blu wrote:
So, to sum up, can we surmise that the bridge collapsed because of the following:
overload (too many construction vehicles, poorly placed, too much traffic)
freight train vibrations/displacement (oh, please say this had something to do with it! It makes such a
simple visual for me!)
You have given some great explanations, pictures even. Thanks for all your work!
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We don’t know why the bridge collapsed, but we are getting a better idea of how it collapsed, the progression of the failure.
In a cantilever bridge like that one, the live load, cars and trucks, construction vehicles, etc., is a pretty small fraction of the dead load, the weight of the bridge structure itself. Sure, extra vehicles will increase the chance of failure, just as one extra straw will break the camel’s back. But it’s not the one straw that does it, it’s the total load, of which heavy traffic probably wasn’t the largest fraction.
I could see vibration from trains disturbing old concrete, but that’s why they inspect bridges periodically. Significant subsidence, or cracks from vibration, even in a sidespan pier, are unlikely to remain unnoticed.
Best guess right now, heavy live loads, train vibration, construction mistakes, and metal fatigue look good, with metal fatigue being a critical element. Something brought down the supports for the bridge deck, either at the north main span pier, the next sidespan pier north of that, or both.
I’m less likely to look for footing or concrete issues because concrete usually shows visible problems before they are fatal.
Metal fatigue shows problems too, but it can be very difficult to judge precisely how severe they are. Fatigue occurs when metal is stressed beyond it’s elastic limit. Bend or stress metal, let go, and it returns to it’s original shape, fine. Bend or stress it too far, deform it permanently, and internal issues start to cascade. Internal means “hard to see”.
Vibration from a train or construction work puts much or all of the dead load in motion. Energy calculations involving motion include a velocity squared parameter, a force magnifier which can quickly become signnifcant, either at the time of a failure, or leading to metal fatigue before a failure.
The devil’s going to be in the details on this one, either in the steel over the north mainspan pier, or the next sidespan pier and/or steel above that. Looks to me like the area around the 1st sidespan pier north of the main is hard to access right now.
TOKYO (AP) - Japan’s Meteorological Agency says strong quake has hit southern Sakhalin, issues tsunami warning for northern Japan.
Jeffers, I am intrigued by your theory on this.
It disturbs me that that the pier on the south(?) side is so out of plumb, post collapse. The north side pier has both towers intact, except for a violent reaction at the top of the piers, where the rocker plates have been ripped off the top of the piers.
The other pier has both rocker plates intact, and the span appears to have snapped cleanly off at the pins.
If something happened at the north side, with a lateral deflection sideways of the span(not the piers), I could see the center span pulling at the south pier, pulling it toward the center of the river. The half arch span to the south broke cleanly off once the southern pier went out of plumb, and leans, almost intact to the south.
But what if there was scour at the south pier, which is at the waterline and has no lateral support similar to the support enjoyed at the northern pier. What if that pier went out of plumb and twisted toward the river, making both spans it supported rip off their rocker pins, and the center span falling into river, tore the northern part of the span and twisted it off of the northern pier, which is not out of plumb post collapse.
The fact that the southern pier is now out of plumb is disturbing, because it shows that, in either case, it was the weaker of the two piers.
The slide show posted by Norms Revenge earlier shows some more shots of the southern pier.
The local news reported that a 2006 inspection noted stress cracks and metal fatigue problems in both the main girders and the diaphragms, but there was no indication of the (now apparent) severity. I would hate to be the engineer who authored that report.
Prayers for all involved in this tragedy.
Metal fatigue is a microscopic process of atomic rearrangement, that always occurs at stress levels below the elastic limit. No macroscopic changes are discernable. Normally it's well below the elastic limit. The elastic limit is always higher than the stress at failure when metal fatigue occurs.
Metal that is stressed beyond it's elastic limit at RT is simply cold worked. In the case of this bridge, cracks were noted. This is mild steel, so those cracks were not likely due to corrosion. Those cracks indicate the fatigue limit of that steel had been reached, and that result could be applied to the rest of the same steel in the rest of the structure. That is the new ultimate limit to be used for that steel. Values for new steel no longer apply and an effective elastic limit doesn't exist, because with fatigue, it's probable that the elastic limit is the same as the ultimate limit. ie, the steel will not bend, it fractures.