There were eight entries to the competition I ran before Christmas to identify the longest possible beam supporting only self-weight. The winner is Felix Wiesner, to whom a bottle of whiskey. His entry, which can be seen here, followed the EC design procedure, noted that lateral-torsional buckling would be important and also included a nice graph of maximum span possible against plastic moment capacity for various standard sections. With this approach something around 33m seems to be the maximum possible.
Other entries included some interesting points. Xiaobo Cheng, for example, touched on the philosophical matter of what “support” means and included a limit on the allowable deflection of a beam, as well bending resistance. I wasn’t convinced such “serviceability” limits were really relevant – surely as long as the beam carries the load it is supporting it?
I also wonder if it is possible to go further with a bit of lateral thinking. As Felix noted using sections that are not suceptible to laterial-torsional buckling, such as square hollow sections, may allow for greater spans. Also would it be possible to reduce mid-span bending moments by allowing the beam to over-hang the supports? Taken to extremes there are a host of other complicating factors too, such as the precise nature of the supports (will friction become important here?), and so on.
Thanks for all the interesting entries.