[Ferro List] Catenary Dome

[Peter Payne]

Best shape for self-supporting arch with no load: Catenary arch, as 
described by Keith.

Best shape for purely vertical load: Pillar (direct vertical weight 
transmission, no bending)

Best shape for resisting pressure from all around: Sphere (as in deep 
sea vehicles)

Best shape for arch with vertical load: somewhere between catenary arch 
and pillar, in other words a steeper, more pointed arch.

Best shape for underground: such a shape must support itself, deal with 
vertical load of the earth above, and deal with lateral pressure of the 
earth (&/or hydrostatic pressure) around it. The amount of these two 
pressures depends on the texture of the earth. A very sandy wet earth 
might act similarly to water, whereas a clayey soil could compact around 
the shape so as to put very little pressure or weight on it. The most 
common situation would be: substantial vertical load, and also fairly 
substantial lateral pressure. So, a shape that would be a cross between 
a pointy arch and a sphere. Case in point: My storage shed is more or 
less a catenary arched vault; but as snow accumulated up the sides this 
winter the sides caved in; a better design would have had the sides 
bulge out in a more sphere-like way, so as to redirect the pressure 
forces of the snow out into skin of the structure.

I tried modelling some of these shapes on a computer program that allows 
you to set up two shapes then draws all the intermediate shapes, 
morphing one into the other.

Peter