Web Bend Buckling

[edbgtr]

G’day All
I’m sure we are all familiar with the Windenburg formula of providing simply supported stability to a compression member free-edge by means of a lip (Bruhn C7.9). There are also formulas for sizing stiffeners that provide a simply supported condition for shear webs (McCombs’ Supplement, Fig A6).
Has anyone seen a similar relationship for providing a simply supported edge condition for a shear resistant web in bending along the compression edge? The difference between the bend-buckling coefficient for a free edge web and a simply supported one is large (0.776 versus 21.7, Poisson’s Ratio included), and one would expect there to be a minimum lateral bending stiffness requirement from the flange to provide this support. For C, I and Z sections, one “normally” checks the compression flange for buckling, crippling and lateral/torsional stability and the web edge stability appears to be ignored. What if the beam length to depth ratio is such that the web compression edge becomes the limiting criteria and not one of the “usual” flange failure modes?
If someone on this forum can shed some light on this, it’d be greatly appreciated.
Ed.

 

[rb1957]

g'day ed,

i would check the flange for crippling and column failures.

you know the compression stress in the flange, the peak bending stress. I'd represent the flange as an angle, with some portion of the web assumed (off the top of my head i'd say the effective web saw the same as the bent flange).

 

[Sparweb]

Is it not safe to assume that the free edge of a flange will cripple before the edge attached to the web? Maybe not in cases of unequal-thickness extrusions.

I'm not sure how much light I can shed, but I'd like to discuss it to see where you're going with the question.

I'll start with a an attempt at ASCII "art" as a FBD.


7| |===============
| M| | V
| | \/
|L |===============

The "7" being the top flange and the "L" being the bottom flange of a Z-section beam. The beam is short, and cantilevered at "M". Shear "V" is applied at the free end.

Assuming the beam is short, then it sounds like the L flange isn't long enough to buckle under the compressive load due the applied shear load "V" in your case, as you state it. In other words, you're happy with the flange and are looking for other problems.

If you're checking the web itself for compressive buckling failure, just above the L flange, you can consider it simply-supported at the very least. If as you say the web is shear-resistant, then it's surely more than s-s.

How is the web fastened to the flange? A series of rivets? Perhaps inter-rivet buckling comes into play.
Have you also checked transverse shear? (VQ/It?) Again, if it's a "shear-resistant" web, then that's probably sized well by the rules-of-thumb that we often go by.

Okay, I've reviewed enough chapters of Bruhn... have I helped or just stated the obvious?


Steven Fahey, CET

 

[Trajano]

Hi edbgtr,

if I didn't misunderstood you, you want to study stability of the web of a bending beam.
If so, I would suggest to consider the next:
- if the Web is not high and thin: beam bending theory: no buckling.
- if the Web is high and thin: diagonal tension


When a beam is submmited to transverse load, the resulting shear loads can cause the buckling of the web **if the web is very high and thin**. If the web is not high and thin, then it is "shear resistant" and then you use the beam bending theory: f=VQ/tI, as SparWeb has said.
You said that your web is shear resistant, in that case, that is all: it will not buckle. If not otherwise, the shear load can cause the bucking of the web, the diagonal tension theory shows that a thin web under transversal load, under shear, doesn't fail when it buckles, but some diagonal waves appear. This waves are working under tension. In this case, the compression load is redistibuted to the flanges. The failure will happen because of the tension in the web or because the buckling of the flanges due to the redistributed load.
This theory is described in NACA Technical Note No. 2661: "A summary of diagonal tension. Part I: Metods of analysis" (Kuhn, Peterson, Ross Levin).
If you have holes in the web they should be properly reinforced in order to avoid permanent deformation or cracks.

 

[edbgtr]

Hi Stressers
Stating the obvious can help refocus the mind from muddled thinking, and debate, on any subject, helps one to look at problems from another perspective.
The idea is to get the PURE BENDING allowable moment for the section, ignoring other secondary failure modes. From background reading I have done on the subject, the web and its bending failure mode appears to be key to the overall analysis of the section and hence, IMHO, a method of establishing the degree of support for the compression edge would be most helpful in this work. There is a huge difference in buckling stress between the unsupported and the supported edge and one would expect there to be partial support conditions in between. To borrow a term from control theory, I would not expect the supported/unsupported condition to be a bang-bang situation.
I am aware of the other failure modes that one encounters in I-beam-type sections and all are catered for by using the interaction MS equation found in Bruhn C3.13, and also considering the minutiae of detail failures as well. Most aircraft companies use this approach in one form or another.
Thanks for all your contributions, your interest is much appreciated.
Ed.