I have an existing 10" flat slab with drop panels projecting 8" below the slab soffit (total thickness 18"), with 40" diameter concrete columns (no capitals). f'c = 4000 psi.

Bay size is 28 feet x 40 feet.  

Shear is 400 kips factored as per CSA A23.3-2004.  

I want to bring down two new steel column loads onto the flat slab, one column load of 80 kips at the north face of the existing round concrete column and another new column load of 80 kips at the south face of the existing round concrete column (total additional load =160 kips).  

Total load = 400 kips existing + 160 kips new = 560 kips factored.

These new  columns will apply their load within about d/2 of the round column face (d average = 18" -1.5" cover - 1" top bar size = 15.5";   d/2 = 7.75').

Question: How can I check whether the flat slab floor works for shear?

 

So the new columns are centered on the face of the existing so that the center to center distance is 40 inches?
 

The new steel columns are 8" x 8" WF sections so the centre-to-centre distance is 40" + 8" = 48"

 

Ref ACI 318 - The shear failure is a pyramidal frustrum with slope angle to the vertical a = 45 deg. The code provides a simpler design eqn. assuming a pseudocritical section located at a dist. d/2.
Ref CRSI Handbook 1996, Chapter 13 - Piles: For a case of a pile cap with reactions from piles located less than d from face of the column, the handbook provides special investigation for two-way shear based on the report by Joint ASCE-ACI Committee 426 "The shear strength of reinforced concrete". For such a case, a < 45 deg. Failure when a < 45 deg can occur but only at increasingly higher values of shear stress. Special investigation for two way shear is made with a critical section located at the face of the column.
I am not sure if the theory in that report would be directly applicable in your case but may provide some pointers.  

I think you should be OK.  The concrete column is lightly loaded, and the steel column reactions will transfer through the deepened slab by concrete strut action.  I would just check the existing slab top bars to take the additional tie force.

Thanks to DST148. That was a really great suggestion. The CRSI method is very straightforward. Thanks again. Very much appreciated.

Thanks to hokie66 too.

Just one thing, when I wrote the description in my original post, I was not in the office and was trying to remember the loads but got them very wrong. They are much heavier, namely 275 kips factored times 2 loads per existibg column location = 550 kips. Nevertheless I think it may still work by the CRSI method. will let you know.

 

Does anyone have the latest CRSI Handbook, and if so, do they still give this method of calculating the shear capacity when the load is within d/2 from the support?

Can anyone explain why the interface shear formulae in CSA A23.1 give such different answer when the load is very close to the column face (about 3" away)?

...by the way. I had the wrong load in my original message. The added loads should have said 250 kips factored, each of 2 sides for a totla added laod of 500 kips per column (not 80 kips each of 2 sides in my original message). The added load is very significant so I have to get this right.

Not familiar with the CRSI publication, but I would just use strut and tie analysis to check it.  You may find that the top bars in the vicinity do not provide enough tie area.

ajk1,
I have had a similar situation in the past. A Strut and tie analysis as suggested would be the most appropriate one. For your loads, like Hokie suggests, you may not have enough top steel to cater for the tie force required to keep the two inclined struts from separating.

One option might be to groove cut the slab and post-install some rebar, if needed.

It's no trick to get the answers when you have all the data. The trick is to get the answers when you only have half the data and half that is wrong and you don't know which half - LORD KELVIN

See attached thread also thread507-256671: Transfer column on a thickned slab

It's no trick to get the answers when you have all the data. The trick is to get the answers when you only have half the data and half that is wrong and you don't know which half - LORD KELVIN

As hokie66 and slickdeals suggested, there is not enough steel to act as tie if I do it by strut and tie model (assuming that the tie steel must be additional to the flat slab top bars), based on compressive strut extending down from the bearing area of a 100 x 400 mm steel base plate.

If I ty to transfer the load all with 24 mm Hilti HSL bolts or equivalent, I need 8 rows of bolts in 2 columns (16 bolts total) extending the full storey height and then this only takes 75% of the load (may be good enough, because it is unlikely that all post-tensioning strands in the girders that are being braced are going to fail, especially since they are currently being dried and grease injected). Would have to do scans of the columns to locate the column verical rebars and then custom fabricate the holes in each plate to suit. Will also require drilling thru the spiral ties in the existing concrete columns, which are at 2.75" centes.

I am thinking of investigating the strut and tie model further by using a curved vertical plate that extends about half way around the perimeter of the existing concrete column, with a curved based plate welded to the bottom of the curved vertical plate. This should allow a narrower base plate and a narrower compression strut, thereby reducing the eccentrity and required tie steel, as well as mobilizing more tie bars. The curved plate would have vertical bending and would have to be designed as a flangeless beam so that the compression edge of the plate does not buckle.

Any comments on any of the above? any other suggestions?

You have lost me. An elevation sketch of your overall problem would help. Where does the additional load come from? How does a 100 x 400 mm base plate relate to an 8" x 8" column?

The 8x8 column is another scheme...sorry for the confusion, I will see if I can scan and attach a skecth on Monday.