articles dealing with problems I'm working ( at a price ).


I sincerely wish you luck!

PS: The link below is where I bought my copy of McCombs book from. Please note that is is totally soft cover (in fact, the cover sheet is nothing more than a yellow piece of paper!)


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Nert