Form Determination - Tensile Fabric Structures: Design, Analysis, and Construction - page 80

g X  g X  g X  P

X C =

1 A 2 B 3 D CX

(5.5.2-3)

g  g  g

1 2 3

= 0.005(0.0) + 0.005(0.0) + 0.005(4000) - 0.0 = 1333
(0.005 + 0.005 + 0.005)

g Y  g Y  g Y  P

Y C =

1 A 2 B 3 D CY

(5.5.2-4)

g  g  g

1 2 3

= 0.005(1000) + 0.005(-1000) + 0.005(0.0) - 2.0 = -133
(0.005 + 0.005 + 0.005)

Check for equilibrium, recalling F i = g i L i (ref 5.5.2-2)

2 2

L 1 = 1333  1133 = 1749

F 1 = 0.005(1749) = 8.75 kN
F 1X = 6.67 kN
F 1Y = 5.67 kN

L 2 = 1333 

2

867

2

= 1590

F 2 = 0.005(1590) = 7.95 kN
F 2X = 6.67kKN
F 2Y = 4.34 kN

2 2

L 3 = 2667  133 = 2670

F 3 = 0.005(2670) = 13.35 kN
F 3X = 13.34 kN
F 3Y = 0.665 kN

At the new location for node C:

 F

= - 6.67 - 6.67 + 13.34 = 0.0 (ref 5.1.3-1)

 F

= 5.67 - 4.34 + 0.67 = 2.0 (ref 5.3.1-2)

An equilibrium configuration has been identified. However, the forces in the bars,
8.75, 7.95 and 13.3 are only moderately close to the targeted 10.0. The force density
value can be modified to find another equilibrium condition.