Shear reinforcement in two way slab 8

[mrzift]

In a two slab (supported on walls), if designing manually using strip methods, should the shear reinforcement required for x direction (Asx) be summed with the shear reinforcement required for the y direction (Asy). The total area (As) be applied to the critical regions?

Otherwise, is it safe to simply design a strip for the maximum shear force (whether its in the x or y direction) without summing up the As.shear required for both directions?

This is an issue that has caused a lot of confusion in my office with many clashing opinions. In a strut and tie model, each direction has a vertical tension force that needs to be resisted, so it does make sense to me to design the slab for a sum of the shear. See diagrams.

 

[hokie66]

cliff234,
That site inspection should be mandatory and done by an engineer who knows what to look for. Yes, columns poured too high are a big issue.

 

[sticksandtriangles]

Ok, after much thought, I think I have proved to myself, there is no "double counting" in load (note I am still in camp, non-additive, but no doubling of load). Merely accounting for 100% of the load in each direction.

Consider a beam and girder system with 150psf of loading as used in the examples I have posted above.

Total shear in the beams simple span beams = 135 kips.
Total shear in girders = 90 kips.

As beam spacing approaches 0, girder shear approaches 135 kips. I think we can all agree that there is no doubling of load.

This also explains the space truss example I posted, I only provided trusses at gridlines. The more and more space trusses I would have made, the closer and closer each direction shear would approach the 1/2 column reaction I believe. In the space truss case, the shear released in the deck/what ever element that is delivering the line loads to the trusses, releasing that shear would yield a total of 135 kips in each direction.



S&T

 

[RFreund]

Good follow up. I accept this conclusion. Thanks.

 

[rapt]

The problem as I see it is the orthogonal simplification. And how to combine the effects.

In flexure, doing the calculation on the Principal direction gives a tension force that can then be resolved into X and Y orthogonal directions for detailing of reinforcement. Or the moments can be resolved to orthogonal and then each direction designed. The complication then is Mxy and what to do with it. The simplification to orthogonal before design causes problems. I see a similar problem in this case. The real design shear is the Principle shear, which has been resolved to X and Y shears.

I would suggest you look at it based on the Principle Shear direction, rather than X and Y directions. Then there is nothing to combine.

The flexural reinforcement forces for the shear calculation would be based on the vector of the tension force in that direction.

 

[sticksandtriangles]

I would suggest you look at it based on the Principle Shear direction, rather than X and Y directions. Then there is nothing to combine.

Based on this, it feels like the whole idea of one way shear reinforcing in a two way flat plate would likely go away. Principal shears would be conically radiating from interior column, right?
Essentially you would extend your punching shear reinforcing out to capture all principal shears and forget about the X Y direction.

Life was better when one shear essentially never controlled in two way plates...
Based on this discussion, I do not understand how one way shear could ever control in a typical regularly spaced column grid on a two way flat plate.



S&T

 

[dik]

I agree, but you could similarly draw a strip diagonally the other perpendicular direction and get the same overlapping strip item that we have been discussing.

If we take the principal shear then there is no perpendicular shear, right?

Based on this, it feels like the whole idea of one way shear reinforcing in a two way flat plate would likely go away.

In a two way flat plate on a column we are essentially just converting a two dimensional perimeter into a one way case. We effectively unroll the perimeter and use the one way shear rules. Instead of a single plane failure, we are looking at a series of one way plane failures.

The OP's case is quite different, because we are talking about two orthogonal shear planes. I've looked at a few examples and the orthogonal directions are always critical - with critical shearing occuring at supports, and away from transverse supports. I'm still curious as to how two orthogonal strips can interact to produce diagonal shearing forces that end up critical.

 

[rapt]

He is talking about 2 orthogonal shear planes because that is how people treat detailing of slabs. They convert the results to 2 orthogonal directions because that is how you place the reinforcement.

For flexure, you could just as easily calculate the reinforcement required based on then principal stress results. And then convert the tension force required to orthogonal results. This would remove the Mxy conundrum that orthogonal X Y design strips causes.

I am suggesting shear is the same.

Orthogonal is simply a simplification used because that is how it is detailed. FEM results are not orthogonal. They are converted to orthogonal for ease of design.

 

[hardbutmild]

@sticksandtriangles In the picture that you show an orthogonal system of beams how would you design such a system if this was made in steel? For example, let's look at the point where a secondary beam connects to a primary beam (away from the column) - do I need to check both secondary and primary beams for shear at that point, each for its own shear or is it okay to check just one direction? It's the same problem, you just have both "beams" cast together in the case of concrete slab.
Regarding your last post I agree with you... if you look at the problem that you've been looking at it will come down to a punching shear problem, that's why I said "make an example without a column". I also agree that one way shear usually does not control, that is why many people asked OP for a picture of their exact problem, it seems unusual.

 

[hardbutmild]

I found something that might be interesting to this discussion.
I recently bought fib model code 2020 - it's a new code type document on concrete that is quite comprehensive. I looked up shear and it seems from that document that shear is checked for a square root of sum of squares of shear.
The more important thing is that it cites a paper:

https://www.concrete.org/publications/internationalconcreteabstractsportal.aspx?m=details&ID=3137

I unfortunately do not have access to ACI, but I guess that a lot of you have. This problem is probably mentioned there so maybe someone can read it and explain to the rest of us since we never got a conclusion.