"Beam Within A Slab", How can it be a beam? 3

[IJR]

This one has been bugging me for quite some time

Usually you have a slab with one edge required to support a point or a line load. And architect wants no beam to support this edge.

So here comes the temptation:

You run a number of "thicker" bars along a "well judged" strip(say 1ft or 1 meter) along the edge of the slab, tie it with some transverse reinforcement, and there man you have a beam. You design the beam to support both the slab and the line load etc.

How can this be a beam?

Reinforcement does not increase stiffness, and my intuition is load goes from zones of lower to higher stiffness. So the slab can not be supported in any way by this "heavily reinforced slab turned into beam".

Does ACI adress this problem?. Is there anything I am missing?

respects
IJR

 

[ishvaaag]

Except for the anisotropy the excess steel introduces, you are right. Forfeiting it you analyze the slab whith thick plates in FEM for yours, say, central point load, and of course, it is a slab, but the presence of the load creates significant tension parallel to the free edge. The load path of course won't be exclusively parallel to the edge, but n-way as the elastic -or whatever meeting the model equilibrium- distribution causes. In any case, be it beam or slab, you will be checking both for strength and deflection. If your 1 m wide beam is to be embedded in the slab and is thick enough to meet required strength and stiffness, with more reason a well reinforced slab capable of embed it will be.

Furthermore, now imagine there are no other loads and you don't reinforce but your edge "beam". Once the tensile capacity of concrete is exceeded, your well reinforced beam will separate from the unloaded part of the slab and still meet strength and deflection: in short, a reinforcement scheme devised to meet some load and its limit deflection constitutes by itself one known secondary load path that we know will remain extant. If you have more redundant paths, how better, your structure will be having more strength and better serviceability even.

The traditional practices know of this and idealize for embedded beams not because it is assumed the structure initially will undergo behaviour as if the line elements were the structural reality (it only would be if the non line elements were utterly weak), but because it is known that once present, strength and serviceability are met.

But you are right in that of course a reinforcement scheme more in accord with, say, an elastic analysis, would be more true to the initial behaviour of the thing as naturally pertains...only that this is many times inimical to good reinforcement poractices such using beams at edges, use orthogonal reinforcement and so on, what has much to do in this kind of simplifications.

 

[StructuralDzine]

A band off heavy reinforcement will increase stiffness, especially after cracking. In addition the band will have a much higher moment capacity, where you need it.

Analysing the full moment field in an anisotropic panel, the properties of which are load dependent, is just too hard. Neither could we practically reinforce exactly for this moment field. The idea of a strong band is a practical idealisation that allows us to analyse and design a safe structure

A good reference is "The strip method of design" by Hillerborg.

Chris Rohde
Editor, Structural D-zine

http://www.topica.com/lists/Structuraldzine

 

[JAE]

Agree partially with both StructuralDzine and isvaaag above. The extra rebar will increase your Ie, but not by a lot. It increases your cracked moment of inertia, but keeping the slab profile, (i.e. keeping d small) doesn't always do you a lot of good.

As stated above, you need to estimate an effective width and use that as a basis for your deflection calculations.

The strength design can take care of the loads. I would be more worried about long term deflections in this case.

 

[IJR]

One more point:

The code I am using requires the depth of a beam to be at least 3.5 times that of a slab it is supporting.

So where does the band fits in?

regards and thanx for the great discussion

IJR

 

[JAE]

What code is it?

 

[ishvaaag]

In any case it maybe a case of wording, except that the reviewing party can't accept this. You may always say that you simply are reinforcing the slab such way.

 

[IJR]

Thanx Ishvaaag , thanx JAE

Response to JAE:

The code I have in hand is the European CEB-FIP model based Turkish Reinforced Concrete Code. This code also heavily borrows from ACI318 to the point that almost similar designs can be made using either code. There is a clause that says the min depth of a beam should be at least 3.0(sorry for the 3.5 misquote above) times the thickness of a slab and never less than 30cm(1ft). Havent gone through documentaries yet and so cant get the reasons why.

My prayers are to all victims of the recent terrorist attack in US.

regs
IJr