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To: RLM

It is and it isn’t a cantilever. It’s a complex truss. There are cantilever forces in play near the piers, but closer to midspan the superstructure acts as a simple truss. There is no floating truss or pivot pin at mainspan center, and no tiebacks or counterweight on the approach sides (except the cantilever/truss dead loads), so treating the structure as two independant cantilevers does not resolve the forces in play consistently with MnDOT’s judgement.

On the other hand, ignoring the cantilever aspect severely restricts understanding of the northern sidespan collapse progression. In order to properly model all the forces at work here we’d need much more complex software, and then we’d have to plug in all the defects that have accumulated since the bridge was built, and already that’s out of my processing horsepower range, without even looking at fatigue effects, wind loads, settlement, etc., etc., etc.

For what it’s worth, MnDOT shows the pier kingposts in compression, though without indicating magnitude. The Johns Hopkins models indicate magnitude, but as stated earlier, I’m uncomfortable using those except in trends and comparison, since my width to depth to length ratios are essentially random, without relation to the prototype truss.

One of my earlier images, and to a much better degree an image Spunkets posted, shows the southeast kingpost was subjected to severe compression forces at some point in the collapse progression, it folded up like a toothpick with a quarter of the weight of a big bridge resting on it.


2,638 posted on 08/05/2007 2:33:09 PM PDT by jeffers
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To: jeffers
Note also that in the above and all previously posted stress resolution diagrams, the left truss support represents a fixed bearing surface, while the right truss support represents and is modeled after a roller bearing. This is a limitation of the modeling software and is mandatory prior to executing the force resolution calculations.

If both support points were fixed, the structure would be redundant unless a member were removed somewhere. One could fix the right support point by adding a member connecting it to the left; one could then remove almost any member and the structure would still be supported (though depending upon the member removed, stress levels on remaining members may become excessive).

2,640 posted on 08/05/2007 3:32:03 PM PDT by supercat (Sony delenda est.)
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To: jeffers
For what it’s worth, MnDOT shows the pier kingposts in compression, though without indicating magnitude. The Johns Hopkins models indicate magnitude, but as stated earlier, I’m uncomfortable using those except in trends and comparison, since my width to depth to length ratios are essentially random, without relation to the prototype truss.

The pier kingposts support almost the entire weight of the bridge. I find the design a little odd, actually. Had the pier had diagonals going down toward it, each of those diagonals would have had to support about half as much compressive load as the kingposts (there would be twice as many of them). If the pier kingpost failed, the bridge would start to drop. The force on the lower chord would increase toward infinity as the bridge did so, until the bridge had fallen enough for the lower chord to start being under tension.

2,647 posted on 08/05/2007 7:52:04 PM PDT by supercat (Sony delenda est.)
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