Arched spaceframes  barrel vaults, cylinders, and hyperboloids 
. 
Arching a spaceframe reduces the required
depth/module ratio of its unit cell by up to one 
half compared to a planar spaceframe with the same
span and loading conditions. That is, 
the lattice can be made thinner.
This is due to the load collecting and displacing abilities 
of the arch discussed previously.
That reduces the stresses experienced by the members 
located midspan of the structure
where the bending
moment is the greatest. 
. 
Barrel vaults and cylinders 
. 
Arched
spaceframes can be built that are simply arched trusses, like the ones
shown 
before,
that are extended in the horizontal direction. Semicircular
structures like these 
are
called truss barrel vaults. The following model has a twoway
rectangular outer grid 
over
lying a twoway square inner grid. The joints of one grid are
aligned vertically with 
the midpoints of the edges of the other grid. 
. 

Fig. 273  Arched truss
structures 

based on the same geometry 
◄ arched truss 
truss barrel vault ► 
(demonstration models) 
click image to enlarge 

. 
The unit
cell of this curved lattice is inherently unstable requiring an additional
bracing 
strut
positioned diagonally across either the square or rectangular opening
for stability. 
. 



a) unstable 
b) stable 
RT (red, blue), ST (orange) 
m = 17 J = 8 
18 = 3 ( 8 )  6 
Fig. 275  Cylinder 
17 < 3 ( 8 )  6, need + 1 M 

(demonstration models) 
click image to enlarge 
Fig. 274  Stability analysis of the arched
truss unit cell 


. 
Vaulting the arched truss stiffens the structure against diagonal twisting
but not entirely so. 
However
if the cells are assembled together to form a ring or cylinder, as in Fig.
275 above, 
the
resulting structure is completely rigid and stable without the need for
any extra bracing 
struts.
The equation describing the stability of this cylinder is M = 3 J. That
is, the number of 
struts
equals three times the number of joints, or hubs. Since the unit
cell is unstable, the 
stability of the cylinder must be due solely to the fact that the arch
curves back on itself. 
. 
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Page 149
 Building stability  Arched spaceframes 

