Axial Compressive Resistance of Steel Deck With Composite Concrete Topping

[Zahait]

I have a foundation wall that is around 20' high. We are anticipating using composite concrete topping over steel deck and steel joists for the main floor framing. I would like to put actual numbers to the capacity of this system and how thick the slab is going to have to be even though it is relatively early in design. Schematically we are showing a 4" concrete topping with 2 1/2" cover on the steel deck. Would it be conservative to calculate the axial compressive resistance of a 2 1/2" "concrete wall" with lateral supports at joists locations (4'-0")? Or is there any better resources to determine this value? My biggest issue is I don't believe the shear diaphragm tables are applicable because it's less of a shear problem and more of a compression problem, since the wall on one side will be supported by the wall on the opposite side.

 

[KootK]

I think that treating it as a plain concrete wall of sorts is reasonable and better than the no check at all that most of us will do for such a condition. Some wrinkles:

1) Your joist won't exactly be rigid supports. I'd not lose any sleep over that.

2) Your slab would tend to buckle downwards and, when it does, it will engage the steel deck flexural which is a nice bonus that you probably won't account for.

3) Based on typical slab reinforcement patterns, it probably does make sense to consider the slab as unreinforced concrete for buckling upwards.

4) In my experience, the axial stresses for these situations end up being pretty low and easy to deal with. That said, your wall is 20' high which, surely, is why you're concerned aobu this particular situation.

I'd be curious to hear what your findings are with this.

 

[MotorCity]

Use the diaphragm tables, that is exactly what they are for. It is a shear problem, think "deep beam". It is not an axial compression problem. The tables consider the stiffness of the steel deck and concrete working together.

 

[KootK]

It is a shear problem, think "deep beam". It is not an axial compression problem.

I disagree. I think that's it definitely a compression problem if there's offsetting active earth pressure at the other end of the building to oppose the lateral soil load coming in from the side being investigated. I'd be inclined to treat that as OP has if that's the case. Whether or not the situation is also a shear problem is open to debate. How much load is resisted by which mechanism based on stiffness etc is not an easy thing to suss out.

 

[MotorCity]

Agreed. I only saw one wall in the sketch so I thought we were only talking about lateral pressure from one side. Now that I re-read it, I see the last line mentions 2 walls. I think the approach makes sense to look at it as a column with fixed ends spanning between the joists (assuming you can convince yourself that a joist can serve as a rigid support in its weak axis...haha.) If you take a 1' wide strip, it certainly cannot rotate or translate within the plane of the floor. Out of plane, it will be continuously supported by the deck and concrete within the composite deck. Having said all that, this is voodoo stuff. If I were to check this, I'd only be doing it out of curiosity. Lastly, as long as we're checking this voodoo stuff, I would be more inclined to check the 4" part of the slab as the "column" since it will more than likely be stiffer than the 2 1/2" topping. Hopefully no code writers are tracking this thread and jumping for joy at the possibility of adding 30 more pages to require a check like this.

 

[Boiler106]

how about rather than taking the compression through the deck, you design the deck to horizontally span between beams/joists to distribute the horizontal force and design the beams/joists/connections as the compression struts from one side of the building to the other.

 

[Zahait]

@kootk I don’t think the joists being rigid is really a problem if I count on a k factor of 1. The design reference of the structure is CSA A23.3 and there is a note that says; walls shall be considered laterally supported if the connection between the wall and its lateral supports are designed to resist 2% of the factored vertical load or 10kN/m whichever is greater. The joists are surely able of supporting this load in the downward direction and I would have to count on the self weight of the slab connection to the deck in the upward direction.

@motorcity yes, perhaps it was my long winded explanation of what the issue was that had you slightly confused. I am glad we agree now. I agree that a compression check is typically not done but when I started calculating the loads coming in from the 2 story retaining wall I started to get… nervous.

@Boiler106 this is an interesting idea and I may end up doing this. Thankyou very much for this suggestion. I would end up with a series of beams in combined bending and axial compression, but that is simple to design and then I can actually count on my diaphragm to do it’s job.

 

[KootK]

...assuming you can convince yourself that a joist can serve as a rigid support in its weak axis...haha.

Why weak axis? I only see the joists being worked in strong axis flexure for this.

Hopefully no code writers are tracking this thread and jumping for joy at the possibility of adding 30 more pages to require a check like this.

