1. ## Buckling in Structures

Referring to the attached picture, which shows 4 examples of a load rigidly attached to a column and/or columns.
Example A shows a load supported by a column.
Example B shows a load exceeding the column's ability to resist buckling.
Exampe C shows an additional column, which together with the original column, provides sufficient resistance to the buckling moment.
Example D shows the two columns in Example C, with the addition of a cross member at top and bottom, rigidly connecting the columns together.

To determine the resistance to buckling in Example C,
is it true that the resistance of each column can be summed,
resulting in the total resistance to buckling?

In Example D, the columns are spaced apart, but are rigidly attached, forming a "structure".
Is it true that this structure resists buckling more than the simple sum of the individual columns?

2. Dale,

Just to make you work a bit, think in extremes. In "D" what would the situation be if the space between the columns was say six-feet? Might help you get a grasp on the concept of things.

By the by, A and B are very poor designs and should be avoided unless there is no other way. The column can twist and the overhang is very severe compared to the column size.

3. Dave says: "By the by, A and B are very poor designs and should be avoided unless there is no other way. The column can twist and the overhang is very severe compared to the column size. "

dale replies: yes, of course. But to facilitate understanding,
this discussion is limited to a single variable,
that being buckling in the left-right direction only.

Dave says: "Just to make you work a bit..."
dale says: Ok, fair enough. Here is my line of thinking:
from another thread recently: " a truss is a beam with the useless bits removed" (or something to that effect).
and from some forgotten book: " an I beam is a rectangular bar with the extra metal removed that was not doing much anyway" (or some such concept).

It seems possible that in Example D, the column has been "widened" by use of the lateral pieces.
I am wondering if this works in a similiar, but probably not as effective, manner as trusses and I beams,
in that some, if not most, of the material is not really doing much to resist the left-right buckling force.

So, in Example D, where the column has been only modestly widened, it may result in more than the simple sum of its parts.
In fact, it seems possible that the column in Example D might have 95% of the strength of the total width of the "structure".

But, you encourage me to think in extremes, which I did, but I kept running into another limiting factor:
the lateral piece itself starts to become subject to a failure by (horizontal) buckling.

If all of this is true, there is a "cost/benefit ratio" of how much material one can remove without reducing strength to an unacceptable degree.
Or, put another way, a open "structure" can duplicate the function of a solid column, up to a point.

Having said all that, according to Euler's formula, the way to increase resistance to buckling is to increase MofI;
and it does not really seem like adding a couple of horizontal braces does that.

Or am I missing something?

4. Originally Posted by dalecyr
from another thread recently: " a truss is a beam with the useless bits removed" (or something to that effect).
and from some forgotten book: " an I beam is a rectangular bar with the extra metal removed that was not doing much anyway" (or some such concept).
I would be VERY surprised to learn that you saw those statements on this Forum. That is more likely to have come from a "Trades" Forum where there seems to be a unilateral belief that Engineers are generally of little use other than for getting the lunches from the burger place. Think about it, IF any parts of a beam, truss or whatever load bearing contraption you are thinking of has "useless" bits then the you would have a formula for adjusting the Moment Of Area to excluded the "useless" bits.

I have often heard the phrase in motor racing circles. "Drill holes to make it lighter and stronger." Hmmmm, a quaint notion.
Originally Posted by dalecyr
Or am I missing something?
It's a bit of a moot point unless you have a specific application in mind. I think it is safe to generalize and say that for any vertical support as you have shown in A, B, C and D, a round (or slightly oval) form is much better suited. Therefore, IMHO, there is little point in exploring the merits of a supporting system that should never be used or encouraged. I am sure a 1/2 ton of concrete and a steel cable tossed from a moving car would be far more effective at stopping the vehicle than brakes. But, I don't see the car manufacturers adopting that any time soon though.

Just one old man's opinions mind you, and I have been wrong before.

