I have an existing slab and I need to find out if the slab can support a raised platform. where do I start to calculate if the slab can support the punch shear and the deflection.
What is the thickness of the slab? Do you have any existing drawings? If not I recommend coring the slab in three locations to determine the thickness and then breaking the cores to determine the existing concrete strength. This can be done by a testing lab. After this information is obtained and evaluated then you have a much better idea of what direction you can take as far as the design is concerned. It would be a good idea to core the slab even if you have the drawings to see what your in place strength and thickness is. Of course the significance and size of your platform will also be a factor in justifying this expense.( perhaps $500 to $1000 dollars )
If design allows, you can also increase the punching shear plane by "spreading" the load using a widened concrete curb at each platform columns (in case existing slab isn't thick enough).
if you know how big the concentrated load imposing the slab, you may start derive slab thickness from "punching shear" equation or you can use appropriate design tables for that kind of slabs.