How to calculate concrete bearing of steel plate that might be loaded unevenly

[Flat Square Parallel]

Hello guys!
Long-time lurker here but first-time poster. Engineer designing steel structures but have less experience with concrete design.

We have an application where a steel structure will be supported via four extending arms that are sitting in pockets made into the side of a fairly green (~1ksi) concrete wall. See the attached image below. The arms are solely transferring a vertical load to the pockets. The concrete wall is 12" cast against rock, and extends left/right/below of the pocket by more than 10'. Concrete is not reinforced.

I need to make sure that I don't exceed the bearing capacity of the concrete in those pockets. If I understand correctly, this would be straightforward if we considered that the arm bearing plate was lying flat against the pocket : it's a matter of making sure the average contact pressure does not exceed the allowable concrete compressive capacity (right?). But considering that there will be flexure in my structure, as shown in the image (where the deformation is very exaggerated), then the actual load transfer will happen at the edge of the pocket. I mean, the tip of the arm might lift by 0.002-0.003" or the like - imperceptible - but an FEA of this clearly shows that the load is transferring at the edge. Do I need to account for this localized high-stress point, or am I overthinking it, with concrete? I know that ideally, the arm would have some kind of swivel between the arm and the bearing plate, but the equipment is existing and new arms cannot be made easily.

Also, would there be other load cases that one would need to consider other than bearing capacity?

Thanks!
FSP

 

[jayrod12]

For bearing plates on masonry, they usually consider a triangular pressure distribution for bearing plates supporting beams unless specifically detailed to apply the load at the centre of the bearing plate.

It's essentially half the bearing capacity of the rectangular.

So maybe it would be prudent to only account for a triangular pressure distribution and keep the maximum bearing pressure below the allowable.

 

[SWComposites]

Why would one use an FEA for this simple loading???

 

[Flat Square Parallel]

SWComposites, the FEA I did was for analyzing the whole structure, and not only to look at the bearing plates.

Thanks Jayrod for your answer. I looked up the triangular distribution. I did find references in Masonry books that I could purchase, but nowhere else. Would you have a code to point to? Also, and to be sure, does the reaction diagram below correspond to what you meant?

 

[JLNJ]

We like to hold the bearing plate back from the face of the wall to avoid that stress riser and crack which wants to form at the edge.

 

[JStephen]

Consider the use of grout, rubber pad, or expansion joint material between the two surfaces for more uniform loading.
Even without the bending effect, the two surfaces are never going to be perfectly flat, so there will always be a single point of contact that contacts first.

You could get a shear failure on an angled surface below the pocket, or tension effects beside the pocket.

 

[dik]

I design nearly all corbels with the load at the outside edge... with ledger angles nearly always near the back edge due to deflection with shelf angles...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik