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# Web-Buckling of Concrete

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• To: "INTERNET:seaint(--nospam--at)seaint.org" <seaint(--nospam--at)seaint.org>
• 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

```