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The challenge:  create a space with minimal height that can accommodate a loft space with adequate head-room below and in the loft.

The roof plane is sculpted slightly to direct the space outward making it feel larger than what is contained within the walls.  The structural thickness must be minimal, but there is a near-20ft span and a 6ft cantilever which makes it very difficult to do structurally. 

Solution:  use a two-way waffle structure with stressed skins.

Since we have CNC plasma capabilities, a waffle structure created from a light gauge steel sheet would be very economical to fabricate and could be prefabricated in long sections, then hoisted and assembled on site.  The issue then becomes designing and analyzing a waffle structure in 20ga. Sheet.

Right:  the 20ga. Steel waffle core at 12" o.c. each way.  This is the second version of the core as the first was at 16" o.c. and resulted in excessive deflection in the composite analysis.  This 12" centers waffle on first round of analysis is resulting in approximately 0.604" deflection.  More analysis is required to verify results at this point, but is seems as if the system will work.

Right:  Step 1 of the analysis is to run a simulation on a piece of the core in which the top edges are uniformly loaded, the beam is a simple span, and the top edges of the steel sheets are restrained in the X direction as they are laterally restrained by the stressed skin.  This will allow only Y & Z deflections to be calculated and produce a situation where one can solve for the composite Elastic Modulus (E) using the deflection value computed by the Finite Element Analysis.  This E can then be used as input for a material physical property for the center core grid along with the resultant density for the 12"o.c. grid. 

Deflection results for the 12" o.c core "simple beam" section used in the first step of the composite analysis.

The resulting E (Elastic Modulus), density, and yield strength (calculated by using the yield strength of the 20ga steel & dividing by the cross sectional area of the overall spanning section) are then used as properties for a "new material"  in a second Finite Element Analysis (FEA) which uses a solid volume as the core material, and a 20ga skin as the stressed skin. 

This image shows the loading and restraint conditions for the composite FEA.  FEA by default is extremely computation intensive and can run for days if one is not careful about the density of the resulting finite element grid or mesh.  This is why the waffle grid core was modeled as a solid with derived physical properties. 

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