Crown without soundboards

[A440A]

Greetings all, 
     I read with interest the postings concerning crown and the rim influence
on it.   I have often wondered if a bridge attached to the ribs, with no
soundboard would be able to withstand the down pressure.  I am skeptical that
the soundboard itself, what with soft thin wood, actually provides much
support.  
   That a board is still crowned with glue joint failure around the rim
doesn't tell me much.  Would not the joints of the ribs to rim actually have a
lot more bearing on  crown maintenance? 
   From a structural standpoint,  the principle  of arches seem to describe
the transfer  and containment of bearing pressure.  When you vector the
downward force from an arch, you see that there is a transfer of pressure from
straight down to a more lateral direction, where the pressure meets the case,
( and any centripedal apparatus that may be in the area.......(:)}} 
   So,  has anyone ever considered that the ribs alone might support a bridge,
and the soundboard itself  does very little? Or to ask another way,  how long
would a board remain crowned if there were no ribs?  
Regards, 
Ed Foote