Page 152 - JCAU-6-2

Journal of Chinese
Architecture and Urbanism RuiXue Multi-Hall in reciprocal structures

to include three distinct types: triangles, squares, and increases to 0.45 and 0.35 m, rendering it a more viable
irregular pentagons. At α=15°, the minimum length of the option for construction. Nonetheless, when considered in
structural edges for the two types of reciprocal geometric conjunction with the number of unit boundaries, achieving
pentagonal units is merely 0.12 m, a dimension smaller than optimal geometric shape effects during the construction
the predefined structural member thickness. This situation process remains challenging.
is highly impractical for construction purposes. However, The comparison between the most basic B and C classes
at α=30°, the shortest edge length for the pentagonal unit
of reciprocal grids reveals notable differences. First, the C
class grid exhibits higher material efficiency than the B
class grid when mapped onto a shell structure with the
same scale and rotation angle. Second, both B and C class
grids can achieve a relatively stable equidistant point shape
during the conversion process of reciprocal structures,
implying that the node where the rods intersect is located
at the equidistant point of the rod. After continuous
adjustment of the rotation angle parameter, α, and inverse
solution, it can be concluded that the B grid can attain a
unique reciprocal state at a 27.6° rotation, while the C grid
can achieve a special reciprocal state at a 16.1° rotation.
On reaching this state, the overall structural performance
Figure 11. Workflow of organizing the application of reciprocal geometry of these two classes of reciprocal grids can be optimized
in shell structures. Source: Drawing by Philip F. Yuan (Figure 15).

Figure 12. The application of B and C grid reciprocal geometric shell. Source: Drawing by Yingzi Hu

Volume 6 Issue 2 (2024) 10 https://doi.org/10.36922/jcau.1635