5. uuummm... er...
from the thread "Constructing a Deck with Beam supports":
06-24-2011 06:36 AM#28
RWOLFEJR

" I'd go with 40 foot W14 x 22 twice (I of 199 each) and some rough cut 2" hardwood planks. If the load will indeed be limited to a mower and/or 2,000 lbs. for your own private residence. The 14" beam is lightest you can get with a high enough moment and light = less steel = less dollars. Or as Kelly mentioned you could look into trusses. Beams with all the useless parts cut out. Space the beams maybe a foot wider than your mowers width. and overhang the boards by a foot each side. Sink some big cut stones in the ground a few feet off the bank each side. Drop the beams on the rocks and poke a bunch of holes for stainless carriage bolts. Further you sink the stones the less need for a ramp. Thrwo some rip rap along the edges of the crick and call it a day. "

but perhaps I have misunderstood his intent...

6. I would like to simplify the question:

Does the structure in right diagram have more resistance to buckling in the left / right direction than the columns in the left diagram?

7. Originally Posted by dalecyr
Or as Kelly mentioned you could look into trusses. Beams with all the useless parts cut out.
Oooops, just changing feet in my mouth as I type. I humbly stand corrected. But, I should then of course, censure Kelly for such a rash statement.

My most profound apologies to the "Trades" forums et al. Wait, no, they probably still think the same about Engineers so I retract that apology. :O

8. Ahh HA! A trick question !! The old insufficient information trick eh??

If the load is mechanically substantial enough
and
the columns have plates welded at the top
and
the load is bolted through the plates
and
the columns have plates welded at the bottom
and
the plates are bolted to embedded bolts in a mechanically substantial enough concrete footing
then
there would be little to no difference between the two options.

Do you have a real-world application in mind?

9. Surely as the load is purely from a vertical plane the option on the right in the simplified diagram should have more rigidity than the the two unsupported beams on the left..... Although if all the stresses are purely from above and the seating of the structure is secure the difference would be small.

10. Originally Posted by PinkertonD
Ahh HA! A trick question !! The old insufficient information trick eh??

<snip> a bunch of appropriate restrictions that must be met to qualify the answer </snip>
then
there would be little to no difference between the two options.

Do you have a real-world application in mind?
Of course. And I will reveal it shortly.

referencing the attached drawing;
is it true that the MofI can be increased by rigidly "attaching" an additional member to the column,
even though that additional member is only a substantial portion of the column height, but not the entire column height?

11. Best guess (which probably isn't allowable here)

Yes, as long as the top and bottom of the structure is secure.

12. Was I... Bob... that added the "...Beams with all the useless parts cut out." to the suggestion of considering a truss. My flippant remark was meant to simply imply the strength to weight ratio improvement, but if I'm deserving of a flogging for that so be it. I have a habit of leaning toward simplification in most of what I say and do. The complex engineering in the design of a truss isn't something that I need to re-invent therefore I take it for granted and I'm happy with that. To me a truss looks like a beam with most of it cut away...?

Here's another over simplification, far as these column choices goes and their resistance to buckling... You've effected a shorter pair of columns when you added the two cross members. Shorter column = Less buckle
Add a slight conical shape to them and you'll really beef them up. You could cut the useless parts out of those conical tubes and rename them towers!!
Oops... there I go again. (humor)

"I have often heard the phrase in motor racing circles. "Drill holes to make it lighter and stronger." Hmmmm, a quaint notion."

There is an instance where the statement is not just quaint but a fact. A tube with heavy enough wall will handle more torque than a solid bar of equal diameter. After reaching a cross section capable of same/ same torque as a bar of same diameter... to increase the cross section will allow the tube to handle more torque than the heavier bar. So you gun drill the axles... Drill holes and make it lighter and stronger... Then there's the added benefit of the drop in spinning weight that robs power. Similar concept with the drive shaft. Light wall tube capable of delivering say maybe 70-80% of the torque of a solid bar of the same diameter... lighter for less hp loss... much higher first critical speed... lower cost... Tube is awesome!!

13. Bob, it was about an hour later that I suddenly realized what you mean about the "useless" parts and your comment became acceptable.

Argghhh, hoisted by my own Petard, I failed to be specific enough. Guilty by common curse of Generalization. With the hole drilling I was referring to plates, sprockets disk brake rotors etc. Things where hole drilling does make them lighter but stronger, I am afraid I can't see how.

When you cite an axle, I had overlooked your love affair with tube. I think we started down this topic-debate road some time back. I shall again Pass.

