On 3/20/12, Henry Baker <hbaker1@pipeline.com> wrote:
You are correct about the catenary not having constant stress, only constant weight/mass per unit length. I think that long anchor chains for boats/ships may thin out towards the anchor itself, because the lower portions don't have to carry as much load.
I think that the reason for the non-constant cross-section of the St Louis arch has more to do with wind loads than static loads.
Ditto for the Eiffel Tower, which was designed more for wind loads than static loads.
Note that the "inversion" principle doesn't depend upon constant stress or constant cross-section, but is more general.
I would be interested in your solution for the constant stress case, because that is more like a real arch made of constant (?) bulk modulus material. I'll have to study it more carefully.
Check out this guy's efforts on "fractal" structures of real materials:
A most enjoyable read! WFL