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Web-Buckling of Concrete
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- Subject: Web-Buckling of Concrete
- From: Mark K Gilligan <MarkKGilligan(--nospam--at)compuserve.com>
- Date: Sun, 25 Oct 1998 01:57:11 -0500
Rafael I once looked at a similar problem where I was using the slab to transfer the horizontal reaction at the base of a retaining wall to the wall on the opposite side of the building. In this process I became aware that you need to reformulate the buckling equations unless you want a very conservative solution. Two things that are unique about the buckling of slabs on grade are: 1) The buckling shape is always above the ground. 2) The self-weight of the slab will resist the tendency of the slab to buckle. The approach I took was similar to that used by Salmon & Johnson to find the critical stiffness of column bracing. The exception was that instead of the resisting force being due to a spring it was due to the tributary weight of the slab and the deflection was assumed to be a function of the length of the strut. The trick is to choose a large enough deflection. For smaller deflections the resistance to buckling is higher. Think of the deflection as the initial distortion of the slab out of a plane and then magnify it. Use the factored axial force in the equation. Then you solve for L. L being the distance between one end of the strut and the point where the resisting weight is applied. For any larger L the weight of the slab will be more than enough to resist the tendency to buckle. You then must check to make sure that the slab is stiff enough not to buckle in the length L. Up until this last step we have assumed that we were dealing with rigid struts between hinges. For this check I treated the slab as a concrete wall with a height L. This approach allowed me to feel comfortable with a moderately thicker slab and a heavier than average level of reinforcing. You can probably develop a more refined solution but this simpler approach is cost effective in most situations. Diagonal tension may be possible but in order to develop the diagonal tension the slab would be pretty well cracked up. The question is what type of a factor of safety would you need so that the cracking wasn't a problem at service level loads. Also remember that the steel in the tension field of a plate girder is continuous from one corner of the web to another. With a concrete slab the reinforcing is typically orientated at an angle to the tension field and in addition the reinforcing is often spliced. Before wanting to rely on the tension field in a concrete slab I would want to assure myself that these were not a problem. Since the buckling must first occur in the direction of the principle compression forces before a tension field can form you might be happy if you could show that the slab would not allow this buckling to form. This could be done with an approach similar to the one described above. I hope that this helps. Mark Gilligan markkgilligan(--nospam--at)compuserve.com
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