So, to start it off, let's talk about the rules. SanderO has offered the following as associated with the diagram:
SanderO wrote:columns will buckle and fail when their yield strength is exceeded. This is only possible from strength reduction due:
to mechanical destruction of part of the column's cross section (cutting explosion)
to removal of bracing
factor if safety
I assumed that the loads of a failed column were shared equally to only adjacent columns. I also assumed the heat / destruction was the same value / rate and in the cartoon...symmetrical about the north south axis.
This is a good starting point. SanderO describes purely local load sharing between adjacent elements. That can be twiddled in more complex ways is subsequent trials. I can definitely see load distribution being extended in a weighted fashion to many close neighbors, especially along the perimeter, and global sharing entering via the hat truss.
Ignoring for the moment both the hat truss and floor assemblies (they will probably be treated as external input, though clearly constrained by the couplings to columns), there are two types of elements, core and perimeter columns. A formal characterization of these elements is necessary.
A column has a capacity which determines the load under which it will fail. We shall not at this point discriminate between the different yield points, elastic or plastic response, or geometric nature of failure mode. Rather, we'll simply say that, when a column is loaded above capacity it fails and is removed from the model. An intact column starts with a given design capacity - which for now is its only explicit attribute - and from that is derived an effective capacity which is some fraction of that value.
The manner in which the effective capacity is determined may as well be arbitrary. At some point, it will be nice to plug in expressions for capacity reduction due to thermal response, eccentricity, increase of unsupported length, etc. But for now it probably suffices to just simply assign reductions with various distributions and see the response. Broad swaths of uninteresting results can be identified and swept aside.
For the first pass, then, it's a pretty simple system. The only explicit state variable is capacity. Under the hood, we can talk about how heating is applied in some gradient or whatever, but the factors merely result in calculated capacity based on simple fractional reductions.