Concrete shear wall buckling/deep beam buckling

[Stazz]

What equation is used for the buckling of a very thing shear wall/beam. In ACI they have the general buckling formula but that's considering a uniform stress over the whole section. In this case it should be a linear varying stress.

I might use AISC's equation for the local buckling of a W shape flange bent about its weak axis. This is similiar to the stress distribution in a shear wall minus the axial load. Fcr = 0.69 E / (bf/(2tf))^2

 

[OCI]

I'm also very interested in this subject. We are working on making some very slender RC shearwalls work and were surprised at the lack of input from ACI on this subject. Roark has an equation for thin plate buckling in shear that might apply. Anyone else have any ideas?

 

[hannis]

In the UK there is a publication by CIRIA (Construction Industry Research & Information Association) The Design of Deep Beams in RC ( by Arup, 1977) it is a useful guide if you could get hold of it since it deals with storey height walls as beams in bending and shear.

 

[ishvaaag]

Perhaps one practical way to ensure you have performed as required is to model the deep beam with component plates and explicit initial deformation (to any required level of imperfection) with P-Delta. You may require some iterative tuning for the stiffness of the plate (Young's modulus used for each plate) once you have sarted the calculation, but since you will have to live within ordinary crack control limits, stiffnesses shouldn't deviate much from what we ordinarily do when not this thin deep beam case.

 

[ash060]

There is an article in the ACI Structure Journal Vol. 104, No.4 p. 412-420; about slenderness effects in concrete beams.

There is an equation in the article for the critical buckling moment.

It is very time consuming, but it may help you out.

 

[ron9876]

I have always checked strips of the wall that are in compression using the column buckling approach.

 

[dhengr]

Stazz:
I don’t have either of the codes (AISC or ACI) that you are looking at, mine are older versions, so I can’t exactly help you with that. But, I suspect the Fcr equation you show is AISC’s critical buckling stress for the outstanding tip of the flange, outstanding leg, supported at the web/radius and free at its tip. I’m not sure this is a good analogy if I understand your problem correctly. I think OCI has the right comparison in the thin pl. buckling with shear on two opposite edges, but I didn’t get a chance to look at that either, and, I’m not sure we know quite how to get from this thin stl. pl. to a thin RC wall, which probably doesn’t fit the thickness criteria any longer. Why is the wall so thin that it’s giving you heartburn and how does it compare to normal h/t ratios for conc. walls?
My analogy would be a 2 or 3' long WF with its bot. flg. bolted to a heavy table top (your lower fl. slab or footing); and the top flg. supported so it can’t move laterally, the same support your upper fl. should provide, from orthogonal shear walls or some such; then apply the bldg. lat. load (from the upper fl. diaphragm) parallel to the long axis of the WF, or parallel to the web (your shear wall). You will have a shear flow (kips/ft) between the flanges and the web, and in your case some added gravity load (kips/ft) vertical. This is probably what Roark’s table shows. Why don’t you thicken the wall and sleep easier, will anyone miss a couple inches in the room dimension? Then you have reinf’g. both ways in both faces, and adequate vert. tension reinf’g. at each end of the wall, I hope.
Deep beams particularly in conc. act like a corbel or a short cantilever. Shear influences stresses and strains much more than bending. Beam theory doesn’t really start to apply until you get 2 or 3 times the wall length (above) away from the lower fl. ( for a RC beam that would be, 2d or 3d). You want the wall to stay intact for service loads and wind loads, and go to ultimate under earthquake loads and the like. Maybe the strut and tie approach comes into play at ultimate, that’s likely the way the wall would start to fail.
The strut and tie analogy may be similar to the way I think of thin stl. shear panels. The shear panel must be bounded on four sides by sufficient structure to take the tensions from the shear panel. Then, the shear panel buckles out of plane slightly and, becomes a diagonal tension field, between diagonally opposite corners, to take the shear load. Within limits the panel will relax and work the same way in the opposite direction.
For a stl. column you only need a few percent of the axial load, as a lateral support reaction load, to restrain the column from buckling. That’s been in the AISC code for a long time now, but I can’t give you a citation for that off the top of my head either. If you look at your RC wall and its h/t ratio, does it have enough reserve moment cap’y. out of its plane to provide this kind of resistence?
I certainly haven’t given you the equation you were hoping for, and maybe I haven’t solved your problem for you either. My hope was to give you some food for thought, and let you do the research. I could probably dig some specific citations and ref. titles (text books) if I had more time. I would like to hear about your final thinking and solution on this wall, please post.