14. Ok, time for the reveal.

One of my many jobs, although this one is volunteer, is to assist in the design and implementation of stage backdrops for a large church.

We recently (last week) designed, fabricated and installed a rather large wall, 24 feet tall by 52 feet long.
see this time lapse video (60 seconds) that shows the install portion:
http://vimeo.com/30609476

The wall consists of 1" x 1.5" x .125 tube steel, with 3/8 inch OSB attached to the steel frame via stand-offs.
The OSB has been "made lighter and stronger" (joke) by cutting holes of various sizes in it.
Coroplast was glued to the upstage (back) side of the OSB, and lighting was suspended behind that,
creating the design goal of multi-colored circles throughout the wall.

The wall is stable in the left/right direction (when facing the wall - it is 52 feet long after all), but "edge on" is extremely slender.
Disregarding the small effect of the OSB, the wall is 1 inch thick in the upstage/downstage direction, and 24 feet tall .

To mitigate any movement of the wall, including buckling, the following was done:
the wall was bolted to the floor
the wall was bolted to the lighting grid (load rated at ~30,000 pounds total)
the wall was braced to the building structure every 10 feet laterally, and half way (12 feet) up vertically.

The braces at 12 feet elevation halved the effective length.

As can be seen in the video, the wall was built in sections; 8 feet high by 12 (center section) or 20 feet long (each side section).
Each completed section was raised into place using chain motors suspended from the grid.
Each section is bolted to the one above/below it.

The lighting grid is fully capable of carrying the suspended load of the entire wall,
so other than doing weight calculations, no other calculations were done.

Mostly for curiosity, I want to do the buckling calculations.
I took a quick tour through Eulers, Young's, slenderness ratio, etc.,
but it seems as though I may have an unusual situation:
there is no "load" at the top of the "column";
the "load" is only the steel itself and the OSB and blinders, all of which are attached via stand-offs,
all on one side of the 1" steel tube.

Not sure how to proceed with that...

15. Originally Posted by dalecyr
Mostly for curiosity, I want to do the buckling calculations.
...
Not sure how to proceed with that...
Well, with all of those holes it should be light enough and strong enough as it is.

Correct me if I have missed something, but you have attached it to the lighting structure above?
Question: Would that not be supporting load or is it just to prevent it moving forward or backward?

Regardless, you have a rather complex structure and nothing closely approaching the single columns and loads you started this thread with. I assume the tubing is welded or bolted together to form one large wall panel, so load is going to be distributed.

Given that, if you wanted to assess deforming the plane of the entire wall, you could perhaps consider using a wind-load assessment approach even though there is no wind. That would allow some quantitative figures, but because of the attachments to floor and lighting structure, it would still be only estimated. Given also that it is a frame with stuff hanging off one side, any buckling (your word) would be assisted by the off-center (cantilevered) load and not centrally as you showed in the original post.

If it hasn't buckled yet then it is probably adequate.

16. Originally Posted by PinkertonD
Well, with all of those holes it should be light enough and strong enough as it is.

Correct me if I have missed something, but you have attached it to the lighting structure above?
Question: Would that not be supporting load or is it just to prevent it moving forward or backward?
It is currently only preventing movement forward or backward, but the wall is rigidly attached to the lighting grid,
and should deformation start to occur, the lighting grid would start to support the wall.

Regardless, you have a rather complex structure and nothing closely approaching the single columns and loads you started this thread with.
I agree. But I did get a qualified answer to the original question.
(generally, and with sufficient qualifications, a "structure" does not equal more than the simple sum of its parts.)
And I also understood that this wall does not resemble such a simple question.

I assume the tubing is welded or bolted together to form one large wall panel, so load is going to be distributed.
Yes, each element (tube) of each section is welded all around.

Given that, if you wanted to assess deforming the plane of the entire wall, you could perhaps consider using a wind-load assessment approach even though there is no wind. That would allow some quantitative figures, but because of the attachments to floor and lighting structure, it would still be only estimated.
Interesting. I had not thought of that approach.

Given also that it is a frame with stuff hanging off one side, any buckling (your word) would be assisted by the off-center (cantilevered) load and not centrally as you showed in the original post.
I do not quite understand the word "assisted" in this context;
do you mean deformation would be more likely, less likely, or just occur in a differant spot?

