Posted on 08/21/2007 3:20:52 PM PDT by jeffers
Wow. Thank you for this wonderful service to FR.
Thanks for the ping jeffers. I can’t believe how small the point is between the truss (?) and the cement post. Hope they get to work soon on the Cayuga and Lafayette bridge!
Thanks for keeping us posted.
So bird droppings and road salt corrosion did not play a part?
BTTT
ping
Couple Qs.
* If you're feeling motivated (insomnia, perhaps), could you redraw that MnDOT diagram so it shows the whole bridge from one side to the other--I'm still never quite sure which are the center spans and which are the landside-spans. And identify what the "king truss"--I'm not sure what a king truss is on a cantilevered tower.
On the diagram, I'm thinking the L9/U10 member on the MnDOT diagram is actually compression, not tension (a typo for MnDOT's consultant). (like the L7/U6 member). For one thing, the photos show it as being a box beam, not an I beam. For another, the bridge wouldn't stand up if it was tension.
* Do you have an opinion as to whether the U10/L10 area failure was or wasn't the initial failure? If the south landside span failed, the center span would be expected to sag and buckle somewhere, is U10/L10 as good as any spot for that?
i.e. if the south landside arm failed somewhere, then the counterweight would be gone from the main span, and the section from U8 to U10 would suddenly be acting in compression, rather than tension. and you'd get a buckling of the tension member somewhere on that stretch, quite possibly at the farthest-extremity of the tension member.
bttt
now THAT’S analysis!!
Check out my diagram below--do I have the labeling right? Now it's a lot easier to talk and see at the same time.
Now, let's establish how the bridge stands up.
* Cantilever bridges are built out from the piers. Chords on top are tension, chords on bottom are compression.
* Truss bridges are built from pier to pier, tension on the bottom, compression on top.
* A Cantilever bridge with a suspended truss span has cantilever arms reaching out from the piers, then a truss span hanging from the ends of each cantilever span.
So, the tension/compression diagrams in the MnDOT doc show that this is a cantilever bridge with a suspended truss span. There's a bit of overlap between the two span types, as can be seen in this labeled diagram. The Cantilever extends out from Pier 6 from U12 to U6, with the compression chords from U12 to U10 and U6 to U4 acting as tension chords. Similarly, the Truss Span extends from L9 to the L9 on the other side of the river (same spot, other side), with the L9 to L11 compression chord also working as a tension (the entire span, except that last 40' segment from L8 to L9 at each end). (Of course, if my whole diagram is backwards, it makes perfect sense, with U6 to U2 and L5 to L1 as "reversal members" -- able to function both ways).
Now, look at where Jeffers determined the failure occurred. U10/L10. It's right at the outer extremity of tension members on the top chord. And, in the video, it looks like the failure at the north end also occurred right at U10/L10.
Now, imagine (hypothetically) the center span standing without the side spans. It now has to function as a truss span, compression across the top, tension on the bottom. What will fail? The compression members on the bottom will probably function pretty well as tension members, they're big and beefy. But the tension members will buckle under compression.
So, I'm thinking, the south arm may have fallen first. Jeffers is exactly right on how the main span fell, but I think the south span triggered the main span. (Mainly because it fell so crooked while the rest of the structure fell straight. With a long, complex set of spans like this, span like this, you'd expect a point failure somewhere to take out one span in an asymetrical way, then the other spans to fall like dominos as they lose their counterbalancing cantilever arms, and the girder spans on each end to be yanked off their piers or shoved off their piers as the main spans go).
So, Jeffers is right on the main span, and this is why.
The south cantilever platform, from U12 to U4, can stand on its own only if its balanced. If, say, the south half (landside) was to collapse, then an unattached north side of the cantilever platform would simply dump itself into the river.
And, the north side, attached to the suspended truss and whole north cantilever platform (over pier 7), wouldn't simply dump itself into the river, it would try to act as a truss span, from pier 6 to pier 7. But, this isn't going to work. It's not designed to hold up that way--it would need a truss network with a continuous compression member across the top. Which it doesn't have--it's tension from U10 to U8. The truss system is fine, actually, from L9 to L9 across the river. But not from L8/U8 to L8/U8.
So it will fail.
Where will it fail?
The tension chord from U10 to U8 will buckle. Crunch. Game over. Which is exactly what you've shown, Jeffers, and the video clip shows happening on the other side of the river.
So, it could have been an initial failure on U10, south side. But, you'd think that would have resulted in the main span twisting much more as it dropped. As it is, it fell pretty flat. It seemed to take a few seconds for things to fail. Maybe those tension members handled the compression for about 5 seconds as they slowly got bent out of shape and twisted apart. That's how long it took the same failure to occur in the north landside arm.
