Memger,
For simplicity, consider what happens to a single span, fixed ended beam carrying a single central point load, and assume perfect elastic-plastic material behaviour.
Without any differential settlement, the beam will collapse when plastic hinges develop at both ends and at the centre.
The load at which this occurs will be 8Mp/L where Mp = plastic moment, and L = span. To get -Mp at both ends and +Mp at the centre, the "free bending moment" due to the applied load must = 2*Mp. (Hence PL/4=2Mp gives P=8Mp/L)
Suppose that one end settles (without rotation). In the worst situation, you could have +Mp (sagging moment) at the lower end, -Mp at the other, even with no applied load.
If you now apply an increasing central point load to this beam, the moment at the upper end will remain constant at -Mp, with a plastic hinge just 'rotating' a bit.
At the other end, the moment will gradually change from +Mp to -Mp. Essentially, until the fixing moment at the lower end reaches -Mp, the beam will behave as a propped cantilever. Collapse can still not occur until there are three plastic hinges forming a mechanism
At collapse condition, the BM diagram will be exactly the same at if there had never been any settlement : -Mp at both ends, +Mp at the centre, and the applied load to cause collapse remains 8Mp/L as before.
Any good reference on plastic theory will confirm this. eg Michael R. Horne "Plastic Theory of Structures" has this to say :
"..provided change of geometry and instability are unimportant, and also provided failure does not occur because of alternating plasticity or incremental collapse... The collapse loads of elastic-plastic structures are unaffected by thermal stresses... Finally, subject to these restrictions, settlement or flexibility of supports and flexibility (as opposed to ultimate strength) of internal connections have no effect on failure loads".