Geometric Optimization of a Reciprocal Floor-Framing System with Self-Weight and Area-Loading Considerations

This paper explores the geometric optimization of a planar reciprocal frame (RF) floor framing structure, focusing on the triangular topology. The structural performance of the frames is computed and plotted against the geometric parameters for various load cases. The load cases modelled include both symmetric and asymmetric loading on a hypothetical surface supported by the frame, and the loads are distributed to the members based on tributary areas. The two key geometric parameters studied are the rotation angle of the members at the unit RF level which defines the geometry, and the total number of members in the grid which defines the grid density. The structural performance is deduced from the total strain energy in the grid. Results show that smaller rotation angles at the unit RF level produce more structurally efficient RF grids. Depending on the grid density and load case, the optimal angle lies between 4 and 8.2 degrees. To some extents, these values mean that optimum geometries for RF under area-loading considerations tend to reduce lever-arms to a minimum. It is also found that the optimal angle remains relatively unchanged for a given grid density between the symmetric and asymmetric load cases.