 

[OCI]

ash060,
Is the ACI Structural Journal article any good? Does it apply to cantilevered deep beams or walls? ACI wants $25 for it and I don't want to order it unless it applies. Thanks.

The CIRIA article mentioned is out of print and it appears it is only available in photocopied hard copy which will take a while to get.

dhengr,
An associate of mine is working on a wall panel product for light commercial and residential(SFD) that consists of 4" thick concrete walls. I'm trying to check what the reality for buckling would be for a 3.5' wide x 9' tall panel. I've noticed that Roark's formula is for plates that are simply supported on all 4 edges while this application would only be supported against out of plane deformation on the top and bottom. I'm also concerned that the assumption of elastic behavior would be innaccurate for this application as you pointed out. I'll post more as I look into this further.
Thanks

 

[dhengr]

OCI:
I’m kinda new at this forum thing and much less new at structural engineering. I read all over the place that we should not exchange names, phone numbers or e-mail addresses on this forum for various reasons. You have to explain to me how we would get in touch to exchange some info. I was not taking the time last night to dig out various references, etc. These kinds of discussions do not lend themselves well to three sentence questions and answers, typed and flying through the either. A phone call would be best for me to understand your concept, and to comment on same, I can’t type as fast as we can talk.
3.4" thick conc. panel (to fit in 2x4 stud wall), by multiples of 16" less 1.5" for width, by various heights, may be what you really need if I understand where you’re going with this. And, while we would have to work a bit to come up with some analytical buckling force, I don’t think buckling will be your biggest problem with your scheme in light construction. BTW the ACI article is interesting but not particularly applicable to the problem at hand, I think I know where a copy could be had for $23.95.

 

[OCI]

dhengr,
I agree, i'm not the fastest typest and would enjoy a phone conversation much more than playing forum tag. Let me think of a way to privatly exchange some info and get back to you.

 

[Stazz]

Ok, I finally got my hands on the ACI publication that ash060 mentioned and it does give a simple reduction factor for slenderness effects. It's essentially the same thing that AISC does for flexure. Its the same curve 1) Plastic Zone -> Linear Transition -> Elastic Buckling


The lateral torsional buckling moment of a slender concrete beam is given by:

Mbuck = C1 C3 sqrt(BK) / ( C2 *L)

When I tell you what these constants are you'll realize that this makes sooo much sense

B = Flexural Rigidy = E = bd^3/12
G = Torsional Rigidiy = G = aprox = G*b^3*d/3
C1 = Nature of applied load -> This is analagus to AISC's Cb = pi for pure bending, 3.54 for uniform, and 4.23 for point load at midspan.
C2 = End condition of beam -> This is analogus to effective length (k)
C3 = Accounts for location of the load w.r.t cross section (This is just an amplification for torsional effect)



When you use the constants we're familiar with you get

M buck = pi / (kL) *sqrt(EG)

The article gives a reduction factor for the linear transition zone (or non compact for steel):

n = 1.1 - (1/3) * (L*d/b^2)/ gamma

where gamma is the limiting slenderness ratio which I'm not quite sure how to calculate for concrete. I beleive this reduction factor is applied to the plastic moment.

Thanks for playing.

 

[Stazz]

I forgot to give some input...

The formulation above is for lateral torsional buckling but I would think a shear wall is braced at each level. What we really need is a local buckling formula for an unbraced equal to the story to story height.