Structural Slab Reinforcing?

[SteelPE]

Hopefully I can explain this properly.

I have a structural slab that is uptight to an existing building. Parallel to the building, I have a grade beam that is 5’-6” away. The slab is being designed as a one-way slab. The question I have relates to the fact that the existing building is set 45 degrees to my one-way slab reinforcing which makes the cantilever reinforcing 45 degrees to the one-way slab reinforcing.

How do you handle this moment with regards to the main one-way reinforcing in the slab? Is it a matter of SRSS (square root of the sum of the squares) or is it much more complicated that this (which I think it is)?

 

[a2mfk]

Someone else will say it so.... provide a sketch.

 

[SteelPE]

Hopefully this will clear it up a little.

 

[csd72]

It is a case of moment vectors.

 

[SteveGregory]

I would design the cantilever (rebar in the top) for the moment = w (5.5)^2/2 and the main slab (rebar in the bottom)as if the cantilever did not exist.

 

[ATSE]

Resolve moment demand and moment capacity as vectors. You can rotate the "X-Y" plane (or you can call it "R-S" plane) anyway you like - probably 45 degrees for your condition - so long as the principal axes are 90 degrees apart.
But you don't need to.
If capacities phiMnx = phiMny, and Mnx > Mu, you're okay for any vector angle between Mnx and Mny.

 

[a2mfk]

OK, not being a RC expert, but couldn't you also conservatively place bars 45 degrees (same direction as your cantilever, perp. to the grade beam) and extend them back into the main slab for development as necessary? From a fabrication and placement standpoint I think this would be just as easy, a bunch of bars of the same length anyway...

Maybe this makes your slab too congested with rebar mats..

 

[hokie66]

Agree with a2mfk. The top bars in the cantilever don't have to be parallel to the bottom bars.

 

[TXStructural]

You can use the top reinforcement from the backspan, and resolve using trig, keeping mind that you may get different crack behavior since the length of bars being loaded are longer. If there is plenty of reinforcement, this should not be an issue.

Otherwise, you probably want to orient the top bars in the cantilever so that the bars work over the shortest length, that is, perpendicular to the cantilever support. You can also extend the main reinforcement into the cantilever to develop it without hooks, if you prefer. Add top bars, hooked at the cantilever end as needed for development, and extending into the backspan for development beyond the negative moment over the support.

 

[pwht1]

I think you guys have complicated this simple procedure just a weeeee bit

I assume you're analyzing this one way slab in strips perpendicular to the main beams. In the analysis just increase the length of the cantilever by SQRT(2) and keep your reo running in the same direction.

Also with such a short cantilever you're likely to have hogging where there is a large backspan and will need bottom reo in the slab crossing over the beams.

 

[hokie66]

Hogging? The bending moment on a cantilever is the same, regardless of the length of the backspan.

 

[rscassar]

I would provide the reinforcement at 45deg to the cantilever for the ease of placement. The moment capacity will be Mx and My (if x and y are orthogonal directions). The bending in the Mx' direction (the principle direction of bending) can be designed for by resolving Mx and My.

 

[SteelPE]

Well, we currently have it designed with the main top reinforcing cantilevering over the grade beam and spanning about 6'-10" or so (angle is not exactly 45 degrees). This is similar to a few posts above (I believe).

I was thinking that it could have been easier to have a bunch of bars that cantilever perpendicular over the top of the grade beam and run a development length into the back span. However, this would mean that the the reinforcing (strong and weak axis) would need to be designed to take the moment that is currently at an angle to the reinforcing in the one-way slab.

I am just not sure if you can do the trig to get the design moments at an angle? It appears from the above that this is possible. So if my moment is 10 ft-kips and my angle is 45 degrees. Then I need to provide an end moment for the reinforcing in the strong and weak axis of .707*10ft-kips = 7.07 ft-kips.

 

[a2mfk]

I would go with TXstruct method to make sure I have good crack control, and place the cantilever bars perp. to the grade beam and extend them a full develop length into the main slab. Though it seems that for strength purposes you would be able to use the main slab rebar, like TX said it would seem that unusual cracking could occur due to stiffness/rebar differences.

Imagine you have no main slab and just a big block of plain concrete, then this is how you would design the cantilever, no?