76 Spatial rings and domes
which can be broken down into
(4.29)
and
.
(4.30)
Eq. (4.29) is identical to Eq. (4.6) whereas Eq. (4.30) is the equation that
determines the relationship among eccentricities. One possible solution to
Eq. (4.30) is
(4.31)
i.e. the eccentricities are proportional to the length of the rods.
4.4.2 Diagonal ties
Rings based on concepts A and C are in general less stiff than those using
concept B owing to the trapezia in the layout instead of triangles. However,
it is possible to triangulate a trapezium by having an alternative intermediate tie diagonally placed. In concept A layout shown in Figure 4.5(a), for
instance, A and C could be bridged by such a tie. The projection length of
AC is
,
(4.32)
in which
.
(4.33)
The alternative intermediate tie can be designed by substituting l into Eq.
(4.20). It forms an integrated part of the ring just like any other elements.
The entire assembly remains mobile.
which can be broken down into
(4.29)
and
.
(4.30)
Eq. (4.29) is identical to Eq. (4.6) whereas Eq. (4.30) is the equation that
determines the relationship among eccentricities. One possible solution to
Eq. (4.30) is
(4.31)
i.e. the eccentricities are proportional to the length of the rods.
4.4.2 Diagonal ties
Rings based on concepts A and C are in general less stiff than those using
concept B owing to the trapezia in the layout instead of triangles. However,
it is possible to triangulate a trapezium by having an alternative intermediate tie diagonally placed. In concept A layout shown in Figure 4.5(a), for
instance, A and C could be bridged by such a tie. The projection length of
AC is
,
(4.32)
in which
.
(4.33)
The alternative intermediate tie can be designed by substituting l into Eq.
(4.20). It forms an integrated part of the ring just like any other elements.
The entire assembly remains mobile.