68 Spatial rings and domes
Substituting these expressions into Eqs (4.7) and (4.8) gives two equations
in terms of a, b and β, from which
(4.10)
and
.
(4.11)
4.2.4 Concept C
This ring is made from n a trapezia and n a triangles arranged so that 2n a
scissor- like elements with beam length 2b form the outside of the ring,
while only n a scissor- like elements with rod length 2a form the inner loop.
In plan view, Figure 4.5(c), this results in a chain of alternate isosceles triangles and isosceles trapezia. The intermediate elements are the same type
as those used in concepts A and B whose heights meet those of the elements to be connected.
It can be shown that
(4.12)
and
,
(4.13)
where
. Noting that
,
and
,
(4.14a, b, c)
we have
(4.15)