I'm in the minority in that I'd actually prefer for there to be more prescriptive requirements in the code so as to make it easier for designers to make smart choices rather than racing one another to the bottom. If I had my way, there would be one line in both he IBC and IRC that said:

All floors at and below grade shall be constructed of CIP concrete not less than 6" thick unless a discrete, horizontal bracing system is provided in liu.

how about rather than taking the compression through the deck, you design the deck to horizontally span between beams/joists to distribute the horizontal force and design the beams/joists/connections as the compression struts from one side of the building to the other.

This is not an alternative but, rather, a must when the framing runs perpendicular to the basement walls. In that scenario, the framing braces the concrete slab against buckling. The math on that for buckling will tend to work out nearly identically whether the compressive stress is assumed to exist in the slab, in the framing, or both. In all cases, the lion's share of the stiffness that resists buckling will come from the framing.

@kootk I don’t think the joists being rigid is really a problem if I count on a k factor of 1.

I disagree and feel that k=1 may be optimistic if one is discounting potential fixity at back spans and wall connections etc which I normally would. If you imagine the meaningful sources of potential misalignment and perturbation for this, that would include:

1) The deflection of the joists.

2) The deflection of the girders supporting the joists.

3) The ponding that you get during concrete pouring that will make the deck non-prismatic and eccentrically loaded.

4) Tolerances in the flatness and levelness of the deck.

The joists are surely able of supporting this load in the downward direction and I would have to count on the self weight of the slab connection to the deck in the upward direction.

I'm not so sure. Consider:

5) 10 kN/m = 685 plf which is actually a significant load for most steel joists.

6) As with all bracing, it is the stiffness of the bracing that is most important, not the strength. The force requirements specified in CSA are likely assuming that the concrete walls are being braced by wildly stiff concrete slabs such that sufficient stiffness is not in doubt. You're steel joists 'aint that, not by a long shot.

 

[Zahait]

@kootk thankyou for your insights, I truly do appreciate getting feedback on my thoughts. I have been creeping here for a long time and always appreciate your comments.
I think I have eliminated potential issues with the deck ponding and unevenness by assuming only the concrete cover will be working for me and disregarding everything else.
In regards to your point number 5), I was meaning that the joists WILL be designed to support this in a downward direction. I was not speculating even though it could have been read that I was. The floor loading in this area is quite substantial.

So here is where I where I am currently at…

I have found reference to the maximum compressive and tensile stresses in unreinforced concrete walls in accordance to CSA A23.3. I have calculated the total axial load from the earth pressure and the maximum moment from the floor loading. I agree with kootk’s comment about the joist deflecting being a potential issue so I have included an additional induced moment created by the axial load acting 3/8” off centre between adjacent joists. I based this off of half of the total maximum allowable deflection since I cant see one joists ever being loaded completely full with adjacent joists taking none of the load. I have taken the total axial load and the total magnified moment and plugged it into the classic P/A+/-M/S. I have come up with 4” cover over 1 ½” deck which I feel to be slightly conservative. I hope I have not grossly oversimplified anything here.

 

[Zahait]

I thought I would also provide a little more information so I have attached a schematic layout of our plan.

When loading from the long sides I agree with Boiler106 that the girders could be designed in compression and I would end up with 3 separate shear diaphragms. That would definitely simplify the issue I am having trying to quantify the axial resistance of the topping. Provided I don't run into constraints with the size of these struts of course.

when loading from the top (narrow) of the plan there is no issue as I will be counting on the diaphragm to get this load back to the longer walls and this is relatively easy to quantify.

 

[KootK]

That would definitely simplify the issue I am having trying to quantify the axial resistance of the topping.

1) Given your proportions, I'm not sure that the axial stresses in the deck will actually spend any amount of meaningful time in the beams. I do feel that it's best to assume that the axial stresses remain within the slab, with the beams serving as plate stiffeners to restrain buckling.

2) I feel that a fairly simple design approach would be this:

a) Check the slab for bearing stresses.

b) Design the beams as though they are axially loaded beam columns with one exception: you don't need to consider a combined, [axial + bending < Fy] stress check separate from the beam column buckling check. That, because the axial load won't really be in the beams. The beams will just be performing the plate stiffening role. In my opinion, this check is necessary no matter what path you chooose.