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 mid-span 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. Semi-circular
structures like these |
are
called truss barrel vaults. The following model has a two-way
rectangular outer grid |
over
lying a two-way 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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to Knowhere |
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Page 149
- Building stability - Arched spaceframes |
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