Question What does graduated compression mean?
I always encounter the term graduated compression. What does it mean?

Best Answer No Best Answer Yet

Question What would the logical steps be to mathematically describe the structural failure of a bridge?
I am under graduate math student trying to write an end of term paper that models the failure of a fictional bridge. I thought about starting off with the cracking of the gusset plates followed by the buckling of the beams due to their fall. What considerations should I make so my paper is not trivial?

Best Answer If you don't have any experience doing complicated stress analysis using computer packages (like Finite Element analysis) I would suggest staying away from that, and doing something with more math content. For example you could take a type of bridge where it is easy to calculate loads and stresses in a simple model (e.g. a truss bridge or a suspension bridge) and consider whether one failure causes the whole structure to fail or if the loads can be safely redistributed through the rest of the structure. Obviously that is desirable in a real structure. For example a truss bridge with a simple Warren girder structure (equliateral triangles) doesn't have much redundancy. All the parts of the truss are supposed to carry the load in tension and compression (which is efficient use of the material) but if one member fails the loads then have to be carried be bending of the remaining structure, which is inefficient. But if there is some cross-bracing in the truss, that may fix the problem. You could investigate different topologies to see how fail-safe they are (e.g. how many components can fail before the entire bridge fails) and compare your conclusions with some real bridge designs. The above is actually the hard part of much real engineering design work. It's straightforward to calculate stresses etc in a complicated structure that is already defined, given the right computer software and the knowledge of how to use it. Given the topology of a structure, it's fairly easy to calculate the size of the various parts (cross section area of rods etc), to meet some criteria for safe stresses without wasting material. But getting a computer to design an optimal structure(however you choose to define "optimal") without any human input is an unsolved problem in general.