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.
