Punching Shear in Foundations - Bending

[Luceid]

Hey all - I've got a concrete structure that we've designed using pinned-base assumptions with a mat foundation system where the columns are delivering vertical point loads at the base.

The SAFE model has a subgrade modulus spring support - so the mat foundation generates flexural moments as it deforms under loading. Many of these columns are near the edges/corners of the mat - so they often get some tricky moments in two directions which are being designed for flexurally.

When it comes to the punching shear of these columns through the raft - are the moments in the raft considered as part of the punching calculation as they are in elevated slab conditions with "restrained/fixed" slab-column collections? Or would you just take the axial load from the column and essentially check V/A - no component due to raft flexure? I have a tough time understanding the flexural component of punching shear in general - with this case I am even less sure what is clear.

 

[HDStructural]

I would think that you do not need to consider the moment. Similar to a spread footing loaded by a pinned column, there would be moment in the footing. We do not consider moment when doing the punching shear check in this case. For a two way slab, we would only consider moment with punching shear when a moment is transferred from the two way slab into the column.

Since no moment is in the column itself, I think no moment would be considered for the punching shear check.

 

[Luceid]

That's a fair point HD - thanks

 

[canwesteng]

Jumping in too late, but it is the portion of unbalanced moment transferred by shear that you design for. No moment in the pier means there is no unbalanced moment.

 

[cliff234]

I agree with canwesteng. It is the unbalanced moment that causes additional punching shear stresses. The unbalanced moment will typically be greatest at columns located at the edges or corners of the mat. All moments at the bases of edge and corner columns are unbalanced moments. You can’t ignore these moments. Regardless of how you modeled your concrete column connections to the mat, there will be fixity at the base of the columns. Unbalanced moments at the base of columns bearing on the interior of the mat are usually pretty small as long as the spans in each direction are about the same. I suggest fixing the column bases in your model. Just because you modeled pinned bases does not mean the actual column bases will be pinned. In my experience these unbalanced moments are usually small enough that they don’t add significant additional shear stresses as long as the mat is thick enough to begin with.

 

[Luceid]

I ended up coming back around to more what you've proposed cliff - using localized strips to integrate the peak moments near the applied columns loads to show unbalanced moments at the centerline of the columns above. These moments are MUCH MUCH smaller than what SAFE was reporting - I have yet to really understand how it is calculating the moments it was using in its internal punching check.

 

[Celt83]

I ended up coming back around to more what you've proposed cliff - using localized strips to integrate the peak moments near the applied columns loads to show unbalanced moments at the centerline of the columns above. These moments are MUCH MUCH smaller than what SAFE was reporting - I have yet to really understand how it is calculating the moments it was using in its internal punching check.

I don't believe this is correct. At the mat foundation the unbalanced moment would just be the column fixed base moment from the building model. For the mat foundation the bearing pressure is in response to the loading so for equilibrium the pressure distribution should result in the unbalanced joint moments equaling the "applied" column base moments.

 

[Luceid]

Alright I'm back around - the approach I described above ended up looking really similar to the unbalanced moment conditions in elevated slabs, so I trusted it at first. However the unbalanced moment was being generated in the slab itself due to the discrete area springs SAFE creates at mesh points - and since the column load was at a mesh point it looked like it was related to the column. But I think the correct approach is what I think you've described Celt.

If I apply a stiffened zone into the foundation using a "column above" with half story height - pinned at the top (assumed inflection point), then read the resulting moment in the column at the slab interface due to whatever fixity it provides - this is the moment that would be multiplied by gamma to get the portion of flexure resisted by shear. Does this seem like an appropriate path?

 

[Celt83]

It's sounds like you're saying:

" I am loading my mat foundation with column reactions assuming pinned bases"

"I am designing my mat foundation with fixed near-pinned top columns"

If this is accurate then your boundary conditions between models are at odds with each other.

If the columns are pinned then there is no unbalanced moment because no moment is transferred from the slab to the columns.

 

[Luceid]

Sure - but couldn't you consider this part of a bounding exercise to work through the non-pinned non-fixed real conneciton behavior?

Design building using pinned base columns. Then I suppose I need to check the column bases assuming a fixed base condition to ensure it can take any additional moment necessary there.

Then on the foundation end - ensure any moment transfer assuming a completely fixed condition is transferable through a punching mechanism as a worst case. If the interface ends up more like a pin under ultimate loading in reality - there is no moment transfer so no problem there.

Essentially studying both the building end and the foundation end for both cases. Is this overkill? Curious how you would treat it, my understanding is this is typically the approach in elevated slabs - test negative moment capacity assuming fixity and test max deflections and positive bending using pinned slab-column joints.

 

[KootK]

I'm not sure that this is your situation but, if it is, this might be of help.

In the past, I've seen significant column base moment develop as a result of insufficient slab stiffness. One strategy for redress, in addition to a stiffer slab, is to ensure that your model isn't overestimating the flexural stiffness of the columns (use the real length, 0.35 Ix etc.)

 

[cliff234]

Luceid – I’m not sure what you’re referring to when you say “localized strips”. The way I see it, the mat foundation is an upside down flat plate. If the mat is bearing on rock the moment at the edge of the mat under the columns will be smaller, and the maximum soil pressure will be higher than if the mat was bearing on soft soil. If you model the soil with a spring constant that should give you an accurate moment in the mat under the column. Conservatively if you assume the mat was floating on water, that assumption would give you the highest and most conservative moment in the mat and you could calculate the moment using the Direct Design Method. Distribute a fraction of the unbalanced moment by flexure per ACI 318-08, Section 13.5.3.2. The remaining moment is transferred to the mat by shear per ACI 318-08, Section 11.11.7. (Sorry. My brain is hard-wired to ACI 318-08.)

(Make sure that you hook your top bars perpendicular to the edge of the mat, and make sure your top hooked bars will develop within the width of the column. (In other words, don’t use big (i.e. #10 or #11) top bars with hooks.)

 

[Luceid]

Cliff - I've steered away from the strips which I was using to average moments in the slab since that reflects something different than I think we need here. As Celt described - it's about the moment that is transferred between the column and slab at the joint that needs to be considered for punching. Not all of the moment around the column-raft interface is being transferred up into the column since we have the bearing supports on the underside of the slab. Noted on the other tips - thanks for those!

Koot - that is helpful yes - I'll investigate the stiffness. Once I've included the columns in the foundation model, the moments don't seem too bad (nothing close to the monstrous moments SAFE's punching output was giving) so I'm not incredibly concerned now.