computing the flat plate punching shear critical section at corner columns

[cliff234]

I am computing the punching shear capacity at a corner column per ACI 318-08 and am confused as to the dimensions of the critical section (see attached sketch). My column is 24"x24", d/2=4" and the slab cantilever is 12". Section 11.11.6 implies that I cannot use the full 4-sided punching shear critical section unless my slab edge is at least 10xt from the column face. So what is the extent of my critical section? Is it a 2-sided critical section that terminates at the slab edges (detail 2) or is it a 2-sided critical section that terminates 4" from the corners of the columns (detail 3)? Are there any references that validate one versus the other? What is the accepted standard practice? Figure 11.11.6 in ACI 318 implies that detail 3 is the correct approach, however this seems to be an overly conservative approach - or is it?

Textbook examples of this condition always seem to show the slab edges flush with the faces of columns - however this is often not the case. The slabs often cantilever past the faces of the columns.

Thanks!

 

[dcarr82775]

ACI318 is annoying silent on this. All the examples I have seen use your Option 3 but most of those are done by the same people. Obviously ignoring the additional contribution of the slab per Option 2 is conservative, but it must provide some real resistance. I might use your Option 2 based on the dimensions given if I was looking at something that already existed.

 

[JoshPlumSE]

It never seemed all that unclear to me. I'm looking at Figure R11.12.5 of ACI 318-2005 and it addresses your exact situation.

 

[cliff234]

JoshPlum, Yes, Figure R11.12.5 is clear but confusing (to me). It implies that I can use a punching shear stress of up to 4 x square root f'c for a critical section that extends beyond d/2 from the face of the column. See my revised (attached) sketch. Envision a corner column with a slab 9.5" thick. 10 x t = 95". That means when my slab cantilever is less than 95" I cannot use the full four-sided punching shear critical section and instead have to use a 2-sided critical section. Imagine a condition where the slab cantilever is 6' on both sides of the corner column. Does my critical section extend all the way to the slab edge as shown in detail 4 (attached)? And if so, can I use a punching shear stress of 4 x square root f'c? That seems unreasonably high. I have no problem using 4 x sq rt f'c within d/2 of the column face but it would seem that 2 x sq rt f'c would be more appropriate beyond d/2. That's just my gut feel. If anyone has any references that would justify using a higher stress, I would be interested in knowing about it. Thanks again!

 

[briancpotter]

The commentary here points to reference 11.3, "Shear and Diagonal Tension" published by ACI-ASCE Committee 326. This reference gives the following instructions for dealing with openings and free edges (corners):

"The shear capacity of the slab in the vicinity of free edges or corners...should be evaluated by applying criterion (a)"

which states the following, referring to the size of the critical section:

"(a) The shortest of all possible sections lying not less than d/2 from the loaded area"

So for your case with a 6' cantilever, the perimeter would be 72+72+24+24+4.75+4.75 = 201.5in when extending the critical section to the edge, and 4*(24+9.5) = 134in when using d/2 on all sides.

Thus, based on this criteria, because the perimeter d/2 from the edge of the column is the shortest, it should be used.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[dcarr82775]

Josh,

Sure, Figure 11.12.5 is perfectly clear for the exact scenario they show where the slab extends about d/2 past the column face. It is not clear what happens when it extends t, 2*t, or 9*t past the column. What then? That is what is very unclear. How far you get to extend that critical section off the face of the column is not well defined.

 

[dhengr]

Cliff:
It seems to me that there have been a couple other threads on this issue over the years, you might try searching older threads. I suspect there has also been some research done on the matter. I haven’t done much detailed conc. design in the last few years, so maybe some of the more knowledgeable conc. guys/gals will be along later. As I recall the 10t cantilever length criteria (likely a number pulled out of thin air), or the question about exactly how to treat this problem, has to do with the way that corner cantilevered slab acts; curls, lifts, acts torsionally, which makes it a little less effective in developing the shear along the two outside faces of the column which would normally make up the four sided shear cone area. I think it’s the likelihood of too little compression in the conc. slab in that cantilevered region, plus potential torsional stresses; either along the two outer col. faces or those extensions out to the edges of the slab. I wouldn’t think your shear area in your details 2 or 4 should ever exceed the std. four sided condition around the column. On the inside two faces you might use those stud-rail shear devices to increase the length/size of your shear surface/cone area.

 

[hokie66]

The maximum shear stress at a corner column only applies at the interior corner of the shear perimeter. Towards the outer edge, the shear stress decreases linearly due to the unbalanced moment. It has always been clear to me that the actual design shear perimeter can extend to the edge of the slab, as long as the perimeter does not then exceed the limit for an interior column.

 

[cliff234]

Thank you for all of the responses. While I am now more comfortable in determining the punching shear capacity of corner and edge columns with slab overhangs, I still feel that ACI 318 Section 11.11.6 is too vague. Punching shear is the most critical limit state in flat plate design, and as such I feel that ACI 318 should be more explicit in what to do when this common situation occurs at edge and corner columns.

 

[JoshPlumSE]

There are cases where it is unclear whether the punching perimeter should be based on an "interior", "edge" or "corner" perimeter per the 2nd ACI punching shear equation. If it's not clear I would recommend investigating all cases. In your diagrams 2 and 4, I would refer to this as an corner perimeter. In case 1, I would refer to this as an interior perimeter. Using the corresponding Alpha_s value for each case. This is the way punching shear works... at least per ACI.

Now, is it possible to get a one-way shear type failure when you have the situation shown in diagram 4? Sure, it is possible. But, that is a different failure mode. It is assumed to happen at a distance d from the face of support, not d/2. It will have a capacity based on 2*sqrt(f'c), not the punching shear formulas. The demand force will be the shear force in your design strip. The width of the one way failure will extend over a different width of the slab (your design strip width). This design strip width is more difficult to set and is based on some engineering judgment.

I think the problem is that you are mixing up the two failure modes in your mind. The punching shear failure is pretty straight forward to calculate per code. The one way shear failure is a bit trickier.