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Table 4.
Optimum Pipe sections for Geodesic Dome with Four Rings
Optimum Pipe Section Designations for Member Groups
1
2
3
4
5
6
7
8
PIP
1393.6
PIP
1143.0
PIP
485.0
PIP
424.0
PIP
423.0
PIP
333.0
PIP
333.2
PIP
213.2
The optimum sectional designations for each group obtained for the dome with five
rings are given in Table 5. The optimum height of the dome is determined as 1.5m.
The maximum displacement in the dome is 32mm and the maximum strength ratio is
0.99. The minimum weight of the dome is attained as 1,477.08kg. The optimum ge-
ometry of the dome obtained is shown in Figure 6(c).
Table 5.
Optimum Pipe sections for Geodesic Dome with Five Rings
Optimum Pipe Section Designations for Member Groups
1
2
3
4
5
6
7
8
9
10
PIP
886.3
PIP
765.0
PIP
763.6
PIP
483.6
PIP
423.2
PIP
333.2
PIP
333.0
PIP
422.6
PIP
263.2
PIP
213.2
The optimum sectional designations for each group obtained for the dome with six
rings are given in Table 6. The optimum height of the dome is determined as 1.5m.
The maximum displacement in the dome is 29.3mm and the maximum strength ratio
is 1.00. The minimum weight of the dome is attained as 1545.3kg. The optimum ge-
ometry of the dome obtained is shown in Figure 6(d).
Table 6.
Optimum Pipe sections for Geodesic Dome with Six Rings
Optimum Pipe Section Designations for member groups
1
2
3
4
5
6
7
8
9
10
11
12
PIP
213.2
The maximum displacement values in each design problem are less than but close
to their upper bound of 33mm while the maximum value of strength constraints are at
their upper value of 1. This indicates that the displacement limitations are not domi-
nant in these design problems. Hence the strength constraints are the ones that decide
the optimum shapes in the design example considered. Variation of the minimum
weights of geodesic domes with different number of rings is shown in Figure 7.
PIP
886.3
PIP
884.0
PIP
763.6
PIP
483.6
PIP
483.6
PIP
333.6
PIP
333.0
PIP
263.2
PIP
263.2
PIP
263.2
PIP
263.2
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