Civil Engineering Reference
In-Depth Information
The resulting prestress in each member is:
F
CA
= 10.0 - 0.73 = 9.27 kN
(ref 5.5.1A-7)
F
CB
= 10.0 - 0.79 = 9.21 kN
(ref 5.5.1A-8)
F
CD
= 10.0 + 0.27 = 10.27 kN
(ref 5.5.1A-9)
The computed prestresses are within 7% of the target prestress. The answer is
converging. For the next estimate, scale the X deflection by 500 and continue to scale
the Y deflection by 100. The new estimate for point C is:
X
C
= 2000 - 406 - 379 - 290 - 471 - 74 = 380
Y
C
= 0 - 699 - 137 + 73 + 63 + 13 = -687
For this configuration:
0
0915
P
=
(ref 5.5.1A-1)
0
4667
The resulting displacements are:
0
031
CX
=
0
063
CY
The resulting prestress in each member is:
F
CA
= 10.0 + 0.32 = 10.32 kN
(ref 5.5.1A-7)
F
CB
= 10.0 - 0.26 = 9.74 kN
(ref 5.5.1A-8)
F
CD
= 10.0 - 0.04 = 9.96 kN
(ref 5.5.1A-9)
This process is converging toward the equilibrium prestress configuration. After five
cycles, the computed prestress is within 3% of the desired prestress. The primary
challenge in developing and using a stiffness approach lies in efficiently predicting
the ideal configuration from information derived in previous estimates.
5.5.2 Force Density
The force density method is an analytic technique to linearize the form finding
equations. Although it may be used in the analysis of applied loads, its primary use is
in identifying the equilibrium shape associated with a specified prestress.
This method allows designers to find shapes in equilibrium with a given topology,
support locations and a set of force density ratios (cable force divided by cable
length). The method is independent of the initial location of the free joints. The
method considers each element framing into each joint. Different force density ratios
produce different geometries, all of which are in equilibrium. A certain amount of
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