Which system is designed with a two-way concrete setup in which the slab reinforcement extends directly to the columns?

The two-way concrete system where the slab reinforcement extends directly to the columns is known as a Flat Plate system. In this design, the concrete slab is relatively thick and consists of a uniform thickness that is directly supported by columns and does not require beams for additional support. This allows for a more open and flexible floor plan, as there are no beams to create obstacles in the space.

In a Flat Plate system, the load is distributed evenly in both directions (hence the term "two-way"), allowing for efficient load transfer directly to the columns. This characteristic makes it well-suited for various building types, particularly when the spans are relatively short, as it can achieve height efficiency and a more aesthetically pleasing ceiling surface without beams interrupting the visual field.

The other options involve different structural systems: Stressed Skin Panels involve a rigid panel construction used typically in lightweight structures; Flat Slab systems, while similar to the Flat Plate, generally incorporate drop panels or thickening at columns for additional support and load distribution; and Beam-and-Girder systems utilize a grid of beams and girders to support the floor slab, which does not create the same direct column connection of reinforcement as a Flat Plate system.