Johnson-Euler Buckling 2

[mathlete7]

Back in my Boeing days I remember that in their Boeing Design Manual (BDM) as well as corresponding IAS tool they had a Johnson-Euler buckling tool. You could select how many "supported edges" the given cross-section had (1 for a "tee" and 2 for a "zee", for example). If you selected "1 supported edge" it would do a standard Johnson-Euler calc because buckling of one of the legs would occur basically simultaneously as global buckling. If there was more than one supported edge you had to enter additional information and it would calculate buckling of each leg and use this in the resulting calc (global buckling a function of local buckling strengths of each leg).
Well, I'm no longer at Boeing and am looking at doing a Johnson-Euler type calc for a cross-section with a couple supported edges. Does anyone know where Boeing got their method from? Do Roark/Bruhn/Niu discuss this? Seems like all I can find are standard Johnson-Euler methods where all you need is a crippling allowable and section properties (area, MOI, E).
Any help is appreciated.
Thanks...

 

[737eng]

I believe that Johnson-Euler is in Flabel or at least mentioned.

 

[inertia4u]

mathlete7,

I think I know what you are referring to. Correct me if I'm wrong, buy you are asking about the interaction of the local buckling on column stability.

I've seen this topic mentioned both in the BDMs when I used to work for Boeing, and I've also seen it in the old Grumman Structures manual. I have not seen it mentioned in other structure books.


However, a quick way to account for this phenomena in J-E equations (which is typically limited by Crippling Stress, Fcc) is to actually limit it to flange buckling stress (Fbuck), *IF* the buckling of the flange decreases the inertia properties parallel to the axis you are checking for column buckling.

In other words. Assume you have a channel section (C) without any lips. Assume you are going to run a column check with buckling about an axis parallel to the web of the C. Also, assume that it is pure compression load on the channel.

buck
axis
|
| + ------
| |
| |
| |
| |
+ ------



Now, since you don't have lips, and you apply a compression load, there may be a point at which the flanges will buckle (Fbuck)-(if the flanges are long and thin). Once the upper and lower flanges of the C buckle, you not longer can count on the inertia in that direction. So, you would set your J-E limited to Fbuck.

Now, assume you have a channel again, but it has effective lips (Per Bruhn) on the ends of the upper and lower flanges. Now, if you apply a load, you can take the structure all the way up to Fcc, since the corners (all 4 corners = 2 lips + 2 for the upper and lower flange attachment to the web) still offer support about the axis parallel to the web of the channel. In this case, you would use Fcc as the limiting stress in J-E.


buck
axis
|
| + -----+
| | |
| |
| |
| | |
+ -----+



Good luck,

NERT

-----
Nert

 

[mathlete7]

hi inertia,
yes! that's exactly what i'm talking about. what you said makes a lot of sense. i also remember doing torsional instability checks at boeing with one of their standard tools. again, oddly enough it seems that the biggies (bruhn, roark, niu) don't really talk about this issue. i've found some equations for calculating torsional instability in the online astronautics structures manual, but am wondering if this represents the latest methodology. Do you know of any references that talk about torsional instability?
Basically I'm trying to put together some standard beam compression stability checks (not getting into web buckling yet) for my company. What I have is johnson-euler buckling (which i'll modify to include provisions for local buckling per your suggestion) and torsional stability. Am I missing anything?
thanks for your input...

 

[inertia4u]

mathlete7,

You are right about the biggies not really talking about it. And I really don't know why it isn't mentioned.

I spent some time investigating compression failures of structure because I find it extremely interesting. Unfortunately, I've only looked into torsional instability in a very limited sense (quickly read some old NACA reports), and haven't spent any time really digging into it. That will be this years study

If I may, I recommend you pick up a copy of William McCombs work on columns (around $30.00 or so):

Engineering Column Analysis
The Analysis of Compression Members
William F. McCombs


Please note, it isn't a very fancy book. In fact, it is more of just a photocopy of many notes that Mr. McComb put together regarding compression members. Very informative and useful (at least for me). He was a stresser in the Aerospace Industry, so a lot of his articles are applicable to what we do today. Note, though, that he doesn't discuss the local instability effects on column buckling as your question of flange buckling.


As far as if you are missing anything.