So, seems to me, it's much more likely that the initial failure was indeed in the south landside span. Between Pier 6 and Pier 5. Something happened on one side or the other, the west side?? since the deck seems to have flopped to the east. Then the east truss/cantilever arm held for the same 5 seconds, and failed. That makes for the twisted deck. And something in there should also account for the rotating king posts. If the west side, south arm failed (around, say, U6 or U4), then the king post would still be intact. Not sure on the rotational movement, but there's probably a few good reasons.
This brings the initial failure back to a small member somewhere, rather than a massive failure of a main structural member, with a result in s similar failure on the other truss arm, which seems more plausible overall to me.
Hope this makes some sense, I'm staying up *way* too late...
Kwuntongchai
And, as to what happened? This photo http://www.flickr.com/photos/s4xton/981290582/in/set-72157601157770382/
might explain something. Why is the location the girders buckled **behind** the pier? You’d think they’d have bent right on top of the pier. It’s not exactly normal for a girder to bend a couple feet out into the span.
It looks like a compression buckle. They got shoved, and bent out of shape? What shoved them, why? Did the whole south landside cantilever arm (U8 to U1) bust loose off Pier 5 because of expansion joint issues and crush the approach span?
There needs to be some explanation of this, curious as to what anyone thinks. This is the spot directly “in front” of the burning Tastee Truck and schoolbus.
The mens' arms are the tension members, the sticks are the compression members. In my diagrams above, red are tension, blue are compression, and green function as either compression or tension.
So, the failure mode I'm thinking is that, say, the guy on the right looses his grip on his stick with his left hand. What happens? the weight in the middle will make him tip inward, causing a complete failure. How will the middle section fail? The right guy tips inward, everything pivots where left guy and right guy's hands meet middle guy. Depending on the strength of middle guy's connection to left guy, he will either hang and dangle from left guy and pull left guy into the river, or (in the 35W case) bust loose from left guy and drop more or less straight down.
Meanwhile middle guy's falling has town loose left guy's right hand loose from the stick, and the stick drops, then left guy tips over to our left.
(Also, the buckle in the girders on the approach span, now that I look at it, appears to be too uniform from left to right to have been caused by the twisting south span... Must be some artifact of how a continuous girder bridge buckles over an intermediate pier if it loses one abutment)
Thanks for the kind words, but I’m not a licensed engineer. I studied CE for a couple years, but financial pressures forced me into full time employment in construction field management. I put 20 years into that, another ten into computers after a fall broke three vertebra, and am now happily retired. If something interesting comes along, I consider it, but mostly engage in private research.
There are more images and more logic as to the mechanics of this failure, but the good engineers can usually look at the rubble and figure out what puzzles them, while the non-engineers don’t need technical gibberish, so I decided to cut it off where it sits now.
There are good reasons why I’m not considering an approach span failure as the trigger event anymore, and other reasons why I see a center span failure further north of pier 6 to be less likely, but so far everyone seems to follow this well so unless questions are raised, no need to delve deeper into the arcane.
Some professionals have weighed in on this thread, others are considering the material and have yet to air comments, it will be interesting to see where the consensus, if any, lies.
Thanks again for your comments and I hope you keep up your own brand of first class work.
I have seen claims that materials and heavy equipment were stored on the bridge, but I can’t say I’ve seen proof of this.
I recall one image showing small, maybe a little bigger than golf carts, buggies for carrying sand or gravel, some images of men with jackhammers breaking deck for replacement, and maybe one or two dump trucks, but that’s all I have photo support for.
I’ve looked for piles of gravel or sand in the post collapse imagery and have not found them. Not saying there weren’t any, just that so far most of the evidence supporting heavy materials and equipment stored on the bridge, from what I’ve actually seen, is hearsay only.
TXnMA wrote:
“...I do notice
some very early-on buckling of the main-span western lower chord — right at the nothern pier end......”
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The bottom chords in the first three truss panels on either side of piers 6 and 7 are integral parts of the cantilever component of this bridge’s truss design. They are in compression, where simple truss design would have them in tension.
Because it wasn’t a pure cantilever design, however, those members are nowhere near stout enough to carry the bridge by themselves.
Sever span 7 just about anywhere along its length, and those bottom chords will go into compression orders of magnitude beyond design limits and buckle almost immediately.
If you see that in differential frame analysis, it is expected and supports the contention that span 7 was severed early in the collapse sequence.
Looking forward to your analysis.
