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I don't know direct design ,perhaps you want to say that in solid slab design (not the flat slab ) you are using ready-made tables of coefficient for finding moment & shear based on long & short span ratio & edge fixidity condition of slab,in this regard I will only remind you that negative moment at support is higher than middle span positive moment.

In flat slab construction , there is no beam .In solid slab there is a beam running column to column & carrying all load of adjoining slabs up-to half of span on both side of beam.In flat slab since there is a column strip in place of beam & this column strip thus designed for higher rigidity & act as beam as it runs between columns.

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