I think a sketch is in order to we can better understand the configuration. Shear Transfer in concrete can be accomplished in several ways. In order to achieve a shear friction joint you would need to have rebar fully developed on each side of the shear plane, this is a common method to achieve the transfer of shear across a cold joint.

If this is a continuation of his other threads, he needs to increase the punching shear capacity of his column to raft slab. It appears he has decided that a concrete sleeve may be the most acceptable solution.

Similar to composite concrete toppings, I expect that the bulk of the actual shear transfer mechanism is bond. If you wanted, you could have them chip keys into the perimeter of the existing column to allow for a more robust interface between the old and new concrete.

Existing column 24x12"
Added concrete Encasement [sleeve] 4"
shear links; steel rebar [#4] 4 embedment length
looking for enquation that [similar to shear studs] that i could apply to calculate the shear transfer between the old column and new concrete layer (to check the required number of shear links @ spacing) also to study the best shape of hooked end (90 degree/direction or ?). Also to study the actual load distribution between the column and the attached concrete encaesment
if that possible ?

thanks jayrod12 for your answers
it is the same problem
but i was thinking if the column is also weak and need to increase its bearing capacity
i did delete the old thread cause of the "..."
still i deeply appreciate/respect your and others inputs
.
i thought i could start with the column encasement then do the RAFT thickening [reinforced top layer]
Tow major parameters here; layer thickness & shear links (numbers & spacing)

Another configuration for column bearing capacity enhancement
to add steel jacket (these pictures from different renovation project)





My second question
if there is similar case studies to read/compare ? (details are always appreciated)
only built-up column i found or composite encased-column

The steel sleeve will not improve your punching shear issue, all it does it provide confinement to enhance bearing capacity. I'd stick with the concrete sleeve.

thanks jayrod12
Any references in mind you recommend ? [concrete columns Strengthening/Repairing techniques] ?

Unfortunately I don't have anything specific for you. I practice in Canada so our references may be slightly different. However you need to provide enough steel on each side of the shear plane to get adequate shear interface transfer (shear friction). Or provide a shear transfer mechanism that doesn't rely on friction, e.g. cutting in regularly spaces keys around the existing column.

thanks jayrod12
all noted ( provide a shear transfer mechanism that doesn't rely on friction )

I am not a fan of doweling the existing concrete to transfer the shear, rather, the existing concrete surface should be roughened to at least a 1/4" amplitude to ensure shear friction in between the concrete. Also, stirrups should be provided for the addition, which shall be fastened to at least 4 vertical bars.