A flat plate floor system is a two-way concrete slab supported directly on columns with reinforcement in two orthogonal directions (Figure 1a). Primarily used in hotels, multi-family residential buildings, and hospitals, this system has the advantages of simple construction and formwork and a flat ceiling, the latter of which reduces ceiling finishing costs, since the architectural finish can be applied directly to the underside of the slab. Even more significant are the cost savings associated with the low-story heights made possible by
the shallow floor system. Smaller vertical runs of cladding, partition walls, mechanical systems, plumbing, and a large number of other items of construction translate to large cost savings, especially for medium and high-rise buildings. Moreover, where the total height of a building is restricted, using a flat plate will result in more stories accommodated within the set height.
The thickness of a flat plate is controlled by the deflection requirements given in Sect. 9.5.3 of ACI 318-05. Minimum slab thicknesses for flat plates with Grade 60 reinforcing bars, based on ACI 9.5.3, are summarized in Figure 2 as a function of the longest clear span between supports.
Flat plate systems are economically viable for short to medium spans and for moderate live loads. Up to live loads of about 50 psf, the deflection criteria usually govern, and the economical span length range is 15 ft to 25 ft. For live loads of 100 psf or more, punching shear stresses at the columns and bending moments in the slab control the design. For these cases, the flat plate is economical for spans between 15 ft and 20 ft. A flat plate floor with a live load of 100 psf is only about 8% more expensive than one with a live load of 50 psf, primarily due to the minimum thickness requirements for deflection. Floor panels with an aspect ratio of 2 would be about 30% more expensive than panels with an aspect ratio of 1; the thickness of the rectangular panel is governed by the greater span length, resulting in a loss of economy.
On average, the formwork costs for flat plates represent approximately 46% of the total floor cost. Concrete material, placing, and finishing account for about 36% of the cost. The remaining 18% is the material and placing cost of the mild reinforcement.
Bottom line: 8 meter (24 ft) sides on hexagons greatly reduces complexity and cost of building the deck, going bigger probably needs a waffle joist built into the deck, which means very complex forms and more expertise.