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Baz replies are very detailed, and here is one item I can re-elaborate on since you have asked it again. Because the way your slabs are being connected to your beam (The slab is connected to the face of the beam), you will always have torsion and you need to deign for that torsion as that is the only load path from slab to beam with the provided connection concept. If you want to reduce or avoid torsion, your slab to beam connection philosophy needs to be revised. For example, if this hollow slab was "casted above the beam" you will not have this issue (torsion will reduce at the center beams but will still have torsion at corner beams), but you will need to connect your slab and beam through some system and in that way your beam depth will be much smaller. Thanks.

Do you understand that the supporting beam is subjected to torsion, in addition to shear and bending moment, due to connection detail chosen for transferring forces from the precast hollow-core slab to RC beam? Can you imagine what will happen if beam has not been designed for the interaction of torsion and shear? Can you imagine that the beam will tend to twist or rotate about its longitudinal axis if the adequate amount of torsional reinforcement is not present? What will be the result of that rotation? In this case, can it lead to an increase in connection forces that may not have been accounted for?

Rigid diaphragm is reasonable assumption for this kind of arrangement for vertical members of lateral-structural system. I already answered the issue of torsion constant. In the first run, analyze the section with out using any reduction in constant for torsion (use 1). Make changes if you are redistricted in the choice of section size for beam. In this case, how will you know if the additional flexural demands in hollow-core panels, due to torsion-related cracking in RC beam, will be taken into account?

Straying away from your questions, I am curious how will the construction of floor-system with these connection details take place? Will they cast the frame with rectangular X-sections of beams first, and then install the panels? Will they drill the dowels afterwards? Will the dowels be left in place during pouring of concrete for RC beams. How will they adjust the dowels at their right position in precast hollow-core panels? For these kind of construction, I have seen following construction methodologies: 1- Hollow-core panels supported on ledges of RC/Pre-case beams. 2- Hollow-core panels supported on horizontal joint of RC beams. In this case, they do not pour concrete on the full depth of beam, leaving room equal to the thickness of floor on top of horizontal joint with-in beam's depth.