One important thing I've noticed after reviewing many stresser analysis is the engineer not knowing when to use long column checks (Euler/Engresser) vs. short column checks (J-E). In fact, just yesterday an experienced engineer used a long column check (Euler) on a short column. So, one thing for sure you want to include for your company is to check the critical L'/rho; the point at which a short column/ long column equation should be used. You can find the Equation of the critical L'/rho in Perry(the original Perry),

Where:

L'/rho crit = sqrt(2) * pi * sqrt(E/Fco) [EQN 1]

(See Perry page 354 for that topic)

All the crit L'/rho really is the intersection of the J-E equation and the Euler equation. You can actually solve this yourself and show that the intersection of the 2 equations is [EQN 1] above.

Good luck,

Nert

-----
Nert

 

[inertia4u]

Let me clarify something.

The very first check for column stability is if the structure resides in the long column (Euler) or short column range (Johnson-Euler). This seems to be missed by a lot of engineers.

-----
Nert

The most important step in column buckling checks is to determine if you are in the Long Column or Short Column Range.

 

[Kwan]

The nasa structures manual covers torsional instability.

http://trs.nis.nasa.gov/archive/00000254/

Volumn 2, section c1.5

 

[mathlete7]

Correct me if I'm wrong, but can't you just do Johnson-Euler as a default since it covers you for the entire length range anyways (overlays the euler curve for longer beams). I guess you get stuck with the extra step of calculating a crippling allowable for some "long" columns when just an euler buckling calc would have been sufficient. But then, unless its painfully obvious that its an euler column, you'd have to do the extra step of applying the Perry equation anyways to see what regime you're in, so you aren't really saving much work in not just applying J-E in the first place...

Thoughts??

 

[inertia4u]

mathlete7,

No, you should not just do J-E as default. In fact, if you were to use J-E on a long column, it is possible to get a negative value (tension) as a result, which of course doesn't make sense.

As an exercise, just plot the J-E equation as a function of L'/rho and then Euler as a function of L'/rho and you will see what I mean. Of course, there will be a region where J-E will be conservative, but this will lead to heavy structure, and really is just plain wrong.

The Perry check of critical L'/rho is relatively painless, in my opinion.



Please, give plotting the equations out and you'll see what I mean.


Godspeed,

Nert


-----
Nert

 

[inertia4u]

One more thing,

It may be that you are assuming that J-E follows along the Euler curve (which is typically shown in structures manuals like Bruhn, etc). But this really isn't the case. The J-E equation and the Euler Eqn are 2 different equations which intersect at 1 point. The J-E curves downward and the Euler eqn curves upward, and intersect at that "Perry point" of EQN 1 above.

Usually what you see in structures manual is a single curve where J-E is in the lower bounds of L'/rho, and then Euler is used in the upper bounds. For some reason, they don't show the entire curve of either.

Godspeed,
Nert

-----
Nert

 

[mathlete7]

good stuff nert. thanks for your help. you're right, i had always assumed that the euler curve and the J-E curve became the same after they intersected but had never bothered plotting out the entire J-E curve myself.
thanks again for your help...

 

[rb1957]

as we all know, euler doesn't appreciate material strength, it only considers the column geometry.

johnson corrects euler for the material strength (fcy for stable sections, fcc for sections that cripple). the johnson parabola is set up to trangent the euler curve at a column stress of 1/2 the johnson cut-off (eg if fcc = 40 ksi, the johnson parabola tangents the euler curve at 20ksi). the johnson parabola is invalid beyond this point, 'cause the long column failur mode (=euler) is appliciable.

 

[RichardHurwitz]

1) Crippling is crippling - first the flanges buckle and then the web (or vice versa) and then the section cripples.
2) For a quick estimate of the crippling stress use equations C7.16 and C7.17 in Bruhn on page C7.11 with 1.9 replaced with 1.7. Once you have the effective lengths multiply them by their thickness and by Fcy. The sum is the maximum load the cross section can cary - dividing by the original area gives the crippling stess, Fcs.
3) If, when you use the Johnson Euler curve on page C7.23, you find that Fc is higher than Fccr for flange buckling simple remove a small portion of the tips of the of the flanges and repeat the proceedure until Fc>Fccr. Do not attempt to set Fc=Fccr because intereaction will fail the column earlier than predicted. Since you are discarding a portion of the structure the method is conservative.
4) If Fccr = Fcy the entire cross section can be used. BUT if Fc>Fcy an adjustment for Et must be made.