2-Way Slab systems 2

[todd2ny]

I am designing some reinforced concrete beams which are supporting a slab which will have 2-way action. Is there a method for determing the load to each beam? One beam is perpendicular to the other. The slab dimensions are roughly 10'x 10'.

Thanks

T.

 

[GoddyMgwasa]

Table 63 from Reinforced concrete designer's Handbook tenth edition by Charles E. Reynolds and James c. Steedman can help.
Good luck.

 

[Structures33]

With a square slab 1/4 of the load would go on each beam.

 

[jike]

ACI 318-02, Fig. R13.6.8 shows how to distribute load to the beams.

 

[apsix]

"With a square slab 1/4 of the load would go on each beam."
And the load distribution is triangular therefore M = WL/6.

 

[NS4U]

you'll need to design those beams for compatibility torsion in addition to just the gravity load

 

[csd72]

For some crazy reason, the code does not cover it very well.

The load distribution is based on yield line analysis. For a square slab as noted abaove, there is a yield line running at 45 degrees from each corner these meet at a single point in the center. For a rectangular slab you have the same 4 yield lines except they dont meet at one point but 2 and there is a 5th yield line running between the intersection points.

Each support then takes the load from the slab on their side of the yield line.

For more info on yield lines look at:

http://www.concretecentre.com/main.asp?page=195

 

[tngolfer]

You can make the slab span however you want by where you put the steel. There are more ideal locations for the steel, of course.

Generally I will provide steel in a one-way layout (trying to keep the same direction as the rest of my slab) and provide transverse top steel in the perpendicular direction along the side supports. This is similar to how ACI 318 covers T-beam flange transverse reinforcement. ACI 318 says you need to provide transverse top steel so the flange can support the loading as a cantilever. (I'm at home w/o ACI 318 but I believe the chapter is 10.8) I'm pretty sure the length of the "cantilever" is equal to the effective flange width of the concrete T-beam so the load the side beams are supporting is equal to the effective flange width and main beams are supporting the rest.

 

[hokie66]

tngolfer,

For two way spanning slabs, I disagree that you can control how a slab spans by where you place the steel. It will span according to the stiffness. Your approach may work on an ultimate basis, but does not take into account undesirable cracking which could develop as a result.

 

[asixth]

todd2ny,

AS3600 (Australian Concrete Code) allows you to distribute loads to your beams based on a triangular allocation of load. This will result in a total static moment of wl^2/12, which must be distributed between the negative support moments and positive midspan moment accordingly.

I understand your probably not using an Australian Standard but the design principles are still valid.

 

[frv]

hokie66..

What tngolfer is referring to is the strip method. And he is right. From an ultimate standpoint, as long as you account for the total static moment, it really doesn't matter how you do so.

Certainly, you could choose to do it inefficiently, but this is a lower bound method, meaning you will always be conservative.

 

[csd72]

tngolfer and hokie66,

You are both right to an extent.

The steel is much stiffer than the concrete so where you heavily reinforce it, it will be stiffer and therefore attract more load. This effect is not proportional to strength though, so if you design it for a completely wrong moment distribution then it will crack.

 

[hokie66]

Thanks, csd. That is what I thought I was saying, albeit clumsily.