Two-Post Truss as Dome
We use a set of four, two-post cable trusses to make a cable dome. We arrange trusses radially. We
replace the horizontal portions of cable in each 2D truss with hoop cables. This change leaves the
middle of the dome open.
Figure 1
Figure 2
Figure 3
Figure 4
Dimensions
We will do a preliminary design for a circular dome with 200 ft diameter. The middle, open portion of
the dome is 100 ft diameter.
Figure 5
Loads on trusses
We use the roof deck and snow loads from our examples for other roof constructions. The deck has self
weight equal to 12 psf. Snow load equals 20 psf. Load at top of a strut is computed from tributary area.
Trib area = 1196 ft2
Deck load = 14.4 k
Snow load = 23.9 k
Statics for Dome
Prestressing cables
The eight upper radial cables provide prestress. We select a value of vertical prestress, Q, then find H
for upper radial cables to deliver Q.
Figure 6
Symbolic relation for H in terms of Q
H = 5Q
Select Q equal to 10 k. Numerical value for H
H = 50k
Symbolic relation for tension in prestress cable in terms of H.
T = H sqrt(26/25)
Numerical value for tension in prestressing cable
T = 51.0 k
Upper hoop cable
An upper hoop cable provides horizontal equilibrium for tension in prestressing cables. We use the plan
geometry of the hoop cable to get a relation of Hprestress to Hhoop.
Figure 7
Symbolic relation for Hhoop
Hhoop = 1/2 Hprestress (38.27’ / 14.64’)
Numerical value for Hhoop
Hhoop = 65.3 k
Load–Carrying Cables
The lower radial cables carry loads to foundations. The lower radial cables carry deck load, snow load,
vertical prestress force, and self weight of cables and post.
Figure 8
Symbolic relation for H in terms of P
H = 2.5 P
Numerical value for H under deck weight plus prestress (this is our reference state)
H = 60.9 k
Numerical value of H under deck weight, snow load and prestress
H = 121 k
Symbolic relation for tension in load-carrying cable
T = H sqrt(29/25)
Numerical value for tension in load carrying cable under deck weight, snow load and prestress
T = 130 k
Lower hoop cable
The lower hoop cable provides horizontal equilibrium at the bottom of struts. Statics are identical to
statics for upper hoop cable.
Symbolic relation for Hhoop in terms of H for lower radial cable
Hhoop. = 1/2 HloadCable (38.27’ / 14.64’)
Numerical value for Hhoop for deck weight plus prestress
Hhoop = 79.5 k
Numerical value for Hhoop for deck weight, snow load and prestress
Hhoop = 158 k
Strut
Struts carry compressions due to deck load, snow load and vertical prestress force.
Numerical value of compression in strut under deck weight load plus prestress
H = 24.35 k
Numerical values of compression in strut under deck weight, snow load and prestress
H = 48.27 k
Cable Lacing
We need one more component. We tie struts together in an X pattern with cables. These provide
stability. Struts could turn-over (invert) for loads applied at top of struts. We’ve got to inhibit this
movement. Lacing cables are 1/2” diameter strand. These have zero force in the reference state.
Select components
Select stands for cable components and HSS for struts
Component
Tu estimate Select
Prestress cable
56.1 tn
1”
Upper hoop
71.9 tn
1 1/8”
Load carrying cable 143 tn
1 9/16”
Lower hoop
173 tn
1 11/16”
Strut
48.3 k
HSS 7 x 7 x 1/4
Values for HSS 7 x 7 x 1/4, KL/r = 131, Fcr = 14.6 ksi, Pallow = 54.1 k
Model
The model file is TrussDome.csxml
Reference state
Find values for H in cables and struts for a permanent load reference state.
Component
Prestress cable
Upper hoop
Load carrying cable
Lower hoop
Strut
H estimate
50 k
65.3 k
60.9 k
79.5 k
-24.4 k
H final
50 k
65.33 k
64.19 k
83.87 k
-24.92 k
Response to snow load
Analysis with 1.0 load factors on all loads.
Vertical deflection is -0.4 ft
For the strut, compare the estimated force to the result from analysis. Update strut size if needed.
Pestimate = -48.3 k
Presult = -47.3 k
New size for strut? keep HSS 7 x 7 x 1/4
Analysis with 2.2 load factors
Check cables. Increase cable size if needed for strength.
Component
Prestress cable
Upper hoop
Load carrying cable
Lower hoop
Tu k
112
144
232
279
Tu tn
56.1
71.9
116
140
New size?
Keep 1”
Keep 1 1/8”
OK, could go to 1 3/8”
OK, could go to 1 9/16”