Untitled

134 Antonio J. Gil
4 Numerical Example: Cable Network
This example, extracted from [23], represents a squared hyperbolic paraboloid with
a 12 foot horizontal side. The difference between the highest and lowest points is
measured as 1.5 feet. The sides of the structural model are composed of rigid beams
which prevent any displacement.
The structure is modelled by means of a cable network depicted at Fig. 5,where
arepresentation of nodes and elements can be observed. The external nodes are
adopted to be fixed and the only allowed displacement is for the inner nodes.
OY axis (in)
100
80
60
40
20
0 37 38 39 40 41 42 43 44 4 45 46 47 48
−20
−40
−60
−80
−100
85 8
−100 −80 −60 −40 −20 0
OX axis (in)
20 40 60 80 100
1
2 3 4
5 6 7 8 8 9
10 11 12 13 14 15 155 16 1
17 18 18 19 19 20 20 21 21 22 222
2 23 23 24 225
2
26 27 27 28 28 29 29 30 30 31 31 32 332
3 33 33 34 34 35 336
3
50 51 51 52 52 53 53 54 54 55 55 56 556
5 57 57 58 58 59 59 660
61 62 62 63 63 64 64 65 65 66 666
6 67 67 68 68 669
70 71 72 73 74 7 75 755 76 7
77 78 79 80 880
8 881
82 83 8 884
8
Fig. 5.Broughton: cable discretization.
All the cables are subjected to a previous prestressed state of 1.2 Kip. In addition
to that, the cables will be represented by a unique material of 0.618e3 Kip for the
mechanical factor EA.
The structural model undergoes under service conditions a downward point load
of value 0.22 Kip applied at node 79 -see figure (5)-. The analysis has been solved
by using a Newton-Raphson numerical scheme in one incremental step.
Figs. 6 and 7 represent both original and displaced shapes. Analogously, Table
1 reflects a survey of displacements according to the different spatial directions for
some remarkable internal nodes. Results according to reference [23] and present work
are displayed.
Fig. 8 gathers the convergence curves for the numerical method which has been
employed. Eventually, a representation of the Cauchy axial forces is shown in Fig. 9.
49 4