If it hasn't buckled yet then it is probably adequate.
Smiley faces noted.

17. Originally Posted by dalecyr
I do not quite understand the word "assisted" in this context;
do you mean deformation would be more likely, less likely, or just occur in a differant spot?
You mentioned "it's own weight" or "the weight of the metal," too lazy to go back and read, but, it is not just that as you have 80 (whatever) sheets of OSB hanging off one side. That would assist deflection in the direction of the OSB. So the calculation-center would need to be biased towards that cantilevered load. Is each OSB resting on the one below or are they each individually attached to the tube frame and have no bearing on adjacent OSBs.

Also the "sum of its parts" all things are not equal. A vertical tube in the center of the frame has a different load to one on the end as the span between uprights would need to be considered with the off-center load.

It really is a complex structure to assess down to the N-th detail. I would have sized the uprights for 3+ safety factor of the total load and left it at that. It would have been way over-designed for the purpose, but it is one-off and the end cost would not differ that greatly after three weeks of finite calculations.

It's like machining tolerances, just because a lathe can cut to 0.0005" repeatability it does not mean that a handle for a chaff-cutter needs to be machined to 0.0005" diameter tolerance. A quarter inch either way will not matter. It's still Fall outside, get out and smell the flowers.

18. Originally Posted by PinkertonD
You mentioned "it's own weight" or "the weight of the metal," too lazy to go back and read, but, it is not just that as you have 80 (whatever) sheets of OSB hanging off one side. That would assist deflection in the direction of the OSB. So the calculation-center would need to be biased towards that cantilevered load. Is each OSB resting on the one below or are they each individually attached to the tube frame and have no bearing on adjacent OSBs.
Ah, it is even more complex than that. Each OSB is individually attached to the frame behind it, and each OSB have a differant standoff amount than it's neighbors. The OSB is attached at the corners only. Each OSB does not touch any other.

Also the "sum of its parts" all things are not equal. A vertical tube in the center of the frame has a different load to one on the end as the span between uprights would need to be considered with the off-center load.
Ah, like a batten suspended by 3 cables; one at each end plus one in the center. The center cable supports 62.5-ish percent of the weight on a uniformly loaded batten.

I would have sized the uprights for 3+ safety factor of the total load and left it at that.
Imagine a 4x8 frame laying on the floor made from 1" tube.
Weld a 6" piece of 'all-thread' in each inside corner.
Using holes drilled in the appropriate spot in each corner of the OSB,
attach it with a nut on each side of the OSB, keeping the OSB about 4 inches above the frame.
Stand this contraption upright.

"sized the uprights for 3+ safety factor of the total load"
I am definately not shy about doing the work; but I must admit, I'm not sure which direction to assign the load.
Can you give me a hint? Which formula do I start with? I will take it from there.

It's still Fall outside, get out and smell the flowers.
Headed to the supply house in just a minute to pick up some Titanium for a customer (coworker) ordered product, then to the shop. Will smell the flowers on the way

19. Originally Posted by dalecyr
"sized the uprights for 3+ safety factor of the total load"
I would assume the weight of the OSB as the total load and work on using the (6 x 4)=24' high x 8' wide rectangle as the structure.
I would assume the load to be the total load of 6 sheets of OSB balanced on top of the structure.
Size the verticals for that load then multiply it by 3 or 3.5.

You have some leeway built in because it is attached to the floor and the lighting structure so it has some stability. The OSB will provide some degree of lozenge prevention depending on their offset with the stand offs. The further out the stand off the OSB is, the more likely to lozenge. I would be concerned about stacking 6 of those 4' x 8' open frames on top of each other.

I would have opted for a real structure rather than 40 - 4' x 8' frames bolted together. Maybe four complete welded panels 13' wide x 24' high and braced accordingly. Or maybe eight panels 13' wide x 12' high. It is probably a good thing you have the thing bolted to the floor and braced off the light structure.

Unless I am imagining it completely incorrectly, it is not a favorable design. I worked in Failure Analysis for about 6 years and it usually required five or six things to all go wrong at the same time before a failure. I am not convinced you have a great deal left in reserve.

20. I may have given the wrong impression.

Please see the attached drawing, which is very close to one of the 'as built' sections.

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