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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Page 149 - Building stability - Arched spaceframes

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