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Re: cracking of concrete in post-tension

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Roger, I am not disputing that the oneway design of twoway slabs "works",
even though it has nothing to do with the analysis method, and that the
final failure is as a oneway structure but I was not talking about this. 

I was simply pointing out that the ACI code allows the designer to place
"NO" bonded reinforcement in the bottom of two way slabs (and in some other
areas such as the top of slabs outside the column zone) under certain
conditions. I was pointing out that in this case, if a crack did occur due
to some extraneous reason such as restraint to movement, then instead of
the crack width being confined to a limited width by reinforcement or
bonded tendons, it would be free to open up in an uncontrolled fashion. I
have seen such cracks in prerstressed slabs and so have many of us seen
them in reinforced slabs where the reinforcement has not been correctly
detailed and a crack has formed in an an area where tensile stresses have
occurred and where there is no bonded reinforcement provided to confine the
expansion of the crack.

Depending on the severity of the restraint and the cracking, these cracks
can be dangerous in terms of strength, but they will definitely be
dangerous in terms of corrosion of the unbonded tendons.

Back to the topic of "oneway designed" twoway slabs.
This does not mean that there will not be "redistribution" cracks for the
elastic twoway slab (before any cracking occurs) to change to a plastic
oneway slab. Remember, the slab does not "know" that it is a oneway slab
until the twoway moments crack the slab and all of a sudded it realises
there is no reinforcement in certain tension areas to allow these areas to
even hold the moment that has cracked them let alone to attract more moment
and so the moments redistribute to where there are sections which will
carry these moments, the ones where we have placed the
tendons/reinforcement. We thus end up with a oneway slab because we have
given it a oneway load path, not a twoway load path. It is not necessarily
how the slab wants to act nor is it the best way for the slab to act. It is
simply how the designer wants it to act to simplify his job and to simplify
the construction. 

My opinion, and the opinion of people much more learned  than I who I have
talked to or have heard talk on the topic of how a structure acts, has
always been that we should design a structure in the way that it wants to
act, not force it to act in another way unfamiliar to itself. This is
inviting trouble. In other words, we should attempt to reinforce a
structure in the way that it wants to act elastically. Otherwise we are
forcing it to act in a wa foreign to itself and therefore requiring
relatively massive redistribution of actions to make it work. An
interesting point is that nowhere does the ACI code say that you can design
prestressed twoway slabs in this way (cl 18.12 commentary would appear to
indicate the opposite). It does however say that you cannot have more that
20% redistribution (cl 18.10.4) of moments. In a oneway designed twoway
slab the designer is allowing 100% redistribution.

If we do not put crack control reinforcement in these areas where the
moments want to develop, but cannot, then unsightly cracking can and will
occur. This does not normally happen under service loads as the combined
effects of prestress uplift and compression normally mean that the slab is
in compression or low levels of tension under these loads and it is not
sufficient to crack the concrete. If, however, there are other "load
conditions" which are not allowed for, such as restraint of shortening,
whose effects can be far higher than the flexure stresses in lightly loaded
slabs, then the cracking will occur and will be unrestrained and will be
very large.

The other case where there is a problem is heavily loaded slabs or lightly
loaded partially prestressed slabs such as the ones we have been designing
for the last 20-25 years. In these cases, the stresses in the concrete at
service are sufficient to crack the slab. If there are areas where
excessive stresses develop and crack control reinforcement is not provided,
even though it may not be on the failure condition load path and therefore
not immediately critical to the failure strength of the slab, large (I mean
in the order of 1/12 inch or 2-3 mm) cracks can easily occur. These cracks
are dangerous and also the client does not like them no matter what you
say. The strength area in which I think that the main area of danger lies
is punching shear as well, obviously, as corrosion which will cause
flexural strength problems.

At 11:46 22/10/98 -0400, you wrote:
>Gil Brock wrote:
>
>. > The way the ACI code minimum reinforcement rules work for unbonded slabs
>. > (especially 2 way slabs), it is very possible to have large areas of slab 
>. > in tension and cracked and there will be no unprestressed reinforcement or
>. > bonded reinforcement to limit the crack width. 
>
>
>The ACI provisions for a two-way prestressed slab that permit the tendons to 
>be banded in one direction means that you end up with a one-way slab spanning 
>in the direction of the distributed tendons.  The only reason that this 
>method "works" is because it was based on analysis using the equivalent frame 
>method:  *ALL* of the loads are supported by an equivalent frame in one 
>direction, AND, *ALL* of the loads are supported by an equivalent frame in 
>the other direction.  The crack pattern in the tests that were conducted to 
>justify banding tendons in one direction clearly show that the failure 
>occurred as a one-way slab.
>
>A. Roger Turk, P.E.(Structural)
>Tucson, Arizona
>
>

Regards  Gil Brock
Prestressed Concrete Design Consultants Pty. Ltd.
5 Cameron Street Beenleigh Qld 4207 Australia
Ph +61 7 3807 8022		Fax +61 7 3807 8422
email:	gil(--nospam--at)rapt.pcdc.com.au