I think fatigue played a critical part in this collapse, and as a result, find it hard to look away from the U6 gusset area.
At that point, the top chord goes into reversal from being in tension nearer the south piers. It’s carrying the upper end of the U6-L5 tension diagonal, and the upper end of U6-L6 also in tension. Further, its got the upper end of the L7-U6 compression diagonal.
There’s many opposing forces coming together at that critical point, and repeated loading and unloading of the span over decades of carrying traffic essentially have to focus fatigue inducing alternating and differential stresses there.
Awesome work.
placemark
XR7 wrote:
Thanks for keeping us posted.
So bird droppings and road salt corrosion did not play a part?
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I’d guess road salt corrosion and possibly bird droppings probably did play a part, but it is impossible for me to say how large of a part at this point.
Regardless of where the triggering failure took place, metal fatigue, rust, corrosion and cracked welds would not have helped the bridge carry its gravity loads. But pinning the failure to one specific cause of weakening is beyond my ability.
Jim Trent has favored corrosion fatigue and cracking as significant causal factors in the past, and I tend to agree with that assessment, in theory at least.
I don’t have empirical data in this case to assess causes of component failure, but anything that weakens steel in fracture critical structures can’t be viewed as beneficial, whether the structure fails or not.
kwuntongchai wrote:
Great analysis—thanks for piecing it all together. You’ve certainly nailed the point, mechanism and sequence as to how the main span failed.
Couple Qs.
* If you’re feeling motivated (insomnia, perhaps), could you redraw that MnDOT diagram so it shows the whole bridge from one side to the other—I’m still
never quite sure which are the center spans and which are the landside-spans. And identify what the “king truss”—I’m not sure what a king truss is on a
cantilevered tower.
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I don’t know about drawing the whole bridge. I’ve got a pretty busy schedule right now as it is, and that’d take some time to do. I know once I got into it, I’d start adding more and more detail, until I’d redrawn the full set of working plans, and I’d also veer off into stress and failure analysis such that a project like that might stretch into years.
In your post 45 photo, pier 8 is in color at far left. Span 8 starts there and ends at the next pier to the right, pier 7, the north end of the main river span, span 7. Pier 6 is on the right side of the river, and span 6 stretches right from there to pier 5, the farthest right member you’ve highlighted in color, save for that last diagonal.
(There’s a LOT going on at that diagonal, but that’s another book that isn’t written yet. For now, at least note the expansion joint in the road deck above that far right diagonal.)
Kingpost is a vernacular term we’ve always used to refer to the tallest vertical member in a truss. In practice I and the people I’ve worked with usually used it in connection with Pratt or Howe truss designs, in this analysis, we used the term to refer to the vertical members above piers 6 and 7, on either end of the main river span.
Keep in mind, this truss isn’t a pure cantilever either, it is a complex truss, which is about as far as I want to get into that, absent specific questions.
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kwuntongchai wrote:
On the diagram, I’m thinking the L9/U10 member on the MnDOT diagram is actually compression, not tension (a typo for MnDOT’s consultant). (like the
L7/U6 member). For one thing, the photos show it as being a box beam, not an I beam. For another, the bridge wouldn’t stand up if it was tension.
*************
I believe you are almost certainly correct here, except the member in question is L9’-U10’, not L9-U10. L9-U10 would be in span 6, south of pier 6, while L9’-U10’ resided north of pier 7 in span 8.
I believe the origin was designated at the center of the main span, span 7, with normal numbered junctions incrementing south from there, and primed numbered junctions incrementing north from there.
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kwuntongchai wrote:
* Do you have an opinion as to whether the U10/L10 area failure was or wasn’t the initial failure? If the south landside span failed, the center span would be
expected to sag and buckle somewhere, is U10/L10 as good as any spot for that?
i.e. if the south landside arm failed somewhere, then the counterweight would be gone from the main span, and the section from U8 to U10 would suddenly
be acting in compression, rather than tension. and you’d get a buckling of the tension member somewhere on that stretch, quite possibly at the
farthest-extremity of the tension member
************
In your later posts, you use a connection labelling scheme inconsistent with that used by MnDot, so I’m not completely sure I know what you ask here.
However, your labelling scheme here seems consistent with the rest of your question, and in any event, a general answer will suffice.
If I was to look for a triggering failure anywhwere on the southern approach, the first, (and possibly last) place I’d look would be at the pier 5 endbeam/crossbeam/rockerbearing assemblies, on both the east and west trusses, the far right diagonal in your image, mentioned above.
A lot of significant history there, and I refer you to the 2006 Inspection Report for more detail before getting deeper into this.
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